Scott J. Wilderman

List-mode maximum likelihood reconstruction of Compton scatter camera images in nuclear medicine

A Maximum Likelihood (ML) image reconstruction technique using list-mode data has been applied to Compton scattering camera imaging. List-mode methods are appealing in Compton camera image reconstruction because the total number of data elements in the list (the number of detected photons) is significantly smaller than the number of possible combinations of position and energy measurements, leading to a much smaller problem than that faced by traditional iterative reconstruction techniques. For a realistic size device, the number of possible detector bins can be as large as 10 billion per pixel of the image space, while the number of counted photons would typically be a very small fraction of that. The primary difficulty in applying the list-mode technique is in determining the parameters which describe the response of the imaging system. In this work, a simple method for determining the required system matrix coefficients is employed, in which a back-projection is performed in list-mode, and response coefficients determined for only tallied pixels. Projection data has been generated for a representative Compton camera system by Monte Carlo simulation for disk sources with hot and cold spots and energies of 141, 364, and 511 keV, and reconstructions performed.

C-SPRINT: a prototype Compton camera system for low energy gamma ray imaging

An electronically-collimated imaging system is being built using pixellated, low-noise, position-sensitive silicon as the first detector, and a sodium iodide scintillation detector ring as the second detector. The system consists of a single 3/spl times/3/spl times/0.1 cm/sup 3/ silicon pad detector module with 1 keV FWHM (noise-limited) energy resolution centered at the front face of a 50 cm diameter, 10 cm long NaI detector annulus. Custom acquisition and timing electronics have been manufactured to minimize system dead time. Monte Carlo modeling is used to predict system sensitivity and position resolution. Simulations using the existing setup show angular uncertainties of 4.1/spl deg/ and 2.1/spl deg/ FWHM for /sup 99m/Tc and /sup 131/I point sources, respectively (7.2 mm and 3.7 mm at 10 cm). Sensitivity can be improved by more than a factor of a hundred over the existing setup by stacking five 1 mm thick 9/spl times/9 cm/sup 2/ silicon arrays and redesigning the second detector geometry to accept a wider range of scattering angles. Lower bound calculations show that our electronically-collimated camera system challenges current mechanically-collimated systems for both /sup 99m/Tc and /sup 131/I despite the deleterious effects of Doppler broadening. Preliminary measurements show a timing resolution of 41 ns FWHM between the silicon detector and a single SPRINT module.

131I-Tositumomab Radioimmunotherapy: Initial Tumor Dose–Response Results Using 3-Dimensional Dosimetry Including Radiobiologic Modeling

For optimal treatment planning in radionuclide therapy, robust tumor dose–response correlations must be established. Here, fully 3-dimensional (3D) dosimetry was performed coupling SPECT/CT at multiple time points with Monte Carlo–based voxel-by-voxel dosimetry to examine such correlations. Methods: Twenty patients undergoing 131I-tositumomab for the treatment of refractory B-cell lymphoma volunteered for the study. Sixty tumors were imaged. Activity quantification and dosimetry were performed using previously developed 3D algorithms for SPECT reconstruction and absorbed dose estimation. Tumors were outlined on CT at multiple time points to obtain absorbed dose distributions in the presence of tumor deformation and regression. Equivalent uniform dose (EUD) was calculated to assess the biologic effects of the nonuniform absorbed dose, including the cold antibody effect. Response for correlation analysis was determined on the basis of the percentage reduction in the product of the largest perpendicular tumor diameters on CT at 2 mo. Overall response classification (as complete response, partial response, stable disease, or progressive disease) used for prediction analysis was based on criteria that included findings on PET. Results: Of the evaluated tumor-absorbed dose summary measures (mean absorbed dose, EUD, and other measures from dose-volume histogram analysis), a statistically significant correlation with response was seen only with EUD (r = 0.36 and P = 0.006 at the individual tumor level; r = 0.46 and P = 0.048 at the patient level). The median value of mean absorbed dose for stable disease, partial response, and complete response patients was 196, 346, and 342 cGy, respectively, whereas the median value of EUD for each of these categories was 170, 363, and 406 cGy, respectively. At a threshold of 200 cGy, both mean absorbed dose and EUD had a positive predictive value for responders (partial response + complete response) of 0.875 (14/16) and a negative predictive value of 1.0 (3/3). Conclusion: Improved dose–response correlations were demonstrated when EUD incorporating the cold antibody effect was used instead of the conventionally used mean tumor-absorbed dose. This work demonstrates the importance of 3D calculation and radiobiologic modeling when estimating absorbed dose for correlation with outcome.

Improved modeling of system response in list mode EM reconstruction of Compton scatter camera images

An improved List Mode EM method for reconstructing Compton scattering camera images has been developed. First, an approximate method for computation of the spatial variation in the detector sensitivity has been derived and validated by Monte Carlo computation. A technique for estimating the relative weight of system matrix coefficients for each gamma in the list has also been employed, as has a method for determining the relative probabilities of emission having some from pixels tallied in each list-mode back-projection. Finally, a technique has been developed for modeling the effects of Doppler broadening and finite detector energy resolution on the relative weights for pixels neighbor to those intersected by the back-projection, based on values for the FWHM of the spread in the cone angle computed by Monte Carlo. Memory issues typically associated with list mode reconstruction are circumvented by storing only a list of the pixels intersected by the back-projections, and computing the weights of the neighboring pixels at each iteration step. Simulated projection data has been generated for a representative Compton camera system (CSPRINT) for several source distributions and reconstructions performed. Reconstructions have also been performed for experimental data for distributed sources.

