Mixture modeling for PET neuroreceptor studies

Abstract

Standard compartmental kinetic modeling is commonly used for quantifying PET neuroreceptor binding. Drawbacks with this approach are its reliance on the choice of model and that the nonlinear least squares (NLLS) algorithm used for fitting such models requires substantial computational expense. One alternative to kinetic modeling is the graphical analysis of Logan, et al., (1990) (and its variants), which allows estimation of distribution volume without requiring a specific compartmental model. Another alternative is the method of Gunn, et al. (2002), in which each voxel time-activity curve (TAC) is expressed as a weighted sum of basis functions. We offer another alternative, building on the general mixture modeling framework described by O'Sullivan (1994). In our construction, an approximation to the full unconstrained kinetic model, each voxel TAC is modeled as a sum of exponentials, each convolved with a plasma input function, with the time constant for each term constrained to be the same across all voxels. Thus, each voxel's TAC is modeled as a mixture of sub-TACs, which can roughly be regarded as curves expressing a variety of binding levels. Fitting a mixture model with K components involves computing K coefficients for each voxel and a total of K time constants. For a given choice of time constants, all coefficients can be computed efficiently by applying a nonnegative linear least squares algorithm. With this as a nested step, estimation of time constants may be accomplished using a standard NLLS algorithm. The choice of model order K may be made using standard model selection criteria, such as AIC. By constraining the time constants to be the same for all voxels, this method borrows strength across voxels and thus allows both for the ability to fit approximations to higher order compartmental systems than could not be modeled using one-voxel-at-a-time methods and also for greater stability of estimation of the shared parameters. In addition, this framework allows for the creation of maps of the contributions of each component separately. The computational expense involved in fitting our mixture model is no greater than that required for competing methods and is considerably less than usual kinetic modeling. Through simulation, we demonstrate that the mixture model has good agreement with standard kinetic modeling when estimating binding outcome measures even for general kinetic structure (i.e., no shared time constants in the simulated data). Figure 1 displays a sample VT map from a WAY study using K=4 components