Download Segmentation and Alignment of 3-D Transaxial Myocardial Perfusion Images and

Segmentation and Alignment of 3-D Transaxial
Myocardial Perfusion Images and
Automatic Dopamine Transporter Quantification
Leo Bergnéhr
April, 2008
Reg nr: LiTH-IMT/MI30-A-EX--08/465--SE
Segmentation and Alignment of 3-D Transaxial
Myocardial Perfusion Images and
Automatic Dopamine Transporter Quantification
Master’s Thesis in Biomedical Engineering
at Linköping University
by
Leo Bergnéhr
April, 2008
Reg nr: LiTH-IMT/MI30-A-EX--08/465--SE
Supervisor:
Joakim Rydell
Examiner:
Magnus Borga
Abstract
Nuclear medical imaging such as SPECT (Single Photon Emission Tomography) is an
imaging modality which is readily used in many applications for measuring physiological properties of the human body. One very common type of examination using SPECT
is when measuring myocardial perfusion (blood flow in the heart tissue), which is often
used to examine e.g. a possible myocardial infarction (heart attack). In order for doctors
to give a qualitative diagnose based on these images, the images must first be segmented
and rotated by a medical technologist. This is performed due to the fact that the heart
of different patients, or for patients at different times of examination, is not situated and
rotated equally, which is an essential assumption for the doctor when examining the
images. Consequently, as different technologists with different amount of experience
and expertise will rotate images differently, variability between operators arises and can
often become a problem in the process of diagnosing.
Another type of nuclear medical examination is when quantifying dopamine transporters in the basal ganglia in the brain. This is commonly done for patients showing
symptoms of Parkinson’s disease or similar diseases. In order to specify the severity of
the disease, a scheme for calculating different fractions between parts of the dopamine
transporter area is often used. This is tedious work for the person performing the quantification, and despite the acquired three dimensional images, quantification is too often
performed on one or more slices of the image volume. In resemblance with myocardial
perfusion examinations, variability between different operators can also here present a
possible source of errors.
In this thesis, a novel method for automatically segmenting the left ventricle of the heart
in SPECT-images is presented. The segmentation is based on an intensity-invariant
local-phase based approach, thus removing the difficulty of the commonly varying intensity in myocardial perfusion images. Additionally, the method is used to estimate the
angle of the left ventricle of the heart. Furthermore, the method is slightly adjusted, and
a new approach on automatically quantifying dopamine transporters in the basal ganglia
using the DaTSCANTM radiotracer is proposed.
Sammanfattning
Nukleärmedicinska bilder som exempelvis SPECT (Single Photon Emission Tomography) är en bildgenererande teknik som ofta används i många applikationer vid mätning
av fysiologiska egenskaper i den mänskliga kroppen. En vanlig sorts undersökning
som använder sig av SPECT är myokardiell perfusion (blodflöde i hjärtvävnaden), som
ofta används för att undersöka t.ex. en möjlig hjärtinfarkt. För att göra det möjligt för
läkare att ställa en kvalitativ diagnos baserad på dessa bilder, måste bilderna först segmenteras och roteras av en biomedicinsk analytiker. Detta utförs på grund av att hjärtat
hos olika patienter, eller hos patienter vid olika examinationstillfällen, inte är lokaliserat
och roterat på samma sätt, vilket är ett väsentligt antagande av läkaren vid granskning
av bilderna. Eftersom olika biomedicinska analytiker med olika mängd erfarenhet och
expertis roterar bilderna olika uppkommer variation av de slutgiltiga bilder, vilket ofta
kan vara ett problem vid diagnostisering.
En annan sorts nukleärmedicinsk undersökning är vid kvantifiering av dopaminreceptorer i de basala ganglierna i hjärnan. Detta utförs ofta på patienter som visar symptom
av Parkinsons sjukdom, eller liknande sjukdomar. För att kunna bestämma graden av
sjukdomen används ofta ett utförande för att räkna ut olika kvoter mellan områden runt
dopaminreceptorerna. Detta är ett tröttsamt arbete för personen som utför kvantifieringen och trots att de insamlade bilderna är tredimensionella, utförs kvantifieringen allt
för ofta endast på en eller flera skivor av bildvolymen. I likhet med myokardiell perfusionsundersökningar är variation mellan kvantifiering utförd av olika personer en möjlig
felkälla.
I den här rapporten presenteras en ny metod för att automatiskt segmentera hjärtats
vänstra kammare i SPECT-bilder. Segmenteringen är baserad på en intensitetsinvariant
lokal-fasbaserad lösning, vilket eliminerar svårigheterna med den i myokardiella perfusionsbilder ofta varierande intensiteten. Dessutom används metoden för att uppskatta
vinkeln hos hjärtats vänstra kammare. Efter att metoden sedan smått justerats används
den som ett förslag på ett nytt sätt att automatiskt kvantifiera dopaminreceptorer i de
basala ganglierna, vid användning av den radioaktiva lösningen DaTSCANTM .
Acknowledgements
This project has been carried out at Exini Diagnostics AB and I would like to thank
everyone there for their support and friendliness. Special gratitude goes to my company
supervisor, professor Lars Edenbrandt, who initiated the project and invited me to work
on it. Thank you; bringer of good confidence!
Additionally, I would like to thank my university supervisor, Joakim Rydell, at the Department of Biomedical Engineering. In the beginning of this project I had a lot of
questions, to which you always had enlightening answers, despite completing a PhD at
the same time.
Finally, I give a special acknowledgement to my family and near friends; not for helping
me while formulating mathematical expressions, but for just being there when I was not.
Thank you!
Table of Contents
1
Introduction
1.1 Background
1.2 Objectives .
1.3 Method . .
1.4 Outline . .
1.5 Notation . .
2
Scintigraphy
2.1 Nuclear medicine physics . . . . . . . . . . . .
2.1.1 Decay of radioactive isotopes . . . . .
2.1.2 Detection of radiation . . . . . . . . .
2.2 Single Photon Emission Computed Tomography
2.2.1 Image quality . . . . . . . . . . . . . .
2.3 Scintigraphic examinations . . . . . . . . . . .
2.3.1 Myocardial perfusion SPECT . . . . .
2.3.2 DaTSCAN Quantification . . . . . . .
2.4 Summary . . . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3
Image Segmentation
3.1 Segmentation methods
3.1.1 Thresholding .
3.1.2 Region growing
3.1.3 Active shapes .
3.2 Image registration . . .
3.3 Summary . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
The Morphon Method
4.1 Displacement field estimation . .
4.1.1 Quadrature phase . . . .
4.1.2 Least square solution . .
4.2 Displacement field accumulation
4.3 Displacement field regularisation
4.4 The model . . . . . . . . . . . .
4.4.1 Deformation . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
1
2
2
3
4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5
5
5
6
8
8
9
9
10
11
.
.
.
.
.
.
.
.
.
.
.
.
13
13
13
14
15
15
17
.
.
.
.
.
.
.
19
20
20
24
24
25
26
26
.
.
.
.
.
.
.
.
.
.
.
.
8
Table of Contents
4.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Rotation of Myocardial Perfusion Images
5.1 Pre-processing of images . . . . . . .
5.2 2-D Morphon segmentation . . . . . .
5.2.1 Locating the heart . . . . . .
5.2.2 Segmentation . . . . . . . . .
5.3 3-D Morphon segmentation . . . . . .
5.4 Angling of the heart . . . . . . . . . .
5.4.1 Angle estimation . . . . . . .
5.4.2 Rotation . . . . . . . . . . . .
5.5 Summary . . . . . . . . . . . . . . .
6
Dopamine Transporter Quantification
6.1 3-D Morphon segmentation . . . . . . . . . . .
6.1.1 Locating the basal ganglia . . . . . . .
6.1.2 Segmentation . . . . . . . . . . . . . .
6.2 Quantification . . . . . . . . . . . . . . . . . .
6.2.1 Weighted principal component analysis
6.3 Summary . . . . . . . . . . . . . . . . . . . .
7
Results
7.1 Segmentation and alignment of 3-D transaxial myocardial perfusion images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Automatic dopamine transporter quantification . . . . . . . . . . . . .
7.2.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
9
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
27
.
.
.
.
.
.
.
.
.
29
29
30
31
31
32
33
34
35
35
.
.
.
.
.
.
37
37
38
39
40
41
43
45
45
45
46
46
52
52
Discussion
8.1 Segmentation and alignment of 3-D transaxial myocardial perfusion images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Automatic dopamine transporter quantification . . . . . . . . . . . . .
59
59
61
Conclusions
63
1
Introduction
1.1
Background
Scintigraphy is a widely used medical imaging modality for observing physiological
properties in the human body. Two examples that are considered in this thesis are scintigraphic heart images and images of the basal ganglia in the brain.
At the time of writing, a scintigraphic examination of the heart is at hospitals carried
out by a technologist. The main tasks for the technologist is to prepare the patient for
the diagnostic procedure, and later on to perform a sequence of manual operations on
the acquired images. These operations includes positioning the location of the heart to
a predefined area in the images, determining the orientation of the heart and concluding
whereas the image quality is sufficient for the doctor to base a diagnosis on. The reorientation of the heart is necessary due to the simple fact that different individuals do not
look the same; not on the outside, nor on the inside of the body. In heart scintigraphy,
this presents a problem.
For a doctor to give a qualitative diagnosis, the result of an examination is compared
to other images. This may occur directly, by looking at different images from other
patients, or indirectly, by taking into account the vast amount of images in the past that
is the experience of the doctor. However, both these methods depend on the presumption
that the images have been observed from the same point of view, which would not be
the case if the technologist did not manually compensate for angular and rotational
differences of the orientation of the heart, between different scintigraphic examinations.
However, as different technologists have different experience and slightly different ways
of making these adjustments, the result will not be consistent for all examinations. An
automatic process for doing this would not only hopefully make the result more consistent, but also save time that the technologist has to spend on performing these tasks
manually. One method for doing this has been proposed by Germano et al. [1], hoping
2
Chapter 1. Introduction
to move more and more into a fully automated process [2]. However, as this method is
based on intensity of the images, a more insensitive method may be desired.
Moreover, scintigraphic images of the basal ganglia in the brain are beginning to be
more and more popular to diagnose Parkinson’s disease. At the time of writing, quantification is used to measure a number of properties from the images of the basal ganglia, thus being able to determine the state of the patient. This process is tedious and
can present difficulties if the state of the basal ganglia is poor. An automatic method for
doing this quantification would benefit in much the same ways as the case with scintigraphic heart examinations. The process would be much faster compared to manual
quantification, and the variability between medical staff would be eliminated. Additionally, manual quantification is performed in two dimensions and hence it could be
beneficial to quantify in 3-D. Morton et al. [3] has evaluated two computer driven methods in the same field and found that a 3-D based method gives better concordance with
visual assessments.
1.2
Objectives
The primary aim of this project is to investigate if an automatic reorientation of threedimensional, transaxial myocardial perfusion SPECT images is possible, and if so, to
design and implement an automatic segmentation method that can distinguish, and compensate for, differences in anatomical structure of the heart; particularly the angle and
position of the left ventricle. The method should be able to segment and reorient the left
ventricle from transaxial images into short-axis (oblique) images.
