Download A S C -A S

A S YSTEM FOR C OMPUTER -A SSISTED S URGERY WITH
I NTRAOPERATIVE CT I MAGING
by
A NTON O ENTORO
A thesis submitted to the
School of Computing
in conformity with the requirements for
the degree of Master of Science
Queen’s University
Kingston, Ontario, Canada
August 2009
c Anton Oentoro, 2009
Copyright Abstract
Image-guided interventions using intraoperative three-dimensional (3D) imaging can be
less cumbersome than systems dependent on preoperative images, especially by needing
neither image-to-patient registration nor a lengthy process of segmenting and generating
a 3D model. In this dissertation, a method for computer-assisted surgery using direct
navigation on intraoperative images is presented. In this system the registration step of
a navigated procedure was divided into two stages: preoperative calibration of images to
a ceiling-mounted optical tracking system, and intraoperative tracking during acquisition
of the 3D image. The preoperative stage used a custom-made multi-modal calibrator that
could be optically tracked and also contained fiducial spheres for radiological detection; a
robust registration algorithm was used to compensate for the high false-detection rate that
arose from the optical light-emitting diodes. Intraoperatively, a tracking device was attached to bone models that were also instrumented with radio-opaque spheres; a calibrated
pointer was used to contact the latter spheres as a validation. The fiducial registration error
of the calibration stage was approximately 0.1 mm with the Innova 3D X-ray fluoroscope
and 0.7 mm with the mobile-gantry CT scanner. The target registration error in the validation stage was approximately 1.2 mm with the Innova 3D X-ray fluoroscope and 1.8 mm
with the mobile-gantry CT scanner. These findings suggest that direct registration can be a
highly accurate means of performing image-guided interventions in a fast, simple manner.
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Acknowledgments
I would like to thank Dr. Randy Ellis for his supervision and providing me with the opportunity to conduct research in the operating room. I would like to thank Dr. Elvis Chen and
Amber Simpson for their help over the two years I was working in the Medical Computing
Laboratory. I would especially like to thank Dr. Burton Ma for providing great support and
guidance to me throughout this work. I would also like to thank all the staff, surgeons, and
nurses at Kingston General Hospital and Human Mobility Research Center especially, Paul
St. John for his help with the work in the ACT operating room. I would also like to thank
Dr. Purang Abolmaesumi, Dr. Parvin Mousavi, and Dr. David Gobbi for the help during
the early stages of my graduate studies. And of course, I would like to thank my friends
and family.
This research was supported in part by the Canada Foundation for Innovation, the Canadian Institutes of Health Research, Kingston General Hospital, the Ontario Research and
Development Challenge Fund, and the Natural Sciences and Engineering Research Council
of Canada.
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Contents
Abstract
i
Acknowledgments
ii
Contents
iii
List of Tables
vi
List of Figures
ix
1 Introduction
1.1 Subject Matter . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Replacing the Preoperative Planning Stage . . . . . .
1.1.2 Replacing Surface-Based Image to Patient Registration
1.2 Organization of the Dissertation . . . . . . . . . . . . . . . .
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2 Literature Review
2.1 Image-Based Computer-Assisted Surgery . . . . . . . . . .
2.1.1 An Overview of Computer-Assisted Surgery using
Imaging . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Image-to-Patient Registration . . . . . . . . . . . . . . . . .
2.2.1 Paired-Point Fiducial Registration . . . . . . . . . .
2.2.2 Surface-Based Registration . . . . . . . . . . . . . .
2.2.3 Other Registration Methods . . . . . . . . . . . . .
2.3 Intraoperative Imaging . . . . . . . . . . . . . . . . . . . .
2.3.1 Intraoperative 2D Imaging Devices . . . . . . . . .
2.3.2 Intraoperative CT Imaging . . . . . . . . . . . . . .
2.3.3 Intraoperative MRI . . . . . . . . . . . . . . . . . .
2.3.4 Summary of Intraoperative Imaging . . . . . . . . .
2.4 Overview of Computer-Assisted Orthopedic Surgery . . . .
2.4.1 Surgical Procedures on the Spine . . . . . . . . . .
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Preoperative
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2.4.2 Surgical Procedures on the Pelvis . . . . . .
2.4.3 Surgical Procedures on the Lower Extremity
2.4.4 Surgical Procedures on the Upper Extremity .
2.4.5 Excision of Osteoid Osteoma . . . . . . . . .
Volume Rendering . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . .
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3 Materials and Methods
3.1 Coordinate Frames, Vectors, and Transformations . . . . . . . . . . . . .
3.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The Innova 3D X-Ray Fluoroscope . . . . . . . . . . . . . . . .
3.2.2 The Mobile-Gantry CT Scanner . . . . . . . . . . . . . . . . . .
3.2.3 The Optotrak Optoelectronic Position Sensor . . . . . . . . . . .
3.2.4 The Multi-Modal Calibrator . . . . . . . . . . . . . . . . . . . .
3.2.5 Bone Models For Validation . . . . . . . . . . . . . . . . . . . .
3.2.6 Custom Optoelectronic Instruments . . . . . . . . . . . . . . . .
3.2.7 The VSS Navigation System . . . . . . . . . . . . . . . . . . . .
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Transformation between {C} and {M} . . . . . . . . . . . . . .
3.3.2 Transformation between {M} and the coordinate frame of the Image Spaces {S} and {V} . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Registration of the Innova . . . . . . . . . . . . . . . . . . . . .
3.3.4 Registration of the CT . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Experiment with the Plastic Models . . . . . . . . . . . . . . . .
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4 Results and Analysis
4.1 Results from Bead Detection . . . . . . . . . . . . . . . .
4.2 Results of the Innova Registration Experiment . . . . . . .
4.3 Results of CT Registration Experiment . . . . . . . . . . .
4.4 Results from the Plastic-Bone Validation Experiment . . .
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Analysis of the Innova Results . . . . . . . . . . .
4.5.2 Analysis of the CT Registration . . . . . . . . . .
4.5.3 Analysis of the Plastic-Bone Validation Experiment
4.5.4 Summary . . . . . . . . . . . . . . . . . . . . . .
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5 Conclusions and Future Work
5.1 Summary . . . . . . . . . . . . . . . . . . .
5.1.1 Simplicity of the New System . . . .
5.1.2 Replacing Intraoperative Registration
5.1.3 Accuracy of the New System . . . . .
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5.2
5.3
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Bibliography
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A Appendix
A.1 Calibration Results for the Innova . . . . . . . . . . . . . . . . . . .
A.2 Calibration Results for the Mobile-Gantry CT Scanner . . . . . . . .
A.3 Results of the Bone-Model Validation Study . . . . . . . . . . . . . .
A.3.1 Results for the Bone-Model Validation Study with the Innova
A.3.2 Results for the Bone-Model Validation Study with CT . . . .
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Glossary
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v
List of Tables
4.1
4.2
4.3
4.4
4.5
Average rotational and translational errors calculated from ∆C T for the
Innova registration experiment. . . . . . . . . . . . . . . . . . . . . . . . .
Average rotational and translational errors calculated from ∆S T for the
Innova registration experiment; µ is the mean and σ is the standard deviation.
Average rotational and translational errors calculated from ∆V T for the CT
registration experiment; µ is the mean and σ is the standard deviation. . . .
The Innova target registration for 4 bone models, each in 4 poses; σ is
the standard deviation. The corrected values compensated for the 0.4 mm
radius of each fiducial marker . . . . . . . . . . . . . . . . . . . . . . . . .
The CT target registration for 4 bone models, each in 4 poses; σ is the standard deviation. The corrected values compensated for the 0.4 mm radius of
each fiducial marker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 Deviation of the angles in the rotational component of ∆S T in degrees;
columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . . . . .
A.2 Deviation of the angles in the rotational component of ∆S T in degrees;
columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . . . . .
A.3 Deviation in the translational component along the X axis of ∆S T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . .
A.4 Deviation in the translational component along the X axis of ∆S T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . .
A.5 Deviation in the translational component along the Y axis of ∆S T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . .
A.6 Deviation in the translational component along the Y axis of ∆S T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . .
A.7 Deviation in the translational component along the Z axis of ∆S T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . .
A.8 Deviation in the translational component along the Z axis of ∆S T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . .
A.9 Deviation in the norm of translational component of ∆S T in millimeters;
columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . . . . .
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A.10 Deviation in the norm of translational component of ∆S T in millimeters;
columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . . . . . . 128
A.11 Deviation in the translational component along the X axis of ∆C T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . 129
A.12 Deviation in the translational component along the X axis of ∆C T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . 129
A.13 Deviation in the translational component along the Y axis of ∆C T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . 130
A.14 Deviation in the translational component along the Y axis of ∆C T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . 130
A.15 Deviation in the translational component along the Z axis of ∆C T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . 131
A.16 Deviation in the translational component along the Z axis of ∆C T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . 131
A.17 Deviation in the norm of the translational component of ∆C T in millimeters; columns are for Innova scans 1 to 7. . . . . . . . . . . . . . . . . . . . 132
A.18 Deviation in the norm of the translational component of ∆C T in millimeters; columns are for Innova scans 8 to 14. . . . . . . . . . . . . . . . . . . 132
A.19 Deviation in the angle of the rotational component of ∆V T in degrees. . . . 133
A.20 Deviation in the translational component along the X axis of ∆V T in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.21 Deviation in the translational component along the Y axis of ∆V T in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.22 Deviation in the translational component along the Z axis of ∆V T in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.23 Deviation in the norm of the translational component of ∆V T in millimeters.134
A.24 Target Registration Errors for the Fiducial Markers on Femur Model #1 at
the initial position (long shaft of the bone parallel to the table) with the Innova135
A.25 Target Registration Errors for the Fiducial Markers on Femur Model #1 at
90 ◦ counter-clockwise rotation from the initial position (long shaft of the
bone parallel to the table) with the Innova. . . . . . . . . . . . . . . . . . . 135
A.26 Target Registration Errors for the Fiducial Markers on Femur Model #1 at
180 ◦ counter-clockwise rotation from the initial position (long shaft of the
bone parallel to the table) with the Innova . . . . . . . . . . . . . . . . . . 136
A.27 Target Registration Errors for the Fiducial Markers on Femur Model #1 at
270 ◦ counter-clockwise rotation from the initial position (long shaft of the
bone parallel to the table) with the Innova . . . . . . . . . . . . . . . . . . 136
A.28 Target Registration Errors for the Fiducial Markers on Femur Model #2 at
the initial position (long shaft of the bone is parallel with the table) with
the Innova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
vii
A.29 Target Registration Errors for the Fiducial Markers on Femur Model #2
90 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone is parallel with the table) with the Innova . . . . . . . . . . . . . . . . 136
A.30 Target Registration Errors for the Fiducial Markers on Femur Model #2
180 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone is parallel with the table) with the Innova . . . . . . . . . . . . . . . . 137
A.31 Target Registration Errors for the Fiducial Markers on Femur Model #2
270 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone is parallel with the table) with the Innova . . . . . . . . . . . . . . . . 137
A.32 Target Registration Errors for the Fiducial Markers on Tibia Model #1 at
the initial position (long shaft of the bone parallel to the table) with the Innova137
A.33 Target Registration Errors for the Fiducial Markers on Tibia Model #1 at
90 ◦ counter-clockwise rotation of the initial position with the Innova . . . . 137
A.34 Target Registration Errors for the Fiducial Markers on Tibia Model #1 at
180 ◦ counter-clockwise rotation of the initial position with the Innova . . . 138
A.35 Target Registration Errors for the Fiducial Markers on Tibia Model #1 at
270 ◦ counter-clockwise rotation of the initial position with the Innova . . . 138
A.36 Target Registration Errors for the Fiducial Markers on Tibia Model #2 at
the initial position (long shaft of the bone parallel to the table) the Innova . 138
A.37 Target Registration Errors for the Fiducial Markers on Tibia Model #2 at
90 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone parallel to the table) the Innova . . . . . . . . . . . . . . . . . . . . . 138
A.38 Target Registration Errors for the Fiducial Markers on Tibia Model #2 at
180 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone parallel to the table) the Innova . . . . . . . . . . . . . . . . . . . . . 139
A.39 Target Registration Errors for the Fiducial Markers on Tibia Model #2 at
270 ◦ counter-clockwise rotation of the initial position (long shaft of the
bone parallel to the table) the Innova . . . . . . . . . . . . . . . . . . . . . 139
A.40 Target Registration Errors for the Fiducial Markers on Femur Mocdel #1
with the CT Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.41 Target Registration Errors for the Fiducial Markers on Femur Model #2
with the CT Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.42 Target Registration Errors for the Fiducial Markers on Tibia Model #1 with
the CT Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.43 Target Registration Errors for the Fiducial Markers on Tibia Model #2 with
the CT Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
viii
List of Figures
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
A diagram that illustrates the principal axes of the Innova image space . .
A diagram that illustrates the principal axes of the CT image space . . . .
A diagram that illustrates the coordinate frame of the Certus. . . . . . . .
Computer aided design of multi-modal calibrator. . . . . . . . . . . . . .
Computer aided design of the multi-modal calibrator in a profile view . .
Computer aided design of the multi-modal calibrator in a profile view . .
Computer aided design of the multi-modal calibrator in a profile view with
dimensions of the sides of the MMC. The dimensions are in millimeters. .
The multi-modal calibrator. . . . . . . . . . . . . . . . . . . . . . . . . .
An IRED marker embedded in the multi-modal calibrator . . . . . . . . .
A meshed rendering of the multi-modal calibrator with the axes and origin
One of the femur models used in the study. . . . . . . . . . . . . . . . . .
One of the tibia models used in the study. . . . . . . . . . . . . . . . . .
The location of the fiducials in the first of two femur models. The circles
highlight the location of the fiducials. . . . . . . . . . . . . . . . . . . .
The location of the fiducials in the second of two femur models. The circles
highlight the location of the fiducials. . . . . . . . . . . . . . . . . . . .
The location of the fiducials in the first of two tibia models. The circles
highlight the location of the fiducials. . . . . . . . . . . . . . . . . . . .
The location of the fiducials in the second of two tibia models. The circles
highlight the location of the fiducials. . . . . . . . . . . . . . . . . . . .
The digitizing probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A side shot of the multi-modal registration device . . . . . . . . . . . . .
Pseudo-Code of the modified RANSAC algorithm . . . . . . . . . . . . .
A diagram that illustrates the transformation between all of the coordinate
frames that are involved in the registration of the Innova . . . . . . . . . .
A tracked array was attached to a stand is placed at the foot of the CT
gantry. The Innova was positioned to allow the Certus to detect the multimodal calibration device during a CT scan. The arrows indicate the location
of the Certus and the origin of the CT image frame. . . . . . . . . . . . .
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3.22 This diagram describes the relevant transformations for the calibration of
the CT scanner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.23 A view of the special holder for the bone model and the tracked array. . . . 87
3.24 A screen shot of VSS during the validation study. . . . . . . . . . . . . . . 88
4.1
4.2
A volume rendered image of the multi-modality calibrator using the Innova
system. The circled regions are the IREDs and the uncircled white dots are
the beads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A volume rendered image of the multi-modality calibrator using the CT
images. The circled regions are the IREDs. The white dots are the beads
and line from the IREDs are the wires. . . . . . . . . . . . . . . . . . . . . 91
x
Chapter 1
Introduction
Integration of computers in the operating room has enabled the visualization and real-time
navigation of surgical procedures. It is especially beneficial in minimally invasive procedures where direct visualization of the anatomy is not often possible. At the time of writing,
the predominant use of computer-assisted surgical systems are with pre-operative imaging
and planning. To use such a system, a three-dimensional (3D) image of the patient prior
to surgery is acquired with computed tomography or magnetic resonance imaging. A virtual model must then be generated from the segmented 3D images, so that a surgeon can
use this model for planning and simulation. Intraoperatively, the pre-operative image must
be aligned, or registered, with the anatomy of the patient; this is commonly done first by
tracking surgical tools in 3D, then by optimizing the match between data collected from
the patient’s anatomy with data from the image. A computer, using the 3D transformation
calculated by the registration process, can then provide a surgeon with images of the tools
overlaid on top of the virtual model, all updated in real-time to reflect the actual position
of the surgical tools in the operating room. For certain type of surgeries the pre-operative
planning stage, although lengthy, is needed in order to simulate the outcome of the surgery.
1
CHAPTER 1. INTRODUCTION
2
However, minimally invasive surgical procedures using a computer-assisted surgical
system with pre-operative planning can be less than ideal, in part because:
• Segmentation of the 3D images is a time consuming procedure. Manual segmentation
of CT or MRI slices is often needed to ensure that the region of interest selected
accurately. This procedure could take a technician hours to complete.
• It is difficult to use pre-operatively acquired images for visual guidance intraoperatively, because the position of the anatomy during surgery might not correspond well
with the pre-operatively acquired 3D images due to poor registration. It easy to move
bones in a joint transporting the patients to the OR. Additionally, a patient’s joint may
be at a different angle during imaging and surgery.
• It is difficult or impossible to measure points from the surface of some anatomy such
as the spine, during image to patient registration.
Regarding the last point, the literature shows previous attempts to supplant surfacebased image to patient registration by using intraoperative X-ray equipment to acquire fluoroscopic images of the patient and then, using image registration, to register these fluoroscopic images to pre-operative CT images. There are two common alternatives to solving
this 2D/3D registration problem. One alternative is to use back-projected lines from the
X-ray source to the X-ray images and match either the contours of the 3D models to perform the registration. Another alternative is to construct digitally reconstructed radiographs
from the CT images and match these to the fluoroscopic images, using a similarity measure
such as normalized correlation. These algorithms are, however, usually very expensive
computationally and have not yet achieved sufficient accuracy for routine clinical use.
CHAPTER 1. INTRODUCTION
3
Alternatively, 2D fluoroscopic images can be used instead of 3D CT images for guidance. In this computer-assisted workflow, a calibrated frame that could be detected by a
tracking system is attached to a fluoroscope. Via information from the calibrated frame,
image distortion and C-arm deformation can be corrected to improve accuracy during navigation. Use of 2D images for guidance eliminates the pre-operative stage, which can involve a lengthy segmentation process. The images that are used for navigation are captured
intraoperatively, more accurately reflecting the position of the anatomy during surgery; this
technique also avoids surface-based registration. Despite its intellectual appeal, navigation
from 2D fluoroscopic images has not seen wide clinical adoption.
The next logical advance from intraoperative 2D navigated images is to use 3D navigated images. Although conventional CT scanners are not designed for fully sterile operations, recent developments in mobile-gantry CT scanners and flat-panel 3D fluoroscopes
have made it feasible to integrate intraoperative 3D imaging devices into an operating room.
An integrated operating room could be equipped with an intraoperative imaging modality, an accurate tracking system, ceiling mounted monitors, and an adjoining control room
for the technicians and storage of the workstations. A new operating room in Kingston
General Hospital (Kingston, Canada) has recently been built with the above specifications
thus making it, at time of writing, one of the most technological advanced operating rooms
in North America. The operating room is integrated with an Optotrak Certus tracking
system and two intraoperative imaging modalities: a mobile-gantry CT scanner and a flatpanel 3D fluoroscope. In addition to having a sterile operating area with ceiling mounted
monitors, the operating room also contains an adjoining control room for the technicians
and workstations. This operating room was, in effect, the laboratory for the work described
in this dissertation.
CHAPTER 1. INTRODUCTION
4
1.1 Subject Matter
The focus of this dissertation is to demonstrate that it is technically feasible to conduct
computer assisted surgery in an integrated surgical suite without relying on a pre-operative
planning stage or an intraoperative image to patient registration procedure. The following
section will provide a brief description of using real time intraoperative images for planning
and using direct registration for performing the image to patient registration process.
1.1.1 Replacing the Preoperative Planning Stage
To replace the pre-operative planning stage the images are acquired intraoperatively, using
one of the imaging modalities in the operating room. Subsequently, the 3D images are
rendered using real-time volume rendering. A modified version of an existing surgical navigation system was used to show that volume-rendered models can be used for navigating
a calibrated probe to a desired location.
1.1.2 Replacing Surface-Based Image to Patient Registration
Predominantly, some form of intraoperative surface-based registration has been used in
computer-assisted interventions. In this dissertation I describe a new, quick, and robust
procedure to perform the image to patient registration that is carried out pre-operatively.
In this new technique, the alignment between the image coordinate frame (Innova system
or CT scanner) and another fixed coordinate frame (ceiling mounted tracking system or a
patient’s anatomy) were determined using a custom made multi-modal calibration device.
Because the accuracy of this registration depended on the mechanical stability of the imaging modalities, I conducted a series of experiments to measure the mechanical stability of
CHAPTER 1. INTRODUCTION
5
the Innova system and the mobile-gantry CT scanner. Additionally, an experiment that
navigated a calibrated probe to a set of fiducials on plastic bone models was conducted to
illustrate the target registration error of this system.
1.2 Organization of the Dissertation
This dissertation is organized as:
Chapter 2 reviews point-based and surface-based image to patient registration, developments in intraoperative imaging, computer assisted orthopedic surgery, and finally an
overview in volume rendering.
Chapter 3 describes the workflow of performing a computer-assisted surgery in the operating room as well as the studies to test the reliability and accuracy of the system.
Chapter 4 reports the results from the experiments in Chapter 3 as well as an analysis of
the results.
Chapter 5 summarizes the significant contribution of this dissertation along with future
areas of research.
Appendix A Section A.1 contains the tabulated result of the Innova calibration experiment.
Appendix A Section A.2 contains the tabulated result of the CT calibration experiment.
Appendix A Section A.3 contains the tabulated results of the accuracy experiments using
the plastic bone models.
Chapter 2
Literature Review
This chapter reviews the relevant literature needed to understand the technology and clinical work flow of computer-assisted surgery using intraoperative 3D imaging. The following
areas will be covered in the review: an overview of computer assisted surgery, image-topatient registration, intraoperative imaging, integration of intraoperative imaging in computer assisted surgery, computer assisted orthopedic surgery, and volume rendering.
2.1 Image-Based Computer-Assisted Surgery
An image-guided intervention uses computers to enhance the visualization of a surgical
procedure. Typically, these procedures are accompanied intraoperatively by navigational
guidance according to a pre-surgical plan. Primarily, the goal of image-guided intervention
is to improve the accuracy of surgeons in difficult surgeries, such as minimally invasive
procedures where ordinarily a high level of expertise is required.
6
CHAPTER 2. LITERATURE REVIEW
7
2.1.1 An Overview of Computer-Assisted Surgery using Preoperative
Imaging
The most common type of computer-assisted surgery can be broken down into four distinct
components: the preoperative planning stage, real-time tracking, registration, and calibration.
Pre-operative Planning Stage
In the preoperative planning stage, an anatomical model is generated from 3D image data,
usually obtained from computer tomography (CT) or magnetic resonance imaging (MRI).
The 3D image data is constructed from a stack of 2D images that are captured at set intervals along an axis and arranged parallel to each other. Subsequently, a segmentation
process is used to extract the anatomy of interest from the 2D images;this process is usually performed manually after pre-processing with various image processing filters. After
segmentation, a surface-meshed model is generated. The surgeons can then use this model
to establish a virtual plan, which may involve simulating the procedure or using virtual
landmarks to mark entry points and drill paths.
Real-Time Tracking
Real-time tracking is most commonly provided by a camera system that can accurately
measure the location of infrared emitting diode (IRED) markers within its detection volume. The camera system is capable of tracking targets that have been characterized by
using three or more IRED markers. Because the local coordinate frames of the targets can
be expressed in the common coordinate frame of the camera, transformations between any
two targets can be determined. Conventionally, all targets used in the surgical procedure
CHAPTER 2. LITERATURE REVIEW
8
are expressed with respect to the local reference frame of the target that is fixed to the
patient. Instead IRED markers, passive spheres can also be used. These spheres have a
special coating that reflects the infrared light from the position sensor.
