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 fordedicated prostate imaging. These include detectors designed for imaging the biodistribution ofradiopharmaceuticals labeled with single gamma as well as positron-emitting radionuclides. Newdetectors and acquisition geometries present challenges and opportunities for imagereconstruction. In this contribution various strategies for image reconstruction for these specialpurpose imagers are reviewed. Iterative statistical algorithms provide a framework forreconstructing prostate images from a wide variety of detectors and acquisition geometries forPET and SPECT. The key to their success is modeling the physics of photon transport and dataacquisition and the Poisson statistics of nuclear decay. Analytic image reconstruction methodscan be fast and are useful for favorable acquisition geometries. Future perspectives on algorithmdevelopment 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:

Phone: +1 757-269-5539

FAX: +1 757-269-6248

1. Introduction

There is increasing interest in the design and construction of dedicated nuclear medicinedetectors for organ specific prostate imaging. These include detectors designed for imaging thebiodistribution of radiopharmaceuticals labeled with single gamma [1-10] as well as positronemittingradionuclides [11-14]. The general design goal of these detectors is to provide improvedprostate imaging performance (e.g. sensitivity, resolution) or equivalent performance at lowercost compared with conventional whole body imaging systems. With these new detectors there isthe potential to improve the diagnosis and staging of prostate cancer, as well as monitoring theefficacy of therapy. This interest in dedicated prostate imagers has been spurred in part by thedevelopment 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 imagereconstruction. In this contribution various strategies for dedicated prostate imagers arereviewed. In section 2 general considerations for image reconstruction with dedicated detectorsare discussed. Section 3 examines image reconstruction strategies for several dedicated prostateimaging devices. A broader view is taken in section 4 with a discussion of future perspectives onimage reconstruction and data analysis for prostate specific nuclear medicine imaging.

1. General considerations for image reconstruction with dedicated detectors

Analytic image reconstruction methods (e.g. filtered backprojection) for positron emissiontomography (PET) and single photon emission computed tomography (SPECT) are generallyfast, robust and well-suited for regular acquisition geometries and for clinical use withconventional PET scanners and SPECT cameras. Iterative statistical image reconstructionmethods have gained widespread use and acceptance in both research and clinical applicationsover the past two decades with the advent of cheaper and faster computers.These statistical methods estimate the radiopharmaceutical distribution by solving thematrix equation

y = A x + b (1)

for the discretized source distribution x, given the observed data vector y and a computed systemmatrix A, usually with some explicit or implicit regularization scheme to suppress image noiseresulting from statistical noise in the observations. The matrix element Aij represents theprobability that a radioactive decay in source voxel (or other basis element) j is detected by dataelement (line of response for PET, projection pixel for SPECT) i. The vector b may incorporateeffects such as randoms, scatter (if not modeled in the system matrix), electronic noise or otherbias.The most widely used iterative statistical methods are maximum likelihood expectationmaximization (MLEM) [25, 26], its accelerated versions such as ordered subset expectationmaximization (OSEM) [27] and maximum a posteriori (MAP) methods such as penalizedweighted least-squares [28]. For MLEM image reconstruction with Poisson variables, forexample, the log likelihood function

(2)