3D image reconstruction for a Compton SPECT camera model

Proposes a 3D image reconstruction algorithm for a 3D Compton camera being developed at the University of Michigan. The authors present a mathematical model of the transition matrix of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemispheres. By using this sampling pattern the system matrix is reduced to a product of a (approximately) block circulant matrix and a sparse interpolation matrix. This representation reduces the very high storage and computation requirement inherent to 3D reconstruction using transition matrix inversion methods. The authors geometrically optimize their hemispherical sampling and propose a 3D volumetric interpolation. Finally, the authors present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective.

Microfocus X-ray sources for 3D microtomography

Abstract An analytic model for the performance of cone beam microtomography is described. The maximum power of a microfocus X-ray source is assumed to be approximately proportional to the focal spot size. Radiation flux penetrating the specimen is predicted by a semi-empirical relation which is valid for X-ray energies less than 20 keV. Good signal to noise ratio is predicted for bone specimens of 0.1 to 10 mm when scanned at the optimal energy. A flux of about 1 × 10 10 photons/mm 2 /s is identified for 0.2 mm specimens. Cone beam volumetric microtomography is found to compare favorably with synchrotron based methods.

Fast algorithm for list mode back-projection of Compton scatter camera data

A fast algorithm is presented for back-projection of Compton camera projection data in a list mode fashion for which the number of operations per photon per image slice scales at less than the dimension of the image space. The method focuses on the mesh of grid lines which delineate pixel (or voxel) boundaries, rather than on the pixels themselves, and involves computation of the intersection of back-projected Compton cones with just the image space boundaries and those grid lines near the boundary intersection points for each plane of the image space. Depending on the orientation of the back projected cone and the image grid lines, between 4 and N+4 determinations (by quadratic solution) of cone/mesh intersections are required per image slice per photon, where N is the dimension of the image space. Thus the total number of floating point operations for this method from 4 to N+4 times the number of operations in solving a quadratic for each photon. Back-projections for tomographic reconstructions can be readily obtained by stepping through the sequence of planes n the image space parallel to the Compton aperture. Back-projected images are presented, using data generated by Monte Carlo simulation of a practical detector configuration and various source distributions.

Development of silicon pad detectors and readout electronics for a Compton camera

Abstract Applications in nuclear medicine and bio-medical engineering may profit using a Compton camera for imaging distributions of radio-isotope labelled tracers in organs and tissues. These applications require detection of photons using thick position-sensitive silicon sensors with the highest possible energy and good spatial resolution. In this paper, research and development on silicon pad sensors and associated readout electronics for a Compton camera are presented. First results with low-noise, self-triggering VATAGP ASICs are reported. The measured energy resolution was 1.1 keV FWHM at room temperature for the 241 Am photo-peak at 59.5 keV .

Use of Integrated SPECT/CT Imaging for Tumor Dosimetry in I-131 Radioimmunotherapy: A Pilot Patient Study

Integrated systems combining functional (single-photon emission computed tomography; SPECT) imaging with anatomic (computed tomography; CT) imaging have the potential to greatly improve the accuracy of dose estimation in radionuclide therapy. In this article, we present the methodology for highly patient-specific tumor dosimetry by utilizing such a system and apply it to a pilot study of 4 follicular lymphoma patients treated with I-131 tositumomab. SPECT quantification included three-dimensional ordered-subset expectation-maximization reconstruction and CT-defined tumor outlines at each time point. SPECT/CT images from multiple time points were coupled to a Monte Carlo algorithm to calculate a mean tumor dose that incorporated measured changes in tumor volume. The tumor shrinkage, defined as the difference between volumes drawn on the first and last CT scan (a typical time period of 15 days) was in the range 5%-49%. The therapy-delivered mean tumor-absorbed dose was in the range 146-334 cGy. For comparison, the therapy dose was also calculated by assuming a static volume from the initial CT and was found to underestimate this dose by up to 47%. The agreement between tracer-predicted and therapy-delivered tumor-absorbed dose was in the range 7%-21%. In summary, malignant lymphomas can have dramatic tumor regression within days of treatment, and advanced imaging methods allow for a highly patient-specific tumor-dosimetry calculation that accounts for this regression.

Experimental results from the C-SPRINT prototype Compton camera

A Compton camera is being tested for nuclear medicine applications. Our design uses a single 3 cm by 3 cm silicon pad detector as the first detector system, and SPRINT, an array of position-sensitive sodium iodide modules, as the second detector. Experimental results with a /sup 99m/Tc point source show coincidence energy spectra agreeing with theoretical predictions. The coincidence energy spectra for both silicon and SPRINT detectors correspond to the geometry-determined scattering angle range. Recorded energy falls outside of strict geometric limits because of Doppler broadening and detector energy resolution effects. The summed energy peak in the initial data run for a /sup 99m/Tc source has a FWHM energy resolution of 33 keV, primarily due to energy uncertainty in the SPRINT modules. A second data run showed an improvement to 25 keV in summed energy resolution due to careful calibration of, and correction for, significant first and second detector gain non-uniformities. Images generated from the second acquired data set result in a backprojection image resolution of 1.5 cm at a source distance of 10 cm. Analytical and Monte Carlo calculations show a very close agreement of 1.6 cm. Using a list-mode maximum likelihood EM reconstruction algorithm, the image resolution is improved to 7 mm, although the resolution recovery is at the expense of increased noise in the image.