Alternatively, an electromagnetic tracking system can be used. In an such a system, a
transmitter is used to create an electromagnetic field. A position sensor detects the strength
of the electromagnetic field to discern the location of the transmitter relative to the sensors. The advantage of using electromagnetic tracking is that a direct line of sight between
the sensor and the target is not needed. Currently, an electromagnetic tracking system is
typically not as accurate as an optical tracking system.
Registration
Registration is used to align two images of the same object that are captured at different
times, perspective or imaging modalities. Image- to-patient registration is a fundamental
task in computer-assisted surgery (CAS), where it is used to align the image coordinate
frame with the coordinate frame of operating room. Predominantly, a surface-based method
is used to solve the image-to-patient registration problem. In a surface-based registration a
digitizing probe is used to measure a set of points from the surface of the patient’s anatomy
intraoperatively. An iterative procedure is used to estimate a rigid-body transformation that
would best align this set of points with another set of points collected from the surface
of the meshed-based model of the same anatomy. Alternatively a fiducial-based method
can be used. In this method, radio-opaque markers are directly placed on the patient. The
fiducials are localized in the image coordinate frame by using image processing on the CT
or MRI images. Intraoperatively, a digitizing probe is used to localized the fiducials in the
coordinate frame of the operating room. A solution to the orthogonal Procrustes problem
CHAPTER 2. LITERATURE REVIEW
9
can be used to find the rigid-body transformation [23].
Calibration
A dynamic reference body (DRB) is a group of IRED markers that have been characterized
within a local coordinate frame. A DRB can be attached to a surgical tool and through a
calibration process the geometry and position of the surgical tool is expressed relative to
the attached DRB. Typically, machined blocks with embedded IREDs are used to facilitate
the calibration of certain tools. The calibration process can be performed pre-operatively
so long as there is no movement of the DRB relative to the tool.
Work Flow of Computer-Assisted Surgery with Preoperative Imaging
Prior to a surgery, a considerable amount of time may be dedicated to segmenting the
anatomy of interest from the CT scan of the patient by the technical team. A surgeon then
plans the surgery using a 3D model generated from the segmented CT images. The surgical tools are calibrated just before surgery, which allows the tracking system to determine
locations relative to the coordinate frame of the DRB attached to the patient. During the
procedure, a surgeon performs a surface-based or fiducial-based image to patient registration. A computer workstation displays images of the various tools superimpose on the
virtual model along with the pre-surgical plan to provide the surgeon with real-time navigational guidance. The advantage of using such a work flow for computer-assisted surgery is
that the planning stage can simulate the outcome of the more complicated procedures such
as total knee and hip replacements. The simulations can assist the surgeons in planning the
surgery more accurately.
CHAPTER 2. LITERATURE REVIEW
10
2.2 Image-to-Patient Registration
Conceptually, medical image registration is the task of relating two different models of
the same anatomy. A more technical description of registration is given as the process
to find a transformation that would align two different coordinate frames. Registration
is a fundamental component of computer-assisted surgery, where it is commonly used to
synchronize the physical pose of the patient in the operating room to a virtual model of
the patient; thus, enabling other key components such as navigation. Numerous different
methods have been developed for performing registration and it is beyond the scope of this
dissertation to provide an overview of medical image registration. Instead, the topics of
paired-point, fiducial-based and surface-based image to patient registration will be covered.
The reader can be directed to the review by Maurer and Fitzpatrick [66] for a more detailed
overview of other topics in registration.
2.2.1 Paired-Point Fiducial Registration
A common theme among all extrinsic registration methods, of which paired-point fiducial
registration is a member, is the usage of foreign objects that have been strategically placed
on the patient such that they appear in the image space [61].
Stereotactic Frames
One form of extrinsic registration, termed framed-based stereotaxy, is the oldest form of
registration with the first system being used over a century ago for neurosurgery [61]. In
framed-based stereotaxy, a frame containing landmarks visible in X-ray images was physically fixed to the head of the patient [85]. The lesions in the brain were located relative
CHAPTER 2. LITERATURE REVIEW
11
to the landmarks in the X-ray images [85]. A set of calculations were performed to transform this position to the coordinate frame of the stereotaxy to allow the surgeons to insert
needles and other surgical tools [85]. With the development of CT and MRI imaging, a
new stereotactic frame was developed that utilized vertical and horizontal struts as landmarks. The struts appeared as dots in the slices of the volumetric data captured by CT or
MRI; thus, the targets were located in reference to the dots in the slices. A computer was
used to perform calculation that would transform the position of the target in the slices to
the coordinate frame of the stereotaxy [58]. A computer-assisted stereotactic system was
also developed that reported the target location in the coordinate frame of the stereotaxy,
allowing the surgeon to plan the surgery and also to simulate the procedure [88].
Frameless Stereotaxy
Frame-based systems yielded a very accurate registration with the only drawback being
the frame itself, which impeded the movement of the surgeons when it was fixed onto the
head of the patient [23]. A frameless method was made possible with the development
of tracking devices (e.g., optical tracking, electromagnetic tracking, acoustic tracking, mechanical tracking) capable of determining the physical location of a point in the operating
room. Generally, in a frameless method, the markers, referred as fiducials, were implanted
directly into the anatomy of the patient (e.g., the skull or bone surface) [23].
Locating the Fiducials
Fiducials have been constructed with metallic alloys (tantalum, titanium) to make them
visible in X-ray images [64]. Similarly, X-ray fiducials can be fabricated using iodine
compounds, or for MRI gadolinium agents can be used [64]. Various tools can be fabricated
CHAPTER 2. LITERATURE REVIEW
12
with special markers that are tracked by a tracking system. For instance, it is common to
attach IREDs to surgical tools in order for an optical tracking system to track its position.
A calibration procedure is then needed to determine the position and orientation of the
surgical tool relative to the IREDs attached to it (e.g., determining the tip of a probe). An
intraoperative coordinate frame can established by using a DRB attached to the patient.
The position of all the surgical tools can then be reported relative to the dynamic reference
body. A calibrated digitizing probe can be used to determine the physical location of each
fiducial in the coordinate frame of the DRB by touching the surface of the fiducials with
the tip of the probe [23].
Image processing is used to localize the fiducials in the image coordinate frame. Wang
et al. [90] used an initial threshold to identify possible candidate voxels for the position
of the fiducials. The voxels connected to the candidate voxel were assessed based on their
intensity value to see whether they were part of a fiducial. The regions were grown based on
the physical dimension of the fiducial. An intensity weighted centroid was then calculated
for each region. Chen et al. [13] developed an automatic fiducial detection algorithm based
on edge map construction and then curvature-based object detection.
A method based on 3D morphological segmentation has been described by Gu and
Peters [31]. Conceptually, the method was to match any regions that would fit inside a
3D sphere slightly bigger than the actual fiducials. A “top-hat” transformation, which is a
morphological algorithm that uses mathematical morphology operators to extract objects
from images with a 3D spherical element, was used to search for possible candidate voxel.
A morphological “C-Dilation” filter was used to reconstruct the fiducial regions that were
lost during the top-hat transformation process. The intensity weighted centroid for each
fiducial region was then calculated.
CHAPTER 2. LITERATURE REVIEW
13
Template matching has also been developed. Tan et al. [86] used edge detection on the
slices of a CT image and then matched those edges against a pre-defined list of template.
Wang and Song [91] also developed a more advanced template matching algorithm. In their
method, a model of the fiducial was generated by creating a projection height image (PHI).
At each voxel, a PHI was generated and the pixel difference between the PHI generated at
each voxel and the PHI generated from the model was calculated. A threshold was used to
assess the pixel difference to determine if that region was a fiducial.
The accuracy of locating the fiducials can be quantified by calculating the fiducial localization error (FLE). Maurer et al. [63] defined FLE as the error in determining the location
of a fiducial from the images. The error is the difference between the actual location of
the fiducial and the location of the fiducial as determined by a bead detection algorithm.
The FLE was specific to the method that was used to localize the fiducials. Typically, FLE
occurred in locating the fiducials in the image coordinate frame F LEI and locating the
fiducials in the physical patient coordinate frame F LEP . In order to lower F LEI , it was
recommended that the dimensions of the fiducials should be considerably larger than the
voxel dimension of the imaging device [89]. The F LEI can also be estimated from the
fiducial registration error. Maurer et al. [64] also determined F LEI experimentally to be
approximately 0.4 mm for a CT image device with a voxel dimension of 0.5x0.5x4 mm,
using fiducials with a diameter of 7 mm and a height of 5 mm. The F LEP depended on
the accuracy of the tracking system. For an optical tracking system, which is usually the
most accurate tracking method, the F LEP was approximately 0.3 mm.
CHAPTER 2. LITERATURE REVIEW
14
Solutions to Point-Based Registration
The problem of point-based registration consists of two stages. The solution to the first
stage has already been outlined in the sections above, which is to determine the location
of the corresponding points in the two coordinate frames (e.g., the image coordinate frame
and the physical patient coordinate frame). The second stage is to align the two coordinate
frames by finding a rigid-body transformation using the two corresponding point sets. The
problem can be better formulated using the following definitions.
Given a point set Z with points z~i that is measured experimentally, and another point
set X with points x~i that is derived from a model that should align with Z, find a rigid
transformation T (consisting only of a rotation and a translation) that maps the points set
Z to coordinate frame of X. To determine the best transformation T , the root mean square
error of the Euclidean distance between T (Z) and X is most commonly used. Thus, the
rigid-body registration problem, when correspondence between the point set is established,
is a least sum of squares estimation problem. This problem is otherwise known as the
absolute orientation problem or the orthogonal Procrustes problem [84, 35].
arg min(
T
n
X
kT (~
zi ) − x~i k2 )
(2.1)
i=1
Many methods have been developed to find a solution to this problem. The first closedform solution was developed in 1966 by Schonemann [65]. Arun et al. [3] solved the problem using a similar method to Schonemann by using a singular value decomposition (SVD)
of the covariance matrix of the centroid-subtracted position vectors in the two coordinate
frames. Horn [35] developed a closed form solution that used quaternion to represent the rotation. The method found the unit quaternion by finding the eigenvector that corresponded
to the most positive eigenvalue of a 4x4 symmetric matrix. A dual-quaternion method to
CHAPTER 2. LITERATURE REVIEW
15
solve the problem has also been developed by Lorusson et al. [56]. They performed a study
utilizing Arun’s method, two versions of Horn’s method, and the dual quaternion method
to solve the orthogonal Procrustes problem, finding no significant differences among these
four methods.
Clinical Studies
A greater concern is the accuracy of the image guided navigational system, which can
be assessed by measuring the distance between a point in one coordinate frame and its
corresponding point in the other coordinate frame after registration has been performed.
This error is termed the target registration error (TRE) and if a fiducial-based pair point
registration is used, the TRE is calculated on points other than the fiducials [29]. Fitzpatrick
et al. [29] have illustrated that the TRE is proportional to FLE, inversely proportional to
the square root of the number of markers, and is strongly dependent on the configuration
of the markers.
Image-guided navigational systems based on using fiducials for pair-point registration
have been proposed for various areas of surgery. Kato et al. [41] have proposed a frameless
and armless navigational system for neurosurgery. Maurer et al. [65] designed a commercial system for image guided surgery based on using fiducials for paired-point registration
for MRI or CT images. Barnett et al. [6] used a fiducial based image guided system for
brain biopsies, and reported a high success rate in 218 cases. Additionally, Taylor et al. [88]
have compiled a review of cases using fiducial-based image guided system for performing
surgical procedures in neurosurgery and orthopedic surgery.
CHAPTER 2. LITERATURE REVIEW
16
2.2.2 Surface-Based Registration
The accuracy obtained from fiducial based registration is accepted widely as the gold standard for image to patient registration [23]. However, the introduction of fiducials on the
patient requires an additional invasive procedure; surface-based registration is a more attractive method, wherein points are obtained by measuring from the surface of the patient’s
anatomy, and afterwards matched against the surface of the model based on a similarity
criterion [5].
Generally, there are many methods that are used for the representation of surfaces. In
this discussion we concentrate on feature-based or landmark-based methods, and free-form
point-based methods, which have been used in orthopedic application for solving the image
to patient registration problem. We point the readers to the review from Audette et al. [5]
for a thorough discussion of surface-based registration.
Features
Features are usually classified into three categories, namely sparse points, curves, and regions. Sparse points are selected in well localized areas on the surface that exhibits a
defined geometric significance, such as extreme curvature (e.g., local peaks and pits). The
similarity criterion used to match features based on sparse points are surface curvature values (e.g., the type of extremal points) and the position of vectors to neighboring points [5].
Curves are selected based on ridge lines on the surface of the anatomy. Additionally,
lines separating the boundaries of different regions can be used as features. Curves are
matched by finding the longest contiguous sub-curves appearing in the two curves [5].
Regions are defined on the surface based on the homogeneity of an area or an area
CHAPTER 2. LITERATURE REVIEW
17
inscribed by a boundary. Matching of regions is then performed by using specific characteristics of the regions [5].
A rigid-body transformation is usually determined as part of the matching process due
to the sparseness of the points from the features. The methods of determining the rigidbody transformation are usually one of the solutions to the orthogonal Procrustes problem.
Free-Form Point-Based Registration
Feature-based methods often depend on landmarks on the anatomy, which are sometimes
hard to locate depending on the surgical procedure. Alternatively, the surface of the anatomy can be represented by physically measuring points from it [5]. This method is termed
a free-form surface registration. Typically, in a computer-assisted intervention, one set of
points is derived from the surface of CT image and the another set of points is measured
directly on the anatomy of the patient by using the tip of a calibrated probe that is tracked
by a tracking system. The two set of points are assumed to be relatively closely aligned
and an iterative method is used to establish a correspondence between the two point sets.
Afterwards, any solution to the orthogonal Procrustes solution can be applied to solve for
the rigid-body transformation [66]. The formula below is the same as Equation 2.1 except
that the point set Y , which is the set of points y~i closest to Z, is used instead of X:
arg min(
T
n
X
kT (~
zi ) − y~ik2 )
(2.2)
i=1
Many methods exist to solve for the correspondence between two set of points that are
assumed to be relatively closely aligned. The most popular method is the iterative closest
point (ICP) algorithm from Besl and McKay [9], which matched the two point sets by
minimizing a similarity criterion based on the point registration error. In each iteration, the
CHAPTER 2. LITERATURE REVIEW
18
closest model point (y) was updated until either a local minimum to the PRE was reached
or a limiting number of iterations have been tried.
Modifications have been made to ICP to increase its effectiveness in performing the
registration for computer-assisted interventions. The following is a small sample of the
modified ICP algorithms in the literature. Tang [87] derived a special case of ICP for
performing a fiducial based 2D/3D registration by forcing a fixed correspondence between
the points of the surface models and the back projected lines from the X-ray images to the
X-ray source. Betting et al. [10] modified ICP to handle 6-D data and used a k-d tree to
perform the closest-point operation. Cuchet et al. [17] tried to accelerate the ICP algorithm
by using a chamfer map to find the closest points by approximating the Euclidean distance.
The ICP algorithm is prone to failure if the initial transformation is extremely far from
the final alignment or if statistical outliers are present in the point sets (e.g., points are
measured far from the actual anatomy or outside of the images). The former problem was
addressed by Besl and McKay [9], who suggested slightly perturbing the initial transformation during each run of ICP to ensure that the local minimum to the objective function
is not far from the global minimum. However, the traditional ICP algorithm cannot properly address the latter problem; thus, statistically robust algorithms have been designed to
handle cases where outliers are present into the dataset.
Previous works have shown that it is possible to use robust statistics to solve the registration problem. The following is a brief description of the least median of squares (LMS)
and the random-sample consensus (RANSAC) algorithm.
arg min(med(kT (~
zi) − x~i k2 ))
T
i
(2.3)
In the LMS algorithm, Equation 2.3 has a replacement of the summation operator in
CHAPTER 2. LITERATURE REVIEW
19
Equation 2.1 with the median operator; in other words, the LMS of the registration residual
is calculated among all of the points once a correspondence between the two datasets was
established [81].
To find the minimization of the registration residuals, a brute-force method has been
used, finding the LMS of the registration residual for all possible combinations of correspondence among the two data sets [81]. This method is inefficient computationally, but
various heuristics have been used to make the algorithm more efficient by reducing the
search space to a fixed number of randomly generated subsets.
RANSAC is a paradigm for fitting experimental data into a predefined or selected
model, originally proposed by Fischler and Bolles [28]. This problem is generally broken down into two tasks. The first task, which is known as the classification problem,
requires selecting the data points that would best fit the model. The second task is to estimate the parameters of the models. The RANSAC paradigm avoids the pitfalls of averaging
techniques, such as least squares, for model fitting because RANSAC does not succumb to
the effects of gross outliers. They first selected the minimum number of points that could
instantiate the model and estimated the free parameters from these points. Afterwards, this
instantiated model was used to include other data points that were within a given error
tolerance. This new set of points was called the consensus set. The consensus set should
contain as many of the original outliers as possible, usually determined by the user. If the
consensus set passed this threshold then a new model was calculated; otherwise, a new set
of minimum points were used to instantiate a new model. This process continued until the
criterion was satisfied or it terminated and returned failure after some predetermined number of iterations. Meer et al. [69] have observed experimentally that LMS and RANSAC
produce similar results. There are many other robust registration algorithms, such as the
CHAPTER 2. LITERATURE REVIEW
20
one proposed by Kumar and Hanson [49] that used the Tukey-M estimator to register 3D
lines with 2D lines when correspondence was provided.
A robust version of ICP has been designed by Masuda and Yokoya [62] that used the
LMS estimator for the point registration error objective function. Additionally, a statically
robust version of the ICP algorithm was reported by Luck et al. [57] that used simulated
annealing to find the rigid-body transformation that corresponded to the global minimum
of the objective function.
The spotlight algorithm designed by Ma and Ellis [60] was a robust surface-based registration system for performing image to patient registration during computer-assisted orthopedic surgery. The spotlight algorithm initially directed the surgeon to contact the points
with a calibrated probe on regions on the patient that corresponded to highlighted “spotlight” regions in the model. The measured points were then matched against the spotlighted
points on the model using the standard ICP. Additional points were collected on the exposed surface of the bone; this larger set of points was used to constrain the translational
and rotational components of the registration. An iterative procedure was used to determine
the best initial registration; for each iteration, the initial registration was slightly perturbed
and the residual from the resulting registration was calculated. The best initial registration
produced the highest number of residuals that were below a user specified threshold. Afterwards, an ICP algorithm based on the Tukey-biweight M-estimator was used to refine
the initial registration.
A unified method to surface based registration has also been proposed by Ma [59].
The method provided guidance for the surgeon to select the next optimal point that would
lead to a more accurate registration; additionally, as each point was acquired feedback was
provided on the resulting accuracy of the registration by estimating the uncertainty in the
CHAPTER 2. LITERATURE REVIEW
21
registration parameters.
Besides robust algorithm and ICP, the objective function described in Equation 2.1 can
be solved by using standard optimization methods such as the Nelder and Mead [72] downhill simplex method, conjugate-gradient methods that require the first partial derivative of
the objective function to be found [76], or a quasi-Newton method that uses Newton’s
method to find a line direction to minimize [76]. There are many other classes of methods and the reader can refer to the paper by Press et al. [77] for a description of some
algorithms.
Clinical Studies with Surface-Based Registration
Surface based registration is primarily used in computer-assisted orthopedic surgery to perform the image to patient registration. Computer-assisted orthopedic surgical procedures
based on surface based registration have been used successfully on patients for knee replacement [19], pedicle screw placement [70], high tibial osteotomy [25], distal radius
osteotomy [16], and excision of osteoid osteoma [60] among many other clinical applications.
2.2.3 Other Registration Methods
The most useful current mode of registration is surface-based, whereby a surgeon uses a
calibrated probed to gather a set of points from the surface of the patient’s anatomy [23].
Despite all the advances to guide surgeons to perform the registration process, it is still a
technical feat that is best left in the hands of experts. Hence, methods have been developed to register the image to the patient without the surgeon having to participate. These
methods include atlas-based registration, where an atlas of an anatomy is morphed to fit the
CHAPTER 2. LITERATURE REVIEW
22
anatomy of a specific patient, and image-based registration, where images of the same object captured at different time or modality are matched based on a similarity measure [66].
One of the topics in the next section is the use of intraoperative imaging modalities to facilitate a direct navigation scheme where the image to patient registration is not performed
intraoperatively.
2.3 Intraoperative Imaging
This section provides an overview of recent developments in intraoperative imaging with a
focus on their integration into computer-assisted interventions.
2.3.1 Intraoperative 2D Imaging Devices
A C-arm fluoroscope uses X-rays to provide intraoperative images, especially where direct
visualization of the anatomy is not possible. It is especially common in orthopedic surgery
and also has many application in cardiac and vascular surgery. Ultrasound can also be used
intraoperatively, with a particular attraction being that no ionizing radiation is emitted from
this device [12]. This section describes various areas where a conventional C-arm fluoroscope and a ultrasound machine have been used in a computer-assisted surgical system.
Computer-Assisted Surgery with Intraoperative 2D Imaging
The focus of this section is to provide a general overview of using a 2D intraoperative
imaging device to facilitate the process of registration, or to provide the visualization for
navigation in a typical computer integrated surgical workflow.
Common methods to extract the pose of the patient as a point set, which is used to
CHAPTER 2. LITERATURE REVIEW
23
register against a 3D model, include digitizing points from the surface of the anatomy
(e.g., surface-based registration) and implanting markers into the patient (e.g., fiducialbased registration) [66]. Alternatively, 2D images of the patient can be captured using an
intraoperative imaging device such as an ultrasound system or a C-arm fluoroscope. The
ensuing registration is to determine a rigid-body transformation that relates the coordinate
frame of the model (generally generated with CT) with the coordinate frame of the 2D
images [66].
2D/3D registration is regarded as a challenging process and the associated computationally expensive algorithms are an impediment for routine use in a clinical setting. Typically,
a calibration process is required to determine the physical location of each 2D image in the
operating room with the coordinate frame of the optical tracker acting as the global or world
coordinate frame [75]. For example, a custom jig containing several optical markers can be
attached to a C-arm fluoroscope or an ultrasound transducer in order to deduce the location
of the imaging source and other important characteristics of the imaging device, which are
then used to locate each 2D image relative to the tracking system [87]. Examples of a calibration process include a study from Tang [87] that outlined a calibration technique for a
C-arm fluoroscope and the study from Chen et al. [12], which is a calibration technique for
an ultrasound transducer.
The physical location of each 2D image is used, in conjunction with the features of the
patient’s anatomy captured in each 2D image, to formulate a method to solve the 2D/3D
registration problem. For radiographic 2D images the back-projection lines, from the 2D
images to the X-ray source, can be used for the registration of the contours of the anatomy
derived from the 2D images with the shape features extracted from the shape of the anatomy
from the CT model [27]. Another method is to match the 2D images against a digitized
CHAPTER 2. LITERATURE REVIEW
24
reconstructed radiograph (DRR) from the CT model based on a similarity metric such as
phased-based mutual information [18]. Furthermore, fiducial markers have been used as a
method for solving the 2D/3D registration problem [87, 82].
