Download Image Reconstruction for Prostate Specific Nuclear Medicine Imagers

Image Reconstruction for Prostate Specific Nuclear Medicine Imagers
M. F. Smith
Thomas Jefferson National Accelerator Facility
Newport News, Virginia, USA
Abstract
There is increasing interest in the design and construction of nuclear medicine detectors for dedicated
prostate imaging. These include detectors designed for imaging the biodistribution of
radiopharmaceuticals labeled with single gamma as well as positron-emitting radionuclides. New
detectors and acquisition geometries present challenges and opportunities for image reconstruction. In
this contribution various strategies for image reconstruction for these special purpose imagers are
reviewed. Iterative statistical algorithms provide a framework for reconstructing prostate images from a
wide variety of detectors and acquisition geometries for PET and SPECT. The key to their success is
modeling the physics of photon transport and data acquisition and the Poisson statistics of nuclear
decay. Analytic image reconstruction methods can be fast and are useful for favorable acquisition
geometries. Future perspectives on algorithm development and data analysis for prostate imaging are
presented.
Key Words: image reconstruction, nuclear medicine, prostate, emission computed tomography
Presented at the Topical Symposium on Advanced Molecular Imaging Techniques in the
Detection, Diagnosis, Therapy and Follow-Up of Prostate Cancer
Rome, Italy; December 6-7, 2005
Submitted to Physica Medica; Version: August 25, 2006
Corresponding Author:
Mark F. Smith
Jefferson Lab
12000 Jefferson Avenue, Suite 10
Newport News, VA 23606
USA
E-mail: [email protected]
Phone: +1 757-269-5539
FAX: +1 757-269-6248
1. Introduction
There is increasing interest in the design and construction of dedicated nuclear medicine detectors for
organ specific prostate imaging. These include detectors designed for imaging the biodistribution of
radiopharmaceuticals labeled with single gamma [1-10] as well as positron emitting radionuclides [11-
14]. The general design goal of these detectors is to provide improved prostate imaging performance
(e.g. sensitivity, resolution) or equivalent performance at lower cost compared with conventional whole
body imaging systems. With these new detectors there is the potential to improve the diagnosis and
staging of prostate cancer, as well as monitoring the efficacy of therapy. This interest in dedicated
prostate imagers has been spurred in part by the development of other organ specific imagers such as
breast specific gamma [15-18] and positron [19-24] imaging devices. New detectors and acquisition
geometries present challenges and opportunities for image reconstruction. In this contribution various
strategies for dedicated prostate imagers are reviewed. In section 2 general considerations for image
reconstruction with dedicated detectors are discussed. Section 3 examines image reconstruction
strategies for several dedicated prostate imaging devices. A broader view is taken in section 4 with a
discussion of future perspectives on image reconstruction and data analysis for prostate specific nuclear
medicine imaging.
2. General considerations for image reconstruction with dedicated detectors
Analytic image reconstruction methods (e.g. filtered backprojection) for positron emission tomography
(PET) and single photon emission computed tomography (SPECT) are generally fast, robust and wellsuited for regular acquisition geometries and for clinical use with conventional PET scanners and
SPECT cameras. Iterative statistical image reconstruction methods have gained widespread use and
acceptance in both research and clinical applications over the past two decades with the advent of
cheaper and faster computers. These statistical methods estimate the radiopharmaceutical distribution
by solving the matrix equation
y=Ax+b
(1)
for the discretized source distribution x, given the observed data vector y and a computed system
matrix A, usually with some explicit or implicit regularization scheme to suppress image noise
resulting from statistical noise in the observations. The matrix element Aij represents the probability
that a radioactive decay in source voxel (or other basis element) j is detected by data element (line of
response for PET, projection pixel for SPECT) i. The vector b may incorporate effects such as
randoms, scatter (if not modeled in the system matrix), electronic noise or other bias. The most widely
used iterative statistical methods are maximum likelihood expectation maximization (MLEM) [25, 26],
its accelerated versions such as ordered subset expectation maximization (OSEM) [27] and maximum a
posteriori (MAP) methods such as penalized weighted least-squares [28]. For MLEM image
reconstruction with Poisson variables, for example, the log likelihood function
L y | x    [ yi ln y i  y i  ln yi !]
