Positron Emission Tomography Compartmental Models: A Basis Pursuit Strategy for Kinetic Modelling

A kinetic modelling approach for the quantification of in vivo tracer studies with dynamic positron emission tomography (PET) is presented. The approach is based on a general compartmental description of the tracer’s fate in vivo and determines a parsimonious model consistent with the measured data. The technique involves the determination of a sparse selection of kinetic basis functions from an overcomplete dictionary using the method of basis pursuit denoising. This enables the characterization of the systems impulse response function from which values of the systems macro parameters can be estimated. These parameter estimates can be obtained from a region of interest analysis or as parametric images from a voxel based analysis. In addition, model order estimates are returned which correspond to the number of compartments in the estimated compartmental model. Validation studies evaluate the methods performance against two pre-existing data led techniques, namely graphical analysis and spectral analysis. Application of this technique to measured PET data is demonstrated using [C]diprenorphine (opiate receptor) and [C]WAY-100635 (5-HT1A receptor). Whilst, the method is presented in the context of PET neuroreceptor binding studies, it has general applicability to the quantification of PET/SPET radiotracer studies in neurology, oncology and cardiology.