In a study from Chen et al. [12], a system was designed for ultrasound-guided computerassisted orthopedic surgery. Ultrasound images were captured pre-operatively using a calibrated ultrasound transducer to construct a 3D model of the patient’s anatomy. Intraoperative ultrasound images of the patients anatomy were acquired with a calibrated ultrasound transducer. A mutual-information based registration was used to match the intraoperative 2D ultrasound images against the collection of ultrasound images captured preoperatively. This matching process could be used to find the image to patient registration
because the coordinates of each 2D ultrasound image within the 3D ultrasound volume
were known; in addition, the locations of the 2D ultrasound images acquired intraoperatively were given relative to the coordinate frame of a position sensor in the operating
room.
Other attempts at designing a system based on ultrasound guidance relied on using a
surface-based method for performing the image to patient registration. This method suffered from the series of complex image processing that needed to be applied to the images
in order to identify the features of the anatomy correctly from the ultrasound images. This
segmentation process is an active area of research, with some of the recent developments
utilizing phase congruency [32] and intensity-based information [74]. Other techniques
include using a dynamic programming algorithm to search for surfaces of the bone in ultrasound images [30]. An extensive overview of this area is provided by the review from
Noble and Boukerroui [74].
CHAPTER 2. LITERATURE REVIEW
25
Fluoroscopic images have also been used directly in fluoroscopic-guided computerassisted surgical systems. To enable navigation with real-time visual feedback of the surgical procedure, two components need to be determined. The first component was to determine the position of the C-arm fluoroscope relative to the coordinate frame of the optical
tracking system CA
C T (CA stands for the coordinate frame of the C-arm and C stands for
the coordinate frame of the optical tracking system) [75]. The solution was to simply attach
a plate containing IREDs directly on to the C-arm fluoroscope [75]. The second component
was to determine the relationship between the position of the C-arm fluoroscope and the
2D X-ray images. The solution to the second problem was not straightforward because the
X-ray images were distorted by pin-cushion effects due to the spherical shape of the image
intensifier, and also distortion can arise from the position of the image intensifier to the
earth’s and other external magnetic field. Additionally, the C-shaped frame of the fluoroscope also experienced deformation when it was rotated [75]. Calibration plates were used
to correct the deformity allowing for an accurate derivation of the transformation between
the coordinate frame of the C-arm fluoroscope as defined by the IREDs attached to it and
the coordinate frame of the 2D X-ray images
CA
S T
(S stands for the coordinate frame of
CA
the image) [87]. The transformation CA
S T was concatenated with the transformation C T
to complete the image to patient registration [75]. The images of the surgical tools were
then overlaid on top of the fluoroscopic images to provide for navigation with visual feedback. During fluoroscopic-guided navigation, an anterior-posterior fluoroscopic image and
a lateral image are commonly used to aid the surgeon [75]. An example of such a system
is described in the study from Mayman et al. [67] that demonstrated the use of fluoroscopic images for navigating surgeons in inserting guide-wires into the femoral heads for
open reduction and internal fixation of hip fractures. However, navigating on 2D images
CHAPTER 2. LITERATURE REVIEW
26
is less than ideal for certain procedures; thus, certain studies had integrated an intraoperative imaging device capable of capturing CT images into the operating room. The topic of
the next section is a general overview of intraoperative imaging device that are capable of
providing CT-like images.
2.3.2 Intraoperative CT Imaging
3D images, captured intraoperatively, can be used to guide the surgical team during minimally invasive procedures. The benefit of using an intraoperative CT scanner was made
apparent by a study from Nelson and Duwelius [73] where a difficult procedure for locating
entry points in internal fixation was averted by using 3D images acquired intraoperatively.
The study demonstrated how 3 CT images captured throughout the procedure were used,
instead of palpating the pelvic region, for the proper placement of a 7.0 mm cannulated
screw. Similarly, Mayr et al. [68] also used an intraoperative CT scanner for guidance in
correcting calcaneal osteosynthesis. Additionally, the possibility of using a mobile gantry
CT scanner intraoperatively in the trauma and critical center was demonstrated by Mirvis
et al. [71].
Alternatively, CT images could be reconstructed from cone beam X-rays emitted by
a flat panel C-arm fluoroscope. Siemens released a mobile flat panel C-Arm fluoroscope
(Siremobil ISO-C-3D system, Erlangen, Germany) that was capable of performing a 190◦
spin acquisition in 100 seconds. During this spin acquisition 100 cone-beam X-ray images
were captured and were subsequently used to re-create a 3D isotropic volume with a dimension of 2563 voxels and a voxel size of 0.46 mm [55]. The CT images produced by
the ISO-C 3D system were inferior in quality to the CT images from a helical CT scanner.
However, it was reported [47] that the diagnostic accuracy of an ISO-C 3D system was
CHAPTER 2. LITERATURE REVIEW
27
equal to that of a conventional scanner.
The floor-mounted Integris 3DXR biplane scanner (Phillips Medical Solutions, Best,
the Netherlands) was a more powerful flat panel C-Arm fluoroscope than the ISO-C 3D.
The 3DXR system was capable of performing a 180◦ spin acquisition in 8 seconds, with 100
projection images were captured during the spin. A 3D isotropic volume with dimensions
of 2563 voxels and a voxel size of 0.23 mm was reconstructed from the projections [78].
The Integris 3DXR system had also been used in clinical studies [42].
Computer-Assisted Surgery with Intraoperative CT Imaging
Direct navigation on the 3D volumetric data acquired intraoperatively by a CT imaging
device has been developed recently. An image-guided system that utilizes such a scheme
absolves the surgical team from having to perform registration during the surgical procedure. Instead, a direct navigation scheme uses a preoperative calibration stage to register
the coordinate frame of the image space to a fixed frame visible to a tracking system. In
this regard, the workflow is similar to the stereotactic frame-based registration, but the fixed
frame is used only to find a relationship between the image and tracking coordinate frame
so the fixed frame is not attached to the patient. During the surgical procedure, the information from the calibration process is used in conjunction with the position of the patient
relative to the fixed frame in order to provide image guided navigation.
A version of direct navigation with a stationary CT scanner was designed by Jacob et
al. [37], which they termed the modality-based navigation system (MBNS). Essentially, the
stationary scanner captured an image in the same physical space of the interventional room
during each scan. Thus, it was possible to register that fixed physical space to the coordinate frame of an optical tracker. This registration was performed prior to surgery with the
CHAPTER 2. LITERATURE REVIEW
28
aid a manufactured calibration block that contained several fiducial markers. By positioning the block correctly, a 3D image of the markers could be obtained and an intensity-based
method could then be used to determine the location of the markers. Subsequently, a digitizing probe was used to localize the position of the markers in the coordinate frame of
the optical tracker. The problem of finding a transformation between the coordinate frame
of the CT image space and the optical tracker then resembled a fiducial-based registration
problem. Thus, a simple solution to the absolute orientation problem could be used to find
the transformation. One drawback in the framework that was presented in the study by Jacob et al. [37] was limited movement of the patient because the patient could not be moved
relative to the imaging device during the entirety of the procedure. Some studies found this
drawback to be impractical and thus reverted to using a fiducial-based registration with an
intraoperative CT scanner in their navigated surgical procedure [2].
The MBNS framework was used to provide navigation to some minimally invasive procedures. In a subsequent study by Jacob et al. [39] the surgical procedure of percutaneous
fixation of the coronal acetabular was carried out under CT-navigation using the MBNS
scheme. The Merle-d’Aubigne score was used to rate the procedure that was performed on
four patients. The Merle-d’Aubigne score is a system designed to rate spinal surgery. A
score is assigned based on the accuracy of the drilling and also the postoperative feedback
such as pain and other complications. The MBNS navigated method scored 18 (highest
score) for three of the fixations and a score of 17 for the remaining fixation. Huegli et
al. [36] also used the MBNS system successfully to perform a CT-navigated closed reduction and percutaneous fixation of a displaced anterior column acetabular fracture on a
patient. Finally, Eggers et al. [22] used a modified MBNS method with a mobile gantry
intraoperative CT scanner. The CT gantry was tracked by attaching IRED markers on the
CHAPTER 2. LITERATURE REVIEW
29
cover. A one-time calibration procedure was performed to determine the coordinate frame
of the CT image space relative to the fixed IRED markers on the cover. Intraoperatively, the
position of a dynamic reference body (DRB) attached to the patient was determined with
respect to the fixed IRED markers on the CT gantry. The resulting registration allowed the
procedure to be navigated by using the 3D images acquired intraoperatively. Additionally,
the DRB on the patient provided the surgical team with the flexibility of repositioning the
patient anywhere within the detection volume of the optical tracker.
Direct navigation with a flat-panel 3D fluoroscope was carried out in a manner similar
to that of Eggers et al. [22]. In a study by Ritter et al. [80], direct navigation was used
with a Siemens ISO-C 3D system. In the study, a preoperative registration process was
performed by attaching a reference plate to a location on the C-arm that was visible to
the optical tracker. Using the information from a manufactured calibration device that
contained IRED’s and radio-opaque markers, a transformation between the image volume
and the reference plate on the C-arm was determined. This calibration process only needed
to be performed daily because the motion of the C-arm was highly repeatable, thus ensuring
the same physical space in the operating room was captured during every spin acquisition.
Intraoperatively, a DRB was attached to the patient in order to track the position of the
patient relative to the tracker plate on the C-arm. The accuracy of direct navigation with
a flat-panel 3D fluoroscope depended heavily on the mechanical reproducibility of the Carm spinning motion. Ritter et al. [80] found a deviation of 0.91 mm in the mechanical
motion of the C-arm in the ISO-C 3D system and reported the navigational error based on a
phantom study to be 1.65 mm. Kraats et al. [48] utilized the same direct navigation scheme
on the Integris 3DXR system and experimentally determined the mechanical stability of
the C-arm motion to be 0.23 mm and reported the navigational error based on a phantom
CHAPTER 2. LITERATURE REVIEW
30
study to be around 1.1 mm.
Hamming et al. [33] recently reported another direct navigational scheme that was
based on using a stereotactic frame. The frame contained several special multi-modality
markers that were detected by an optical tracking system. Additionally in the center of each
multi-modality markers was a 3 mm ball bearing that could readily detected by a C-arm
3D fluoroscope. The locations of the multi-modality markers in the coordinate frame of
the optical tracking system were obtained using the camera system API. A two-stage process was used to localize the the ball bearing component of multi-modality markers in the
coordinate frame of the image. The first stage was to use an intensity-based thresholding
algorithm to detect the centers of the ball-bearing from the 2D X-ray cone beam projection.
The 3D coordinates of the ball bearings were obtained in the second stage, which involved
applying a transformation to the 2D coordinates of the ball bearing. The transformation
was obtained through a calibration process, which was used to obtain information on the
geometry of the C-arm. A solution to the orthogonal Procrustes problem was used on the
two point sets to determine the transformation between the coordinate frame of the image
and the tracking system. The advantage of using this method was that the entire process
was automated. In a normal stereotactic frame-based registration, the fiducials have to been
manually digitized.
2.3.3 Intraoperative MRI
An overview of intraoperative imaging modalities is not complete without addressing some
of the developments in intraoperative MRI, which has been used in recent years.
There is a compelling case for using magnetic resonance imaging (MRI) in imageguided surgery because it can capture multiplanar images that could be used to discern
CHAPTER 2. LITERATURE REVIEW
31
normal and abnormal soft tissues [40]. Recent studies have shown the feasibility of using
MRI intraoperatively for biopsy, thermal therapy, endovascular applications, and prostate
brachytherapy [40].
The closed-bore design of traditional MRI imaging device makes it difficult to integrate into image-guided therapy because of restricted access to the patient during imaging [40]. In recent years, advances have been made in MRI technology that allows for the
development of an open-magnet device capable of using pulse sequences to obtain images
quickly [40]. These open MRI systems allow for real-time, or near real-time, visualization
of a surgical procedure. The first open MRI system was the “double doughnut” design of
the Signa SP/I (GE Medical System, Milwaukee, WI, USA) with a field strength of 0.5 T.
The Signa had a 54 cm gap between two halves of the superconducting cylindrical magnet that can accommodate two medium-size physicians. Alternatively, a biplanar magnet
design allowed for the patient to be sandwiched between two flat panel magnetic poles.
The low-field permanent or resistive magnets that were typically used in this system could
generate a field strength ranging from 0.2 to 0.6 T. The Magnetom Open Vivia (Siemens
Medical Solution, Germany) is a MRI system that follows the biplanar design. The Magnetom allowed a surgeon to conduct a minimal invasive surgical procedure similar to using
a C-arm fluoroscope. The traditional MRI closed-bore system can still be used intraoperatively in monitoring type procedure such as thermal ablation of solid tumors in the head,
breast, neck, and liver [83].
Modifications to surgical instruments also need to be taken into consideration when an
MRI is used for image-guided intervention [40]. Surgical instruments constructed from
magnetic alloys such as iron cannot be used [40]. Stainless steel, which can be nonmagnetic, can be used; however, stainless steel tools that are brought close to the image
CHAPTER 2. LITERATURE REVIEW
32
volume can cause distortion in the images [40]. Currently, instruments such as biopsy needles are constructed from titanium alloy or ceramic material. The artifact that is caused by
a titanium needle can be characterized as roughly twice its actual size in the images [83].
Intraoperative MRI has been used successfully in neurosurgery for the resection of
brain tumors [40]. Recently, it has also been used in endovascular procedures where it
was used to track the position of a tool in the vessels [83]. To highlight the tool in the
images, conducting coils were used to wrap around the wire. However, the conducting
coils generated heat, which may cause complications to the nearby tissues [83]. Contrast
agents were also used to highlight certain regions, similar to X-ray imaging. MRI has also
been used to monitor thermal ablation, where temperature from cryotherapy or laser is used
to cause irreversible tissue damage in tumors [83].
Computer-Assisted Surgery with Intraoperative MRI
A common minimally invasive procedure is percutaneous biopsy with needles. Using MR
imaging simplifies these type of procedures because of its ability to capture multiplanar
high resolution images and the surgeons can use these images for tissue classification. An
intraoperative MRI system has been used for prostate cancer biopsy, where a needle was
inserted percutaneously to retrieve tissues from the peripheral zone of the prostate. The
position of the needle was localized using the artifacts that it caused in the imaging. Hata
et al. [34] demonstrated the workflow for a MRI navigated system for performing transperineal prostate biopsy. The process is similar to the stereotactic frame-based navigation that
was used in neurosurgery. A special template was designed with holes to guide the needle
trajectory and fiducials, detectable in MR imaging, were fabricated at specific locations of
the template. The template was attached to the table and placed beside the perineum. An
CHAPTER 2. LITERATURE REVIEW
33
optical tracking system was used to measure the fiducials in the coordinate frame of the
tracking system. A rigid-body transformation could then be found by using the location
of the fiducials in the MR image coordinate frame and its corresponding location in the
coordinate frame of optical tracking system. The registration aligned the position of the
template with the patient’s anatomy; thus, the needle trajectory could be tracked by fitting
the needle through one of the holes in the template. The trajectory of the needle was usually
determined by obtaining a scan right before the procedure to determine the location of the
biopsy.
Blumenfeld et al. [11] performed a thorough analysis to quantify the errors from this
surgical system and reported the following areas that were responsible for the inaccuracy:
localization of the fiducials on the template, needle deflection during the biopsy procedure,
and that imaging artifacts of the needle might not accurately reflect its actual location. A
similar intraoperative MR system for prostate needle biopsy has been developed by DiMaio
et al. [21], where a robot was used to guide the placement of the needle instead of using
a template. A pre-operative image of the patient was acquired with a closed bored MRI
system with field strength of 1.5T. The pre-operative image was then registered to the preprocedural image of the patient, which was acquired from an open-bored MRI system with
field strength of 0.5T, using a deformable registration to compensate the shifting of the
anatomy during the biopsy procedure. During the procedure, real-time 2D fast gradient
recalled (FGR) images were taken to visualize the surgery. The quality of the FGR images
did not convey tissue contrast adequately so, a navigational system was used to resample the
T2-weighted (T2W) values from the pre-procedural scan to provide surgeons with images
that illustrated the tissue contrast. The robot was then calibrated to the coordinate frame
of the image using an optical tracking system. The proper location of the needle was then
CHAPTER 2. LITERATURE REVIEW
34
determined using the robot and the insertion was performed manually.
2.3.4 Summary of Intraoperative Imaging
Ultimately, image-guided therapy using direct navigation on 3D volumetric data acquired
intraoperatively could only be fully realized and made practical by equipping an operating
room with a MRI, CT and/or flat panel 3D fluoroscope along with a navigational system [38]. Building such an operating room was expensive and complex, as shown by a
report from Jacob et al. [38]. Furthermore, it required training the nursing staff, surgeons,
emergency staff, and radiologists to understand the workflow and how to use the technology
correctly. Despite the challenges, there was a growing interest with having a multifunctional sterile suite, as indicated by BrainLAB offering an operating room (BrainSUITE
iCT, BrainLAB, Heimstetten, Germany) that was fully integrated with their navigational
system (VectorVision sky, BrainLAB, Heimstetten, Germany) and a CT scanner (Somatom
Emotion 6, Siemens Medical System, Erlangen, Germany) or an MRI since late 2007.
2.4 Overview of Computer-Assisted Orthopedic Surgery
With the development of stereotactic frames, the first application of computer aided surgery
was in neurosurgery [23]. Since then, many computer-assisted systems have been modified
to support computer-assisted orthopedic surgery. Orthopedic surgery is an ideal paradigm
for computer integration because most bone has a rigid structure. It is easier to work with
rigid structures, where the anatomy will not deform when it is probed or drilled; thus, the
shape and geometry of the patient’s anatomy continues to correspond accurately with the
CHAPTER 2. LITERATURE REVIEW
35
virtual model during the surgical procedure [75]. This section reviews some of the orthopedic surgical procedures that have been performed on patients using computer-assisted
surgical systems.
2.4.1 Surgical Procedures on the Spine
The spine is composed of 24 vertebrae and, because it surrounds the spinal chord, surgical
procedures in this region can benefit from computer assistance. The following section will
review internal fixation of fractures in the vertebrae.
Pedicle Screw Placement
Fractures, and deformities in the spine (e.g., scoliosis), can be treated with internal fixation
by a screw [70]. The only region of a vertebral bone that can safely accommodate a screw
is a region known as the pedicle; depending on the section of the spine, the diameter of
the pedicle can be from 3 mm to 10 mm [70]. Conventionally, the surgery requires a
high level of expertise because drilling of the screw is performed with limited or no direct
visibility of the spinal cord, lung, vessels, and nerves. Sometimes it is necessary to repeat
the procedure several times to locate the right position of the screw [53]. However, even
when the correct location has been located the depth of the screw cannot be discerned. A
computer-assisted system can be used to ameliorate these shortcomings by using a preoperative CT scan to generate a virtual model of the spine for surgeons to plan the drill
path. A surface-based method can be used to perform the image to patient registration, and
a navigational system can then track the tools and relay its position in real time relative
to the virtual model [53]. Merloz et al. [70] reported that a computer-assisted technique
performs better than manual insertion. In 52 patients that underwent computer assisted
CHAPTER 2. LITERATURE REVIEW
36
pedicle screw placement, no neurological complications were observed. Kim et al. [45]
has also tried to extend computer-assisted pedicle screw placement to the thoracic region
and found that 23 of 120 pedicle screw placement were outside of the safe zone. However,
14 of the 23 violations were deemed to be only minor.
Acosta et al. [1] performed a percutaneous screw placement using the intraoperative
ISO-C 3D fluoroscope. A direct navigation scheme is used in their study (StealthStation
Treon, Medtronics, Louisville, CO); hence, the image to patient registration was performed
in a pre-operative procedure. A DRB was drilled into the L3 spinous process and an optical
tracking system was used. An intraoperative 3D image of the L4 and L5 region of spine was
acquired with the ISO-C 3D fluoroscope. The 3D image was transferred to the workstation
which is then used by the surgeon to navigate the placement of K-wires in the pedicles
of the L4 and L5. The holes from the K-wire were then used for the placement of a screw
using the Sextant instrumentation. Post-operative CT was used to verify the accuracy of the
drilling, and Acosta et al. [1] reported accurate placement of all pedicle screws. Follow-up
with the patients showed a reduction in leg pain with no new neurological deficits.
Cervical Screw Placement
Percutaneous cervical screw placement requires exceptionally high level of expertise due
to the cervical spine being in close proximity to the spinal chord and vertebral artery [52].
Furthermore, there is high variability in the anatomical structures of the cervical spine
among individuals [52]. A traditional computer-assisted workflow relying on an intraoperatively anatomically based (e.g., surface-based or fiducial-based) image to patient registration cannot be used, because for this type of procedure the surgeon has no direct access to
the surface of the anatomy [52]. Computer-assisted fluoroscopic navigation only provides
CHAPTER 2. LITERATURE REVIEW
37
2D X-ray images for visualization, which is far from ideal. In the study from Langston
and Foley [52], a computer-assisted surgical system using the ISO-C 3D fluoroscope with
a direct navigational scheme was used for the percutaneous placement of cervical screws.
The direct navigation was provided by a StealthStation Treon (Medtronics, Louisville, CO)
and the reconstructed multiplanar slices from the intraoperatively acquired 3D images were
used for visualization. The study reported an accurate placement of 41 out of 42 screws on
cadavers.
2.4.2 Surgical Procedures on the Pelvis
The pelvis is a region that receives a lot of attention in orthopedic surgeries. It is common among the elderly to receive hip replacement surgery or fixation of fractures in the
pelvis. This section will describe the following computer-assisted surgical procedures on
the pelvis: total hip replacement, hip resurfacing, and fixation of pelvic fractures.
Total Hip Arthroplasty
Complications following total hip replacement such as dislocation and impingement arise
mainly due to malposition of the acetabular component [20]. Additionally, malposition of
the acetabular component can cause advanced wearing of the acetabular rim [20]. Conventionally, the surgeons only utilize a single anterior-posterior X-ray of the pelvis for visualization and a template tool to estimate the correct size of the acetabular implant. Very little
guidance is provided to the surgeon to locate the correct placement of the acetabular implant [20]. A mechanical guide is commonly used to help the surgeons align the acetabular
component intraoperatively, but the guide is configured using a pre-determined orientation
CHAPTER 2. LITERATURE REVIEW
38
of the pelvis and trunk, and not the orientation of the patient in the operating room; furthermore, the guide does not account for individual variations of the anatomy [20]. Therefore,
it is not a reliable method for guiding the placement of the acetabular implant. DiGioia et
al. [20] designed a computer-assisted system for total hip replacement that allowed a surgeon to establish an accurate plan for the surgical procedure, such as selecting the proper
size of the implant and mapping out the correct position. Additionally, a range of motion
simulation was performed after the plan was established, which allowed the surgeon to
view possible impingements caused by the implant. Navigation was provided by an optical tracking system and a surface-based method was used to perform the image to patient
registration. A DRB was attached to the pelvis as well as the handle of an acetabular cup
holder; thus, the pelvis and the implant could be located intraoperatively. This method has
been used successfully in patients and, because the procedure was navigated, the incision
was minimal [20].
Hip Resurfacing
Hip resurfacing is a procedure that re-shapes the surface of the femoral head for the attachment of a hemispherical metallic shell that fits into a metal acetabular cup [8]. The procedure is used as an alternative to total hip arthroplasty for young and active patients [50]. A
hip resurfacing procedure preserves most of the bone in the femoral neck which allows for
the possibility of total hip arthroplasty in the future [50]. A computer-assisted technique
based on using intraoperative fluoroscopic images has been proposed by Belei et al. [8].
Three points on the femur were digitized to complete the registration for the navigation
procedure. Two calibrated fluoroscopic images were acquired intraoperatively for planning
and guidance. Additional information for the planning stage was facilitated by using 3D
CHAPTER 2. LITERATURE REVIEW
39
and profile models from a database.