Secondarily, the same method should, after little modification, be applicable to scintigraphic images of the basal ganglia. These should be segmented, and a variety of useful
parameters should be extracted. These parameters should correspond to parameters that
are extracted in manual quantification.
1.3
Method
The work in this project has been divided into two different parts. First, the segmentation algorithm was implemented, and secondly the algorithm was applied on the two
problems at hand, which first required some pre-processing in each case. ComputaR
tions and simulations have been carried out with the help of M ATLAB!
, version 6 and
7, from The MathWorks, Inc. The main part of the functions and methods used has
been implemented with the help of M ATLAB-included primitive functions. However,
to decrease computation time, a C-compiled version of convolution has been used, with
courtesy of Gunnar Farnebäck at the Department of Biomedical Engineering, Linköping
1.4 Outline
3
university. To decrease the time of implementation, some functions from the M ATLAB Image Processing Toolbox have also been used. These are the bwlabel() and
regionprops() for some simple morphological operations, and tformarray()
for rotating 3-D volumetric objects.
All the images used for development of the algorithm have been provided by Swedish
hospitals. The scintigraphic heart images originate from Sahlgrenska university hospital
in Gothenburg, Sweden, while the DaTSCAN-images of the basal ganglia have been
provided by The university hospital of Norrland in Umeå, Sweden.
1.4
Outline
Here follow a short summary of the contents of each chapter of this thesis.
Chapter 2 The basics of nuclear physics is presented along with the essential parts of a nuclear medical examination. In this chapter, relevant facts about myocardial perfusion examinations and DaTSCAN examinations are also introduced.
Chapter 3 In this chapter, image segmentation and registration is introduced. Some commonly used techniques are presented along with their good and poor properties.
Chapter 4 The main method in this thesis, the Morphon method, is gone through in some
detail in this chapter.
Chapter 5 Here the problem with the estimation of angles of the heart in myocardial perfusion images is addressed with the help of the earlier presented methods and some
complementary techniques.
Chapter 6 This chapter involves applying the Morphon method on the problem of automatic
quantification of dopamine transporters and introduces some additional tools for
solving this.
Chapter 7 The results of both parts of the thesis are presented in this chapter.
Chapter 8 The results of the previous chapter are discussed and some future development of
the methods is proposed.
Chapter 9 This chapter concludes the whole thesis, its results and possible effects on the
problems at hand.
4
1.5
Chapter 1. Introduction
Notation
This thesis inevitably involves some mathematics. The notations used are presented
below.
s, S
v
v̂
|v|
M
v T , MT
M−1
s∗
(s1 ∗ s2 )(x)
E[x]
Scalar
Vector
Unit vector
Norm of vector
Matrix.
Transpose of vector and matrix
Inverse of matrix
Complex conjugate of the complex signal s
Convolution of s1 and s2
Expectation value of the stochastic variable x
2
Scintigraphy
To be able to understand the process of generating scintigraphic images using nuclear
medical methods such as SPECT (Single Photon Emission Computed Tomography), the
basic physics behind it is laid forward in this chapter. Details on the physical aspects and
more information regarding different isotopes can be found in [4] and [5, 6] respectively.
2.1
Nuclear medicine physics
Nuclear physical applications in medicine have been in clinical use for many decades.
The first experiments started somewhere around 1935, when Chiewitz and de Heversy
[7] tested the technique on rats. At first, nuclear medicine was mainly used in therapeutical treatments, such as that of cancer, introduced by Lindgren [8]. However, as
acquisition instruments and radiotracers improved, it also became a very popular way
of examining physiological and anatomical properties of many parts of the human body,
for example the heart [9] and the brain [10].
2.1.1
Decay of radioactive isotopes
In all imaging modalities, some kind of conceptual probe is used to gather information
about the observed object at hand. This probe can be very different in different situations. For example, at an ultra sound examination, mechanical waves are used to gather
information about the object, by propagation and reflection between different acoustic impedances, and in magnetic resonance imaging, radio frequency fields, interacting
with fundamental properties of matter, are the probes at hand. In nuclear imaging, radiation is used to acquire information about an object. Radiation, which originates from
radioactive isotopes1 .
1
An isotope of an element is a specific variation of that element, where the number of neutrons in the
nucleus differ between different isotopes.
6
Chapter 2. Scintigraphy
There are a variety of radioactive isotopes used in nuclear medicine. Depending on the
type of examination and the region of interest in the body, the energy of the decaying
particles from the isotopes has to be taken into consideration. For example, in SPECT,
which is the modality of interest in this thesis, the most common isotope used is 99m Tc
(technetium), which is suitable due to, among other things, its half-life and the energy
of its emitted photons [11]; that is about the same as for conventional X-ray γ-energies2 .
A radioactive isotope (radioisotope) is, by definition, unstable. That means that the
nucleus of that element can, and will, spontaneously decay with a certain probability,
given a period of time. The faster the nucleus decays, the faster will it reach its half-time
value; that is when 50 percent of the amount of isotope has vanished in favour of decay
radiation of some sort. There is a tremendous amount of different isotopes, both occurring naturally on Earth and synthetically produced with the help of nuclear reactions.
There are also many different types of decaying processes for different types of nucleus.
These different types of decay have been categorised after the type of particle emitted in
the process. The most known particle emission, or radiation, is γ-radiation, where the
emitted particles are photons, or light. Other common types of radiation are α-, β − - and
β + -radiation [4]. β- and γ-radiation is of much interest from a nuclear medical point of
view since they are the key particles in SPECT, while α-radiation is attenuated quickly
in most media and is more harmful to human tissue, and therefore is used sparsely in
medical diagnostics [5]. β −/+ -particles are more commonly known as electrons (e− )
and positrons3 (e+ ).
2.1.2
Detection of radiation
As was stated earlier, γ- and β-radiation is preferable in nuclear medical diagnostics,
however the methods for collecting images with the two methods differ. In SPECT
imaging, isotopes like 99m Tc, mentioned in the first paragraph of 2.1.1, are used for
different purposes. While some have been stated, the one more important for the basic
principles of this imaging modality is that these kind of isotopes decay with a single
emission of a γ-particle.
Since the nucleus decays spontaneously, it will have an equal probability of emitting a
photon in any direction [4], which is illustrated in Figure 2.1. The emitted photon will
have a total energy of about 140 keV, which is suitable for many photon detectors at
the time of writing [6]. To detect the emitted γ-rays, different types of detectors can
be used. However, particularly in nuclear medicine scintigraphy, a common method
is to use a so called scintillator for this purpose. A scintillator is basically a type of
2
The Greek letter γ is in physics often used as a symbol for photon or light.
The positron is the antiparticle of the electron, which means it has exactly the same properties, except
for electrical charge, which is the opposite.
3
2.1 Nuclear medicine physics
7
!
Figure 2.1: The one-step process when a radioactive isotope decays with γ-radiation.
crystal4 with specific characteristics. These crystals have in common that they undergo
a process called fluorescence when interacting with γ-rays of an energy matching the
characteristics of the crystal. Fluorescence is a process where an element will absorb
a γ-ray and immediately emit light within the visible range. This is due to the photo
electric effect, where electrons in an atom can be pushed to a higher energy state and
then, when falling back to the original state, send out a flash of light [4]. This light can
later be amplified, for example with the help of a photomultiplier, and then detected.
Guerra [6] points out that while the scintillator is more sensitive and therefore preferable
in many applications, other detectors are used, such as gas-filled chambers and solid
state semiconductors.
1
e+
2
ee+
!
Figure 2.2: The two-step process when a radioactive isotope decays with a positron (β-decay),
which shortly thereafter reacts with an electron, creating γ-radiation.
While single photon emitters (SPE) such as 99m Tc are used to detect one γ-ray at a time,
4
Common crystals that are used in nuclear medicine are: Cerium doped lutetium orthosilicate (LSO),
cerium doped gadolinium orthosilicate (GSO) or yttrium aluminium perovskite (YAP) [6].
8
Chapter 2. Scintigraphy
there is another method used in nuclear medicine that utilise positron emitters (PE),
such as Oxygen-15. In accordance to the name, positron emitters decay by emitting
positrons; that is with β + -decay (see figure 2.2) [5]. However, as an antiparticle to the
electron, the positron will readily react with electrons it encounters, annihilating both
particles and sending out two photons near exactly in the opposite direction to each
other. In vivo, the positron will react almost instantly with an electron, producing two
photons that will radiate from the same source [4]. Consequently, even though another
type of nuclear decay is the source of radiation, photons will, in the end, be detected
by both type of radioisotopes. In nuclear medicine, the imaging modality using PE is
referred to as PET (Positron Emission Tomography). PET-images are very similar to
SPECT-images, but they will not be studied any further in this thesis due to the lack of
PET-image material.
2.2
Single Photon Emission Computed Tomography
The imaging modality that is the source of all images in this thesis is SPECT. In SPECT,
photons from single photon emitters are detected in a manner as described in 2.1.2.
SPECT is a widely used modality and has been used for some time. One of the great advantages of SPECT compared to projectional modalities like X-ray imaging is its ability
to acquire images in 3-D, thereof the word tomography in the abbreviation. Larsson [12]
presented one of the first working tomographic systems and the image quality has been
much improved ever since.
2.2.1
Image quality
What should be mentioned about the images generated in a SPECT examination is that
they are low in resolution and signal to noise ratio compared to images from other
imaging modalities, such as CT (computed tomography) and MRI (magnetic resonance
imaging). A typical SPECT-image has a resolution of 643 voxels5 , while the other
modalities can have resolutions of 5123 voxels and above [5]. The low resolution in
SPECT-images originates from the fact that the photon count, i.e. the number of photons
that are detected, is quite low and that SPECT registers physiological processes in the
body, not anatomical structures as CT and MRI are mainly used for. Further more, even
though the photon count could probably be increased with a more radiating radioisotope,
it would consequently increase the dose of radiation applied to the patient.
5
The three-dimensional correspondence to an image pixel.
2.3 Scintigraphic examinations
2.3
9
Scintigraphic examinations
There are many steps involved in a clinical scintigraphic examination. In this section,
the process of examining myocardial perfusion as well as dopamine activity in the basal
ganglia, and some problems that arrises with manual diagnoses in such examinations,
will be presented.
In most nuclear medical applications the radioisotope that generates the image signal
is tagged to a compound of some sort, called a pharmaceutical agent, which is injected
into the patient. Together, the isotope and the agent are named a radiotracer, which is
used to attach itself to the organ that is to be investigated, and to make the radioisotope
less hostile to the body. For example, as exemplified by Wilson et al. [13], in myocardial
perfusion SPECT examinations, tert-butyl is commonly used, and for the brain images
studied in this thesis, the popular DaTSCANTM radiotracer from GE Healthcare [14]
has been used.
