Development and evaluation of convergent and accelerated penalized SPECT image reconstruction methods for improved dose–volume histogram estimation in radiopharmaceutical therapy
Authors: Cheng Lishui , Hobbs Robert F. , Sgouros George , Frey Eric C. 
Published: October 2014

Purpose:Three‐dimensional (3D) dosimetry has the potential to provide better prediction of response of normal tissues and tumors and is based on 3D estimates of the activity distribution in the patient obtained from emission tomography. Dose–volume histograms (DVHs) are an important summary measure of 3D dosimetry and a widely used tool for treatment planning in radiation therapy. Accurate estimates of the radioactivity distribution in space and time are desirable for accurate 3D dosimetry. The purpose of this work was to develop and demonstrate the potential of penalized SPECT image reconstruction methods to improve DVHs estimates obtained from 3D dosimetry methods.Methods:The authors developed penalized image reconstruction methods, using maximum a posteriori (MAP) formalism, which intrinsically incorporate regularization in order to control noise and, unlike linear filters, are designed to retain sharp edges. Two priors were studied: one is a 3D hyperbolic prior, termed single‐time MAP (STMAP), and the second is a 4D hyperbolic prior, termed cross‐time MAP (CTMAP), using both the spatial and temporal information to control noise. The CTMAP method assumed perfect registration between the estimated activity distributions and projection datasets from the different time points. Accelerated and convergent algorithms were derived and implemented. A modified NURBS‐based cardiac‐torso phantom with a multicompartment kidney model and organ activities and parameters derived from clinical studies were used in a Monte Carlo simulation study to evaluate the methods. Cumulative dose‐rate volume histograms (CDRVHs) and cumulative DVHs (CDVHs) obtained from the phantom and from SPECT images reconstructed with both the penalized algorithms and OS‐EM were calculated and compared both qualitatively and quantitatively. The STMAP method was applied to patient data and CDRVHs obtained with STMAP and OS‐EM were compared qualitatively.Results:The results showed that the penalized algorithms substantially improved the CDRVH and CDVH estimates for large organs such as the liver compared to optimally postfiltered OS‐EM. For example, the mean squared errors (MSEs) of the CDRVHs for the liver at 5 h postinjection obtained with CTMAP and STMAP were about 15% and 17%, respectively, of the MSEs obtained with optimally filtered OS‐EM. For the CDVH estimates, the MSEs obtained with CTMAP and STMAP were about 16% and 19%, respectively, of the MSEs from OS‐EM. For the kidneys and renal cortices, larger residual errors were observed for all algorithms, likely due to partial volume effects. The STMAP method showed promising qualitative results when applied to patient data.Conclusions:Penalized image reconstruction methods were developed and evaluated through a simulation study. The study showed that the MAP algorithms substantially improved CDVH estimates for large organs such as the liver compared to optimally postfiltered OS‐EM reconstructions. For small organs with fine structural detail such as the kidneys, a large residual error was observed for both MAP algorithms and OS‐EM. While CTMAP provided marginally better MSEs than STMAP, given the extra effort needed to handle misregistration of images at different time points in the algorithm and the potential impact of residual misregistration, 3D regularization methods, such as that used in STMAP, appear to be a more practical choice.