An alternative method has been proposed by Kunz et al. [50] based on using an individualized template. Using the 3D model from a CT scan, a specific template was manufactured from plastic that could fit a patient specific bone structure. Holes and other markings
were also made into the template for positioning of the tools. Therefore, the template replaced the need for registration and navigation because the positioning and orientation of
the tool relative to the bone was encapsulated in the template and its markings. Intraoperatively, the template was fitted onto the anatomy of the patient and tools were inserted
using the holes and markings. Kunz et al. [50] used the template for placing a pin down
the central axis of the femoral head for the hip resurfacing procedure. The resurfacing of
the femoral head and the preparation of the acetabulum were performed using conventional
tools, which were guided by a central pin.
Pelvic Osteotomies
An osteotomy is a surgical procedure where realignment of a bone is performed, often involving removing a section of it [60]. A computer-assisted technique has also been applied
to pelvic osteotomies where it is commonly used to correct a dysplastic hip. Langlotz et
al. [51] used a 3D model based on CT images and navigation provided by an optical tracking system. The image to patient registration was performed by a surface-based algorithm.
The system was used to guide the surgeons to perform a series of cuts in the ischium, pubis,
and ilium to remove the acetabular cup. The pre-operative plan was used to guide the surgeon to re-orient and fixed the acetabular cup correctly so it properly covered the femoral
head.
CHAPTER 2. LITERATURE REVIEW
40
Pelvic Fracture Fixation
Percutaneous sacroiliac fixation is used for osteosynthesis of unstable fractures in the posterior pelvic ring [39]. Without computer assistance navigation, this minimally invasive
procedure is difficult to perform due to the nature of the 2D images that are captured by
a traditional C-arm fluoroscope. Citak et al. [14] designed a computer assisted workflow
that utilized the ISO-C 3D fluoroscope in a laboratory setting. Similar to other interventions
with intraoperative CT imaging modalities, a direct navigation scheme was used to perform
the image to patient registration. The 3D images were acquired intraoperatively and direct
navigation was provided by the SurgiGATE system (Praxi-Medivision, Grenoble, France).
In the study, Citak et al. [14] evaluated the accuracy of the fixation by accounting for perforation of the cortex. Using this evaluation scheme, they reported that the computer-assisted
technique using an ISO-C 3D fluoroscope was more accurate than a computer-assisted
technique with a conventional C-arm.
A similar study has been conducted by Jacob et al. [39], where an intraoperative CT
scanner was used instead of the ISO-C 3D fluoroscope. In the study, a CT imaging suite
was converted to a sterile environment. A direct navigational scheme was used with their
in-house system, thus avoiding the intraoperative image to patient registration process. The
surgical tools were optically tracked and real-time visual feedback of the surgery was provided by the reconstructed multiplanar images from the CT images acquired intraoperatively with the CT scanner. A surgeon performed the percutaneous fixation of the pelvic
ring using their computer assisted surgical system. The Merle-d’Aubigne score, which is
based on the range of hip joint motion, walking distance, and pain on a scale of 1–6, was
used to assessed the outcome of the surgery. All four patients were given a score of 18 (the
highest).
CHAPTER 2. LITERATURE REVIEW
41
Huegli et al. [36] has also performed a closed reduction and percutaneous fixation of a
displaced anterior column acetabular fracture on a patient using the same system as Jacob
et al. [37]. In their study, Huegli et al. used a post-operative CT of the patient to conclude
that the fracture was fully consolidated and that there was no sign of osteoarthritis.
2.4.3 Surgical Procedures on the Lower Extremity
The lower extremity consists of the region starting with the thigh and ending with the
foot. This following section will provide a review of computer-assisted surgeries in the
lower extremity which includes total knee arthroplasty (total knee replacement) as well as
surgical procedures concerning the tibia and the ankle joint.
Total Knee Arthroplasty
Following the popularity of using CAOS for total hip arthroplasty, a computer assisted system has been designed for total knee arthroplasty [75]. In total knee arthroplasty, it is crucial to correctly align the prosthesis components with the tibia and femur in order to avoid
complications after the surgical procedure [19]. Conventionally, mechanical guides and
jigs are used to refine the alignment; however, the jigs and guides are not patient-specific,
and it is difficult to attach these guides on patients who are obese or have deformities [19].
Typically, a computer-assisted method for total knee arthroplasty is similar to the system
for total hip arthroplasty: preoperative CT scans are acquired for planning, optical tracking
is used for tracking the surgical tools, DRB’s are mounted on the tibia and femur to locate
them in the operating room, and a surface-based method is used to establish the image to
patient registration [75]. The computer is also used to calculate the mechanical axes of the
leg by attaching optically tracked reference pins on the distal femur; afterwards, the thigh
CHAPTER 2. LITERATURE REVIEW
42
is rotated in a circular manner and the computer can track this circular motion to determine
the center of rotation of the hip. A similar method is performed with the knee and ankle
to established the center of rotation of the knee. The mechanical axis of the femur is the
axis from the center of rotation of the knee to the hip. Once the mechanical axis of the
femur is established, reference markers are attached to the cutting block, which allowed
for navigation with the computer system to guide the surgeon in placing the cutting block
correctly on the patient. The surgeons can then make the cuts with a oscillating saw [19].
There is an ongoing debate on the clinical efficacy of computer-assisted systems for total knee arthroplasty [75]. Some commercial companies that concentrate on manufacturing
computer-assisted surgical systems have discontinued development for total knee arthroplasty. However, there are still ongoing research by many institutions on developing better
systems for computer-assisted total knee arthroplasty [75].
High Tibial Osteotomy
In a closing-wedge high tibial osteotomy (HTO), a lateral wedge of bone is removed from
the proximal tibia in order to realign the lower limb [25]. HTO is usually performed on
young and active patients who are suffering from osteoarthritis in the medial compartment
of the knee [25]. The realignment is used to alter the biomechanics of the knee so most of
the load is transmitted to the lateral compartment instead [25]. High accuracy in the incision
of the wedge is needed to ensure proper healing and realignment. The traditional procedure
is performed by mapping out the procedure on a X-ray image. The proper correction angle
places the upper plane of the wedge parallel to the tibia’s plateau and the lower plane of
the wedge above the tibia tubercle [25]. The outcome of the surgery is dependent on the
correction angle; thus, computer-assisted surgical systems have been developed to improve
CHAPTER 2. LITERATURE REVIEW
43
the accuracy of HTO. Ellis et al. [25] proposed a computer-assisted system for HTO with a
preoperative planning stage using a 3D model from CT images. Additionally, a simulation
was performed by the computer to illustrate the result of the osteotomy from the plan.
Image to patient registration was performed by using fiducials and navigation was provided
to guide the surgeon in placing Kirschner wires on the resection planes. An alternative
method was proposed by Ma and Ellis [60] that utilizes the same system except a robust
surface-based method was used to perform the image to patient registration instead of a
fiducial-based method.
Revascularization of Osteochondral Defects
An osteochondral defect affects the bone and the underlying cartilage of a joint [79]. It is
commonly found in the talus, which is a bone in the ankle joint. Revascularization of the lesion, the recommended surgical procedure to correct an osteochondral defect, is facilitated
by subchondral drilling of the lesion. In a study from Richter et al. [79], osteochondral
defect in the talus was corrected by a computer-assisted retrograde drilling of the lesion
using 3D images acquired intraoperatively by the ISO-C 3D fluoroscope. Direct navigation was provided by the SurgiGATE system (Praxi-Medivision, Grenoble, France) and the
drilling trajectory was planned intraoperatively using a virtual model constructed from the
3D image acquired using the ISO-C 3D fluoroscope. A DRB was drilled into the talar
head to provide the patient’s reference frame. A customized drill was tracked by an optical
tracking system during the navigated procedure. Arthroscopy was used after the drilling to
ensure that the cartilage was intact. Richter et al. [79] concluded from their study that using
a direct navigation scheme was ideal for the surgical procedure since the 28 bones and 30
joints of the foot are subjected to slight movements; thus, the position and orientation of the
CHAPTER 2. LITERATURE REVIEW
44
bones in the operating room might not correspond with the preoperative CT scans, which is
problematic for performing the image to patient registration using pre-operative imaging.
2.4.4 Surgical Procedures on the Upper Extremity
The upper extremity, more commonly referred to as the arm, consists of the region from
the shoulder to the fingertips. This section reviews computer-assisted surgeries in the upper
extremity which includes surgical procedures on the radius (forearm) and the wrist.
Distal Radius Osteotomy
A distal radius osteotomy (DRO) is use to correct deformities caused by a malunion of a
fracture [60, 16]. Traditionally, DRO is performed with very little guidance. The surgeon
performs an incision at the location of the original fracture and the realignment procedure
is accomplished using an X-ray image [60, 16]. This procedure is often difficult to perform
correctly because the plan is on a 2D image and also because of soft tissue contractures
around the malunion [60, 16]. After realignment, a trapezoidal bone graft is used to fill the
bone gap and a fixation plate is screwed into place [60, 16]. Besides providing the navigation for the initial incision and correctly placing the fixation plate, a computer-assisted
surgical system can allow the surgeon to plan the DRO using a 3D model constructed from
CT images. Ma and Ellis [60, 16] devised a scheme where a mirror image of the healthy
wrist of the patient was used as a template to aid the realignment process during the preoperative planning stage. A robust surface-based method is used for the image to patient
registration during the actual clinical procedure.
CHAPTER 2. LITERATURE REVIEW
45
Scaphoid Fixation
The scaphoid is a small carpal bone in the wrist and fractures along its waist are commonly
reported after using one’s hand to break a fall [7]. Cast immobilization can take a period
of up to 6 weeks and malunion might occur. Thus, it is desirable to mend the fracture by
using internal fixation so as to avoid later complications. Because of the location of the
scaphoid, an open fixation might damage the cartilage and ligaments of the wrist. The
preferred procedure is to insert a screw percutaneously using a conventional fluoroscope
for guidance. The main drawback of using this technique is having to use 2D X-ray images
for guiding the surgical procedure and for locating the central axis of the scaphoid. It
is difficult to adapt this procedure to the traditional computer-assisted surgical workflow
because a surface-based or fiducial-based registration cannot be used successfully in the
region of the wrist. Furthermore, there is no ideal location for the attachment of a DRB
in the wrist [7]. Beek et al. [7] proposed a solution for performing the image to patient
registration for this procedure by using intraoperative ultrasound. A calibrated ultrasound
transducer was used to image a model of the scaphoid. An image processing algorithm was
used to segment the surface of the scaphoid, which was then represented by a set of points.
This set of points from the ultrasound images was registered to a set of surface points from
the CT model using a modified ICP algorithm. The surgical tools were tracked optically
for navigation. The accuracy of the surgical procedure was comparable to the conventional
fluoroscopically guided method in a laboratory setting.
An alternative surgical workflow was proposed by Kendoff et al. [43], where a radiotransparent arm splint board was used for holding the wrist in a flexed position and additionally, the board contained special holders for a DRB. Kendoff et al. [43] used a direct
CHAPTER 2. LITERATURE REVIEW
46
navigational scheme with the ISO-C 3D fluoroscope, so intraoperative image to patient registration was avoided. The VectorVision Sky system (BrainLAB, Heimstetten, Germany)
was used for the navigation. Under the computer-assisted guidance, a surgeon successfully
placed a screw down the central axis of the scaphoid in five cadavers.
2.4.5 Excision of Osteoid Osteoma
An osteoid osteoma is a small benign osteoblastic lesion of the cortical bone [60]. Traditionally, an en bloc resection is used to remove the osteoma [60]. A computer-assisted
technique to remove the osteoma was used by Ma and Ellis [60]. Their system performed
a robust surface-based image to patient registration percutaneously by using a calibrated
needle probe that was tracked optically. Segmentation of the pre-operatively acquired CT
images allowed a semi-transparent visualization of the osteoma with its nidus displayed in
a different color. The visualization allowed the surgeon to remove the osteoma successfully
from a patient with minimal incision [4].
The technique proposed by Ma and Ellis [60] for the excision of osteoma required having to perform a intraoperative image to patient registration, and the system did not provide
real-time feedback in the form of a 3D images. Based on these shortcomings, Kendoff et
al. [44] used the ISO-C 3D fluoroscope in their computer-assisted surgical system. Using
an intraoperative imaging device like the ISO-C 3D fluoroscope absolved the surgical team
from having to perform the image to patient registration intraoperatively. A direct navigational scheme was used instead, where the registration was performed in a calibration
process prior to surgery. Furthermore, 3D images could be acquired during the surgery,
providing the surgical team with real-time feedback of the surgical procedure. In their
study, an osteoma was removed from the proximal medial tibia. A DRB was rigidly fixed
CHAPTER 2. LITERATURE REVIEW
47
to the patella of the patient. Navigation of the surgical procedure was provided by an optical tracking system and virtual visualization was provided by a 3D model along with
the reconstructed multiplanar images from the intraoperative CT scans. A surgeon then
navigated a tracked drill to the site of the osteoma and it was removed percutaneously.
2.5 Volume Rendering
Visualization of a 3D medical image has been described above, in Section 2.4, mainly as
surface rendering of a triangulated polygon mesh that has been extracted from the image
by segmentation. An alternative that was proposed by Levoy [54] is volume rendering,
which uses the interaction of light in the space surrounding the 3D image as well as the
interior of the image. This provides a powerful complete view of 3D volumetric data. The
following is a brief explanation of a few popular volume rendering techniques; the reader
can refer to the text by Engel et al. [26] for a much more complete review of real-time
volume rendering and its implementation.
Generally, volumetric ray casting produces visualization of the highest quality but it
is computationally expensive. The concept behind this technique is to evaluate the volume
rendering equation directly by using the information that is collected at sample points along
a ray that is emitted from the camera. As with ray tracing of surfaces, rays are cast from
each pixel of the image plane to the volume for rendering [26].
There are two primary components to rendering voxels along a ray, opacity and local
shading. To render opacity, the intensity values of each voxel hit by the ray are composited
(typically as an arithmetic average) in a process similar to alpha blending of surfaces. If
only opacity is used, for X-ray images such as CT this is equivalent to computation of a
digitally reconstructed radiograph.
CHAPTER 2. LITERATURE REVIEW
48
Local shading can be accomplished using the Phong model from computer graphics
[92]. The Phong model uses the 3D location of a point, the direction to one or more light
sources, and the local surface normal to produce surface shading. For medical images the
local surface normal can be approximated using a local gradient, possibly with additional
filters as desired. The visual effect can be quite similar to that from a surface rendering,
without requiring a potentially tedious segmentation process. The reader can refer to the
textbook by Watt [92] for a more detailed review in computer graphics.
For medical imaging, which has large data sets, there has been substantial work on using the graphics processing unit (GPU) on an ordinary commercial graphics card to speed
the visualization. One common method is to use texture mapping, or slicing, which is
supported by most current commercial GPU’s. In texture slicing, a 2D image in the coordinate frame of the three dimensional volumetric data is used to sample the volumetric
dataset. The 2D slices are then combined based on a compositing equation. On a typical current commercial GPU, this method is fast enough for real-time interaction. The
volume-rendered images that are included in this dissertation were generated using 3D texture mapping [26].
There are other techniques such as shear-warping (which is closely related to textureslicing), a technique called splatting which uses a projection of a reconstructed 3D kernel,
and cell projection which is a technique that is used for volume rendering of tetrahedral
grids or other complex unstructured meshes [26].
An area of great interest in volume rendering of medical data set is the transfer function, which is a function to map the Hounsfield unit to the opacity domain. The purpose
of the transfer function is to map the range of CT or MRI scalar values of different tissues to the desired opacity values. Regrettably, there are few current studies on designing
CHAPTER 2. LITERATURE REVIEW
49
user interfaces for setting transfer functions. However, one study from Kniss et al. [46]
demonstrated an interactive interface that allowed users to design multi-dimensional transfer function (the gradient of the scalar value being the second dimension with the second
derivative being the third). Using a multi-dimensional transfer function allows for clear
visualization of the boundaries between different types of materials.
2.6 Summary
Most computer-assisted surgical systems rely on using a meshed-based 3D model generated
from preoperatively acquired images and anatomic-based (e.g. surface-based and fiducialbased) registration. Several computer-assisted surgical procedures utilizing this workflow
have been described in this chapter. However, there are some complications that arise from
using this workflow, such as the time it takes to generate a meshed-based surface model
and the invasiveness of the intraoperative procedure for completing the anatomically-based
registration.
To address these shortcomings, intraoperative imaging modalities have been introduced
into the computer-assisted surgical workflow. Recently, this mode of computer-assisted
surgery have expanded to include intraoperative image modalities capable of capturing 3D
data. Consequently, a new registration scheme between the image coordinate frame and
the patient has been developed that directly couples the image coordinate frames to a fixed
coordinate frame in the intervention room. This method has been termed direct registration
or navigation, and it is made possible by the fact that these intraoperative imaging modalities are mechanical stable, thus ensuring the iso-center or origin of the imaging coordinate
frame remains in the same physical location in the intervention room during every spin acquisition. Some surgical procedures utilizing this method have also been described in this
CHAPTER 2. LITERATURE REVIEW
50
chapter.
In Chapter 3, a new procedure for performing direct registration for a flat-panel 3D
fluoroscope and a mobile gantry CT scanner in an integrated operating room is presented.
Additionally, Chapter 3 describes a computer-assisted workflow using intraoperative planning with volume-rendered models and direct registration.
Chapter 3
Materials and Methods
Conventional computer-assisted surgical systems rely on registration to find the transformation between the world coordinate frame, usually the coordinate frame of an optical
tracker, and the coordinate frame of the imaging space. However, the registration step is
not needed in the work flow of the operating room; because the transformation between
the coordinate frame of the Certus optical tracker and the coordinate frame of the Innova
imaging space, can be determined through the information that is provided by a registration
device. The focus of this chapter is then to outline the steps of this registration process.
The chapter will first describe the various coordinate frames that are pertinent to a discussion of the registration process. Next, the materials used and, where relevant, their
coordinate frames will be described. Third, derivations of finding the transformation between the coordinate frame of the Innova imaging space and the Certus will be presented.
Finally, the methods used for validation of the registrations will be described.
51
CHAPTER 3. MATERIALS AND METHODS
52
3.1 Coordinate Frames, Vectors, and Transformations
This dissertation uses the notation developed by Craig [15]. To represent the coordinate
frame J, the notation {J} will be used. A point is denoted using a 3x1 column vector,
for example ~p. When a specific coordinate frame is used to locate a point, the coordinate
frame is written as a leading superscript; for example, the location of point p~ in frame {J}
is written as J~p.
Here, a coordinate transformation from an originating frame to a destination frame is
a rigid transformation, being a rotation about the origin of the originating frame plus a
translation. For example, a transformation T from coordinate frame {J} to frame {K} is
p, it transforms the location J p~ to the location K p~.
written as K
J T ; applied to a point ~
Transformations are performed right-to-left, as they would if applied to column vectors.
For example, to transform a point from frame {J} to frame {K} and then to frame {L},
the resulting transformation from frame {J} to frame {L} would be
L
JT
=
L
KT
∗K
JT
There were eight coordinate frames used in this work. The devices, and the associated
coordinates, will be further described in subsequent sections. The coordinate frames were:
{A}: acute-tipped surgical probe.
{B}: ball-tipped laboratory probe.
{C}: Optotrak Certus position sensor.
{G}: CT gantry.
{M}: Multi-Modal Calibrator.
CHAPTER 3. MATERIALS AND METHODS
53
{P}: dynamic reference that was attached to a plastic bone model.
{S}: Innova 3D “spin” image.
{V}: CT 3D “volume” image.
3.2 Materials
The major devices used in this work were an Innova 4100 3D X-ray fluoroscope, a mobilegantry CT scanner, and an Optotrak optoelectronic position sensor. A custom Multi-Modal
Calibrator (MMC) was developed to relate the various coordinate frames. Plastic models
of bones, instrumented with radio-opaque markers, were used to validate the registrations.
In addition, a small number of custom optoelectronic instruments and fixtures were
needed.
3.2.1 The Innova 3D X-Ray Fluoroscope
The Innova (General Electric, Buc, France) was a floor-mounted X-ray fluoroscope that
was capable of acquiring both 2D and 3D images; a picture of an Innova, installed in an
operating room, is shown in Figure 3.1. The X-ray generator and flat-panel detector were
mounted on a mechanically rigid C-shaped arm that could rotate in space; 2D images could
be acquired during a “spin” of the arm and subsequently reconstructed as a 3D image by
the manufacturer’s software. Originally developed for interventional radiology, the Innova
also has a flat, radiolucent table on which a patient would lie during a procedure; the normal
location for the patient’s head is substantially narrower than the rest of the table and will
be described as the head of the table.
CHAPTER 3. MATERIALS AND METHODS
Figure 3.1: A diagram that illustrates the principal axes of the Innova image space
54
CHAPTER 3. MATERIALS AND METHODS
55
The coordinate frame of the Innova image space is best described with respect to the
table. The X direction was parallel to long axis of the table of the Innova system and was
positive away from the head of the table. The Y direction was perpendicular to the plane
of the table and was positive towards the ceiling. The Z direction was the conventional
cross-product of X and Y, producing a right-handed coordinate frame.
The Innova could perform a 3D acquisition scan resulting in a cubic volume dataset that
had a dimension of 5123 voxels. This dimension in voxels can be converted to millimeters
by multiplying the dimensions in voxels by the voxel spacing of 0.464263 mm/voxel.
1
Thus, the dimension of the 3D dataset from the Innova was 2353 mm.
The origin of the Innova image coordinate frame was located in the lower left corner of
the 3D image.
3.2.2 The Mobile-Gantry CT Scanner
The mobile-gantry CT LightSpeed Scanner (General Electric, Milwaukee, WI,USA) was
part of an operating room that included an Innova, a movable radiolucent table, and an
adjoining control room where the workstations to communicate with the CT scanner and
Innova were housed. The mobile-gantry CT scanner was mounted on two 1850 mm long
metal rails that had been embedded into the floors of the operating room. A motorized belt
between the two metal rails was used to move the CT gantry along the rails. Scan acquisition was programatically similar to that of a conventional CT scanner but was mechanically
quite different: whereas a conventional scanner had a fixed gantry and mobile table, this
system had a fixed table and mobile gantry. Reversing the mechanisms allowed a surgical
team greater access to a patient, because the gantry could be moved well outside of the
1
Seven digits of precision were required to accurately compute the actual field of view of the 3D image.
CHAPTER 3. MATERIALS AND METHODS
56
sterile field of the operative procedure.
The mobile-gantry CT was a 16-slice scanner that was capable of acquiring scans in
either helical or axial formats. Depending on the imaging protocol and the anatomy that
needed to be scanned, the CT scanner could have a field of view as large as 500 mm or as
small as 150 mm. The slice thickness could be set to 0.625 mm, 1.25 mm, 2.5 mm, 5 mm,
or 10 mm. Each slice had a dimension of 512x512 pixels with the pixel spacing being a
function of the field of view, e.g., a field of 250 mm yielded a spacing of 0.488281 mm/pixel
2
.
The coordinate frame of the CT image space can be described with respect to the bore
of the CT scanner and the metal rails. The X direction was across the CT gantry, parallel
to the floor. The Y direction was in the direction of gravity, with the positive direction
pointing towards the ceiling. The Z was parallel with the rails and was positive towards the
head of the table. The origin of the coordinate frame was located at the lower left corner of
the 3D image.