2.3.1
Myocardial perfusion SPECT
Myocardial perfusion SPECT examinations are widely used as a routine examination for
patients with chest pain. Some time after the technologist has injected the radiotracer
into the patient, he/she will be placed in a camera station, often referred to as γ-camera,
with a detector suitable for SPECT γ-energies [6]. After the camera has finished with
the acquisition the image is reconstructed using some reconstruction technique, e.g. as
proposed by Perkins [5]; filtered back-projection or iterative reconstruction. This will
Figure 2.3: A 3-D volume image displayed as iso-surfaces (left) and two slices (center and
right), with the left ventricle of the heart marked with an arrow.
yield the images, which are tomographic 3-D volume data, i.e. each voxel in space
has three space-coordinates (x, y, z) as well as an intensity level. In practice, the 3-D
volume consists of a number of slices. This makes it convenient to display the volume
in the form of a stack of 2-D images, which is often used clinically. Strauss and Miller
10
Chapter 2. Scintigraphy
[15] describes the procedure in more detail. An example of a 3-D volume acquired using
SPECT can be found in Figure 2.3.
The next task for the technologist is to rotate the acquired images of the heart into
predefined angles. This is done by choosing two slices from the volume, which the
technologist finds good for estimating the angle of the heart [15]. An example is given
in Figure 2.4.
Figure 2.4: The manual rotation of the heart performed by the technologist. The heart is here
illustrated before (first row) and after (second row) rotation, for slices through each
axis respectively.
It is obvious that the centre line of the left ventricle, which is commonly seen as the line
that should align with the axes after rotation [15], cannot be exactly defined for such an
asymmetrical object as the left ventricle. Even more so when the images acquired are
of poor quality, or if the uptake of radiotracer in the left ventricle is poor, due to, e.g.,
myocardial infarction. This poses a problem for myocardial perfusion SPECT images,
and is discussed in this thesis.
2.3.2
DaTSCAN Quantification
DaTSCAN quantification is another SPECT-application that is very commonly used
to diagnose Parkinson’s disease. If a patient suffers from Perkinson’s disease, the basal
ganglia are often degenerated, i.e. the number of dopamine receptors are reduced. Moreover, the degeneration is generally first observed from the same place of the ganglia.
However, the quantification methods that are used introduces great inter- and intraoperator variability, which is discussed by Tatsch et al. [16]. Often, a two-dimensional
quantification method with predefined or adjustable regions of interest (ROI) is used,
2.4 Summary
11
which requires operator interaction throughout the whole quantification process. Visual
interpretation of the images are also common, which introduces even more sources of
error, e.g. the use of different colour maps; noted in [16] as:
Use of non-continuous color tables may overestimate findings due to abrupt
color changes.
Tatsch et al. [16]
As with myocardial perfusion SPECT images (section 2.3.1), the variability is great
between different images. An example of how the basal ganglia are manually quantified
is given in Figure 2.5, where a typical ROI has been drawn around each of the basal
ganglia, as well as for the background signal of the image. The quantification of the
Figure 2.5: Illustrating a typical ROI of the basal ganglia and background area (4) of a manually
quantified DaTSCAN-image.
images is commonly based on measuring the signal inside the ROI (or different parts
of it) of the basal ganglia, and comparing it to some kind of background signal. The
background signal has traditionally, with 2-D quantification, been chosen as the visual
cortex (see nr. 4 in Figure 2.5), but there is no absolute standard [16]. The quantification
procedure can take a significant amount of time for an inexperienced operator and there
is little standardisation in the way that the different ROI:s are selected and adjusted.
2.4
Summary
After this chapter, the reader should be sufficiently informed on how SPECT-imaging
works, both theoretically, physically and on a more practical level, which has been exemplified with the two applications that are involved in this thesis; myocardial perfusion
12
Chapter 2. Scintigraphy
SPECT and DaTSCAN quantification. Problems that both applications have in common
regarding inter- and intraoperator variability as well as dimensional reduction approximations from 3-D to 2-D, have also been introduced.
3
Image Segmentation
Image segmentation is in principle a method for bringing out certain, more interesting,
parts of a signal, and has been used in medical applications for many years. The signal
may for example consist of a two dimensional image, or as in the case of this thesis, a
three dimensional volume. Both cases are common situations in medical informatics. In
this chapter, a brief overview of common image segmentation techniques will be covered, and since the principles are the same for signals of different dimension, examples
will mainly concern two dimensional images, since they are easier to visualise. Image
segmentation in more detail can be found in [17].
3.1
Segmentation methods
There are many different image segmentation methods. From the very simple and intuitive, to techniques based on advanced mathematical concepts. An important issue to
consider is therefore what type of segmentation method to apply, given a certain situation. This often depends on the image modality used to acquire the image, as well as
the complexity of the part of the image that is to be segmented.
3.1.1
Thresholding
In a very simple and clear image, simple and intuitive segmentation methods can often
be sufficient. In such images, with a good signal to noise ratio, so called thresholding
is often a good choice. Segmentation by thresholding works simply by keeping the part
(pixels/voxels) of the image that lies in a certain intensity interval. This is demonstrated
in Figure 3.1 b), where the pixels above a certain intensity level in the original image has
been set to 1, and the rest of the image to 0, and can also be described mathematically
14
Chapter 3. Image Segmentation
with
Isegmented
!
1, a < I < b
=
,
0,
o.w.
(3.1)
where I is the original image and a and b are the thresholds. However, if the image
signal is bad and mixed with noise, thresholding will often yield a bad result. This is
shown in Figure 3.1 c, where noise has been added to the original image.
Figure 3.1: a) (left): An X-ray image of the hand of Wilhelm Röntgen’s wife. b) (centre): The
image after thresholding. c) (right): The image after thresholding where noise has
been added to the original image.
Furthermore, another problem with thresholding is choosing a good threshold level that
is not specific to one image. This can be done by for example examining the histogram
of the image, or by other more or less sophisticated guesses. At last, segmentation by
thresholding is often not a good choice where the interesting parts of an image has the
same intensity levels as the rest of the image, and is only separated by structure and
shape. In such situations, some kind of image registration is often required for good
results.
3.1.2
Region growing
A segmentation method that resembles thresholding is region growing [17]. However,
in contrast to thresholding, which operates on each point in an image independently
of neighbouring points, region growing takes into account the surrounding connected
pixels. Region growing requires a starting point in the image. This point should be a
known point within the area of interest, and consequently the method requires manual
3.2 Image registration
15
input or some kind of pre-processing. When the point is chosen, the method works
iteratively. A neighbouring point is chosen. If the intensity of that point is within a
certain intensity level from the starting point, the point is considered part of the final
segmentation, and the process starts over, now starting at this point. There are several
more or less advanced techniques for implementing region growing, however, it often
gets very slow with higher image dimensions. More over, region growing can in its
basic form handle images with much noise very poorly. There are ways of reducing
noise, but nevertheless, region growing will not take into account the structure of the
interesting parts of an image and is highly dependent on image intensity.
3.1.3
Active shapes
The thought behind active shapes takes region growing a step further by introducing
prior knowledge of the the object that is to be segmented. The goal in active shapes is
to find a line in 2-D or surface in 3-D, that encloses the object of interest after segmentation. Active shapes works by first defining a model. The model is built from a data set
of other images of the same kind of object that is going to be segmented. In each one
of the images in the data set, the same landmarks (often anatomical) have been marked.
By observing how the position of the landmarks differ throughout the data set, the variance of each landmark can be calculated [17]. In turn, this is used to define how the
model is allowed to move while it is segmented. The actual deformation of the model
can be generated in various ways. One common way is to use the energy in the image
to calculate edges and borders, to where the model should deform. Compared to region
growing techniques, active shapes are much more robust and insensitive to noise. This
is due to the prior knowledge introduced about the object, which prevents the model
from deforming in an unnatural way. The constraint of active shapes is off course the
data set. If the data set is small, the model will not be able to deform sufficiently when
introduced to cases that are not represented in the data set. However, with a large data
set, active shapes is often a good method in more complicated segmentation situations.
3.2
Image registration
In many situations, particularly in medical imaging, simple segmentation methods such
as thresholding is not sufficient to yield good results. The segmentation process can
then often be helped by adding image registration to the segmentation process. Image
registration is in principle a method for deforming one image to align to another image.
In medical informatics this is often used to map one image, with one type of information, to another image, containing other types of information. One example is to map
an image of a brain acquired with computed tomography (CT) or magnetic resonance
16
Chapter 3. Image Segmentation
imaging (MRI) to another image of the same brain, acquired with SPECT. Since the
brain may not be in the same position at both times of examination, image registration
is used to make the same areas of the two images correspond to the same areas of the
brain. In this example, information about the anatomy of the brain, in the CT or MRI
images, will then be complemented with physiological information from the SPECT
image.
Mathematically, image registration can be described by finding a deformation field, or a
displacement field, v(x), that after acting on an image, I2 (x) will deform the image in
such a way that it will map to the target image1 , I1 (x). The mapping in n dimensions
can be described by
v(x) : Rn "→ Rn .
(3.2)
Moreover, to be able to describe the quality of the registration process, the error
$2 = $I2 (x + v(x)) − I1 (x)$2
(3.3)
is introduced. If this error is zero, the registration process has been completely successful. This is not a realistic goal in practice, since the two images do not contain exactly
the same information, in which case image registration would not be necessary. Consequently, v(x) describes how each point in I2 should be moved to minimise $. There are
many attempts of solving this problem, and many involve minimising some variation of
a least square problem. For example, if the following assumptions are made:
1. v(x) can locally be described solely by a spatial displacement.
I(x, t) = I(x + ∆x, t + 1),
(3.4)
where t denotes the time in the discrete registration process.
2. The image can in each point be approximated with a first order Taylor expansion.
I(x + v(x), t + 1) = I(x, t + 1) + ∇I T v, ∇I = [∂I/∂x, ∂I/∂y]T . (3.5)
If equations (3.4) and (3.5) are combined, the equation for the so called optical flow,
denoted by v, can be found.
∇I T v − ∆t = 0, ∆t = I(x, t) − I(x, t + 1).
(3.6)
Optical flow is one of the oldest concepts in image registration and computer vision and
a lot of research has been done around it. Consequently, there are many methods for
1
Target image is usually the name of the image that is left untouched.
3.3 Summary
17
solving the differential equation (3.6). As a matter of fact, there are many solutions for
v in each point in the image; solutions that are not practically usable, since image points
can then have completely independent solutions of each other. This is described in more
detail in [17], chapter 6:6. However, one robust solution that consider the optical flow
as a continuous function is a least square problem formulation:
"
$2 =
([∇I(xi )]T v(xi ) − ∆t (xi ))
(3.7)
i
By assuming different properties for v in equation (3.7), different types of solutions
for the displacement field can be found, with different amount of rigidity [18]. For
example, in some situations a mere translation or rotation of v is a good enough registration model, while in other more complex applications, a non-rigid model must be
used, which allows for any kind of deformation of I2 . The parameterized solutions for
different levels of rigidity can be found in [17].
In this section, the optical flow was found through differences in the intensity of images. While straightforward, this approach is obviously dependent on the assumption in
(3.4). There are, however, other more robust procedures for estimating the optical flow
in a registration process between two images. Differences in local phase is one such
approach, and will be described in more detail in chapter 4.
3.3
Summary
In this chapter, an overview of more and less advanced segmentation methods have
been presented. From thresholding, which is easy to understand and implement, to
registration based methods; derived within a rich mathematical framework and still issue
to much research and algorithm optimisation.
