Locally constrained mixture representation of dynamic imaging data from PET and MR studies

Dynamic positron emission tomography (PET) studies provide measurements of the kinetics of radiotracers in living tissue. This is a powerful technology which can play a major role in the study of biological processes, potentially leading to better understanding and treatment of disease. Dynamic PET data relate to complex spatiotemporal processes and its analysis poses significant challenges. In previous work, mixture models that expressed voxel-level PET time course data as a convex linear combination of a finite number of dominant time course characteristics (called sub-TACs) were introduced. This paper extends that mixture model formulation to allow for a weighted combination of scaled sub-TACs and also considers the imposition of local constraints in the number of sub-TACs that can be active at any one voxel. An adaptive 3D scaled segmentation algorithm is developed for model initialization. Increases in the weighted residual sums of squares is used to guide the choice of the number of segments and the number of sub-TACs in the final mixture model. The methodology is applied to five data sets from representative PET imaging studies. The methods are also applicable to other contexts in which dynamic image data are acquired. To illustrate this, data from an echo-planar magnetic resonance (MR) study of cerebral hemodynamics are considered. Our analysis shows little indication of departure from a locally constrained mixture model representation with at most two active components at any voxel. Thus, the primary sources of spatiotemporal variation in representative dynamic PET and MR imaging studies would appear to be accessible to a substantially simplified representation in terms of the generalized locally constrained mixture model introduced.