3.2.3 The Optotrak Optoelectronic Position Sensor
The Optotrak Certus system (Northern Digital Inc., Waterloo, Canada) was an optical measuring device that could track the position of each infrared emitting diode (IRED) within
a detectable volume. The position sensor of the Certus was mounted to the ceiling of
the operating room. The position sensor was fitted with three cameras which could then
accurately detect the location of an IRED by using a triangulation method developed by
Northern Digital, Inc. (NDI). The position sensor communicated with a host computer via
a System Control Unit. The system control unit had slots for connecting multiple strobers,
2
The order of magnitude was determined by the manufacturer and it could be due to following the IEEE
floating point protocol.
CHAPTER 3. MATERIALS AND METHODS
Figure 3.2: A diagram that illustrates the principal axes of the CT image space
Figure 3.3: A diagram that illustrates the coordinate frame of the Certus.
57
CHAPTER 3. MATERIALS AND METHODS
58
which strobed (pulsed) each IRED and thus ensured that only one IRED was visible at any
instant. Typically, a tool with multiple IREDs was connected to a strober with a single
multi-wire plug. The characterized measurement volume of the Certus, for the far-focus
mode used in this work, was 1700x2200x6000 mm.
The global coordinate frame of the Certus was characterized by the manufacturer. Using
the geometry of the Certus position sensor for reference, the X direction was along the
width of the position sensor. The Y direction was along the length of the position sensor,
and the Z direction was the conventional cross product of X and Y. The origin of the
coordinate frame was at the middle sensor of the position sensor.A schematic drawing with
axes of the coordinate frame is shown in Figure 3.3.
A Certus system was installed in the operating room with its long axis parallel to the
ceiling and floor. In this orientation the positive X direction was towards the ceiling, the
positive Y direction was along the long axis of the sensor, and the positive Z direction was
pointed away from the radiolucent table.
3.2.4 The Multi-Modal Calibrator
The purpose of the multi-modal calibrator was to provide information concerning the coordinate frames of {C} and the 3D images. A transformation could then be established in a
registration process performed prior to a computer-assisted surgery in the operating room.
To be sensed by both the imaging device and the position sensor of the Certus, the
MMC contained radio-opaque markers and IREDs. A computer aided design of the MMC
was created using Solid Edge (Siemens PLM Software, Camberley, UK). The device was
shaped like a hollow cube for ease of manufacture. Diagonal struts in the faces and center
regions of the cube provided additional support for the structure. A computer aided design
CHAPTER 3. MATERIALS AND METHODS
59
of the MMC is depicted in Figure 3.4.
Figure 3.4: Computer aided design of multi-modal calibrator.
The dimensions of the MMC were designed to fit into the field of view of the Innova –
which was smaller than the CT field of view – with dimensions of (235 mm)3 . According
to the NDI specification, at least four IRED markers should be used and the markers should
be spaced out to ensure that the registration accuracy was optimal which was reported to
be 0.15 mm 3 . The MMC was then designed to contain up to eight IRED markers and
had enough room to space out the IRED markers, in order to improve overall registration
accuracy. Based on those constraints, the dimensions of the MMC was 160x160x160 mm.
To provide a location for attaching the radio-opaque landmarks, five divots with a diameter of 3.2 mm were placed at the corners and center region on two faces of the MMC
and an additional 2 beads were attached to a divot that was in between the two faces for a
total of 12 divots. After empirical testing of various compositions and sizes, steel beads of
3 mm diameter were selected as the radio-opaque landmarks for the MMC.
To aid in tracking the MMC by the Certus system, IRED markers were placed on small
3
Optotrak Certus Rigid Body and Tool Design Guide Edition 2, Northern Digital Inc., March, 2006
CHAPTER 3. MATERIALS AND METHODS
Figure 3.5: Computer aided design of the multi-modal calibrator in a profile view
Figure 3.6: Computer aided design of the multi-modal calibrator in a profile view
60
CHAPTER 3. MATERIALS AND METHODS
61
Figure 3.7: Computer aided design of the multi-modal calibrator in a profile view with
dimensions of the sides of the MMC. The dimensions are in millimeters.
Figure 3.8: The multi-modal calibrator.
CHAPTER 3. MATERIALS AND METHODS
62
protrusions from the surface that had inclines of 45 degrees each and an elevations of
120 mm. Each protrusion had a 8 mm circle indent on its surface where an IRED could
be attached. A total of eight protrusions were placed on two faces of the MMC for the
attachment of a total of eight IRED markers.
The CAD design of the MMC was sent to a 3D printer (Dimension/Stratasys, Eden
Prairie, MN) that printed the MMC with an accuracy of 0.1 mm. For rigidity, the MMC
was printed with a hard acrylonitrile butadiene styrene (ABS) plastic.
Figure 3.9: An IRED marker embedded in the multi-modal calibrator
After the MMC was printed, the IRED markers were attached to the surface of the
protrusion by using ordinary cyanoacrylate cement. Pairs of IRED markers were connected
by a twisted pair cable, which was then connected to a marker strober from NDI. The wires
from the IRED markers were taped to the sides of the struts and a plastic coil was used to
bundle the wires. Each IRED marker on the MMC was numbered according to the strober
slot to which it was connected.
The coordinate frame of the MMC was characterized using NDI 6D Architect software
and the Certus system to localize the IRED markers on the MMC in the Certus coordinate
CHAPTER 3. MATERIALS AND METHODS
63
Figure 3.10: A meshed rendering of the multi-modal calibrator with the axes and origin
frame {C}. By default the program selected one of the eight IRED markers on the MMC
to be the origin of {M} and the position vectors to three of the IREDs were used as the
principle axes; this arbitrary origin was subsequently translated to the center of the MMC.
The orientation of the coordinate frame {M} is best explained by using the diagram in
Figure 3.10. A simple alignment was performed between {M} and {C}, resulting with
the coordinates of the IRED markers in {M}. NDI 6D Architect performed the alignment automatically and reported a description of the coordinate frame {M}, as well as the
coordinates of the IRED markers in {M} in a rigid-body file.
3.2.5 Bone Models For Validation
The registrations were validated using plastic models of human bone (Pacific Research
Laboratories, Bellingham, USA). Two femur and two tibia models were used. Each model
had previously been instrumented with small tantalum spheres of 0.8 mm diameter; the
CHAPTER 3. MATERIALS AND METHODS
64
spheres were readily localized in X-ray images but were sufficiently small that they did not
produce streaking or other artifacts.
Figure 3.11: One of the femur models used in the study.
3.2.6 Custom Optoelectronic Instruments
Four optoelectronic instruments were used in this study. One, a ball-tipped probe, was supplied by Northern Digital as part of the Certus position sensing system. This was assigned
coordinate frame {B} with the origin at the center of the ball and the Z axis aligned with
the shaft of the probe (the other axes were not relevant for this instrument).
The other three were produced by Traxtal, Inc. (Toronto, Canada). One was an acutely
tipped surgical probe, model HP005. This was assigned coordinate frame {A} with the
origin at the tip of the probe and the Z axis aligned with the shaft of the probe (the other
axes were not relevant for this instrument).
CHAPTER 3. MATERIALS AND METHODS
65
Figure 3.12: One of the tibia models used in the study.
Figure 3.13: The location of the fiducials in the first of two femur models. The circles
highlight the location of the fiducials.
CHAPTER 3. MATERIALS AND METHODS
66
Figure 3.14: The location of the fiducials in the second of two femur models. The circles
highlight the location of the fiducials.
Figure 3.15: The location of the fiducials in the first of two tibia models. The circles highlight the location of the fiducials.
CHAPTER 3. MATERIALS AND METHODS
67
Figure 3.16: The location of the fiducials in the second of two tibia models. The circles
highlight the location of the fiducials.
An Adaptrax, model TT001, was used as a dynamic reference for the bone models. This
was assigned coordinate frame {P} with origin and axes provided by the manufacturer.
A VersaTrax, model TT004, was used to track the CT gantry. This was assigned coordinate frame {G} with origin and axes provided by the manufacturer.
Miscellaneous hardware was used to attach trackers to objects.
3.2.7 The VSS Navigation System
VSS is commercial software produced by iGO Technologies (Kingston, Canada). The navigation code could read a variety of medical images, including Innova 3D and CT scans, and
provides extensive facilities for preoperative planning and intraoperative guidance. Originally developed for orthopedic navigation, VSS was previously used with point-to-surface
registration that linked an image to a patient’s anatomy.
CHAPTER 3. MATERIALS AND METHODS
68
The registration transformation aligned points – captured in the coordinate frame of the
dynamic reference – to a 3D model in the coordinates of the preoperative image; using the
notation provided above, the transformation was SP T for an Innova image or VP T for a CT
image. This registration could be used to visualize the location of a tracked instrument with
respect to the medical image and/or a 3D surface reconstruction derived from the image.
Most registration-based navigation systems use intermediate transformations and optimizations to find the registration transformation. If d~ is the tip of a probe at the time when
its location is captured, the process for CT-based registration is typically:
~
• Find the tip location in Certus coordinates as C d;
• Find the dynamic-reference frame in Certus coordinates as PC T ;
~
• Transform the point to dynamic-reference coordinates as Pd~ =PC T ∗ Cd;
• When enough points d~i have been found, optimize their fit to a surface model to find
the registration transformation VP T .
VSS was modified by the company to perform three additional tasks in support of this
work. First, it could input a 3D transformation that could be used to effectively replace the
registration transformation. Second, it was extended to perform volume visualization on
the 3D medical image, bypassing the time-consuming process of segmentation and surface
reconstruction. Finally, VSS was extended to output the locations of the acute-tipped probe
so that overall system validation could be performed.
The registration replacement is the technical key to a major change in the workflow of a
navigated procedure. This was done in three steps: using the MMC, image processing, and
robust registration to find the transformation from Certus coordinates to image coordinates,
which was VC T for a CT image and likewise for an Innova image; acquiring an intraoperative
CHAPTER 3. MATERIALS AND METHODS
69
image and, simultaneously, the dynamic-reference coordinates in the Certus frame as PC T ;
and finally, composing the registration transformation as
V
PT
=VC T ∗
C
PT
(3.1)
for a CT image and likewise for an Innova image, where
C
PT
= [PC T ]−1
(3.2)
is simply the inverse of the usual transformation.
3.3 Methods
This section describes the methods for calibrating the Innova and the mobile gantry CT
scanner in the operating room. Additionally, the methods for validating the registrations
by using plastic bone models are also provided. Before the registration processes can be
described in detail, the derivation of the intermediate transformations that were used in the
registration process are first given.
3.3.1 Transformation between {C} and {M}
Deriving the transformation C
M T , which related the coordinate frame of {C} and {M}, was
a relatively straight forward procedure. Various software such as NDI First Principles or
custom software based on the NDI API could be used to determine the point set C~l, which
was the location of the IRED marker on the MMC in the coordinate frame of {C}. The
point set
M~
l was reported in the RIG file. It was trivial to determine the correspondence
between the point sets C~l and M ~l because, by design, the order that M ~l was reported in the
RIG file matched the order that the IRED markers were connected to the marker strober.
Horn’s method could then be used on the two point sets C~l and M ~l to find the transformation
CHAPTER 3. MATERIALS AND METHODS
70
C
MT.
3.3.2 Transformation between {M} and the coordinate frame of the
Image Spaces {S} and {V}
It was essential to determine the coordinates of the steel beads in various coordinate frames
M
in order to find the intermediate transforms M
S T for the Innova and V T for the CT.
Surveying the MMC
The centers of the steel beads were determined via a survey procedure that used a calibrated
ball-tip probe (supplied by NDI). The procedure consisted of inserting the tip of the probe
in one of the divots on the MMC and pivoting the probe, all the while maintaining a line of
sight between the Certus position sensors and the IRED markers on the probe. The purpose
of the survey procedure was to establish the location of the steel bead in {C}, which was
~ Each of the twelve divots was surveyed, forming an unique configuration that
denoted C f.
could be used to distinguish the orientation of the MMC without ambiguity. Afterwards,
the steel beads were glued in place with an ordinary cyanoacrylate adhesive.
The transformation C
M T , which was determined using Horn’s method on the two point
sets C~l and
M~
l, was applied to C f~ to obtain the coordinates of the beads in {M}, which
was denoted M f~.
Bead Detection
This section describes the bead detection algorithm that was used to localize the beads in
the image space. The algorithm was designed based on a method developed by Ellis et
al. [24]. As pointed out by them, the X-ray beam from a CT scanner is shaped like a
CHAPTER 3. MATERIALS AND METHODS
Figure 3.17: The digitizing probe
Figure 3.18: A side shot of the multi-modal registration device
71
CHAPTER 3. MATERIALS AND METHODS
72
fan whereas the reconstructed slice from the sequence of X-ray beams was shaped like a
rectangular block. Because the Innova volume was reconstructed using cone-beam CT,
the physics generalized from axial CT to the more general case and no new algorithm was
required.
Because of the geometry of the slice of the beam, part of the beam imaged a region
not contained within the nominal width of a slice. A radio-opaque bead would thus appear
in multiple adjacent slices because it absorbed radiation from the neighboring X-ray slice
source. Because of this overlapping effect, a bead appeared across multiple adjacent slices
and the center of the bead could be interpolated. It has previously been shown that this
algorithm can locate the center of a bead to within of the width of a slice.
Two versions of this algorithm were implemented for this study. The CT version used
a VTK DICOM filter to extract the 3D data from the DICOM file. A more complicated
procedure was used for the Innova version because the 3D data of the Innova was stored in
a non-standard quasi-DICOM format. After preprocessing, conventional DICOM readers
could not be used to read the files from the Innova; instead of using DICOM readers, the
3D data was read directly and then stored into a binary C array.4
The bead detection algorithm for the Innova was designed to march through the 3D
dataset and record the position and intensity of any voxels that had an intensity value over
the threshold of 3000 Hounsfield units. Using a constraint on the geometry of the beads
(3 mm in diameter) some of the unwanted artifacts, such as wires from the IREDs, were
removed. For the CT version, the image search space was made smaller because there
were more artifacts presented in the CT images. The search space for the CT version
was restricted to search for beads only at the corners of the MMC. Using this method
4
The location of the 3D data within the Innova DICOM was found in the header file under the field
0047.10D3. The program dicom2 by Sebastien Barren was used to read the offset from the Innova quasiDICOM header
CHAPTER 3. MATERIALS AND METHODS
73
resulted in the detection of only ten beads because the two beads in the middle section
were neglected. The ten beads in the corner regions were sufficient for finding the correct
transformation, as well as for maintaining non-symmetry within the configuration of the
beads. The calculation of center of the bead was the same for both CT and Innova versions.
As suggested by Ellis et al. [24], a five-slice window containing a bead’s voxel position
and intensity was used to calculate its center. The following is a description of the formula
for the calculation of the center of a bead.
For a voxel with integer indexes (i, j, k) in an image volume, let (S ~u(i, j, k)) represent
the 3D coordinates of the voxel in the corresponding image frame, and let H(i, j, k) be the
intensity of the voxel in Hounsfield units. Limiting the indexes to a five-slice window, and
examining only those voxels with an intensity above a given threshold, the center of the
bead was calculated as the normalized weighted average of the Hounsfield units. Mathematically, let S f~ be the computed center of a bead in the coordinate frame {S}. Then
S
f~ =
P
i,j,k
(~u(i, j, k) · H(i, j, k))
P
i,j,k H(i, j, k)
(3.3)
The point set that was generated from the bead detection algorithm was denoted as
S
f~Detect or V f~Detect depending on the imaging modality. In the best scenario, the bead
detection algorithm would return only 12 points. However, the bead detection algorithm
detected the location of the IREDs and also other artifacts, which could lead to the algorithm returning from 20 points (12 beads and 8 IREDs) to as many as 100 points. In order to
discern the beads from the IREDs and artifacts, an algorithm based on the Random Sample
Consensus paradigm (RANSAC) was used.
CHAPTER 3. MATERIALS AND METHODS
74
RANSAC
For a set of markers where no symmetries existed, there was only one transformation to
correctly register the two point sets. In the case of the MMC, the location of the beads were
placed purposely to avoid symmetry. Thus, three markers provided enough information to
find an unique rigid-body transformation between the point set S f~Detect and M f~
The goal of the algorithm was to find up to 12 points from the set S f~Detect that corresponded closely to the points from the set M f~. Following the RANSAC paradigm, we first
randomly selected three points from the set S f~Detect . Additionally, three points from the
set
M
f~ were selected but, not randomly: the beads that were selected were in the middle
and lower portion of the registration cube, because the beads that were situated at the top
portion of the cube had a higher risk of getting cut from the image due to the cube not being
centered correctly in the Innova imaging field.
After finding these three points for the two point sets, which were denoted
S
M
f~3 and
f~3 , the next step was to extend the point set S B3 up to twelve if possible. To accomplish
this task, an initial transformation was found between the point sets M f~3 and S f~3 by using
′
Horn’s method. This initial transformation was denoted M
S T and it transformed points from
the image coordinate frame to {M}.
The rest of the algorithm found the transformation using the following procedure: an
exhaustive search that enumerated all the possible subsets of three from S f~Detect , and extending the cardinality of the subsets to twelve. For each iteration, a new transformation
M ′
S Ti
S
was derived using Horn’s method on a different subset of three points from the set
f~Detect and M f~3 . The second step involved determined the extended point set S f~′ , which
was derived by searching for twelve points, if possible, in S f~Detect that were closest to the
CHAPTER 3. MATERIALS AND METHODS
BestError = infinity
error = 0
M
S TBest = identity matrix
M~
f3 = {4 10 11} of M f~ (Three beads in the lower region)
for each unique combination of three in S f~Detect
S~
f3 = a unique combination of three in S f~Detect
M ′
M~
f3 and S f~3
S T = Horn’s method between
S
′
M ′
M T = inverse of S T
S ~′
f = set of up to 12 points in S f~Detect closest to SM T ∗ (M f~)
S ~′
M~
M
f
S T = Horn’s method between f and
M
S ~′
error = RMS error between S T * ( f ) and M f~
if error < BestError
BestError = error
S ~ S ~′
f= f
M
M
S TBest = S T
end if
end for
Figure 3.19: Pseudo-Code of the modified RANSAC algorithm
75
CHAPTER 3. MATERIALS AND METHODS
76
~ in terms of the Euclidean distance metric. It was noted that the transpoint set SM Ti′ ∗ (M f)
′
formation SM Ti′ was the inverse of M
S Ti . Once all subsets of three had been enumerated and
tried, the algorithm would terminate and return the transformation M
S T that best aligned the
coordinate frame {M} and {S}. In addition, the algorithm returned the subset of S f~Detect ,
which could contain up to twelve points, that were closest to M f~ under the transformation
S
MT.
This point set was denoted S f~. Pseudo-code of the algorithm is provided in Figure
3.19.
3.3.3 Registration of the Innova
In this study, the registration step of a navigated procedure was replaced in part by a preoperative registration scheme that coupled the coordinate frame of {C} with the coordinate
frame of the Innova {S} or the CT {V}. In an ideal scenario, where the position and orientation between the imaging modalities and the position sensor of the Certus remain perfectly fix relatively to each other, the registration process would be needed to be performed
only once. However, this is hardly the case in a realistic clinical setting, so the registration
process must be performed more often (perhaps daily) to ensure a high degree of navigation
accuracy.
Prior to a navigated surgical procedure in the operating room, the registration procedure
was performed by first positioning the MMC on top of the radiolucent table to ensure that
it was within the field of view of the Innova and within the detection volume of the position
sensor of the Certus. The pose of the MMC was then captured in the coordinate frame of
{S} by using the Innova to perform a 3D spin acquisition. Simultaneously, the physical
location of the MMC was captured in the transformation C
M T by using a customized program that communicated with the Certus system; thus, it was important to ensure the MMC
CHAPTER 3. MATERIALS AND METHODS
77
remained perfectly stationary until the Certus system had captured its pose during the 3D
acquisition.
The resulting Innova file was transferred to a navigation workstation. A customized
program on the workstation then took the Innova file as input and performed the bead
detection and robust registration to find the transformation
S
MT.
The final output of the
customized program was the concatenation between the two transforms, performed as:
C
ST
M
=C
M T ∗S T
(3.4)
The transformation C
S T , which was known as the Innova registration transform, entailed
the coupling between the coordinate frame of {S} and {C}. The whole registration process
took less than 15 minutes to perform.
Stability of the Innova Registration
The coupling between the Innova system and the Certus required the registration of the
Innova system to be repeatable and reliable. This ensured that the iso-center of the Innova image space occupied the same physical point in the operating room for every scan.
To measure any fluctuation in the registration, including expansion and contraction of the
room due to seasonal temperature variations, a month-long experiment was carried out that
used the MMC to calculate the two transformations C
M T and
M
S T.
By ensuring the MMC
was stationary during the entirety of the experiment, any deviations among the transform
C
MT
could be attributed to the fluctuation in the dimensions of the room. Similarly, any
deviations in the transform
M
S T
could be attributed to movement in the iso-center of the
Innova, including any mechanical instability in the movement of the Innova’s L-arm and
C-arm.
CHAPTER 3. MATERIALS AND METHODS
78
Figure 3.20: A diagram that illustrates the transformation between all of the coordinate
frames that are involved in the registration of the Innova
CHAPTER 3. MATERIALS AND METHODS
79
The experiment was performed by positioning the MMC in the center of the Innova
field of view and within the detection volume of the position sensor of the Certus. It was
important that the MMC remained stationary for the duration of the experiment. The experiment was conducted over a period of three weeks. During the weekend of each week,
three scans of the MMC were performed on each of the three days (Friday to Sunday).
Each scan was separated by at least an eight hour interval. During each 3D acquisition, the
physical pose of the MMC was recorded by using a customized program that communicated with the Certus system to retrieve the transformation C
M T . After each 3D acquisition,
the Innova was moved back to its home (or default) position and the Innova 3D dataset was
used to calculate the transform M
S T by using the methods described above. The experiment
was conducted in late February of 2009, where the outdoor temperature fluctuation was
reported to be -16 to +2 degrees Celsius. A serial numbering system was used to organize
the transforms, e.g., C
M T1 indicated the transform that was associated with the first scan of
the experiment. The results were then separated into two analyses. The first analysis was
a pair-wise comparison for all combinations of the transforms C
M T that were captured with
the Certus system during the acquisition the 14 scans. The second analysis was performed
on all pair-wise combination of the transforms
M
S T
that were calculated by using the In-
nova 3D dataset from the the 14 scans. The pair-wise comparisons were conducted using
the following mathematical operations.
Given two transformations TA and TB , the disparity between the transformation is
∆T = TB ∗ TA −1 .
The rotational component of the transform ∆T was transformed into an angle and axis
notation and the norm of the translational component was then calculated. This net angle
CHAPTER 3. MATERIALS AND METHODS
80
and the norm of the translation vector was used to convey the disparity among the transC
forms. For the analysis with the transform C
M T , the ∆T transform is denoted ∆ T . As for
S
the analysis with the transform M
S T , the ∆T transform was denoted as ∆ T .
3.3.4 Registration of the CT
By calibrating the GE LightSpeed CT Scanner in the operating room, the computer-assisted
surgical workflow would then be very similar to that of the Innova. As pointed out in the
Section 3.3.3, the key to the Innova registration was that its image origin was in the same
position relative to the position sensor of the Certus for every scan. However, that same
registration procedure cannot be replicated with the mobile-gantry CT scanner because
the same physical space of the room not consistently scanned for every image acquisition.
Instead, any interval along the Z axis of {V} might be acquired in any given CT scan.
Therefore, a scheme was designed to locate the image origin of {V}, which was always
found in the lower left corner of the first slice.
The physical location of the first slice in Certus coordinates was determined by the
position of the CT gantry along the rails. The location of the image origin of {V} could
then be determined by tracking the CT gantry when it was positioned to acquire the first
slice. There were two possible solutions to track the mobile CT gantry.