4
The Morphon Method
The Morphon method is a newly developed method for image segmentation and registration, first introduced by Knutsson and Andersson [19]. Since then, the method has been
under refinement and have been applied in several medical applications [20, 21, 22, 23].
This chapter is mainly an overview of the Morphon method, based on [19] and [20]. The
method can be brought to a much more advanced level, nevertheless, this simplified (and
hopefully faster) version is sufficient for the subject of this thesis.
The Morphon method is essentially a registration driven segmentation technique. It
works by first estimating a displacement field through differences in local phase between the segmentation target image and a model image, which resembles the target
image in e.g. intensity variations. The displacement field is further processed to ensure
robustness of the method. The model of the object that is to be segmented is deformed
according to the displacement field, and the whole process is iterated until the process
is satisfactory and the model has mapped on to the target image.
In the beginning of the work of this thesis, a method for solving the stated problem in a
satisfactory way had not yet been proposed. After investigating several image segmentation and registration methods, the conclusion was finally that a phase based approach
such as the Morphon method had several advantages in comparison, given the problematics of this project. The primary reasons for choosing the Morphon method can be
summarised with the following arguments.
1. Phase: As mentioned in section 3.2, a phase based approach on image registration
can be advantageous compared to classical techniques with intensity based optical
flow estimation. Even more so in the images that is considered in this thesis.
Section 2.3.1 shows that SPECT images of the heart can vary considerably in
intensity. Not only among different images, but also between the heart and other
organs. In such situations, intensity based techniques are inferior to a method such
as the Morphon, which, as presented in 4.1.1, is insensitive to intensity variations.
20
Chapter 4. The Morphon Method
2. Noise: If the images are of low quality1 , which is not an unusual case with SPECT
images (see section 2.2.1), assumption 2 (equation (3.5) might very well not hold.
However, the Morphon method uses robust methods such as displacement field
accumulation and regularisation to prevent the displacement field from diverging.
3. Model: The Morphon framework includes an easy and dynamic way for including prior knowledge about the object that is to be segmented. This makes it easy
to develop further for other applications, as will be presented in chapter 7, Segmentation and quantification of DaTSCAN images.
4.1
Displacement field estimation
A displacement field is essentially a vector field. In this approach, the field is dense,
which means that in each point in space, there exists a vector with a certain direction and
magnitude. Since the image space is discretised with pixels or voxels, the vector field
will have the same size as the image that is to be deformed by it. There are, however,
other applications, where the deformation field is not dense, and a vector describes the
movement of a block of discrete points. To estimate a displacement field in the Morphon
method, analysis of the local phase of the images is made.
4.1.1
Quadrature phase
Phase can principally be described as the structure of the image. Mathematically, the
phase, as it is used in this thesis, is the response from a certain set of filters that respond
to edges and borders in the image. These filters are known as quadrature filters and are
defined as follows.
Quadrature filter 4.1.1. A filter, f (x), is a quadrature filter if its Fourier transform,
F (ω), is zero on one side of a hyper plane through the origin in the Fourier domain.
That is, there exists a vector, n̂, such that
!
0,
n̂T ω ≤ 0
F (ω) =
.
(4.1)
F (ω),
o.w.
In this thesis, one special type of quadrature filters have been used, namely lognormal2
filters, which are described, for example in [24], in the Fourier domain as
4
F (ω) = e− B2 ln2 ln
1
2( ω )
ωc
(4.2)
Quality can be hard to define. Here, quality mainly refers to signal-to-noise ratio and the amount of
artifacts.
2
Lognormal filters are often referred to as lognorm filters.
4.1 Displacement field estimation
21
for positive values of ω. Here, B is the relative bandwidth of the filter in octaves and ω c
is the centre frequency of F (ω). In Figure 4.1, a lognorm filter is shown in the spatial
and frequency domain. For displaying reasons it is shown for only 1 dimension, but the
principle is the same for arbitrary dimensions. Due to the quadrature filter definition in
the frequency domain, quadrature filters are always complex in the spatial domain. This
can be understood since
F (ω) '= F (−ω),
(4.3)
F (ω) = F (−ω).
(4.4)
while a necessary requirement for f (x) to be real is that
!&#"
#
'()*
+,)-./)01
$%+
!&#
$%*
$%)
!&!"
$%(
$%'
!
$%&
$%!
!!&!"
$%"
$%#
!!&#
!
"
#!
#"
$!
$"
%!
$
!!
!"
!#
$
#
"
!
Figure 4.1: Lognormal filter with real and imaginary parts in the spatial domain (left) and the
Fourier domain (right)
In computational practice, filters are discrete, and it is often desirable to adjust the finite length of the quadrature filter. A smaller filter will imply less computations while
making calculations with the filter. Moreover, the size of the filter will have impact on
the size of the items that the filter is able to detect. The size of the filter can, and will,
therefore depend on the application at hand. A good way to design a filter kernel, that
introduces much control over the filter properties, is suggested by Knutsson et al. [25]
and is based on a least square formulation of the filter design problem. The main idea is
to introduce a number of ideal filters in each domain where they can be easily described.
Here the quadrature filter has been defined in the Fourier domain (4.1.1), which is suitable for this technique. However, it is also desirable to achieve a filter which is small in
the spatial domain, i.e. ideally resembling δ(x), an impulse3 . In short, the problem can
be formulated as
"
$2 =
$Wj (fj$ − Bj f )$2 ,
(4.5)
j
3
Mathematically known as the Dirac delta function.
22
Chapter 4. The Morphon Method
where f is the desired filter in the spatial domain, Bj is the base matrix that when
multiplied by f will give f described in domain i, and fj$ is the ideal filter for domain
i. Wj is a weight matrix which can be used to make certain parts of the filter more
important, i.e. more sensitive to errors. For this case, the only domain other than the
spatial is the Fourier domain. Thus, Bj will here either be the Fourier base matrix or
the unity matrix. In each case respectively, Bj f will give F (ω) and f .
As mentioned above, the phase, φ, of a signal, s(x), is related to the response from
these filters. More specifically, phase can be defined as the angle of the filter response
between the signal and the filter, derived from
q(x) = (s ∗ f )(x),
(4.6)
where q is the filter response and ∗ denotes the convolution operator. Assuming s(x) is
real valued4 , q is complex and can be rewritten on polar form as
q(x) = A(x)eiφ(x) .
(4.7)
Here A(x) is the magnitude of the filter response, and the phase can now be found
through
φ(x) = arg(q(x)).
(4.8)
Finally, what is left is to generate a displacement field from the phase of two images.
Assuming the two images I1 and I2 , we get two different responses from the same set
of filters. Since lognorm filters, from definition 4.1.1, are dependant on the direction of
n̂, we actually get one response from each filter in the filter set. A filter set can consist
of as many filters wanted, however, there is a minimum of filters needed given a certain
dimension of the images to be able to cover the whole Fourier domain. This is due
to the fact that the filters have a direction and a limited spread. For example, in two
dimensions, at least three filters are needed and in three dimensions, six filters is the
minimum to span over the whole domain. This is discussed in more detail for example
in [26]. The six directions for 3-D given in [26], for a second order filter, and which are
used in this thesis, are
n̂1
n̂2
n̂3
n̂4
n̂5
n̂6
4
= c[b, −a, 0]T
= c[b, a, 0]T
= c[0, b, −a]T
,
= c[0, b, a]T
= c[−a, 0, b]T
= c[a, 0, b]T
The signal in this context is a two or three dimensional image, which in most circumstances is real
valued.
4.1 Displacement field estimation
a = 2,
b=1+
√
5,
c=
23
#
√
10 + 2 5,
where a, b and c is only for normalisation. From above, it is therefore necessary to apply
convolution between the signal and all the n number of filters in the filter set. This leads
to n filter responses for each image, each one representing the phase and magnitude in
the direction of filter j (see Figure 4.2 for an example), i.e.
(4.9)
qj = (s ∗ fj )(x).
From this we have one response from I1 and one from I2 for each filter in the filter set:
Figure 4.2: The original X-ray hand (left) along with the phase (centre) and magnitude (right) of
it after being filtered with a quadrature filter. Here it is seen that the filter captures
edges corresponding to the filter direction, giving more certainty (magnitude) to
structures with a frequency within the passband of the filter.
qj (I1 ) = (I1 ∗ fj )(x),
qj (I2 ) = (I2 ∗ fj )(x).
(4.10)
Further more, the phase difference at position x between the images can be found
through the product between qi, I1 and the conjugate of qi, I2 , or
qj (I1 )qj∗ (I2 ) = Aj (I1 (x))Aj (I2 (x))ei(φj (I1 )−φj (I2 )) .
(4.11)
From this, the phase difference is, analogue to equation (4.8), equal to
∆φi = arg(qj (I1 )qj∗ (I2 )) = φj (I1 ) − φj (I2 ).
(4.12)
dj (x) ∝ ∆φj .
(4.13)
Since this is the difference between the images, it is also locally proportional to the
displacement field estimate at that point:
Moreover, what we now have is a set of n displacement field estimates, each one representing the estimate in direction i.
24
Chapter 4. The Morphon Method
4.1.2
Least square solution
To bring the information from each one of the estimates together into one displacement
field estimate, a least square problem is a suitable way of postulating this problem. Since
least square problems have the great advantage of being able to weight different points
with different importance, as is common in filter design, for example described in [25],
this can also be used for the derivation of the total displacement field. In this case, the
weight function is called the certainty of the filter responses and is defined as
cj = Aj (I1 (x))Aj (I2 (x)).
(4.14)
The certainty will then be high where the two filter responses match each other in structure, which is sensible, and this makes for all the parts in the least square problem to
calculate the whole displacement field, d = (d1 , . . . , dN ), for N dimensions.
"
min
[cj (n̂Tj d − dj )]2 ,
(4.15)
d
j
for each direction, n̂j .
Further more, since the Morphon method is an iterative registration scheme, the displacement field estimate is only valid for the current iteration, and must be updated
with each iteration, thus generating a new field, dk , for iteration k, which brings us to a
central part of the Morphon method.
4.2
Displacement field accumulation
As presented above, each iteration generates a new displacement field, solved from
equation (4.15). However, the field for iteration k might not be a good estimate compared to estimates prior to that iteration. To prevent bad estimates to disrupt the registration process, a field accumulation is therefore used to make good estimates gain greater
influence on the final displacement field.
The accumulation also have another effect on the registration process as it prevents
interpolation smoothing to be spread throughout the iterations. Since the model (I2 here)
has to be deformed in each iteration and a new displacement found from the deformed
model, smoothing would occur if dk would be applied directly on the model for each
iteration. Instead, the newly found field is added to the field found and accumulated in
iterations before, removing interpolation artefacts since the original model is now used
for each iteration. The accumulated displacement field is updated through
d$a =
ca da + ck (da + dk )
,
ca + ck
(4.16)
4.3 Displacement field regularisation
25
where da denotes the accumulated field for the current iteration and d$a is the next,
updated accumulated field. ca and ck both describes certainty measures, associated with
the ones mentioned in equation (4.14). ck is directly coupled with the displacement
estimate for each iteration, dk , and is defined as
ck =
n
"
cj ,
(4.17)
j
i.e. the sum of all certainty measures for each quadrature filter. ca , on the other hand, is
another accumulated entity and is a certainty measure weighted with its own certainty,
expressed as
c$a =
c2a + c2k
,
ca + ck
(4.18)
where c$a , analogue with above, is the updated certainty measure. To summarise; the
accumulation of the displacement field implies that good displacement field estimates
will have a higher effect on the accumulated (final) displacement field than poor ones.