(2)
i
is maximized, where the overbar denotes expectation value. These iterative statistical methods are wellsuited for image reconstruction in nuclear medicine since they enable the physics of photon transport
and the data acquisition process to be modeled as well as the Poisson statistics of nuclear decay. They
are particularly attractive for organ specific imaging devices since models of unconventional and
irregular acquisition geometries can be incorporated in a straightforward manner into the system matrix
calculation. In general, image reconstructions should improve as the data vector includes more
information and as photon transport and detection are modeled better in the system matrix. For
example, smaller crystal elements for pixellated detectors usually permit better image resolution,
though their effect on energy resolution and sensitivity must be considered. Knowledge of depth of
interaction within a scintillation crystal or multiple crystal layers enables improved raytracing for
gamma events (SPECT) and lines of response (PET). Improved energy resolution will reduce the
number of scattered events, improved time resolution will reduce the number of randoms (PET) and
time of flight information will permit better event localization (PET). One guiding principle for image
reconstruction and activity estimation is to model photon transport and detection as best possible, given
constraints on available time and computing power, in order to make optimal use of the information
that has been acquired.
3. Image reconstruction for several dedicated prostate imaging devices
3.1. Dedicated PET prostate tomograph
A dedicated PET prostate tomograph is being developed at Lawrence Berkeley National Laboratory
(LBNL; Berkeley, California, USA) [11, 14]. The tomograph consists of two curved banks of
Siemens/CTI ECAT HR+ PET block detector modules in a clamshell arrangement, forming an
incomplete elliptical ring with a 45 cm minor axis and a 70 cm major axis. Each bank contains 2 rows
of 20 modules, for a total of 80 modules in the PET imager. Each block detector module consists of an
8 8 array of 4.39 4.05 30 mm3 BGO crystals, with crystal pitches of 4.85 mm and 4.51 mm,
respectively. The axial field of view of the scanner is 8 cm. Image reconstruction is performed with a
three-dimensional penalized maximum likelihood algorithm [29]. The program can accept
histogrammed or list-mode [22] data. Its structure is modular and it uses initialization files for
description of detector blocks and detector head positioning. The description of the detector block
includes the number and dimensions of crystals in the axial and transaxial directions, the crystal
thickness and the number of crystal levels. Photon penetration and interaction in different depths in the
crystals are modeled. The detector head description includes the location of the head and its orientation,
the number and placement of blocks in the detector head and the gaps between the detector blocks.
Modeling of object attenuation is optional and crystal elements may be subsampled as desired for more
accurate system matrix modeling. Preliminary image reconstructions from test phantoms show the
effectiveness of this reconstruction method for cylindrical and line sources phantoms [14].
3.2. High resolution prostate imager with dual planar detectors
A prototype prostate imager has been built with dual rotating planar detectors at Thomas Jefferson
National Accelerator Facility (Newport News, Virginia, USA) and tested at Duke University Medical
Center (Durham, North Carolina, USA) [13]. The system consists of two 15 20 cm2 field of view
detectors built with 3 3 10 mm3 LGSO crystal elements and 6 8 arrays of Hamamatsu R7600-00-C8
position sensitive photomultiplier tubes (PSPMTs). The detectors are mounted on a computer
controlled rotating gantry and were built as part of a positron emission mammography project [23].
Image reconstruction is performed using a three-dimensional MLEM code originally developed for
coincidence breast imaging with dual planar detectors [30, 31]. The system matrix is computed by
tracing rays between crystal elements on opposed detector heads through the source volume; the
maximum angle from normal incidence can be set. With acquisition at one angle, image reconstruction
is a form of limited angle tomography. If there is a sufficient number of rotation angles, then angular
sampling is complete and the source activity distribution can be reconstructed without blurring
artifacts.
The imaging system was tested using an elliptical torso phantom with three different sized spheres [13].
Acquisition and image reconstruction were performed with five different angular rotation ranges. There
was considerable blurring orthogonal to the detectors, as expected, when the detectors were in a static
position. This blurring was reduced as the angular rotation range of the detectors increased, and the best
results were obtained when the detectors were rotated through 180 degrees to obtain complete angular
sampling.
