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A method for partial volume correction of PET-imaged tumor heterogeneity using expectation maximization with a spatially varying point spread function

Tumor heterogeneities observed in positron emission tomography (PET) imaging are frequently compromised by partial volume effects which may affect treatment prognosis, assessment or future implementations such as biologically optimized treatment planning (dose painting). This paper presents a method for partial volume correction of PET-imaged heterogeneous tumors. A point source was scanned on a GE Discovery LS at positions of increasing radii from the scanner's center to obtain the spatially varying point spread function (PSF). PSF images were fit in three dimensions to Gaussian distributions using least squares optimization. Continuous expressions were devised for each Gaussian width as a function of radial distance, allowing for generation of the system PSF at any position in space. A spatially varying partial volume correction (SV-PVC) technique was developed using expectation maximization (EM) and a stopping criterion based on the method's correction matrix generated for each iteration. The SV-PVC was validated using a standard tumor phantom and a tumor heterogeneity phantom and was applied to a heterogeneous patient tumor. SV-PVC results were compared to results obtained from spatially invariant partial volume correction (SINV-PVC), which used directionally uniform three-dimensional kernels. SV-PVC of the standard tumor phantom increased the maximum observed sphere activity by 55 and 40% for 10 and 13 mm diameter spheres, respectively. Tumor heterogeneity phantom results demonstrated that as net changes in the EM correction matrix decreased below 35%, further iterations improved overall quantitative accuracy by less than 1%. SV-PVC of clinically observed tumors frequently exhibited changes of ±30% in regions of heterogeneity. The SV-PVC method implemented spatially varying kernel widths and automatically determined the number of iterations for optimal restoration, parameters which are arbitrarily chosen in SINV-PVC. Comparing SV-PVC to SINV-PVC demonstrated that similar results could be reached using both methods, but large differences result for the arbitrary selection of SINV-PVC parameters. The presented SV-PVC method was performed without user intervention, requiring only a tumor mask as input. Research involving PET-imaged tumor heterogeneity should include correcting for partial volume effects to improve the quantitative accuracy of results.