This creates a robustness of the algorithm as well as increases its reliability.
4.3
Displacement field regularisation
As mentioned in section 4.1.1 about quadrature phase of images, the phase is only a
local description of the image. If the accumulated field estimates from equation (4.16)
were to be directly applied to the model image, it would most likely tear the image apart,
diverging into something far from a successful registration operation. However, since
the field represents local changes in the image, it is sensible to think that an averaging
of sorts would represent a change on a more global scale. This averaging can be made
more or less complicated. Often, it is done by means of a basic Gaussian averaging:
dr = (d ∗ g)(x),
(4.19)
where g is a Gaussian kernel and dr is the regularised field, but can be made more advanced in many ways. In this thesis, a special form of normalized convolution, as first
introduced by Knutsson and Westin [27], called normalized averaging, is used. Normalized averaging introduces the great advantage of allowing to include the certainty
measure in the regularisation process as well, adding even more robustness and reliability to the registration. Normalized averaging is defined as
dr =
((ca d) ∗ g)(x)
,
(ca ∗ g)(x)
(4.20)
where the division and multiplication are taken element wise. The effect of a small and
a large standard deviation of a Gaussian kernel is presented in Figure 4.3.
26
Chapter 4. The Morphon Method
Figure 4.3: A displacement field during a Morphon registration process with a small (left) and
large (right) regularisation of the field.
4.4
The model
The model in the Morphon method is the image that is deformed by the displacement
field, and hence contains the information about the registered object after the registration
has finished. However, to perform a successful registration, an appropriate model is
needed. The type of model often depends on the context or problem. Nevertheless, a
good model should contain approximately the same information regarding shape and
intensity variations as the target object. For example, in this thesis segmentation is
performed on SPECT images of the heart. A suitable model could therefore reside in a
manually segmented heart from another SPECT image.
4.4.1
Deformation
The model is deformed, using a suitable interpolation method, by the accumulated displacement field at the end of each iteration and the deformed model is used to generate
the new accumulated deformation field, which in turn deforms the original model. This
is iterated until some kind of accuracy, δ, or a maximum number of iterations is reached.
The accuracy could for example be the change of the accumulated displacement field
between two, in the iteration process, adjacent fields, i.e.
$
$
$ dr, k − dr, k−1 $
$,
$
δ=$
$
dr, k
where the relative difference has been chosen as the accuracy.
(4.21)
4.5 Summary
4.5
27
Summary
Here, a simpler version of the Morphon method has been described in some depth. The
method takes advantage in its local phase based registration scheme, which is iterated
through different resolutions. A displacement field is found for each iteration and is
accumulated and regularised to make the registration more robust, as well as adding the
option to make the model more or less rigid and deformable.
5
Rotation of Myocardial Perfusion Images
As presented in section 2.3.1, there are some problems with the image analysis in scintigraphic heart examinations as they are carried out at the time of writing this thesis. The
main problems are:
• Interoperator and intraoperator inconsistency, that ends in difficulties in comparing images acquired from different technologists, or even from from the same
technologist.
• Time consuming activities for the technologist after images have been acquired.
• Difficulties in manual alignment for images with poor uptake.
The approach in this thesis for designing an automatic method for doing all this is based
on the Morphon from chapter 4. The automatic process involves some pre-processing,
to help the later registration scheme, followed by a 2-D registration and segmentation
to decrease the amount of data. After this, the 3-D image should have been decreased
to a small volume, containing the left ventricle of the heart. A 3-D Morphon is then
applied to the image, from which a displacement field is generated. This displacement
field, with enough regularisation, is a rough description of how the model have been
rigidly transformed to match the target image. By estimating the angle with the help of
two lines, the rotation of the left ventricle can be known, and the target image rotated
correctly. The sequence is in this chapter described in detail.
5.1
Pre-processing of images
The first problem in this application that must be dealt with is that the amount of data
has to be decreased, in order to increase performance of the analysis. This is primary
done in a quite primitive way by cropping the 3-D image along all of its dimensions.
The cropping assumes that the technologist has placed the patient correctly in the γ-
30
Chapter 5. Rotation of Myocardial Perfusion Images
camera and that the heart is not positioned in the right side of the body. The cropping is
illustrated in Figure 5.1.
Figure 5.1: The pre-cropping that will help the registration process. To the left, the original
image, and to the right the cropped image. The left ventricle is marked with a black
rectangle in both images.
5.2
2-D Morphon segmentation
After the image has been cropped, the first Morphon based segmentation is performed.
As this is a 2-D segmentation, the 3-D volume must first be reduced. This is done by
transforming the volume into a max intensity projection (MIP) image, i.e. by generating
a 2-D image where each pixel is the maximum of all the voxels that after a projection
would result in that pixel. This is performed along the y-axis, which is the axis in the
same direction as the nose of the patient, or that is pointing out from the patient’s chest.
This is illustrated in Figure 5.2 a).
Figure 5.2: a) Maximum intensity projection along the y-axis (green). b) Maximum intensity
projection along the x-axis (red). The resulting projections are symbolised by the
purple plane.
5.2 2-D Morphon segmentation
5.2.1
31
Locating the heart
Since other organs can have very similar shape and intensity variation compared to the
left ventricle of the heart, it is important to help the registration as much as possible. This
is done by finding a point of the heart where the Morphon can be initiated. By assuming
that there are only uptake in form of noise in the parts above (in the negative z-direction,
which is symbolised by the blue vector in Figure 5.2) the heart, a thresholding can be
performed to remove any noise, after which the heart should contain the lowest point
in the z-direction. This assumption has been made after investigating a great number of
images (over 600). As presented in section 3.1.1, the threshold level can be found in
different ways. Here, a dynamic way is needed to keep the thresholding from removing
the heart completely. This is done by calculating the histogram of the image. This will
result in a curve with some maxima and minima, where the maxima are a representation
of intensity levels that are more common in the image. As this do not apply to noise to
the same extent, a suitable threshold level that contains the heart can be found. However,
this may not be enough if the noise level is very high. In order to separate noise from the
heart, the size of the binary clusters that are found is calculated. If the size is too small,
it is likely that it does not represent the heart. Additionally, a distance test is performed.
This test calculates the distance from the centre of mass (COM) of the image and the
point that has been found, where the COM is defined as
%
I(xi )xi
%i
, ∀i,
(5.1)
i I(xi )
for a pixel at position xi with intensity level I(xi ). As the intensity levels in the MIP
image are much higher in the lower parts of the body, it is there that the COM will be
found. The distance from the COM to the heart is therefore relatively short, and points
that are found too far away from the COM can be regarded as noise.
5.2.2
Segmentation
When a point of the heart has been found, the 2-D Morphon can be initiated and performed. The model used is a MIP image from another heart, which represents the
intensity variations in a suitable way. Moreover, as the model may still, despite the
tests from above, be initiated quite far from the heart, the registration is first performed
on a lower scale of the image (naturally, with a down sampled model as well). Still,
the same size of the quadrature filters is used, which implies that the model will "see"
longer than on full scale. To perform the registration on different scales is a good way
of preventing the registration to converge locally on details, before it has reached the
heart. When the model has converged, it should be known where the heart is situated
in the 2-D MIP-image. It can then be cut out along the third dimensions, resulting in a
32
Chapter 5. Rotation of Myocardial Perfusion Images
Figure 5.3: The result after two 2-D Morphon segmentations.
cylinder like volume which is oriented along the axis of the maximum intensity projection (y in this case). The resulting volume is then made a MIP along the x-axis, which
is illustrated in Figure 5.2 b), and another 2-D Morphon is initiated. However, as much
of the interfering organs around the heart has been cut away already, it is sufficient to
initiate the model at the COM of the MIP image, which will result in a good registration.
Consequently, when the registration has converged, even more can be cut away in the
same manner as above. The result is a relatively small box, containing the heart and
possibly other organs that lies very close to the heart. An example of the result can be
seen in Figure 5.3.
5.3
3-D Morphon segmentation
From the segmentation covered in the last section, the heart is now separated from the
majority of interfering organs. The last segmentation process is now made in three dimensions to be able to gather information about the orientation of the heart. As the
co-ordinates of a point that is known to have its position somewhere in the heart, this
point is a sensible starting point for the model in the 3-D Morphon registration. However, as the starting point will probably not correspond exactly to the same point in the
model, the 3-D registration is here as well performed in multiple resolutions. The reg-
5.4 Angling of the heart
33
ularisation of the displacement field is relatively large on the lower scales to keep the
model from deforming incorrectly in the absence of the details of higher resolutions. At
full resolution, on the other hand, the standard deviation of the regularisation filter is
relatively smaller. This means that the model can deform into more detail, which is necessary due to the great variation between images from scintigraphic heart examinations.
The model in the 3-D segmentation is as in the 2-D case a manually segmented 3D heart. The model will deform significantly between different types of hearts. An
example of this is illustrated in Figure 5.4.
Figure 5.4: The original model (top-left) and three examples of it after being deformed in the
registration process.
5.4
Angling of the heart
After the 3-D Morphon registration has converged, the model should have aligned itself
to the left ventricle of the heart. The model can then be used to segment the left ventricle,
which is one of the aims of this thesis. Moreover, the rotation of the heart requires some
thought on how to represent the rotation of the model.
34
5.4.1
Chapter 5. Rotation of Myocardial Perfusion Images
Angle estimation
To represent an angle between two objects, a minimum of two lines is needed. The first
line has been manually defined from the original model. The line does not need to be
represented by voxel coordinates in the image, but can be mathematically defined as
desired. Here, the line is situated in the middle of the left ventricle, in the cavity called
the lumen, and has a length that does not exceed the length of the heart in the same
direction. Mathematically, the line can be expressed as
 
 
x0
vx



x0 + tv = y0 + t vy  ,
z0
vz
t = 0 : l,
(5.2)
where x is the starting coordinate of the line, v is the unit direction vector and t is
a parameter which determines the length, l, of the line. The deformation field that has
been found through the 3-D registration can now be used to deform the line accordingly.
However, as a small regularisation has been used on the full scale registration, the line
is likely to be deformed into a discrete curve. This is not desirable and hence the field is
further regularised. With a large regularisation filter, the global displacement will more
and more correspond to a rigid transformation field. However, the deformed line will
nonetheless become slightly bent. This is solved by fitting a line to the deformed points
of the line, resulting in a linear regression problem:
min
α, β
"
i
[zi − (αxi + β)]2 , x = (x, y),
(5.3)
with parameters α and β, or
min $Ax̃ − b$,
x̃
(5.4)
where A is a known basis matrix, x̃ is an unknown parameter vector (here, containing α
and β) and b is a known vector containing the function values (here, the z-axis). From
linear algebra we know that the solution for a least square problem is:
x̂ = (AT A)−1 AT b.