3.3. Compton probe for prostate imaging
Conceptual designs for imaging the prostate with a probe and Compton scatter camera have been
proposed for single gamma tracers [2-5, 7, 10]. Hardware development and component testing for such
systems is progressing [6-10, 32]. The idea is to detect the position where an emitted gamma ray
scatters in a probe that is intrarectal or just outside the rectum close to the prostate and to detect the
position and energy of the Compton-scattered photon with a gamma camera. With the acquired data,
the Compton scatter equation can be used to constrain the origin of the disintegration event, which
without degrading effects is on the surface of a cone. The first reconstruction effort for Compton
imaging for nuclear medicine applications (not prostate specific) was a two step method in which cone
beam projection data were iteratively formed and then used in an iterative algorithm for 3-D activity
estimation [33]. Several years later maximum likelihood methods were applied for image
reconstruction [34]. Due to the demands of computing the entire system matrix, list-mode image
reconstruction [35, 36] is an attractive option when events occur in only a relatively small fraction of
the total number of possible (discretized) position and energy combinations. It is computationally
efficient because forward projection and backprojection are only performed for recorded events. Listmode maximum likelihood methods have been investigated for simulated Compton camera data [3739] and have included a more sophisticated physical model that includes Doppler broadening and the
limited energy and spatial resolutions of the probe and detector. The disintegration event is constrained
to be on the surface of blurred cone and this information can be incorporated into the projectors and
backprojectors. More recent work has applied these methods to simulations of prostate imaging with
Compton cameras [2, 3, 5] and experimental results have been presented for point sources imaged with
a Compton probe prototype [6]. In a new development, a filtered backprojection algorithm has been
reported for Compton camera imaging [40]. This technique uses the fact that the intersection of a
Compton scatter cone with a sphere is a circle. The sphere is stereographically projected onto a 2-D
plane for application of Fourier methods for applying a ramp filter and deblurring of Doppler
broadening. Reprojection onto the sphere is performed for 3-D activity estimation. This method may be
fast enough for routine clinical application and merits more detailed study and comparison with
listmode maximum likelihood approaches.
3.4. High resolution PET system for molecular prostate imaging
A novel high resolution PET system has been proposed for imaging the prostate with positron-emitting
tracers [41]. Coincidences will be detected between an intrarectal probe and an external detector panel.
The internal probe will consist of detector arrays with thin position sensitive avalanche photodiode
arrays that detect scintillation events from the side of the scintillation crystals in order to obtain depth
of interaction information [42]. Image reconstruction will be performed using an iterative algorithm
that models the detection of coincidence events along lines of response (LORs) between any element in
the external detector array and any subcrystal element in the internal probe. The dense web of LORs
will enable high resolution to be achieved, though there will inevitably be some blurring due to the lack
of complete angular sampling. This could potentially be mitigated by rotating the external detector
array around the patient or, at increased cost, by having multiple panels that surround the patient.
Depending on imaging time, source activity and tracer biodistribution, listmode image reconstruction
may be computationally efficient if only a fraction of the LORs are populated with events.
3.5. Discussion
Statistical iterative image reconstruction methods such as MLEM or MAP methods, and their
variations, are widely used for prostate image reconstruction. The key to their success is modeling
photon transport and data acquisition and the Poisson statistics of nuclear decay. They have the
flexibility to model a variety of detector and acquisition geometries have proven to be robust. Listmode algorithms are advantageous for settings where there are no recorded events for a large fraction
of the LORs or position-energy combinations. Analytic image reconstruction methods are useful for
regular acquisition geometries, particularly with conventional PET scanners and SPECT cameras in a
clinical setting, but are less likely to be the method of choice for special purpose instrumentation. A
possible exception may be the case of Compton imaging with a high number of detected events, though
evaluations and a comparison between the newly developed filtered backprojection method and
iterative statistical methods are needed.