One possible solution was to use the “slice location” in the DICOM header file for
each CT slice. The slice location, as indicated by its name, contained the location of the
CT gantry when each slice was captured. However, the location of the CT gantry was
measured against a local origin that was initialized by pressing the zero button on the CT
control panel. The origin of the CT gantry was therefore relative and could reside anywhere
along the Z axis of {V}. To use this method to track the CT gantry, an absolute origin could
CHAPTER 3. MATERIALS AND METHODS
81
be established by pressing the zero button when the CT gantry was pushed all the way back
to one of its ends. Although this method was relatively easy to implement, it was not
user-friendly because it restricted a user from pressing the “zero” button.
Another solution was to attach an optoelectronic target to the mobile gantry and used
the Certus system to track its physical location along the rails. As long as the target was
physically fixed to the CT gantry, the relative position between that target and the origin of
the {V} should be the same for every scan, regardless of which segment along Z axis of the
{V} the CT scanner was capturing. The advantages to this method were that a user could
press the “zero” button and that the Certus system could accurately track the CT gantry.
However, this method was harder to implement and required the addition of a stand, which
was placed at the foot of the CT gantry, to hold the optoelectronic target.
For the tracked array attached to the CT gantry, the local coordinate frame was denoted
{G}. Although it was difficult to find a spot for attaching a tracked array to the mobile CT
gantry that would be appropriate for surgical use, these experiments were conducted with
the array clamped to the base of the gantry as shown in Figure 3.21.
The calibration procedure was designed to be performed prior to a surgical procedure in
the operating room. The MMC was positioned on the radiolucent table so that it was within
the scanning zone of the mobile CT scanner and also in the line of sight was established
with the position sensor of the Certus. During the study, the detector of the Innova was tilted
to one side, which facilitated the process of establishing a line of sight between the MMC
and the position sensor of the Certus. The start position of the CT gantry was determined by
moving the CT gantry so that its laser reference, which was emitted along the CT bore, was
pointed beside the MMC. A customized program was used to communicate with the Certus
system to determine the transformation C
G T that provided the position and orientation of the
CHAPTER 3. MATERIALS AND METHODS
82
Figure 3.21: A tracked array was attached to a stand is placed at the foot of the CT gantry.
The Innova was positioned to allow the Certus to detect the multi-modal calibration device during a CT scan. The arrows indicate the location of the
Certus and the origin of the CT image frame.
CHAPTER 3. MATERIALS AND METHODS
83
tracked array on the CT gantry when the CT gantry was located at the start position of the
scan. The customized program also captured the pose of the MMC during the scan in the
transformation C
M T . After the image acquisition, the DICOM files were transferred to the
navigation workstation. The DICOM files were then loaded into a second custom program
that performed bead detection and robust registration to determine the transformation M
V T.
The final output of the customized program was the CT calibration transform which was
the transformation between {G} and {V}, denoted as G
V T . The CT calibration transform
was calculated as:
G
VT
C
G T0
C
=VM T ∗M
C T ∗G T0
(3.5)
is the transformation between the coordinate frame of the Certus and gantry of the
CT scanner when the gantry is at the start location of the scan.
Stability of the CT Registration
An experiment similar to the Innova calibration was used to ensure stability of the pose
between the {G} and origin of the {V}. The experiment consisted of performing a series
of 9 scans spread over a period of three days. The multi-modal calibration device was
placed on the table and was not moved for the duration of the experiment.
For consistency, the same start and end positions were used for each of the scans. This
was accomplished by pressing the “zero” button only once for the duration of the experiment, so that the position display on the CT gantry could be used to move the gantry to the
zero position as the start position for each scan. For each scan, the transformation between
the tracked array on the CT gantry and the CT imaging space was calculated according to
Equation 3.5.
CHAPTER 3. MATERIALS AND METHODS
84
Figure 3.22: This diagram describes the relevant transformations for the calibration of the
CT scanner.
CHAPTER 3. MATERIALS AND METHODS
85
Any fluctuation between the position of the array on the CT gantry and the origin of
{V} would result in deviation among the CT calibration transforms. Pair-wise comparisons
for all combinations of the CT calibration transforms were conducted by calculating the
matrix ∆V T = TB ∗ TA −1 . The rotational component of ∆V T was then decomposed into
an angle/axis notation and the translational component of ∆V T was then used to calculate
the norm of the translational component.
3.3.5 Experiment with the Plastic Models
The purpose of this experiment was two-fold: it served as an example to illustrate the clinical workflow of a navigated surgical procedure in the operating room, and it also provided
a method to acquire quantitative measurements on the accuracy of the navigational system
in a clinical-like setting.
Experiment with the Innova
The room was calibrated with the MMC before the experiment. A similar protocol would
be followed for an actual surgical procedure. The plastic bone models were placed in a
special holder that also contained an attachment for a tracked array. Initially, the holder was
placed so the long shaft of the plastic bone was parallel with the table. An intraoperative
image of the bone model was captured using the Innova to perform a 3D acquisition and,
simultaneously, the VSS navigation system was used to capture the pose of the tracked
array in frame {C} as the transformation PC T . The registration transformation was then
computed by composing the Innova calibration transform, which was obtained from the
preoperative calibration process with the MMC, with the transformation PC T as:
CHAPTER 3. MATERIALS AND METHODS
P
ST
=PC T ∗C
S T
86
(3.6)
The Innova file was transferred to the navigation workstation and was then loaded into
VSS, which generated a volume-rendered model of the bone model was generated for the
navigation. A single user then placed the tip of the acute-tipped probe to the surface of
each fiducial marker on each bone model; VSS was then used to capture the pose of the tip
~
at those locations, which was denoted P d.
The inverse of the transformation PS T was used to transform the point set P d~ to the
~ The coordinates of the fiducial markers
coordinate frame {S}, which was denoted S d.
that were previously embedded in each plastic bone model were obtained using the bead
detection algorithm. The resulting point set from the bead-detection algorithm was denoted
S~
d. The TRE was calculated for each fiducial marker on each bone model. The L2 norm
function in MATLAB, which calculates the Euclidean distance for a vector was used to
calculate the TRE. The error between each pair of point was calculated as:
T RE = k((SP T ∗ (P d~i )) −S ~bi )k2
(3.7)
~
where i denoted a point in the set P d~ that corresponded to a fiducial marker in the set S d.
The TRE for each fiducial marker on each of the four bones was recorded. The experiment described above was repeated three more times for each bone model. For each of
the three iterations, the bone model was placed in a different rotation by rotating it counterclockwise by 90◦ , 180◦ , and 270◦ . Afterwards, an overall RMS error and standard deviation
were calculated based on the TRE on locating the fiducial markers.
CHAPTER 3. MATERIALS AND METHODS
87
Figure 3.23: A view of the special holder for the bone model and the tracked array.
Experiment with the CT
The CT scanner was calibrated in a procedure very similar to that of the Innova experiment
described above in Section 3.3.5. The difference was that the gantry was tracked along
with the MMC, so the CT tracking transform G
V T was recorded and used. In each trial,
after the CT scanner was set to its start position, a customized program was used to capture
the transformation G
C T0 , which was the transformation between the tracked array on the CT
gantry and the position sensor of the Certus when the CT gantry was located at the start position of the scan. The customized program was subsequently used to capture the dynamic
reference on the plastic bone model in the coordinate frame {C}, as the transformation PC T .
The registration transformation was then calculated as:
P
VT
G
=PC T ∗C
G T0 ∗V T
(3.8)
CHAPTER 3. MATERIALS AND METHODS
Figure 3.24: A screen shot of VSS during the validation study.
88
CHAPTER 3. MATERIALS AND METHODS
89
The rest of the experiment was conducted identically to the Innova validation experiment, using coordinate frame {V} instead of frame {S}. The only difference in the CT
validation study was that only one iteration of the experiment was performed. The plastic
bone model wasn’t rotated from its initial position, which had the long shaft of the bone
parallel to the table, because a line of sight cannot be established with the ceiling mounted
Certus when the bone was rotated.
Comparison Between the Two Studies
A comparison of the two studies was done by performing a Mann-Whitney U test on the
overall median of the navigational error from validation study when the plastic bone model
was positioned at the initial position, which had the long shaft of the bone parallel to the
table. This method provided a way to compare which intra-operative imaging modality, the
CT or Innova, was more accuracy in a direct navigated procedure. A P value of less than
0.05 was considered statistically significant for this study.
Chapter 4
Results and Analysis
The methods for registering the Innova 3D Fluoroscope and CT scanner were described in
the previous chapter. Additionally, a validation experiment using plastic bone models was
described. The results from those studies are presented in this chapter.
4.1 Results from Bead Detection
Using the bead detection algorithm on the CT images approximately 100 beads were identified. Ideally the algorithm should only find 10 beads, but because of the sensitivity of
the CT scanner to metallic artifacts, it falsely detected the wires and IREDs as beads. The
RANSAC algorithm correctly distinguished the beads from the IREDs and artifacts. For the
Innova images, the bead detection algorithm identified approximately 20 bead candidates:
all 12 beads and, additionally, all 8 IREDs as well. Once again, the RANSAC algorithm
was used to distinguish the beads from the IREDs.
The results from the bead detection algorithm suggested that the Innova scanner was
more capable of handling metallic artifacts than the CT scanner.
90
CHAPTER 4. RESULTS AND ANALYSIS
91
Figure 4.1: A volume rendered image of the multi-modality calibrator using the Innova
system. The circled regions are the IREDs and the uncircled white dots are the
beads.
Figure 4.2: A volume rendered image of the multi-modality calibrator using the CT images.
The circled regions are the IREDs. The white dots are the beads and line from
the IREDs are the wires.
CHAPTER 4. RESULTS AND ANALYSIS
92
4.2 Results of the Innova Registration Experiment
As outlined in Chapter 3, the main criterion that must hold for the registration process of the
Innova to be successful was that the transformation between the Certus coordinate frame
and the Innova coordinate frame remained unchanged. The two principal factors for this
criterion were possible thermal effects and that the Innova’s L-arm and C-arm might not
follow the same trajectory in each 3D acquisition.
An experiment was conducted to test this criterion by using the two transforms C
M T and
M
S T.
A total of fourteen scans were collected over a period of nearly a month. For each
M
scan, two transforms C
M T and S T were obtained, with a subscript used to number each one
according to the scan that was used to calculate the transforms. From the set of transform
C
M Ti ,
C
M Ti
where i ranges from 1 to 14, a pair-wise comparison between two transforms in the set
was conducted by calculating the matrix ∆C T . This comparison was performed for all
C
possible subsets of two from the set C
M Ti . ∆ T was then decomposed to provide an angle
and axis representation of its rotational component and the norm was calculated for its
translational component. This data is found in the Appendix in Section A.1 in Table A.17
to Table A.18. For completeness, we also included the translational components of ∆C T
along the X, Y, and Z directions in Tables A.11 to A.16, respectively.
These steps were repeated for the set of transforms M
S Tj , where j ranges from 1 to 14.
∆S T was calculated for each pair-wise comparison among the transforms of the set M
S Tj .
The angle from the angle and axis representation of the rotational component of ∆S T is
presented in Table A.1 to Table A.2 and the norm of the translation component of each
∆S T is presented in Table A.9 to Table A.10. The translation component of each ∆S T
along the X, Y, and Z directions is listed in Table A.3 to Table A.8, respectively.
CHAPTER 4. RESULTS AND ANALYSIS
93
The data show negligible no deviation among the rotational components of ∆C T 1 . The
average error in the translation along the X direction of ∆C T was 0.19 mm with a standard
deviation of 0.06 mm, in a range of 0.00 mm to 0.44 mm. As for the translation along the Y
and Z directions of ∆C T , the average error for Y was 0.06 mm with a standard deviation of
0.01 mm and a range of 0.00 mm to 0.18 mm and the average error for Z was 0.19 mm with
a standard deviation of 0.03 mm and a range of 0.00 mm to 0.67 mm. Finally, the average
error for the norm of the translational component of ∆C T was 0.30 mm with a standard
deviation of 0.18 mm and a range of 0.03 mm to 0.74 mm.
Table 4.1: Average rotational and translational errors calculated from ∆C T for the Innova
registration experiment.
Type of Error
µ
σ
Range
Rotational Error(degrees)
Translational Error for X (mm)
0.19
0.059
0.0035–0.44
Translational Error for Y (mm) 0.059 0.0062 0.00010–0.18
Translational Error for Z (mm)
0.19
0.029 0.00070–0.67
Norm of Translational Error (mm)
0.30
0.176
0.028–0.74
The average error for the angles in the rotational component of all the ∆S T was 0.27◦
with a standard deviation of 0.03◦ and a range of 0.01◦ to 0.61◦. As for the translation
along the X, Y, and Z direction of ∆S T : the average error for the X direction was 0.04 mm
with a standard deviation of 0.00 mm and a range of 0.00 mm to 0.12 mm; the average
error for the Y direction was 0.05 mm with a standard deviation of 0.01 mm and a range
of 0.00 mm to 0.14 mm; and the average error for the Z direction was 0.06 mm with a
standard deviation of 0.01 mm and a range of 0.00 mm to 0.15 mm. The average error in
the norm of the translational component for all of the ∆S T was 0.10 mm with a standard
deviation of 0.01 mm and a range of 0.02 mm to 0.17 mm.
1
Please refer to section 4.5.1 for further explanation of the lack of deviation
CHAPTER 4. RESULTS AND ANALYSIS
94
Table 4.2: Average rotational and translational errors calculated from ∆S T for the Innova
registration experiment; µ is the mean and σ is the standard deviation.
Component
µ
σ
Range
Rotational Error(degrees)
0.27
0.027
0.0065–0.61
Translational Error for X (mm) 0.036 0.0040 0.00030–0.12
Translational Error for Y (mm) 0.053 0.0080
0.0016–0.14
Translational Error for Z (mm) 0.058 0.0083 0.00050–0.15
Norm of Translational Error (mm) 0.097 0.0076
0.020–0.17
4.3 Results of CT Registration Experiment
A similar method was used to present the results from CT registration experiment. The
main objective of the experiment was to show the stability of the position of the optoelectronic target on the gantry relative to the origin of the CT image volume. Therefore,
pair-wise comparisons between all possible combination of the CT registration transforms,
G
VT
, were conducted by calculating the matrix ∆V T for each comparison. The results are
found in Appendix in Section A.2.
As in the Innova study, the rotational component of each ∆V T was converted to an
angle and axis represent and the angle is organized into Table A.19. The translational
component of ∆V T was used to calculate the norm and the data is shown in Table A.23.
The translational component of ∆V T along the X, Y, and Z axis are also displayed in Table
A.20 to A.22, respectively.
Table 4.3: Average rotational and translational errors calculated from ∆V T for the CT registration experiment; µ is the mean and σ is the standard deviation.
Component
µ
σ
Range
Rotational Error(degrees) 0.14 0.019 0.0070–0.33
Translational Error for X (mm) 0.25 0.047
0.027–0.52
Translational Error for Y (mm) 0.38 0.025
0.0055–1.1
Translational Error for Z (mm) 0.43 0.077
0.010–0.92
Norm of Translational Error (mm) 0.70 0.061
0.042–1.3
CHAPTER 4. RESULTS AND ANALYSIS
95
The rotational component of ∆V T , which was generated from the pair-wise comparisons among all of the CT calibration transforms, was converted into an angle/axis representation and the overall average among all the angles was calculated to be 0.14◦ with a
standard deviation of 0.02◦ and a range of 0.01◦ to 0.33◦ degrees. The average error in
the translational component of all the ∆V T along the X axis was 0.25 mm with a standard
deviation of 0.05 mm and a range of 0.02 mm to 0.52 mm. The average error in the translational component of all the ∆V T along the Y axis was 0.38 mm with a standard deviation
of 0.02 mm and a range of 0.01 mm to 1.14 mm. Finally, the average translational error
of all the ∆V T along the Z axis was 0.43 mm with a standard deviation of 0.08 mm and
a range of 0.01 mm to 0.92 mm. The average error of the norm for the translational component of all the ∆V T was 0.67 mm with a standard deviation of 0.06 mm and a range of
0.04 mm to 1.3 mm.
4.4 Results from the Plastic-Bone Validation Experiment
In this section, the results from the bone model experiment are found in the Appendix in
Section A.3. For completeness, the navigational error for the 19 fiducial points over the
four models are listed in Table A.40 to Table A.43 for trials with the CT, and in Table A.24
to Table A.39 for trials with the Innova.
Table 4.4: The Innova target registration for 4 bone models, each in 4 poses; σ is the standard deviation. The corrected values compensated for the 0.4 mm radius of each
fiducial marker
Component
Raw TRE (mm)
corrected TRE (mm)
RMS
1.56
1.15
σ
0.50
0.50
Range
0.43-2.68
0.03-2.28
CHAPTER 4. RESULTS AND ANALYSIS
96
Table 4.5: The CT target registration for 4 bone models, each in 4 poses; σ is the standard
deviation. The corrected values compensated for the 0.4 mm radius of each
fiducial marker
Component
Raw TRE (mm)
corrected TRE (mm)
RMS
2.24
1.84
σ
0.75
0.75
Range
0.90-4.07
0.50-3.67
The overall average TRE for the 19 fiducial points in all four positions for the Innova
experiment was 1.56 mm with a standard deviation of 0.50 mm and a range of 0.43 mm to
2.68 mm. For the CT experiment, the overall average navigational error for the 19 fiducial
points was 2.24 mm with a standard deviation of 0.75 mm and a range of 0.50 mm to
3.67 mm.
The direct navigation using the Innova as the intraoperative imaging modality was significantly more accurate (p < 0.05) in the navigation of the acute probe to the fiducial
marker on the bone models than the direct navigation using the CT scanner as the intraoperative imaging modality.
4.5 Discussion
This section provides a discussion of the results from the experiments measuring the stability of the Innova and the CT scanner and the validation experiments with the Innova and
the CT scanner.
4.5.1 Analysis of the Innova Results
The results from the analysis of ∆S T suggested that the motion of the Innova’s L-arm
and C-arm during a 3-D acquisition were highly repeatable. Additionally, the analysis
CHAPTER 4. RESULTS AND ANALYSIS
97
of ∆C T suggested that the dimension of the operating room was very stable and did not
fluctuate during temperature changes. Thus, the results from the analysis suggested that
the Innova system could be used in a direct navigational scheme for carrying out image
guided intervention in the operating room. The rest of the section is an attempt to provide
possible sources that contributed to the overall error that was observed in the registration of
the Innova system, as well as comparison to other direct navigational system with flat-panel
3D fluoroscope.
The rotational error in the analysis of ∆C T was reported as zero. Although there may
have been slight rotations in the position sensor from thermal expansion or contraction,
the magnitude of the rotation was too small to detect with the Certus system. An average
translational deviation of 0.30 mm was observed. It was speculated that the actual translational movement of the position sensor from thermal effects was even smaller than the
value that was reported here because the accuracy of the Certus system was only reported
to be 0.25 mm in its specification.
Analyzing the deviations of ∆S T revealed that the mechanical movement of the spin
acquisition was highly repeatable, with very little rotational error and the majority of the
error in the translational component attributable to deviations along the Y and Z axes. One
possible explanation for the observing higher error in the Y and Z components might be
that the Innova C-arm spun roughly about the Certus Y axis and the L-arm spun roughly
about the Z axis during an acquisition. Slight deviations in the trajectories of the L-arm
and C-arm could shift the physical location of the origin of {S} along the Y and Z axes.
Another factor that may have contributed to inaccuracy in an Innova registration was
reconstruction of the 3D dataset by the Innova system. Inaccuracy in the reconstruction
process might lead to errors in the localization of the steel beads in {S}. Using the “3D”
CHAPTER 4. RESULTS AND ANALYSIS
98
setting the Innova captured 148 images, which was roughly one scan every 0.82 degrees.
The Innova system then used these 148 slices to reconstruct the volume data. However,
there were certain instances where the Innova reported a frame drop, so the cubic volume
was reconstructed from 147 slices. A dropped frame might affect the accuracy of the 3D
reconstruction if the slice that was dropped happened to be the first in the series, which
could lead to errors during the interpolation process that was used to reconstruct the 3D
dataset from the slices. At the time of this study there was no method to detect which
slice was dropped in the series so a 3D acquisition was disregarded if it was found to be
constructed from fewer than 148 slices. (This requirement is acknowledged to be less than
ideal in practice, because it might result in excessive radiation exposure to a patient from
multiple scans.)
Furthermore, the setup for acquiring a 3D acquisition could also affect the reconstruction of the 3D dataset. At least one fluoroscopic image must be taken during the “Test Spin”
sequence in order for the Innova to reconstruct the 3D dataset accurately. The Innova system used the parameters from this fluoroscopic image to reconstruct the 3D dataset from
the slices. To capture the proper set of parameters, the foot pedal should be pressed firmly
to capture the fluoroscopic images. Even though during this experiment the foot pedal was
pressed firmly for each fluoroscopic scan, it was not possible to ensure that the parameters
were the same for each reconstruction. Thus, one can expect small deviations among the
parameters from two different scans. This in turn might cause slight inaccuracy in the 3D
reconstruction of the dataset, which would directly affect the location of the origin of {S}.
From analyzing the results of the experiment concerning ∆S T , one could observe that the
summation of the errors from the following processes: repeatability of the L and C-arm,
reconstruction of the 3D dataset by Innova system, and the bead detection algorithm, was
CHAPTER 4. RESULTS AND ANALYSIS
99
below the detection error of the Certus, which is stated as 0.25 mm.
In earlier works, direct navigation had been used with other 3D Fluoroscope such as the
ISO-C3D system [80] and more recently the Integris 3DRX BV5000 system [48]. These
studies performed registration between the 3D image space and a tracking plate that was
rigidly attached on the C-arm. In our direct navigation system with the Innova 3D Fluoroscope, we directly registered the 3D image space of the Innova to the ceiling mounted
position sensor of the Certus in the operating room. Thus, a tracking plate was not needed
and the coupling process was simpler to perform. Furthermore, the Innova 3D Fluoroscope
was a more powerful system than the Integris and ISO-C3D systems. The Innova was capable of capturing 148 cone-beam projection images of 5122 pixels per 3D acquisition, which
were then used to construct a 3D isometric volume of 5123 voxels, whereas the Integris
3DXR and the ISO-C system could only capture 100 cone-beam projection images of 5122
pixels per 3D acquisition that were then used to construct a 3D isotropic volume of only
2563 voxels. Our direct navigation system also used the Certus, which was more accurate
than the Polaris camera that was used in previous study.
A direct navigation system had also been developed by Jacob et al. [37] for a stationarygantry helical CT scanner. The coupling process was similar to the one we used for the
Innova. In addition to the obvious difference that we did not use a stationary CT scanner,
the other main differences were that we performed an additional intra-operative step that
concatenated the Innova registration transform to the transformation between the coordinate frames of the Certus to that of the dynamic reference coordinates of the patient. By
making the coordinate frame of the imaging space relative to the dynamic frame instead
of the tracking camera, a patient can be re-positioned after image acquisition. The only
constraint in our method was that the target anatomy of the patient cannot move relative to
CHAPTER 4. RESULTS AND ANALYSIS
100
the dynamic reference, which in an orthopedic procedure can be accomplished by drilling
the dynamic array into the patient’s anatomy during the surgical procedure.
4.5.2 Analysis of the CT Registration
As pointed out in Chapter 3, the CT scanner in the operating room had a moving gantry,
thus the method used by Jacob et al. [37] cannot be used for our setting. Hence, a method
was described that used an array to track the gantry. The registration process for direct
navigation using the mobile-gantry CT scanner was performed by finding a relationship
between the origin of the 3D image volume and the CT gantry. The results from the experiment involving the CT registration suggested that this system was less stable than that of
the Innova. Table 4.3 shows that the rotational component deviated very little among the
CT registration transforms, and the main deviation was from the translational component.
A possible explanation for the majority of the error residing in the translational component
was the inaccuracy of locating the CT gantry when it was positioned to take the first slice
of the CT image volume. In Chapter 3, we described a method to track the CT gantry by
utilizing an array that was attached to a stand, which was then placed on the foot of the CT
gantry. The movement of the CT gantry caused the tracked array to sway, which introduced
error into the calculation of the transformation C
G T that in turn affected the derivation of the
CT registration transform. Furthermore, the CT scanner was located approximately 6 meters from the position sensor of the Certus; at this distance, a small rotation of the gantry’s
tracked array relative to the position sensor could turn into large translational errors.
CHAPTER 4. RESULTS AND ANALYSIS
101
4.5.3 Analysis of the Plastic-Bone Validation Experiment
The reported navigational errors for the Innova and CT systems did not entirely reflect the
accuracy of the system. The bead detection algorithm from Ellis et al. [24] was used to
localize the center of the fiducial markers on each of the bone models, which was then used
as ground truth for this study. Experimentally, the fiducial markers were localized in {P}
using an acute-tipped calibrated probe that could only report the location of the surface of
the fiducial markers. Thus, an adjustment must be made by subtracting 0.4 mm (which was
the radius of the fiducial markers) from all the reported TRE. After the compensation, the
overall average TRE for the Innova was 1.15 mm and for the CT was 1.84 mm.
A direct comparison between the Innova and the CT was conducted using the MannWhitney U-Test on the results from the plastic bone validation studies. The Mann-Whitney
U-Test was used because the test was robust and also the data did not follow a normal
distribution. The results for the test suggested that using the Innova as the intraoperative
imaging modality significantly increased the accuracy of the direct navigated procedure on
the bone models with a p = 0.00643. However, there were potential modifications that
could be made to increase the accuracy of the CT system. One method might be to improve
the accuracy of tracking the CT gantry. For instance, inadvertent movement of the tracked
array could be decreased by creating a rigid mount on the cover of the CT gantry, possibly
also using a damping material to absorb the vibrations. Also, the CT gantry was rather far
away from the ceiling mounted position sensor of the Certus in the operating room; one
alternative is that a portable Certus could be moved into the operating room and could be
positioned closer to the CT gantry. It must be acknowledged that using a portable Certus
might introduce additional complexity into the clinical workflow. Furthermore, the accuracy of direct navigation with an intraoperative CT scanner could be improved by reducing
CHAPTER 4. RESULTS AND ANALYSIS
102
the slice thickness from 1.25 mm to 0.625 mm (which, because of tight collimation, has
the same radiation burden as a thicker slice but is more subject to motion artifacts).
4.5.4 Summary
The navigational accuracy of our direct navigation system with the Innova was 1.15 mm
and the CT version was 1.84 mm. Based on our experiment, we found the Innova system
to be significantly more accurate than the CT system in terms of navigation. However,
some modifications had been suggested for the CT workflow to improve its navigational
accuracy.
Chapter 5
Conclusions and Future Work
A system for computer-assisted surgery in an integrated operating room has been described.
The following summarizes the significant findings and contributions from the work in this
dissertation.
5.1 Summary
Three main benefits accrue from utilizing direct registration and a volume-rendered model
for intraoperative surgical navigation. First, the resulting system has a much simpler workflow than those of systems that rely on preoperative images. Second, direct registration is
more accurate and less invasive than surface-based registration. Finally, the system is more
accurate than previously reported direct-registration systems.
5.1.1 Simplicity of the New System
A computer-assisted surgical system with preoperative imaging relies on a virtual 3D model
constructed from preoperatively acquired images from for pre-surgical planning and visual
103
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
104
guidance intraoperatively. One limitation of this framework is the possibility that the position of the target anatomy might change in the time span between the preoperative stage
and the surgery; as a result, the 3D model and the pre-surgical plan may not correspond
accurately with the anatomy of the patient during the surgical procedure. This is ameliorated in the new system because the virtual 3D model is constructed from 3D data that is
acquired intraoperatively. A surgeon can then use this volume-rendered virtual model to
establish a plan while in surgery. Using real-time volume rendering also saves the technical
team from having to perform a lengthy segmentation process of the 3D dataset to generate
a meshed-based model.
The feasibility of using volume rendered images captured intraoperatively for visual
guidance during navigation is demonstrated in the study with bone models using VSS,
where volume rendered images of the bones are used to find the location of the fiducials.
5.1.2 Replacing Intraoperative Registration
There are some surgical procedures where a surgeon has no direct access to the surface
of the anatomy (e.g., most closed internal fixation procedures for bone fractures); in such
instances it is not possible to use a surface-based or fiducial-based method to complete
the image to patient registration. Furthermore, a surface-based or fiducial-based approach
requires additional operating time because the surgeon has to perform a minimally invasive
procedure in order to digitize the surface of the anatomy or the fiducials.
Quick procedures for performing direct registration with the intraoperative CT scanner
and Innova system were developed using a customized multi-modal calibration device.
The new system used this direct registration method for completing the image to patient
registration. This method was not dependent on using the surface or markers that were
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
105
attached to the anatomy; rather, it relied on the mechanical stability of the intraoperative
imaging devices to scan the same physical space during every acquisition. Our experiments
found the mechanical reproducibility of the Innova to be approximately 0.1 mm. In a study
from Kraats et al. [48], they reported the mechanical reproducibility of the Integris 3DXR
to be approximately 0.23 mm and Ritter et al. [80] reported the mechanical reproducibility
of the ISO-C3D system to be approximately 0.91 mm. Hence, the results suggest that the
Innova is at least as mechanically reliable as the Integris 3DXR and the ISO-C3D system,
and may be even more reproducible. As for the mechanical reproducibility of the CT
scanner, it was determined experimentally to be approximately 0.7 mm.
A similar direct navigation scheme with an intraoperative CT scanner was proposed
previously by Jacob et al. [37]. Our approach utilized the Certus tracking system, which
provided a much bigger detection volume than the detection system in the study by Jacob et
al. Furthermore, our registration process only took 20 minutes to complete. Our registration
procedure is much faster to carried out than the registration process from Jacob et al., which
reportedly took approximately 2 hours to complete. One advantage of being able to perform
a fast registration is that, if necessary, an operating room could be re-calibrated after every
surgery; thus any movement in the ceiling mounted tracking camera or the imaging system,
e.g., if a surgical boom accidentally collided with a tracking device, this could be quickly
corrected during or after the surgery.
Using direct registration can save a surgeon performing a minimal invasive procedure
from exposing the surface of the anatomy, may reduce the overall operating time, and
most importantly, removes technical details that may otherwise distract a surgeon during a
complex operative procedure.
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
106
5.1.3 Accuracy of the New System
The accuracy of the navigation system depended on the mechanical stability of the intraoperative imaging modalities and also on the dimensional stability of the operating room.
Thorough experiments have shown that, mechanically, the intraoperative imaging modalities are quite stable. Additionally, the dimensions of the room do not fluctuate when subject
to changes in external ambient temperature. Furthermore, a preliminary validation study
has shown that the overall TRE with using the Innova was 1.15 mm and the TRE with using
the CT scanner was 1.84 mm.
Earlier works on direct navigation with an intraoperative CT scanner were conducted
by Eggers et al. [22] and Jacob et al. [37]. They reported the overall average TRE for
their marker experiment in a clinical-like setting, respectively, as 1.20 mm with a standard
deviation of 0.48 mm and 1.9 mm with a standard deviation of 1.1 mm. Here, the adjusted overall average TRE for the marker experiment using the mobile gantry CT scanner
calibrated for direct navigation with the MMC was 1.84 mm. The average TRE from our
experiment was lower than the TRE reported by Jacob et al. [37] However, the average
TRE from our experiment was higher than the TRE reported by Eggers et al. [22]. It was
speculated that our system was less accurate due to the movement of the DRB attached to
the gantry. In the study from Eggers et al. [22], a passive DRB consisting of four passive
IRED markers were directly attached to the cover of the gantry.
The Innova system was originally designed for angiographic imaging and in our study
we have modified the Innova system for image-guided interventions. To our knowledge,
we were the first to modify the Innova system for image-guided intervention. Thus, we
can only compare the accuracy of our system with other flat-panel fluoroscopes such as
the ISO-C3D system and the floor mounted Integris 3DXR. In an accuracy study involving
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
107
the ISO-C3D system, the reported TRE was 1.6 mm [80]. Kraats et al. [48] performed
a similar study with the Integris 3DXR and reported TRE with a glass rod model to be
1.1 mm and the TRE with a cadaver to be between 2.1 mm and 2.8 mm. Kraats speculated
that low TRE in the glass rod model was due to the large ring DRB marker that was used.
For the cadaver experiment, Kraats et al. used a DRB that was similar in design to the ones
that were used in surgery [48]. For our bone validation experiment, all the surgical tools
and DRB were obtained from a surgical kit that was routinely used in computer-assisted
surgery in the Kingston General Hospital.
It was speculated that by directly coupling the image spaces to the Certus coordinate
frame, the resulting direct navigational system would have accuracy that is comparable or
better than earlier works that utilized a tracker plate. This was confirmed by the results
of our validation study with the Innova system. The average TRE for our experiment was
1.15 mm, which was lower than the TRE in the report from Ritter et al. [80] and it was
almost the same as the TRE in Kraats et al. [48] validation experiment with the glass rod
model, and it was lower than the TRE reported in their cadaver experiment.
5.2 Contributions
The significant contributions of this dissertation include:
• Designing a new, quick, and robust preoperative procedure for establish direct registration for the Innova system and the mobile gantry CT scanner in the operating
room. Using direct registration replaces the surface-based or fiducial-based intraoperative image to patient registration.
• Developing methods to measure the mechanical stability of the Innova system and
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
108
the mobile gantry CT-scanner.
• Illustrating that a high degree of accuracy in the navigation can be achieved with
using a direct registration approach with the Innova system and the mobile-gantry
CT scanner.
• Presenting a technically feasible workflow for performing computer-assisted surgery
without utilizing preoperative planning and intraoperative registration in an integrated operating room.
5.3 Future Work
This dissertation has described one way of performing a computer-assisted intervention
using an integrated operating room. However, the final goal is to make this system practical
for routine clinical use. More work is needed in order to make this a reality, including:
• Real-time volume rendering is a promising visualization technique for computerassisted surgery. However, to generate images of high quality, a multi-dimensional
transfer function may be needed. Designing a user interface for assigning multidimensional transfer function in real-time is an active area of research and a very
complex problem.
• A better system is needed to track the CT gantry accurately. The current configuration
of using a stand is not robust or stable enough for clinical use. It is believed that the
most elegant solution is to extract the location of the CT gantry directly from the
machine. However, this is not possible without collaborating with the manufacturer.
CHAPTER 5. CONCLUSIONS AND FUTURE WORK
109
• It is possible to determine the transformation between the CT coordinate frame and
the Innova coordinate frame. Finding a relationship between the two imaging coordinate frames may provide a fast and easy method to merge or compare the data if it
is needed.
• A mechanism to detect whether or not the Certus has been bumped or moved from
the calibrated position.
• Besides the technological improvements, many human factors need to be considered
such as: training of the staff in using the various machines, designating areas for the
anesthesiologist and nursing staff, and coordinating between the various departments
to work together in order to use the operating room to its full potential.
• More studies may need to be conducted in the operating room, with a full staff, in
order to finely tune the new system and to get a better understanding of the range of
surgical procedures that are supported by this system.
The concept of integrating technology directly into an operating room is still in its infancy. In the near future such an integrated operating room will be used routinely. At the
time of writing there are very few institutions in the world that have such an advanced
operating room. Developing the technical details is only the beginning of making the operating room fully operational; some work is still needed to make the system more robust
and to train the staff and surgeons on using the room for image-guided surgery. However, it is believed that once the new operating room is used routinely in surgery, it will
serve as a salutary example of how technology can be merged seamlessly into an operating
room. Hopefully, in the near future, positive results from the operating room will generate
a greater interest in using an integrated operating room in the field of surgery.
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Appendix A
Appendix
This Appendix contains detailed data results that were summarized statistically in Chapter 4
of this dissertation. Each table exhaustively compares calibrations derived from a sequence
of 14 Innova scans and 9 CT scans. The numbering system indicates which two scans were
used to calculate the relevant value. In each case, the numbers have been rounded to two
significant digits.
A.1 Calibration Results for the Innova
The results from 14 calibration experiments with the Innova are displayed in this section.
Some of the datasets are too large to be displayed adequately in a single table, in which
cases two tables have been used to display the results.
123
APPENDIX A. APPENDIX
124
Table A.1: Deviation of the angles in the rotational component of ∆S T in degrees; columns
are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.61
0.5
0.41
0.38
0.3
0.32
Scan2
0.61
0
0.16
0.34
0.27
0.34
0.32
Scan3
0.5
0.16
0
0.18
0.24
0.2
0.19
Scan4
0.41
0.34
0.18
0
0.31
0.13
0.15
Scan5
0.38
0.27
0.24
0.31
0
0.21
0.18
Scan6
0.3
0.34
0.2
0.13
0.21
0
0.04
Scan7
0.32
0.32
0.19
0.15
0.18
0.04
0
Scan8
0.32
0.31
0.18
0.15
0.18
0.04
0.01
Scan9
0.09
0.53
0.42
0.34
0.29
0.23
0.24
Scan10
0.18
0.47
0.39
0.36
0.21
0.24
0.23
Scan11
0.15
0.54
0.46
0.42
0.28
0.3
0.29
Scan12
0.32
0.3
0.18
0.15
0.17
0.05
0.04
Scan13
0.25
0.54
0.49
0.49
0.28
0.36
0.35
Scan14
0.5
0.19
0.04
0.16
0.25
0.2
0.18
Table A.2: Deviation of the angles in the rotational component of ∆S T in degrees; columns
are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.32
0.09
0.18
0.15
0.32
0.25
0.5
Scan2
0.31
0.53
0.47
0.54
0.3
0.54
0.19
Scan3
0.18
0.42
0.39
0.46
0.18
0.49
0.04
Scan4
0.15
0.34
0.36
0.42
0.15
0.49
0.16
Scan5
0.18
0.29
0.21
0.28
0.17
0.28
0.25
Scan6
0.04
0.23
0.24
0.3
0.05
0.36
0.2
Scan7
0.01
0.24
0.23
0.29
0.04
0.35
0.18
Scan8
0
0.24
0.23
0.29
0.04
0.35
0.18
Scan9
0.24
0
0.11
0.11
0.25
0.21
0.42
Scan10
0.23
0.11
0
0.07
0.23
0.14
0.4
Scan11
0.29
0.11
0.07
0
0.3
0.12
0.47
Scan12
0.04
0.25
0.23
0.3
0
0.35
0.18
Scan13
0.35
0.21
0.14
0.12
0.35
0
0.5
Scan14
0.18
0.42
0.4
0.47
0.18
0.5
0
APPENDIX A. APPENDIX
125
Table A.3: Deviation in the translational component along the X axis of ∆S T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.04
0.02
0.01
0.02
0.01
0.02
Scan2
0.04
0
0.02
0.05
0.02
0.05
0.06
Scan3
0.02
0.02
0
0.03
0
0.03
0.04
Scan4
0.01
0.05
0.03
0
0.02
0.01
0.01
Scan5
0.02
0.02
0
0.03
0
0.03
0.04
Scan6
0.01
0.05
0.03
0.01
0.03
0
0.01
Scan7
0.02
0.06
0.04
0.01
0.04
0.01
0
Scan8
0.01
0.05
0.03
0
0.03
0
0.01
Scan9
0.04
0.08
0.06
0.03
0.06
0.03
0.02
Scan10
0.04
0.08
0.07
0.04
0.06
0.03
0.03
Scan11
0.08
0.12
0.1
0.07
0.09
0.06
0.06
Scan12
0.02
0.06
0.04
0.01
0.04
0.01
0
Scan13
0.01
0.03
0.01
0.02
0.01
0.03
0.03
Scan14
0.03
0.01
0.01
0.04
0.01
0.04
0.05
Table A.4: Deviation in the translational component along the X axis of ∆S T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.01
0.04
0.04
0.08
0.02
0.01
0.03
Scan2
0.05
0.08
0.08
0.12
0.06
0.03
0.01
Scan3
0.03
0.06
0.07
0.1
0.04
0.01
0.01
Scan4
0
0.03
0.04
0.07
0.01
0.02
0.04
Scan5
0.03
0.06
0.06
0.09
0.04
0.01
0.01
Scan6
0
0.03
0.03
0.06
0.01
0.02
0.04
Scan7
0.01
0.02
0.03
0.06
0
0.03
0.05
Scan8
0
0.03
0.03
0.06
0.01
0.02
0.04
Scan9
0.03
0
0.01
0.04
0.02
0.05
0.07
Scan10
0.03
0.01
0
0.03
0.03
0.06
0.07
Scan11
0.06
0.04
0.03
0
0.06
0.09
0.1
Scan12
0.01
0.02
0.03
0.06
0
0.03
0.05
Scan13
0.02
0.05
0.06
0.09
0.03
0
0.02
Scan14
0.04
0.07
0.07
0.11
0.05
0.02
0
APPENDIX A. APPENDIX
126
Table A.5: Deviation in the translational component along the Y axis of ∆S T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.11
0.03
0.03
0.1
0.02
0.04
Scan2
0.11
0
0.09
0.14
0.01
0.09
0.08
Scan3
0.03
0.09
0
0.05
0.07
0
0.01
Scan4
0.03
0.14
0.05
0
0.13
0.05
0.06
Scan5
0.1
0.01
0.07
0.13
0
0.08
0.06
Scan6
0.02
0.09
0
0.05
0.08
0
0.02
Scan7
0.04
0.08
0.01
0.06
0.06
0.02
0
Scan8
0.06
0.06
0.03
0.08
0.04
0.03
0.02
Scan9
0.08
0.04
0.05
0.1
0.02
0.05
0.04
Scan10
0.1
0.01
0.08
0.13
0
0.08
0.06
Scan11
0.11
0
0.08
0.14
0.01
0.09
0.07
Scan12
0.07
0.05
0.04
0.09
0.03
0.04
0.03
Scan13
0.12
0
0.09
0.14
0.02
0.09
0.08
Scan14
0.08
0.04
0.05
0.1
0.02
0.05
0.04
Table A.6: Deviation in the translational component along the Y axis of ∆S T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.06
0.08
0.1
0.11
0.07
0.12
0.08
Scan2
0.06
0.04
0.01
0.01
0.05
0
0.04
Scan3
0.03
0.05
0.08
0.08
0.04
0.09
0.05
Scan4
0.08
0.1
0.13
0.13
0.09
0.14
0.1
Scan5
0.04
0.02
0
0.01