is maximized, where the overbar denotes expectation value.These iterative statistical methods are well-suited for image reconstruction in nuclearmedicine since they enable the physics of photon transport and the data acquisition process to bemodeled as well as the Poisson statistics of nuclear decay. They are particularly attractive fororgan specific imaging devices since models of unconventional and irregular acquisitiongeometries can be incorporated in a straightforward manner into the system matrix calculation.In general, image reconstructions should improve as the data vector includes moreinformation and as photon transport and detection are modeled better in the system matrix. Forexample, smaller crystal elements for pixellated detectors usually permit better image resolution,though their effect on energy resolution and sensitivity must be considered. Knowledge of depthof interaction within a scintillation crystal or multiple crystal layers enables improved raytracingfor gamma events (SPECT) and lines of response (PET). Improved energy resolution will reducethe 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 guidingprinciple for image reconstruction and activity estimation is to model photon transport anddetection as best possible, given constraints on available time and computing power, in order tomake 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 NationalLaboratory (LBNL; Berkeley, California, USA) [11, 14]. The tomograph consists of two curvedbanks 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 bankcontains 2 rows of 20 modules, for a total of 80 modules in the PET imager. Each block detectormodule consists of an 8 8 array of 4.39 4.05 30 mm3 BGO crystals, with crystal pitches of4.85 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 likelihoodalgorithm [29]. The program can accept histogrammed or list-mode [22] data. Its structure ismodular and it uses initialization files for description of detector blocks and detector headpositioning. The description of the detector block includes the number and dimensions of crystalsin 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 detectorhead description includes the location of the head and its orientation, the number and placementof blocks in the detector head and the gaps between the detector blocks. Modeling of objectattenuation is optional and crystal elements may be subsampled as desired for more accuratesystem matrix modeling. Preliminary image reconstructions from test phantoms show theeffectiveness 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 ThomasJefferson National Accelerator Facility (Newport News, Virginia, USA) and tested at DukeUniversityMedicalCenter (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 8arrays of Hamamatsu R7600-00-C8 position sensitive photomultiplier tubes (PSPMTs). Thedetectors are mounted on a computer controlled rotating gantry and were built as part of apositron emission mammography project [23].Image reconstruction is performed using a three-dimensional MLEM code originallydeveloped for coincidence breast imaging with dual planar detectors [30, 31]. The system matrixis computed by tracing rays between crystal elements on opposed detector heads through thesource volume; the maximum angle from normal incidence can be set. With acquisition at oneangle, image reconstruction is a form of limited angle tomography. If there is a sufficient numberof rotation angles, then angular sampling is complete and the source activity distribution can bereconstructed without blurring artifacts.

The imaging system was tested using an elliptical torso phantom with three different sizedspheres [13]. Acquisition and image reconstruction were performed with five different angularrotation ranges. There was considerable blurring orthogonal to the detectors, as expected, whenthe detectors were in a static position. This blurring was reduced as the angular rotation range ofthe detectors increased, and the best results were obtained when the detectors were rotatedthrough 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 havebeen proposed for single gamma tracers [2-5, 7, 10]. Hardware development and componenttesting for such systems is progressing [6-10, 32]. The idea is to detect the position where anemitted gamma ray scatters in a probe that is intrarectal or just outside the rectum close to theprostate and to detect the position and energy of the Compton-scattered photon with a gammacamera.With the acquired data, the Compton scatter equation can be used to constrain the origin ofthe disintegration event, which without degrading effects is on the surface of a cone. The firstreconstruction effort for Compton imaging for nuclear medicine applications (not prostatespecific) was a two step method in which cone beam projection data were iteratively formed andthen used in an iterative algorithm for 3-D activity estimation [33]. Several years later maximumlikelihood 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 totalnumber of possible (discretized) position and energy combinations. It is computationallyefficient because forward projection and backprojection are only performed for recorded events.List-mode maximum likelihood methods have been investigated for simulated Compton cameradata [37-39] and have included a more sophisticated physical model that includes Dopplerbroadening and the limited energy and spatial resolutions of the probe and detector. Thedisintegration event is constrained to be on the surface of blurred cone and this information canbe incorporated into the projectors and backprojectors. More recent work has applied thesemethods to simulations of prostate imaging with Compton cameras [2, 3, 5] and experimentalresults 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 Comptoncamera imaging [40]. This technique uses the fact that the intersection of a Compton scatter conewith a sphere is a circle. The sphere is stereographically projected onto a 2-D plane for applicationof 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 fastenough for routine clinical application and merits more detailed study and comparison with listmodemaximum 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 withpositron-emitting tracers [41]. Coincidences will be detected between an intrarectal probe and anexternal detector panel. The internal probe will consist of detector arrays with thin positionsensitiveavalanche photodiode arrays that detect scintillation events from the side of thescintillation crystals in order to obtain depth of interaction information [42].Image reconstruction will be performed using an iterative algorithm that models thedetection of coincidence events along lines of response (LORs) between any element in theexternal detector array and any subcrystal element in the internal probe. The dense web of LORswill enable high resolution to be achieved, though there will inevitably be some blurring due tothe lack of complete angular sampling. This could potentially be mitigated by rotating theexternal detector array around the patient or, at increased cost, by having multiple panels thatsurround the patient. Depending on imaging time, source activity and tracer biodistribution, listmodeimage reconstruction may be computationally efficient if only a fraction of the LORs arepopulated with events.