4. Future perspectives
4.1. Algorithms and data analysis
Predicting image reconstruction algorithm development for dedicated prostate imaging is difficult,
though image reconstruction and detector developments in other areas of nuclear medicine may provide
some insight into future applications for prostate imaging. The iterative image reconstruction approach
permits almost arbitrary new detector configurations for SPECT and PET. For example, flexible
positioning of the detector heads has been investigated for breast-specific gamma imaging [17] and a
similar approach may be feasible for prostate imaging. The LBNL prototype prostate imager could be
augmented by adding additional detector modules between the legs of the patient. The modular design
of these researchers’ iterative reconstruction code would allow modified detector configurations to be
modeled easily in the system matrix. Tracking and incorporating torso motion information into image
reconstruction may prove valuable for achieving improved resolution, which is particularly important
in assessing whether cancer has spread outside the prostate capsule. Bayesian priors using anatomical
information from other modalities, e.g. ultrasound, x-ray CT or magnetic resonance imaging, have not
yet been applied to prostate imaging, though the use of transrectal ultrasound from a dual modality
PET/ultrasound study could be used to provide boundary constraints for image reconstruction or to
correct for prostate motion [43]. An analytic image reconstruction algorithm for dual circular arc
coincidence detectors (two-dimensional case) has recently been developed [44]. The method uses a fast
Hilberttransform- based filtered backprojection formula, without any rebinning. The technique may
prove useful for fast image reconstruction for detectors built with partial rings of detectors around the
torso as in the LBNL imager or for other partial ring prostate imaging systems built using curved
detector arrays. Algorithm performance evaluation for detection and quantitation tasks is being studied
and such efforts are important. For example, the use of non-Gaussian priors for MAP image
reconstruction was investigated for prostate study simulations with an 82.6 cm diameter ring PET
system in an effort to see whether edge-preserving priors had a benefit. It was found, however, that
non-Gaussian Huber and Geman-McClure priors did not improve the detection or quantitation of small
lesions [45]. A recent simulation study of statistical image reconstruction methods for a dedicated
prostate imager compared a conventional quadratic penalty function yielding anisotropic image
resolution with a Gaussian post-smoothed MLEM approach yielding isotropic resolution for tasks of
lesion detection and region of interest quantitation. The results showed superior performance for the
method with anisotropic resolution [46]. Data analysis in the future may provide more than just
reconstructed images to the physician or scientist. It is likely that estimates of spatial-dependent kinetic
rate constants and uptake-washout parameters will be provided for some research studies at academic
medical centers, as is already the case for some studies with conventional PET and SPECT imagers.
4.2. Computer hardware advances
The lower cost of computer clusters and the introduction of multicore processors enable faster image
reconstructions for appropriately structured code. Faster computers also enable more sophisticated
modeling of detector physics in image reconstruction, though parameterized system models are also a
powerful tool to speed image reconstruction.
4.3. Image reconstruction to aid detector design and use
Image reconstructions of Monte Carlo and analytically simulated studies will continue to play an
important role in the development of novel prostate imager designs and their use [2, 11]. Quantitative
metrics have long been employed for the design and characterization of nuclear medicine imaging
systems, e.g. resolution, sensitivity, signal-to-noise ratio (SNR) and noise equivalent count rate
(NECR). For example, the SNR and NECR have been used to study septa design for a dedicated
prostate imager [12]. An as yet unresearched area is the use of multiple pinholes or coded apertures for
SPECT prostate imaging. These collimation methods have the potential to improve the
sensitivity/resolution/SNR/detection tradeoffs, however they must be evaluated against optimally
designed parallel hole or converging beam collimators. Analytic tools such as the linearized local
impulse response [47] and Cramer-Rao bounds for variance resolution tradeoffs [48] that use the Fisher
information matrix [49] are being used more widely in nuclear medicine imager design and evaluation
and may be of value in the development of dedicated prostate imagers.
5. Conclusions
Iterative statistical image reconstruction algorithms provide a framework for reconstructing prostate
images from a wide variety of dedicated imagers and acquisition geometries for PET and SPECT.
Analytic image reconstruction methods can be fast and may be useful for favorable acquisition
geometries. Taking a broader perspective, image reconstruction and data analysis methods can be used
to aid the design of equipment and patient imaging protocols and to extract additional task-dependent
physiological information from the acquired data. When imaging the prostate, it is important to
consider the combination of detector hardware and image reconstruction on total system performance.
Consideration of the system in its entirety in collaboration with the nuclear medicine physicians and
scientists who will use the resulting images and data analyses should enable improved detection,
localization and characterization of prostate tumors for specific clinical tasks.
Acknowledgements
I thank Neal Clinthorne, Jennifer Huber and Jinyi Qi for reviewing a draft of this manuscript and for
their comments. This work was supported in part by the Office of Biological and Environmental
Research of the Office of Science of the U.S. Department of Energy. Jefferson Science Associates,
LLC operates Thomas Jefferson National Accelerator Facility for the United States Department of
Energy under U.S. DOE Contract No. DE-AC05-06OR23177.
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