(5.5)
This will yield a straight line that has been approximately rigidly transformed from the
original line, and the angle, θ, for each axis respectively can be calculated from the
definition of the scalar product between two vectors, u and v, given as
uT v = |u||v|cosθ.
(5.6)
5.5 Summary
5.4.2
35
Rotation
As the angles of rotation around each axis have now been estimated, the remaining
task is to rotate the image heart with the corresponding angles. This can be done in a
multitude of ways, e.g. applying a rigid rotation matrix and interpolating the image to
the new position. The segmented and rotated heart can then be displayed in any way
desired, however, the common clinical way is in slices through each axis. An example
of a segmented heart, before and after rotation, can be found in Figure 5.5, where a
surface of the volume object is displayed, and in Figure 5.6, where one slice through
each axis is shown.
Figure 5.5: Iso-surface plot of an automatically segmented heart (left) and the same heart after
rotation (right).
Figure 5.6: Three slices through the rotated heart as they are commonly displayed in clinical
use.
5.5
Summary
The segmentation and alignment of myocardial SPECT-images is performed with the
aid of two 2-D and one 3-D registrations, based on the Morphon method from chapter 4.
The angles are consequently found through deforming a line along with the deformation
of the model in the method.
6
Dopamine Transporter Quantification
From section 2.3.2, it is clear that there are currently some problems involved in quantification of 3-D scintigraphic brain images which aims at diagnosing e.g. Parkinson’s
disease. This relies both in the variability between operators and the fact that much
quantification is made in two dimensions, while the acquired images are in fact in 3-D.
Thus, The 3-D segmentation method used in chapter 5 has been somewhat modified and
complemented, and then applied on the quantification problem at hand.
The algorithm for automatic 3-D quantification works by first dividing the SPECT-brain
image into two parts and quantifying each part individually. This is followed by an initiation of the 3-D Morphon segmentation process. The segmented basal ganglia are then
further analysed and quantified with methods comparable to the manual 2-D quantification commonly used clinically. To be able to do this, a method called weighted principal
component analysis (wPCA) is introduced.
6.1
3-D Morphon segmentation
Compared to the segmentation process of the heart in chapter 5, specifically section
5.3, very little pre-processing is necessary in the case of DaTSCAN SPECT images.
In myocardial perfusion SPECT images, the image signal from the left ventricle of the
heart constitutes a small part of the total image signal. This is in contrast to DaTSCAN
SPECT images of the brain, where the basal ganglia (the region of interest) stand out in
a much clearer way. This is illustrated in Figure 6.1. Consequently, the initiation of the
3-D segmentation can be greatly simplified compared to the pre-processing in chapter
5; e.g. the two 2-D segmentations from section 5.2.2.
38
Chapter 6. Dopamine Transporter Quantification
Figure 6.1: Two iso-plots of a myocardial perfusion SPECT image (left) and a DaTSCAN
SPECT image (right). The left ventricle is marked with an arrow and the basal
ganglia are the red bean-shaped objects.
6.1.1
Locating the basal ganglia
As mentioned above, the brain image is first divided into two halves, each containing at
least one whole basal ganglia. The division is simply done by examining the intensity
profile through the axis going through both of the basal ganglia and dividing the volume
at the minimum between the two maxima, as illustrated in Figure 6.2. This makes it pos4
x 10
4.5
4
Intensiity
3.5
3
2.5
2
1.5
1
5
10
15
20
25
Position
30
35
40
Figure 6.2: The intensity profile of the brain (left), with marked local maxima and local minimum, taken along the x-axis, shown to the right.
sible to divide the brain in approximately the two brain halves, each image containing
one basal ganglia.
Further more, since the basal ganglia in almost all cases have a significantly higher signal than the rest of the brain, locating the basal ganglia in each side is generally not a
very difficult task. Choosing the point of maximum intensity as the starting point for
6.1 3-D Morphon segmentation
39
further segmentation is often good enough, however, to increase the robustness of the
algorithm, the brain is first multiplied with a weight function, which makes intensity
levels closer to the centre of the brain (where the basal ganglia are located) more important. After this, the point of maximum intensity is selected as the initiation point for the
3-D segmentation of each basal ganglia.
6.1.2
Segmentation
With a point inside the basal ganglia, the model for the 3-D Morphon segmentation can
be initiated. The model here is simply a healthy basal ganglia, which is mirrored when
used in the other side of the brain. As explained in section 2.3.2, the basal ganglia are
degenerated from the same place if a patient suffers from Parkinson’s disease. This fact
can be used as an advantage in the segmentation process. If it is assumed that the relatively unaffected part of the basal ganglia is still high in image signal, the corresponding
part of the model can be initiated at the highest intensity point in the image. This is illustrated in 2-D in Figure 6.3, while it is in practice performed in three dimensions.
a
b
Degenerated basal ganglia
Model
Figure 6.3: a) The model (white) and a degenerated basal ganglia (gray) with the fixed initiation
point of the model (square) and the maximum intensity point of the image (circle).
b) The model and image after the initiation point of the model has been initiated at
the maximum intensity point in the image.
With the model initiated at a spot relatively close to the object that is to be segmented,
the 3-D Morphon segmentation process can be performed. As with the case of the
segmentation of chapter 5, 5.3, the registration process is performed sequentially in
multiple resolutions to help the model to fit on a more global scale at first. One question
that one might ask is that if the basal ganglia have degenerated, how can the model fit
to something that is not there anymore? As a matter of fact, degenerated basal ganglia
40
Chapter 6. Dopamine Transporter Quantification
tend to leave a trace, where there used to be dopamine transmitters before degeneration
(see Figure 6.4). Since the Morphon is phase based, this trace is as good a structure to
fit to as a healthy basal ganglia. Moreover, the model transformation is made relatively
rigid to keep the model from deforming too freely in cases where little or none signal is
left in some parts of the basal ganglia.
Figure 6.4: The faint signal (red) that is left where the basal ganglia has degenerated still works
as a structure to register on.
After the registration process has completed, the model is thresholded to a small extent
in order to remove possible noise or interpolation artifacts, introduced during the registration. The model has now very likely been deformed into a shape that fits well into the
area of the brain where the basal ganglia are situated, even if the dopamine transporters
have been degenerated. The result of two segmentation processes is presented in Figure 6.5, where the slice of maximum signal intensity of the images has been selected for
displaying reasons.
6.2
Quantification
After the area of interest, containing whole or parts of basal ganglia, has been successfully segmented the process of quantifying the segmented data remains. This has traditionally been done by medical staff, as described in section 2.3.2, from two-dimensional
slices of 3-D volumetric scintigraphic images. However, the method used here will rely
on the whole three-dimensional data that has been acquired from the segmentation process. Nonetheless, it will be influenced by the traditional methods in order to be able to
compare the results with previous examinations. Quantification is presently performed
by selecting multiple regions inside the ROI (the basal ganglia). These regions are then
compared by calculating quotes of various kinds. This method has been compared to a
manual segmentation method where the region of the basal ganglia has been divided into
two parts; one front and one rear part, as can be seen from the contour in Figure 6.5.
6.2 Quantification
41
Figure 6.5: Two examples after the 3-D segmentation process. For displaying reasons, the segmented area is illustrated by a contour on 2-D slices of the 3-D volumetric images.
Additionally, the segmented areas have been divided into two parts by a dividing
line, in order to extract corresponding parameters.
Consequently, the need for finding the long axis of the basal ganglia was needed. In
order to achieve this, tools from the statistical domain were used.
6.2.1
Weighted principal component analysis
Principal component analysis (PCA) can effectively be used in a dataset to find the
direction where the data is varying the most. PCA can be derived in many different
ways, depending on the context, however, one property of PCA is that it finds high
variance in data. This suits the problem at hand well, as the direction of high variance
of voxels is very likely the main axis of the basal ganglia. As maximum variance is
desired, finding the local maxima of the variance can be used to derive PCA. If the
empirical mean of the dataset is assumed to be zero (without loss of generality), the
variance in direction ŵ can be expressed as
2
σŵ
= E[xT ŵ] = E[(ŵT x)(xT ŵ)] = ŵT E[xxT ]ŵ = ŵT Cŵ =
wT Cw
,
wT w
(6.1)
where E denotes the expectation value operator, x a data vector and C the co-variance
matrix of x. By differentiating the variance we get
2
∂σŵ
2
= K(Cw − σŵ
w) = 0,
∂w
(6.2)
42
Chapter 6. Dopamine Transporter Quantification
where K '= 0. Moving around some of the terms and disposing K yields
2
Cw = σŵ
w,
(6.3)
which is identified as an eigenvalue equation:
Ce = λe.
(6.4)
The eigenvectors will, consequently, indicate the direction of highest variance, next
highest variance and lowest variance respectively, with all vectors being orthogonal.
However, in its original version, PCA on images works with the positions of the pixels
(or voxels) in the image only. As low intensity noise will then be as important as the
high intensity parts in the centre of the basal ganglia, the direction of variance will much
likely not correspond to the long axis of the basal ganglia. To make the procedure more
robust, the co-ordinates of the data (voxels) in the image are first weighted with the
intensity level at the corresponding position. This can be expressed mathematically if x
is the data vector with observations (pixels or voxels) ordered as columns, and the rows
representing the different variables (in this case, the co-ordinates (x, y) or (x, y, z)). The
weighted data, xw , for row, k, is then expressed as
x(k)w = x(k)W, ∀k
(6.5)
where W is a diagonal weight matrix with the intensity values of the image in the
diagonal. The result of this method is illustrated in Figure 6.6.
Figure 6.6: Principal component analysis (left) compared to intensity weighted principal component analysis (right) with test data where a brighter color indicates higher intensity values. The solid line illustrates the eigenvector with the corresponding highest
eigenvalue, i.e. the direction of highest variance or highest weighted variance.
This will give the means to approximate the long axis of the basal ganglia in order to
find the front and back of the organ, as illustrated by the dividing line in Figure 6.5. The
front and back part of the basal ganglia is here defined as dividing the ganglia at a certain
point along the long axis. If the segmentation was successful, this would approximate
dividing the ganglia with a plane, having the long axis vector as the normal vector.
6.3 Summary
6.3
43
Summary
The quantification of DaTSCAN-images can be performed through first dividing the
brain into two halves. Each part will then be target for a single 3-D Morphon segmentation, which leads to the localisation of the basal ganglia. By finding the long axis of the
two ganglia, they can then be divided into parts, and several fractions and values can be
extracted.
7
Results
In this chapter, the results from the automatic segmentation and alignment of the myocardial perfusion images and the quantification of DaTSCAN SPECT-images will be
presented in two separate parts. Regarding the current implementation of the methods, it
can be noted that they both take around 15 seconds per image to perform their respective
task.
7.1
Segmentation and alignment of 3-D transaxial myocardial perfusion images
The segmentation and alignment algorithm can be divided and tested in two parts; the
segmentation of the left ventricle, and the angling of the left ventricle after segmentation. The segmentation is obviously a necessary step for the alignment to work properly,
but can nonetheless be interesting as a separate segmentation method.