3.5. Discussion

Statistical iterative image reconstruction methods such as MLEM or MAP methods, andtheir variations, are widely used for prostate image reconstruction. The key to their success ismodeling photon transport and data acquisition and the Poisson statistics of nuclear decay. Theyhave the flexibility to model a variety of detector and acquisition geometries have proven to berobust. List-mode algorithms are advantageous for settings where there are no recorded eventsfor 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 areless likely to be the method of choice for special purpose instrumentation. A possible exceptionmay be the case of Compton imaging with a high number of detected events, though evaluationsand a comparison between the newly developed filtered backprojection method and iterativestatistical methods are needed.

4. Future perspectives

4.1. Algorithms and data analysis

Predicting image reconstruction algorithm development for dedicated prostate imaging isdifficult, though image reconstruction and detector developments in other areas of nuclearmedicine may provide some insight into future applications for prostate imaging.The iterative image reconstruction approach permits almost arbitrary new detectorconfigurations for SPECT and PET. For example, flexible positioning of the detector heads hasbeen investigated for breast-specific gamma imaging [17] and a similar approach may be feasiblefor prostate imaging. The LBNL prototype prostate imager could be augmented by addingadditional detector modules between the legs of the patient. The modular design of theseresearchers’ iterative reconstruction code would allow modified detector configurations to bemodeled easily in the system matrix.Tracking and incorporating torso motion information into image reconstruction may provevaluable for achieving improved resolution, which is particularly important in assessing whethercancer has spread outside the prostate capsule. Bayesian priors using anatomical informationfrom other modalities, e.g. ultrasound, x-ray CT or magnetic resonance imaging, have not yetbeen applied to prostate imaging, though the use of transrectal ultrasound from a dual modalityPET/ultrasound study could be used to provide boundary constraints for image reconstruction orto 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 mayprove useful for fast image reconstruction for detectors built with partial rings of detectorsaround 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 andsuch efforts are important. For example, the use of non-Gaussian priors for MAP imagereconstruction was investigated for prostate study simulations with an82.6 cm diameter ring PETsystem 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 orquantitation of small lesions [45]. A recent simulation study of statistical image reconstructionmethods for a dedicated prostate imager compared a conventional quadratic penalty functionyielding anisotropic image resolution with a Gaussian post-smoothed MLEM approach yieldingisotropic resolution for tasks of lesion detection and region of interest quantitation. The resultsshowed 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 anduptake-washout parameters will be provided for some research studies at academic medicalcenters, 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 enablemore sophisticated modeling of detector physics in image reconstruction, though parameterizedsystem 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 toplay 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 nuclearmedicine imaging systems, e.g. resolution, sensitivity, signal-to-noise ratio (SNR) and noiseequivalent count rate (NECR). For example, the SNR and NECR have been used to study septadesign for a dedicated prostate imager [12]. An as yet unresearched area is the use of multiplepinholes or coded apertures for SPECT prostate imaging. These collimation methods have thepotential to improve the sensitivity/resolution/SNR/detection tradeoffs, however they must beevaluated against optimally designed parallel hole or converging beam collimators. Analytictools such as the linearized local impulse response [47] and Cramer-Rao bounds for variance resolutiontradeoffs [48] that use the Fisher information matrix [49] are being used more widelyin nuclear medicine imager design and evaluation and may be of value in the development ofdedicated prostate imagers.

5. Conclusions

Iterative statistical image reconstruction algorithms provide a framework for reconstructingprostate images from a wide variety of dedicated imagers and acquisition geometries for PETand SPECT. Analytic image reconstruction methods can be fast and may be useful for favorableacquisition geometries. Taking a broader perspective, image reconstruction and data analysismethods can be used to aid the design of equipment and patient imaging protocols and to extractadditional task-dependent physiological information from the acquired data. When imaging theprostate, it is important to consider the combination of detector hardware and imagereconstruction on total system performance. Consideration of the system in its entirety incollaboration with the nuclear medicine physicians and scientists who will use the resultingimages and data analyses should enable improved detection, localization and characterization ofprostate tumors for specific clinical tasks.