Application of Gamma Statistics in the Analysis of Kinetic Models for Dynamic PET Time Course Data .

Objectives Accurate representation of the statistical character of PET time-course data can be used to enhance the efficiency of methods used for inferences associated with kinetic models. PET measurements are known to have a pseudo-Poisson structure in which variability is proportional to the mean (e.g. Carson et al 1993). While standard methods for parameter inference take the variance structure into account, via weighted least squares, they fail to address the impact of the non-Guassian and typically skewed nature of PET data. Proper attention to this aspect can impact assessment of goodness of fit including evaluation of residual diagnostics. In formal estimation theory terms addressing this issue could lead to more efficient processing of dynamically acquired PET data.

Methods Dynamic quality assurance data for a physical phantom were acquired on a GE-Discovery (PET-CT) scanner according to a protocol established by the CQIE project of the American College of Radiology Imaging Network (Scheuermann et al, 2013). Histograms of region of interest data were extracted and examined as a function of time-frame and axial position. Gaussian and Gamma distributional forms were evaluated as descriptors for these data. Appropriate modifications for model fitting and normalized residual diagnostics were developed for use in the Gamma distribution framework. These methods were evaluated in the context of the standard compartmental models using time course data from dynamic PET studies with FDG, FLT and H2O.

Results The measured phantom data are strongly supportive of the Gamma distributional form across a range of time-frame durations and axial locations within the scanner field of view. The implementation of model fitting methods that incorporate the Gamma distribution is readily accomplished as an adaptation to existing non-linear weighted least squares techniques. Normalized Gamma-based residuals for kinetic model analysis fits can be evaluated using standard diagnostics tools. An open-source implementation and demonstration of these methods in R is provided. This implementation allows the assessment of the kinetic model and the Gamma distributional form to be routinely accomplished.

Conclusions The Gamma distribution is a well-founded and statistically efficient basis for kinetic modelling of dynamic PET data. Implementation of the approach is straightforward and yields a set of normalized residual diagnostics that can be subjected to standardized and well-understood assessment. The methodology has implication for more elaborate tasks, including image segmenation and parametric imaging mapping. [Supported by SFI/PI 11-1027]

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