7.1.1
Segmentation
In order to test the success of the segmentation algorithm implemented in this thesis,
a large number of randomly selected myocardial perfusion images has been used. The
original images have all been acquired immediately after image reconstruction in the γcamera workstation; often called transversal or transaxial images. No attention has been
paid to different reconstruction algorithms, as they are estimated to have little effect on
the final result. The material consists of images from both male and female patients,
varying in age. Moreover, as only patients showing symptoms of a heart disease are
examined at the hospital where the images have been acquired, the images are not representative to the perfusion of an average person, but often indicates some kind of heart
disorder.
46
Chapter 7. Results
100 images have been used to test the algorithm. Since automatic evaluation can be
difficult for segmentation algorithms, all the images have been visually evaluated after
the segmentation. The importance of the segmentation in this context is to crop the
large transversal image volumes into a small image volume containing essentially only
the left ventricle. No effort has been made to remove noise and/or other organs that may
be situated close to the heart, as they can be of help to medical staff when examining
the images. The segmentation was evaluated to have been completely successful in 100
of the 100 cases, that is in 100 percent. Some examples from the 100 tested images can
be seen in figure Figure 7.1.
Another factor that may be of interest when evaluating the segmentation process is how
well the 3-D model deformed into the target image. Examples of this are shown in
Figure 7.2, where the deformed model, corresponding to the images in Figure 7.1, are
displayed. Note that the above images have not yet been rotated, but only target for
segmentation.
7.1.2
Alignment
After the 100 images above had been segmented, some of these were rotated with corresponding estimated angles. Two angles was used to rotate the heart and thus the rotation
around the axis of the heart was neglected as it has lower priority compared to the main,
global, rotation. Manual rotation of the same images was also performed by a technologist on 60 of the 100 images. These manual operations were made in the ordinary
clinical environment that is used when manually adjusting the images after image reconstruction. The manual alignment was therefore carried out completely independently of
the algorithm. Angles estimated from an application at the workstation were also included to give further data to compare to. This software, however, works on already
manually segmented images. The estimated angles for each of the involved parts (the
algorithm used in this thesis, the manual estimation and the additional semi-automatic
estimation) are presented in Figure 7.3 and 7.4. The mean difference for the automatic
method was approximately 6 and 7 degrees for the two estimated angles. However,
there were peaks of differences of up to 30 degrees. Additionally, in Figure 7.5 there
are some examples of more and less successful rotations made by the automatic algorithm, displayed in the same way as above.
7.2
Automatic dopamine transporter quantification
As there are few developed commercial applications performing automatic 3-D quantification of DaTSCAN-images, the results of this part of the thesis consist much in
considering the correlation between the automatic method introduced here with manual
7.2 Automatic dopamine transporter quantification
47
Figure 7.1: Results from the automatic segmentation displayed as appropriate slices along all
three axes in each image. Note the great variation between the different hearts.
48
Chapter 7. Results
Figure 7.2: The deformed models corresponding to the images in Figure 7.1, displayed in the
same slices.
7.2 Automatic dopamine transporter quantification
49
*!
)!
(!
'!
&!
%!
$!
#!
"!
!+
!
"!
#!
$!
%!
&!
,-./01.23
415-16
,-./!015+72889:9539
;902!1-./01.23
;902!1-./!015+72889:9539
+
'!
Figure 7.3: The first of the two angles in degrees, named HLA, estimated with different methods. The dotted and dashed horisontal lines indicate the mean difference for the
automatic and semi-automatic methods respectively.
50
Chapter 7. Results
"!!
*!
)!
(!
'!
&!
%!
$!
#!
"!
!+
!
"!
#!
$!
%!
&!
,-./01.23
415-16
,-./!015+72889:9539
;902!1-./01.23
;902!1-./!015+72889:9539
+
'!
Figure 7.4: The second of the two angles in degrees, named VLA, estimated with different
methods. The dotted and dashed horisontal lines indicate the mean difference for
the automatic and semi-automatic methods respectively.
7.2 Automatic dopamine transporter quantification
Figure 7.5: Slices through volumes after rotation has been performed.
51
52
Chapter 7. Results
2-D quantification methods. As in the previous section, the results from the automatic
quantification can be divided into a segmentation part and a quantification part. The
material that the method was tested on was made up of 70 images, taken directly after
image reconstruction in the γ-camera.
7.2.1
Segmentation
The segmentation process was here, as in the previous results, evaluated manually for
each image and failed in one case of the 70 images. This was due to the fact that the
uptake in the basal ganglia of one side of the examined brain was lower than in other
parts of the brain, resulting in that the model of the segmentation process was initiated
too far from the basal ganglia. The segmentation did, however, succeed for the other
side of the brain. This gives a rate of success of approximately 99 percent. Images of
successful segmentations are presented in Figure 7.6.
Figure 7.6: Illustrating the results from the segmentation process, where the contour line around
the basal ganglia indicates the segmented area.
7.2.2
Quantification
As have been mentioned, there are, at the time of writing, few algorithms that perform
automatic 3-D quantification of DaTSCAN-images, and the quality of the result can
7.2 Automatic dopamine transporter quantification
53
therefore be difficult to define. Nevertheless, even though the technique presented here
operates in three dimensions, it should, if performing well, correlate with manual two
dimensional approaches. Automatic quantification has therefore been performed on
the same images as the segmentation process, and a set of different values have been
calculated, which are often used in clinical quantification of this kind of images. The
quantification values are defined by different fractions between whole or parts of the
basal ganglia signal and the background signal in the brain, as well as fractions between
the left and right basal ganglia, and the front and back parts (as defined in the last
paragraph of section 6.2.1) of each ganglia. These values are explained and clarified
further in Figure 7.7. With these areas, a number of different fractions, fi , can be defined
A1
A2
B1
C
B2
Figure 7.7: The different fractions between different parts of the basal ganglia and the background signal are defined by the areas above.
as
f1 =
f5 =
A1 +A2 −C
2 −C
, f2 = B1 +B
,
C
C
f1
A2
B2
, f6 = B1 , f7 = f2 ,
A1
f3 = A2C−C ,
f8 = ff34
f4 =
B2 −C
C
(7.1)
where C is the mean signal of the whole brain, excluding the basal ganglia. The different
fractions are illustrated in Figure 7.8, 7.9, 7.10 and 7.11.
54
Chapter 7. Results
5
5
4
4
3
3
2
2
1
1
10
20
30
40
50
10
Correlation:0.89803
20
30
40
50
Correlation:0.91175
4
4
3
3
2
2
1
1
1
2
3
4
5
1
2
3
4
5
Figure 7.8: The fractions f1 and f2 with the values of manual (green) and automatic (blue)
quantification as well as the relative difference (red) along with scatter plots for
both sides.
7.2 Automatic dopamine transporter quantification
5
5
4
4
3
3
2
2
1
1
10
20
30
40
50
55
10
Correlation:0.91397
20
30
40
50
Correlation:0.9189
4
4
3
3
2
2
1
1
1
2
3
4
5
1
2
3
4
5
Figure 7.9: The fractions f3 and f4 with the values of manual (green) and automatic (blue)
quantification as well as the relative difference (red) along with scatter plots for
both sides.
56
Chapter 7. Results
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
10
20
30
40
50
10
Correlation:0.79792
20
30
40
50
Correlation:0.84629
1.1
1
1
0.9
0.9
0.8
0.8
0.7
0.6
0.7
0.5
0.6
0.8
1
1.2
0.6
0.8
1
1.2
Figure 7.10: The fractions f5 and f6 with the values of manual (green) and automatic (blue)
quantification as well as the relative difference (red) along with scatter plots for
both sides. The manual values available were rounded to one digit, which explains
the discretization of the horizontal axis.
7.2 Automatic dopamine transporter quantification
57
%!!&!!
%!!
&!
&!
&!!
!
!
!&!!
!&!
!
!&!!
!&!
!%!!
!"!!
!%!!
!"!!
!
!%&!
!
"!
#!
$!
!%!!
!%&!
! !
"! "!
#! #!
$! $!
!%!!
()**+,-./)01!2345"5
'())*+,-.(/0!12&222
'())*+,-.(/0!12&222
&! '!
'!
!
! !
!
!&!
!&!!'!
!'!
!%!!
!%!!
!&!!
!&!!
!&!
!
&!
!%!!
!%!!
!&!
!"!!
!
!&!!
"!
#
()**+,-./)01!2345
&!
!%!!
!
!&!
Figure 7.11: The fractions f7 and f8 with the values of manual (green) and automatic (blue)
quantification as well as the relative difference (red) along with scatter plots for
both sides.
!%!!
!"!!
!&!!
8
Discussion
In this chapter, some general comments will be made to the results in chapter 7. Furthermore, possible future improvements to the presented methods that, due to the time
limit of this project, were not implemented, will be proposed.
8.1
Segmentation and alignment of 3-D transaxial myocardial perfusion images
From the results it is quite obvious that the automatic segmentation scheme presented in
this thesis is near to flawless when applied to myocardial perfusion SPECT-images. The
relatively large dataset along with the great variation among these kind of medical images, gives great credibility to this local phase based registration scheme for segmenting
the left ventricle of the heart. The initial 2-D segmentation is probably essential in that
it removes other organs that can resemble the left ventricle to quite some extent from
time to time. Additionally, the 3-D segmentation fine-tunes the model to the target image, and if desired, an even tighter cropping could probably be performed than the one
illustrated in Figure 7.1. As noted though, the surrounding organs of the left ventricle
can be helpful for medical staff when diagnosing the images.
Performing the registration with different models have not been performed to any substantial extent in this thesis. However, from the results it is obvious that the choice of
model can not be crucial when it comes to segmentation; backed up by the great variance among different hearts. However, in some cases, where the target heart has been
overly large, the 2-D segmentation can cut away some parts of the heart due to restraints
in rigidity. While this does not generally have any impact on the final result after the
3-D segmentation has been performed, it does increase the possibility of a bad angle
estimation.
The results from the alignment can, compared to that of the segmentation, be directly
60
Chapter 8. Discussion
compared to other data, such as the manual angle estimations. As the angling is a more
complex process, the automatically estimated angles do vary some with the manual measurement and as could be seen, the semi-automatic method have a lower mean difference
than the fully automatic method used in this thesis. It should be noted though, that the
difference between the manual and the semi-automatic methods sometimes reaches a
value of zero. This can be explained due to the fact that the semi-automatic method
is built in to the workstation where the operator performs the manual estimations. The
operator is first presented with angles from the semi-automatic application, and could
possibly deem the presented angles as sufficient; therefore not changing them further
manually.
Moreover, as the deformation of the model to the target images seems very well performed, the flaw of the angle estimation might be founded in the way that the difference
in angles is described and defined. Not uncommonly, the left ventricle of the examined
image is somewhat curved, in which case a line description for describing the orientation of the object could be insufficient. Tests with two lines as describing the angle
difference has been performed, but without any obvious improvement.