0.03
0.02
0.02
Scan6
0.03
0.05
0.08
0.09
0.04
0.09
0.05
Scan7
0.02
0.04
0.06
0.07
0.03
0.08
0.04
Scan8
0
0.02
0.04
0.05
0.01
0.06
0.02
Scan9
0.02
0
0.02
0.03
0.01
0.04
0
Scan10
0.04
0.02
0
0.01
0.04
0.02
0.03
Scan11
0.05
0.03
0.01
0
0.04
0.01
0.03
Scan12
0.01
0.01
0.04
0.04
0
0.05
0.01
Scan13
0.06
0.04
0.02
0.01
0.05
0
0.04
Scan14
0.02
0
0.03
0.03
0.01
0.04
0
APPENDIX A. APPENDIX
127
Table A.7: Deviation in the translational component along the Z axis of ∆S T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.06
0.09
0.03
0.06
0.01
0.05
Scan2
0.06
0
0.03
0.03
0.12
0.07
0.01
Scan3
0.09
0.03
0
0.06
0.15
0.1
0.04
Scan4
0.03
0.03
0.06
0
0.08
0.04
0.02
Scan5
0.06
0.12
0.15
0.09
0
0.05
0.11
Scan6
0.01
0.07
0.1
0.04
0.05
0
0.06
Scan7
0.05
0.01
0.04
0.02
0.11
0.06
0
Scan8
0.02
0.03
0.07
0
0.08
0.03
0.03
Scan9
0.09
0.03
0
0.06
0.14
0.1
0.04
Scan10
0.09
0.03
0
0.06
0.15
0.1
0.04
Scan11
0.06
0.01
0.03
0.04
0.12
0.07
0.02
Scan12
0.01
0.05
0.08
0.02
0.06
0.02
0.04
Scan13
0.01
0.07
0.1
0.04
0.05
0
0.06
Scan14
0.05
0.1
0.14
0.07
0.01
0.04
0.09
Table A.8: Deviation in the translational component along the Z axis of ∆S T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.02
0.09
0.09
0.06
0.01
0.01
0.05
Scan2
0.03
0.03
0.03
0.01
0.05
0.07
0.1
Scan3
0.07
0
0
0.03
0.08
0.1
0.14
Scan4
0
0.06
0.06
0.04
0.02
0.04
0.07
Scan5
0.08
0.14
0.15
0.12
0.06
0.05
0.01
Scan6
0.03
0.1
0.1
0.07
0.02
0
0.03
Scan7
0.03
0.04
0.04
0.02
0.04
0.06
0.09
Scan8
0
0.06
0.07
0.04
0.02
0.03
0.07
Scan9
0.06
0
0.01
0.02
0.08
0.1
0.13
Scan10
0.07
0.01
0
0.03
0.08
0.1
0.14
Scan11
0.04
0.02
0.03
0
0.06
0.08
0.11
Scan12
0.02
0.08
0.08
0.06
0
0.02
0.05
Scan13
0.03
0.1
0.1
0.08
0.02
0
0.03
Scan14
0.07
0.13
0.14
0.11
0.05
0.03
0
APPENDIX A. APPENDIX
128
Table A.9: Deviation in the norm of translational component of ∆S T in millimeters;
columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.13
0.1
0.04
0.12
0.03
0.06
Scan2
0.13
0
0.1
0.15
0.12
0.12
0.1
Scan3
0.1
0.1
0
0.09
0.17
0.11
0.06
Scan4
0.04
0.15
0.09
0
0.15
0.06
0.07
Scan5
0.12
0.12
0.17
0.15
0
0.09
0.13
Scan6
0.03
0.12
0.11
0.06
0.09
0
0.06
Scan7
0.06
0.1
0.06
0.07
0.13
0.06
0
Scan8
0.06
0.08
0.08
0.08
0.1
0.05
0.03
Scan9
0.12
0.09
0.08
0.12
0.16
0.11
0.06
Scan10
0.14
0.09
0.1
0.15
0.16
0.13
0.08
Scan11
0.15
0.12
0.13
0.16
0.15
0.13
0.09
Scan12
0.07
0.09
0.1
0.1
0.08
0.05
0.05
Scan13
0.12
0.07
0.14
0.15
0.05
0.1
0.1
Scan14
0.09
0.11
0.15
0.13
0.03
0.07
0.11
Table A.10: Deviation in the norm of translational component of ∆S T in millimeters;
columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.06
0.12
0.14
0.15
0.07
0.12
0.09
Scan2
0.08
0.09
0.09
0.12
0.09
0.07
0.11
Scan3
0.08
0.08
0.1
0.13
0.1
0.14
0.15
Scan4
0.08
0.12
0.15
0.16
0.1
0.15
0.13
Scan5
0.1
0.16
0.16
0.15
0.08
0.05
0.03
Scan6
0.05
0.11
0.13
0.13
0.05
0.1
0.07
Scan7
0.03
0.06
0.08
0.09
0.05
0.1
0.11
Scan8
0
0.07
0.09
0.09
0.02
0.07
0.08
Scan9
0.07
0
0.03
0.05
0.08
0.12
0.15
Scan10
0.09
0.03
0
0.04
0.1
0.12
0.16
Scan11
0.09
0.05
0.04
0
0.09
0.12
0.16
Scan12
0.02
0.08
0.1
0.09
0
0.06
0.07
Scan13
0.07
0.12
0.12
0.12
0.06
0
0.06
Scan14
0.08
0.15
0.16
0.16
0.07
0.06
0
APPENDIX A. APPENDIX
129
Table A.11: Deviation in the translational component along the X axis of ∆C T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.08
0.13
0
0.41
0.44
0.41
Scan2
0.08
0
0.05
0.07
0.33
0.36
0.34
Scan3
0.13
0.05
0
0.12
0.28
0.31
0.28
Scan4
0
0.07
0.12
0
0.40
0.43
0.41
Scan5
0.41
0.33
0.28
0.40
0
0.03
0
Scan6
0.44
0.36
0.31
0.43
0.03
0
0.03
Scan7
0.41
0.34
0.28
0.41
0
0.03
0
Scan8
0.35
0.28
0.23
0.35
0.05
0.08
0.06
Scan9
0.36
0.23
0.23
0.35
0.05
0.8
0.05
Scan10
0.04
0.03
0.08
0.03
0.36
0.39
0.37
Scan11
0.32
0.24
0.19
0.31
0.09
0.12
0.09
Scan12
0.30
0.22
0.17
0.29
0.11
0.14
0.11
Scan13
0.21
0.14
0.08
0.21
0.19
0.22
0.20
Scan14
0.16
0.08
0.03
0.15
0.25
0.28
0.25
Table A.12: Deviation in the translational component along the X axis of ∆C T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.35
0.36
0.44
0.32
0.30
0.21
0.16
Scan2
0.28
0.28
0.03
0..24
0.22
0.14
0.08
Scan3
0.23
0.23
0.08
0.19
0.17
0.08
0.03
Scan4
0.36
0.35
0.04
0.31
0.30
0.20
0.15
Scan5
0.05
0.04
0.36
0.09
0.11
0.19
0.25
Scan6
0.08
0.08
0.39
0.12
0.14
0.22
0.28
Scan7
0.06
0.05
0.37
0.09
0.11
0.20
0.25
Scan8
0
0
0.31
0.04
0.06
0.14
0.20
Scan9
0
0
0.31
0.04
0.06
0.15
0.20
Scan10
0.31
0.31
0
0.27
0.25
0.17
0.11
Scan11
0.04
0.04
0.27
0
0.02
0.11
0.16
Scan12
0.06
0.06
0.25
0.02
0
0.09
0.14
Scan13
0.14
0.15
0.17
0.11
0.09
0
0.06
Scan14
0.20
0.20
0.11
0.16
0.14
0.06
0
APPENDIX A. APPENDIX
130
Table A.13: Deviation in the translational component along the Y axis of ∆C T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.08
0.11
0.07
0.02
0.02
0.02
Scan2
0.08
0
0.03
0.02
0.10
0.07
0.07
Scan3
0.11
0.03
0
0.04
0.13
0.10
0.10
Scan4
0.07
0.02
0.04
0
0.08
0.05
0.05
Scan5
0.02
0.10
0.13
0.08
0
0.03
0.03
Scan6
0.02
0.07
0.10
0.05
0.03
0
0
Scan7
0.02
0.07
0.10
0.05
0.03
0
0
Scan8
0
0.09
0.11
0.07
0.01
0.02
0.02
Scan9
0.07
0.15
0.18
0.13
0.05
0.08
0.08
Scan10
0.07
0.02
0.04
0
0.08
0.05
0.05
Scan11
0.04
0.12
0.15
0.11
0.03
0.06
0.06
Scan12
0.01
0.07
0.10
0.06
0.03
0
0.01
Scan13
0.03
0.11
0.14
0.10
0.01
0.04
0.04
Scan14
0.03
0.05
0.08
0.04
0.05
0.02
0.02
Table A.14: Deviation in the translational component along the Y axis of ∆C T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0
0.07
0.07
0.04
0.01
0.03
0.03
Scan2
0.09
0.15
0.02
0.13
0.07
0.11
0.05
Scan3
0.11
0.18
0.04
0.15
0.10
0.14
0.08
Scan4
0.07
0.13
0
0.11
0.06
0.10
0.04
Scan5
0.01
0.05
0.08
0.03
0.03
0.01
0.05
Scan6
0.02
0.08
0.05
0.06
0
0.04
0.02
Scan7
0.02
0.08
0.05
0.06
0.01
0.04
0.02
Scan8
0
0
0.06
0.07
0.04
0.01
0.02
Scan9
0.06
0
0.13
0.02
0.08
0.04
0.10
Scan10
0.07
0.13
0
0.11
0.06
0.10
0.04
Scan11
0.04
0.02
0.11
0
0.05
0.02
0.08
Scan12
0.01
0.08
0.06
0.05
0
0.04
0.02
Scan13
0.03
0.04
0.10
0.02
0.04
0
0.06
Scan14
0.03
0.10
0.03
0.08
0.02
0.06
0
APPENDIX A. APPENDIX
131
Table A.15: Deviation in the translational component along the Z axis of ∆C T in millimeters; columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.13
0.35
0.5
0.60
0.56
0.55
Scan2
0.13
0
0.22
0.37
0.47
0.43
0.41
Scan3
0.35
0.21
0
0.14
0.25
0.21
0.20
Scan4
0.50
0.37
0.15
0
0.10
0.06
0.05
Scan5
0.60
0.47
0.24
0.10
0
0.04
0.05
Scan6
0.56
0.43
0.20
0.06
0.04
0
0.01
Scan7
0.54
0.41
0.20
0.04
0.05
0.01
0
Scan8
0.48
0.35
0.13
0.02
0.12
0.08
0.07
Scan9
0.60
0.46
0.25
0.10
0
0.04
0.05
Scan10
0.46
0.32
0.10
0.04
0.14
0.10
0.09
Scan11
0.67
0.53
0.31
0.17
0.07
0.11
0.12
Scan12
0.01
0.07
0.10
0.06
0.03
0
0.01
Scan13
0.50
0.37
0.14
0
0.10
0.06
0.04
Scan14
0.53
0.39
0.17
0.03
0.07
0.03
0.02
Table A.16: Deviation in the translational component along the Z axis of ∆C T in millimeters; columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.48
0.60
0.46
0.68
0.44
0.50
0.53
Scan2
0.35
0.46
0.32
0.53
0.30
0.37
0.39
Scan3
0.13
0.24
0.10
0.31
0.08
0.15
0.17
Scan4
0.02
0.1
0.04
0.17
0.06
0
0.03
Scan5
0.12
0
0.14
0.07
0.16
0.10
0.07
Scan6
0.08
0.04
0.10
0.11
0.12
0.06
0.03
Scan7
0.07
0.05
0.09
0.12
0.11
0.04
0.02
Scan8
0
0.12
0.02
0.18
0.04
0.02
0.04
Scan9
0.12
0
0.14
0.07
0.16
0.1
0.07
Scan10
0.02
0.14
0
0.21
0.02
0.04
0.07
Scan11
0.18
0.07
0.21
0
0.23
0.17
0.14
Scan12
0.01
0.08
0.06
0.05
0
0.04
0.02
Scan13
0.02
0.10
0.04
0.17
0.06
0
0.03
Scan14
0.04
0.07
0.07
0.14
0.09
0.03
0
APPENDIX A. APPENDIX
132
Table A.17: Deviation in the norm of the translational component of ∆C T in millimeters;
columns are for Innova scans 1 to 7.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7
Scan1
0
0.18
0.39
0.50
0.73
0.71
0.69
Scan2
0.18
0
0.23
0.37
0.58
0.56
0.54
Scan3
0.39
0.23
0
0.20
0.39
0.38
0.36
Scan4
0.50
0.37
0.19
0
0.42
0.44
0.41
Scan5
0.73
0.58
0.39
0.42
0
0.06
0.06
Scan6
0.71
0.56
0.38
0.44
0.06
0
0.03
Scan7
0.67
0.53
0.37
0.41
0.06
0.03
0
Scan8
0.60
0.45
0.29
0.36
0.13
0.11
0.09
Scan9
0.70
0.56
0.38
0.39
0.07
0.12
0.11
Scan10
0.47
0.33
0.14
0.06
0.40
0.41
0.38
Scan11
0.74
0.60
0.40
0.37
0.11
0.17
0.16
Scan12
0.53
0.38
0.22
0.30
0.20
0.18
0.16
Scan13
0.54
0.41
0.22
0.23
0.22
0.24
0.21
Scan14
0.55
0.40
0.19
0.16
0.27
0.28
0.26
Table A.18: Deviation in the norm of the translational component of ∆C T in millimeters;
columns are for Innova scans 8 to 14.
Scan8 Scan9 Scan10 Scan11 Scan12 Scan13 Scan14
Scan1
0.60
0.70
0.47
0.74
0.53
0.54
0.55
Scan2
0.45
0.56
0.32
0.60
0.38
0.40
0.40
Scan3
0.28
0.38
0.14
0.40
0.22
0.22
0.19
Scan4
0.36
0.39
0.58
0.37
0.30
0.23
0.16
Scan5
0.13
0.06
0.40
0.11
0.20
0.22
0.27
Scan6
0.11
0.12
0.41
0.17
0.18
0.23
0.28
Scan7
0.01
0.11
0.38
0.16
0.16
0.21
0.26
Scan8
0
0.13
0.32
0.19
0.07
0.15
0.21
Scan9
0.13
0
0.37
0.08
0.19
0.18
0.24
Scan10
0.32
0.37
0
0.36
0.26
0.20
0.14
Scan11
0.19
0.08
0.36
0
0.23
0.20
0.23
Scan12
0.07
0.19
0.26
0.23
0
0.11
0.17
Scan13
0.15
0.18
0.20
0.20
0.11
0
0.09
Scan14
0.21
0.24
0.14
0.21
0.17
0.09
0
APPENDIX A. APPENDIX
133
A.2 Calibration Results for the Mobile-Gantry CT Scanner
The results from 9 calibration experiments with the CT scanner are presented in this section.
Table A.19: Deviation in the angle of the rotational component of ∆V T in degrees.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7 Scan8 Scan9
Scan1
0
0.02
0.09
0.07
0.02
0.02
0.03
0.26
0.31
Scan2
0.03
0
0.07
0.04
0.03
0.03
0.04
0.25
0.30
Scan3
0.10
0.07
0
0.03
0.10
0.10
0.11
0.23
0.28
Scan4
0.07
0.04
0.03
0
0.06
0.07
0.08
0.25
0.30
Scan5
0.02
0.03
0.10
0.06
0
0.01
0.01
0.28
0.33
Scan6
0.02
0.03
0.10
0.07
0.01
0
0.01
0.28
0.33
Scan7
0.03
0.04
0.11
0.08
0.01
0.01
0
0.29
0.34
Scan8
0.26
0.25
0.23
0.25
0.28
0.28
0.29
0
0.05
Scan9
0.31
0.30
0.28
0.30
0.33
0.33
0.33
0.05
0
Table A.20: Deviation in the translational component along the X axis of ∆V T in millimeters.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7 Scan8 Scan9
Scan1
0
0.09
0.37
0.25
0.07
0.12
0.09
0.40
0.34
Scan2
0.09
0
0.27
0.16
0.16
0.22
0.18
0.31
0.25
Scan3
0.37
0.27
0
0.11
0.43
0.49
0.46
0.03
0.03
Scan4
0.25
0.16
0.11
0
0.32
0.37
0.34
0.15
0.09
Scan5
0.06
0.16
0.43
0.32
0
0.05
0.02
0.47
0.41
Scan6
0.12
0.22
0.49
0.37
0.05
0
0.03
0.52
0.46
Scan7
0.09
0.18
0.46
0.34
0.02
0.03
0
0.49
0.43
Scan8
0.40
0.31
0.04
0.15
0.47
0.52
0.49
0
0.06
Scan9
0.34
0.25
0.03
0.09
0.41
0.46
0.43
0.06
0
APPENDIX A. APPENDIX
134
Table A.21: Deviation in the translational component along the Y axis of ∆V T in millimeters.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7 Scan8 Scan9
Scan1
0
0.10
0.42
0.60
0.60
0.48
0.46
1.14
0.70
Scan2
0.10
0
0.32
0.49
0.50
0.38
0.36
1.03
0.60
Scan3
0.42
0.32
0
0.18
0.18
0.06
0.04
0.72
0.28
Scan4
0.60
0.49
0.18
0
0.01
0.12
0.13
0.54
0.10
Scan5
0.60
0.50
0.18
0.01
0
0.13
0.14
0.53
0.10
Scan6
0.48
0.38
0.06
0.12
0.13
0
0.01
0.66
0.22
Scan7
0.46
0.36
0.04
0.13
0.14
0.01
0
0.67
0.24
Scan8
1.14
1.03
0.71
0.54
0.53
0.66
0.67
0
0.43
Scan9
0.70
0.60
0.28
0.10
0.10
0.23
0.24
0.43
0
Table A.22: Deviation in the translational component along the Z axis of ∆V T in millimeters.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7 Scan8 Scan9
Scan1
0
0.39
0.85
0.60
0.06
0.07
0.05
0.57
0.68
Scan2
0.39
0
0.46
0.20
0.44
0.46
0.44
0.18
0.29
Scan3
0.85
0.46
0
0.26
0.91
0.92
0.90
0.28
0.17
Scan4
0.60
0.20
0.26
0
0.65
0.66
0.64
0.02
0.09
Scan5
0.06
0.45
0.91
0.65
0
0.01
0.01
0.63
0.74
Scan6
0.07
0.46
0.92
0.66
0.01
0
0.02
0.64
0.75
Scan7
0.05
0.44
0.90
0.64
0.01
0.02
0
0.62
0.72
Scan8
0.56
0.18
0.28 0.026
0.63
0.64
0.62
0
0.11
Scan9
0.67
0.29
0.17
0.09
0.74
0.75
0.73
0.11
0
Table A.23: Deviation in the norm of the translational component of ∆V T in millimeters.
Scan1 Scan2 Scan3 Scan4 Scan5 Scan6 Scan7 Scan8 Scan9
Scan1
0
0.41
1.02
0.88
0.61
0.50
0.48
1.33
1.03
Scan2
0.41
0
0.62
0.56
0.69
0.63
0.60
1.09
0.71
Scan3
1.02
0.62
0
0.33
1.02
1.04
1.01
0.77
0.33
Scan4
0.88
0.56
0.33
0
0.73
0.77
0.74
0.56
0.16
Scan5
0.61
0.69
1.02
0.73
0
0.14
0.14
0.95
0.85
Scan6
0.50
0.63
1.05
0.77
0.14
0 0.041
1.05
0.91
Scan7
0.48
0.60
1.01
0.74
0.14 0.041
0
1.04
0.88
Scan8
1.33
1.09
0.77
0.56
0.95
1.06
1.04
0
0.88
Scan9
1.03
0.71
0.33
0.16
0.85
0.91
0.88
0.45
0
APPENDIX A. APPENDIX
135
A.3 Results of the Bone-Model Validation Study
The results for the bone model study, using both the the Innova and the mobile-gantry CT
for intraoperative imaging, are presented in this section.
A.3.1 Results for the Bone-Model Validation Study with the Innova
Table A.24: Target Registration Errors for the Fiducial Markers on Femur Model #1 at the
initial position (long shaft of the bone parallel to the table) with the Innova
Fiducial Marker TRE (mm)
1
1.54
2
1.54
3
1.78
4
1.45
5
2.33
6
1.77
Table A.25: Target Registration Errors for the Fiducial Markers on Femur Model #1 at 90 ◦
counter-clockwise rotation from the initial position (long shaft of the bone
parallel to the table) with the Innova.
Fiducial Marker TRE (mm)
1
1.21
2
1.26
3
0.80
4
1.75
5
0.43
6
1.93
APPENDIX A. APPENDIX
136
Table A.26: Target Registration Errors for the Fiducial Markers on Femur Model #1 at
180 ◦ counter-clockwise rotation from the initial position (long shaft of the
bone parallel to the table) with the Innova
Fiducial Marker TRE (mm)
1
1.16
2
1.94
3
1.24
4
0.87
5
1.33
6
2.27
Table A.27: Target Registration Errors for the Fiducial Markers on Femur Model #1 at
270 ◦ counter-clockwise rotation from the initial position (long shaft of the
bone parallel to the table) with the Innova
Fiducial Marker TRE (mm)
1
0.87
2
1.56
3
1.02
4
2.01
5
0.95
6
1.77
Table A.28: Target Registration Errors for the Fiducial Markers on Femur Model #2 at the
initial position (long shaft of the bone is parallel with the table) with the Innova
Fiducial Marker TRE (mm)
1
1.77
2
1.99
3
01.43
4
2.06
Table A.29: Target Registration Errors for the Fiducial Markers on Femur Model #2 90 ◦
counter-clockwise rotation of the initial position (long shaft of the bone is
parallel with the table) with the Innova
Fiducial Marker TRE (mm)
1
2.15
2
0.84
3
1.45
4
1.56
APPENDIX A. APPENDIX
137
Table A.30: Target Registration Errors for the Fiducial Markers on Femur Model #2 180 ◦
counter-clockwise rotation of the initial position (long shaft of the bone is
parallel with the table) with the Innova
Fiducial Marker TRE (mm)
1
0.92
2
1.14
3
1.14
4
1.71
Table A.31: Target Registration Errors for the Fiducial Markers on Femur Model #2 270 ◦
counter-clockwise rotation of the initial position (long shaft of the bone is
parallel with the table) with the Innova
Fiducial Marker TRE (mm)
1
1.00
2
2.51
3
1.63
4
1.59
Table A.32: Target Registration Errors for the Fiducial Markers on Tibia Model #1 at the
initial position (long shaft of the bone parallel to the table) with the Innova
Fiducial Marker TRE (mm)
1
1.71
2
1.31
3
1.70
4
1.61
5
0.95
6
1.21
Table A.33: Target Registration Errors for the Fiducial Markers on Tibia Model #1 at 90 ◦
counter-clockwise rotation of the initial position with the Innova
Fiducial Marker TRE (mm)
1
1.25
2
1.47
3
2.68
4
1.82
5
1.50
6
1.54
APPENDIX A. APPENDIX
138
Table A.34: Target Registration Errors for the Fiducial Markers on Tibia Model #1 at 180 ◦
counter-clockwise rotation of the initial position with the Innova
Fiducial Marker TRE (mm)
1
1.37
2
1.74
3
1.14
4
1.06
5
1.56
6
1.25
Table A.35: Target Registration Errors for the Fiducial Markers on Tibia Model #1 at 270 ◦
counter-clockwise rotation of the initial position with the Innova
Fiducial Marker TRE (mm)
1
2.04
2
1.64
3
2.15
4
1.35
5
1.75
6
2.32
Table A.36: Target Registration Errors for the Fiducial Markers on Tibia Model #2 at the
initial position (long shaft of the bone parallel to the table) the Innova
Fiducial Marker TRE (mm)
1
1.95
2
1.94
3
1.97
Table A.37: Target Registration Errors for the Fiducial Markers on Tibia Model #2 at 90 ◦
counter-clockwise rotation of the initial position (long shaft of the bone parallel to the table) the Innova
Fiducial Marker TRE (mm)
1
1.45
2
2.1
3
0.80
APPENDIX A. APPENDIX
139
Table A.38: Target Registration Errors for the Fiducial Markers on Tibia Model #2 at 180 ◦
counter-clockwise rotation of the initial position (long shaft of the bone parallel to the table) the Innova
Fiducial Marker TRE (mm)
1
0.83
2
0.97
3
0.61
Table A.39: Target Registration Errors for the Fiducial Markers on Tibia Model #2 at 270 ◦
counter-clockwise rotation of the initial position (long shaft of the bone parallel to the table) the Innova
Fiducial Marker TRE (mm)
1
1.59
2
0.90
3
1.09
APPENDIX A. APPENDIX
140
A.3.2 Results for the Bone-Model Validation Study with CT
The results for the bone model study using the CT for intraoperative imaging is presented
in this section.
Table A.40: Target Registration Errors for the Fiducial Markers on Femur Mocdel #1 with
the CT Scanner
Fiducial Marker TRE (mm)
1
1.59
2
0.90
3
1.51
4
1.33
5
1.61
6
1.3
Table A.41: Target Registration Errors for the Fiducial Markers on Femur Model #2 with
the CT Scanner
Fiducial Marker TRE (mm)
1
3.01
2
2.13
3
2.48
4
2.11
Table A.42: Target Registration Errors for the Fiducial Markers on Tibia Model #1 with the
CT Scanner
Fiducial Marker TRE (mm)
1
2.56
2
2.32
3
4.07
4
2.36
5
2.94
6
2.94
APPENDIX A. APPENDIX
141
Table A.43: Target Registration Errors for the Fiducial Markers on Tibia Model #2 with the
CT Scanner
Fiducial Marker TRE (mm)
1
1.926
2
2.06
3
1.88
Glossary
Calibration A technical procedure to establish a local coordinate frame among a group
of IRED or passive markers.
Cervical
The seven cervical vertebrae are the smallest movable vertebrae in the neck
region [93].
Condyle
Knuckle-shaped articular surfaces [93].
Digital Reconstructed Radiographs (DRR)
X-ray like images generated from 3D mod-
els.
Dynamic Reference Body (DRB)
A specific holder that contains a group of IRED or
passive markers that have been characterized with a local coordinate frame.
Femur
Also known as the thigh bone, it longest and strongest bone in the body. The
upper extremity has a rounded articular head which is connected to the pelvis.
The distal or inferior extremity has the shape of a double knuckle or condyle
that is associated with the tibia [93].
Fiducial
Radio-opaque markers that are implanted into the surface of the anatomy or
fabricated on a stereotactic frame.
142
GLOSSARY
Fiducial Registration Error
143
The root mean square distance between corresponding fidu-
cials after registration [29].
Infrared Emitting Diodes (IRED)
Active markers that emit infrared light which can be
detected by the Optotrak Certus system.
Knee
The knee joint consists of two condylar joints between the corresponding condyles
of the femur and tibia and a sellar joint between the patella and the patellar surface of the femur [93].
Osteoma A small benign osteoblastic lesion of the cortical bone [60].
Osteotomy An osteotomy is a surgical procedure where realignment of a bone is performed, often involving removing a section of it [60].
Pedicle
The two pedicles are short, thick, and rounded bars projecting back from the
body of the vertebrae at the junction between its lateral and dorsal surfaces, and
nearer the superior [93].
Pelvis
The skeletal ring formed by two innominate bones and the sacrum, the cavity of
this arrangement, and by extension, to the entire region where trunk and lower
limbs meet. Often referred as the hip bone [93].
Process
A bone projection of considerable size [93].
Radius
It is the lateral bone of the forearm Its upper and lower ends are expanded, but
the lower end is much the wider of the two [93].
Revascularization A surgical procedure to provide blood flow to a body part or organ
[79].
GLOSSARY
144
Rigid Body Transformation A transformation that consists of only a rotation and a translation.
Sacrum
It is a large, triangular and formed by fusion of five sacral vertebrae. It is
situated at the upper and posterior part of the pelvic cavity, inserted like a wedge
between the two innominate bones [93].
Talus
It is a bone that connects the rest of the foot and the bones of the leg. [93].
Target Registration Error
The distance between corresponding points after registra-
tion. In calculating this distance, the points other than fiducials are used [29].
Tibia
It is the medial and strongest bone in the leg [93].