Since the deformation field of the 3-D registration is known and probably a good description of some kind of difference between the model and target image, future implementations of angle estimation can be easily done. Moreover, performing the registration with a different kind of model might prove itself useful when it comes to the angle
estimation since the difference between the target image and the model could correlate
better with the difference in angle for another model. Furthermore, the absolute angle of
the left ventricle may not be important in an absolute, single estimation, but is probably
more important when comparing different images from the same patient. One solution
to this could then be to register the left ventricle in one examination to the same ventricle
in another examination. Since the two images will probably be more alike compared to
a general model, the angle difference estimation between the hearts of the different examinations could be easier determined. It is, however, difficult to determine how much
the rotation of a single heart can vary from a "perfect" rotation and still be sufficient for
a doctor to base a diagnose on. Generally though, a difference of more than 10 degrees
often results in a poor rotated image. Furthermore, a perfect rotation is hard to define,
as different operators will rotate the same heart differently. Therefore, to gain a full
understanding on how successful the algorithm of this thesis is in rotating the images,
a study involving more human operators is desirable. It is also difficult to compare this
method to already proposed methods, since information about image type and quality is
not available in enough detail for such studies.
8.2 Automatic dopamine transporter quantification
8.2
61
Automatic dopamine transporter quantification
The automatic quantification of DaTSCAN-images showed itself to be quite successful
when it comes to correlation to manual 2-D quantification. There is very high correlation in some cases of the different fractions, however, a relevant question to ask is if
the correlation should be higher. Probably not, since the two methods differ very much.
The automatic method uses volume quantification, while the manual quantification is
performed on a number, or sometimes only one, two dimensional slices of the volume.
The segmentation process was successful in most cases, and could probably be even
more so if a more sophisticated method for initiating the registration model was developed. A pre-registration of the whole brain could primarily be performed, which would
give a better estimation of where the basal ganglia should, or more important should
not, be located.
For very low uptake, the registration model could sometimes float away, in lack of
structure to register on. This behaviour could be removed to some extent if one of the
two basal ganglia have a higher uptake. By first registering on the side with high uptake,
a rough approximation of the other basal ganglia could be generated. By then increasing
the regularisation kernel (increasing the rigidity of the model), and mirroring the result
from the first registration, the registration of the basal ganglia with low uptake could
probably be helped; taking into account that the two basal ganglia of the same brain do
not differ much from each other.
Coinciding with suggestions of the earlier section, other registration models should be
evaluated to investigate if that could yield a better result. However, as the uptake of
the basal ganglia is due to a physiological process, this is unlikely. If CT and/or MRI
images of the same brain are available, the registration could be performed on these
images (with much higher resolution) and later mapped onto the SPECT-images of the
dopamine activity in the basal ganglia.
9
Conclusions
In this thesis, it has been showed that a phase based registration scheme can be very successful when performing fully automatic segmentation of myocardial perfusion SPECTimages. Such a method has been implemented and when performed in three dimensions,
this segmentation can be used to estimate the angle of the left ventricle. To reduce variability between different operators, such a method can further more be used to take one
step closer to a fully automatic examination of myocardial perfusion images.
Additionally, a method for automatically quantifying DaTSCAN-images in three dimensions was presented with promising results. Manual quantification can be difficult
and tedious and is often performed on slices instead of whole volume data. This method
can therefore increase the quality of examinations and vastly decrease the time that it
takes to quantify each image. As the research on automatic algorithms for dopamine
transporter quantification is currently quite sparse, the hope that this method will give
medical staff future tools for increasing examination quality is likely well founded.
Bibliography
[1] G. Germano, P.B. Kavanagh, Hsiao-Te Su, M. Mazzanti, H. Kiat,
R. Hachamovitch, K.F. Van Train, J.S. Areeda, and D.S. Berman. Automatic reorientation of three-dimensional, transaxial myocardial perfusion spect
images. The Journal of Nuclear Medicine, 1995.
[2] G. Germano, P.B. Kavanagh, J. Chen, P. Waechter, Hsiao-Te Su, H. Kiat, and D.S.
Berman. Operator-less processing of myocardial perfusion spect studies. The
Journal of Nuclear Medicine, 1995.
[3] R.J. Morton, M.J. Guy, R. Clauss, P.J. Hinton, C.A. Marshall, and E.A. Clarke.
Comparison of different methods of datscan quantification. Nuclear medicine
communications, pages 1139–1146, 2005.
[4] P.A. Tipler and R.A. Llewellyn. Modern Physics. W. H. Freeman and Company,
New York, USA, fourth edition, 2004.
[5] A.C Perkins.
Nuclear Medicine in Pharmaceutical Research, chapter 2.
CRC Press, London, UK, fourth edition, 1999.
URL http:
//site.ebrary.com.lt.ltag.bibl.liu.se/lib/linkoping/
Doc?id=10054842&ppg=5.
[6] A. Del Guerra.
Ionizing Radiation Detectors for Medical Imaging.
World Scientific Publishing Company, Incorporated, Singapore, third edition, 2004. URL http://site.ebrary.com.lt.ltag.bibl.liu.se/
lib/linkoping/Doc?id=10082183&ppg=5.
[7] O. Chiewitz and G. de Heversy. Radioactive indicators in the study of phosphorus
metabolism in rats. Nature, 1935.
[8] E. Lindgren. Versuche mit radioaktiven isotopen bei leukämibehandlung. Acta
Radiologica, 1944.
[9] H.W. Strauss, K. Harrison, and J.K. Langee. Thallium-201 for myocardial imaging. relation of thallium-201 to regional myocardial perfusion. Circulation, 1975.
[10] B. Bodforss. Radioisotope scanning of the brain. (32), 1965.
[11] P.V. Harper, G. Andros, and K. Lathrop. Technetium-99 as a biological tracer. The
Journal of Nuclear Medicine, 1962.
66
Chapter 9. Conclusions
[12] S.A. Larsson. Gamma camera emission tomography. development and properties
of a multi-sectional emission computed tomography system. 1980, Acta Radiologica.
[13] C.G. Wilson, Y.P. Zhu, and M. Frier.
Nuclear Medicine in Pharmaceutical Research, chapter 8.
CRC Press, London, UK, fourth edition,
1999.
URL http://site.ebrary.com.lt.ltag.bibl.liu.se/
lib/linkoping/Doc?id=10054842&ppg=5.
[14] GE Healthcare. Datscan.com, January 2008. URL http://www.datscan.
com.
[15] H.W. Strauss and D.D. Miller. Society of Nuclear Medicine Procedure Guideline
for Myocardial Perfusion Imaging. Society of Nuclear Medicine, 3.0 edition, June
2002.
[16] K. Tatsch, S. Asenbaum, P. Bartenstein, A. Catafau, C. Halldin, L.S. Pilowsky, and
A. Pupi. European Association of Nuclear Medicine Procedure Guidelines For
Brain Neurotransmission SPET using 123 I-labelled Dopamine Transporter Ligands. European Association of Nuclear Medicine, October 2001.
[17] G.H. Granlund and H. Knutsson. Signal Processing for Computer Vision. Kluwer
Academic Publishers, 1995. ISBN 0-7923-9530-1.
[18] B. Svensson, J. Pettersson, and H. Knutsson. Bildregistrering: Geometrisk
anpassning av bilder, May 2007. URL http://www.imt.liu.se/edu/
courses/TBMI45/pdfs/registration.pdf.
[19] H. Knutsson and M. Andersson. Morphons: Paint on priors and elastic canvas for
segmentation and registration. In Proceedings of the Scandinavian Conference on
Image Analysis (SCIA), Joensuu, June 2005.
[20] J. Pettersson. Automatic generation of patient specific models for hip surgery simulation. Lic. Thesis LiU-Tek-Lic-2006:24, Linköping University, Sweden, April
2006. Thesis No. 1243, ISBN 91-85523-95-X.
[21] B. Rodrìguez-Vila, J. Pettersson, M. Borga, F. Garcìa-Vicente, E.J. Gómez, and
H. Knutsson. 3d deformable registration for monitoring radiotherapy treatment
in prostate cancer. In Proceedings of the 15th Scandinavian conference on image
analysis (SCIA’07), Aalborg, Denmark, June 2007.
[22] J. Pettersson, K.L. Palmerius, H. Knutsson, O. Wahlström, B. Tillander, and
M. Borga. Simulation of patient specific cervical hip fracture surgery with a volume haptic interface. IEEE Transactions on Biomedical Engineering, 2007.
67
[23] A. Parraga, A. Susin, J. Pettersson, B. Macq, and M. De Craene. Quality assessment of non-rigid registration methods for atlas-based segmentation in headneck radiotherapy. In Proceedings of IEEE International Conference on Acoustics,
Speech, & Signal Processing, Honolulu, Hawaii, USA, April 2007.
[24] H. Knutsson, C-F. Westin, and G.H. Granlund. Local multiscale frequency and
bandwidth estimation. In Proceedings of the IEEE International Conference on
Image Processing, pages 36–40, Austin, Texas, November 1994. IEEE. (Cited in
Science: Vol. 269, 29 Sept. 1995).
[25] H. Knutsson, M. Andersson, and J. Wiklund. Advanced filter design. In Proceedings of the 11th Scandinavian Conference on Image Analysis, Greenland, June
1999. SCIA.
[26] M. Andersson and H. Knutsson. Controllable 3-D filters for low level computer vision. In Proceedings of the 8th Scandinavian Conference on Image
Analysis, Tromsø, May 1993. SCIA. URL http://www.imt.liu.se/mi/
Publications/Papers/scia93_ak.pdf.
[27] H. Knutsson and C-F. Westin. Normalized convolution: A technique for filtering
incomplete and uncertain data. In Proceedings of the 8th Scandinavian Conference on Image Analysis, Tromsö, Norway, May 1993. SCIA, NOBIM, Norwegian
Society for Image Processing and Pattern Recognition. Report LiTH–ISY–I–1528.
Linköpings tekniska högskola
Institutionen för medicinsk teknik
Rapportnr: LiTH-IMT/MI30-AEX--08/465--SE
Datum: 2008-04-04
Svensk
titel
Segmentering och uppvinkling av tredimensionella, transaxiella myokardiska
perfusionsbilder och automatisk dopaminreceptorkvantifiering
Engelsk
titel
Segmentation and Alignment of 3-D Transaxial Myocardial Perfusion Images and
Automatic Dopamin Transporter Quantification
Författare
Leo Bergnéhr
Uppdragsgivare:
EXINI Diagnostics
Rapporttyp:
Examensarbete
Rapportspråk:
Engelska
Sammanfattning
Abstract
In this thesis, a novel method for automatically segmenting the left ventricle of the heart in
SPECT-images is presented. The segmentation is based on an intensity-invariant localphase based approach, thus removing the difficulty of the commonly varying intensity in
myocardial perfusion images. Additionally, the method is used to estimate the angle of the
left ventricle of the heart. Furthermore, the method is slightly adjusted, and a new approach
on automatically quantifying dopamine transporters in the basal ganglia using the
DaTSCAN™ radiotracer is proposed.
The results for both applications are promising. The segmentation for myocardial perfusion
images succeeded in 100 of 100 cases with a mean difference to manually estimated angles
of around 8 degrees. The automatic quantification algorithm showed good correlation with
manual quantification, with a correlation coefficient of up to 0.95 for 70 images.
Nyckelord
Keyword
Segmentation, Morphon, SPECT, Myocardial, DAT
Bibliotekets anteckningar: