Use of ridge regression for improved estimation of kinetic constants from PET data

The estimation of parameters in radio-tracer models from positron emission tomography (PET) data by nonlinear least squares (NLS) often leads to results with unacceptable mean square error (MSE) characteristics. The introduction of constraints on parameters has the potential to address this problem. We examine a ridge regression technique that augments the standard NLS criterion by the addition of a term which penalizes estimates which deviate from physiologically reasonable values. A variation on a plug-in methodology of Hoerl et al. (1975) is examined for data-dependent selection of the degree of reliance to place on the penalizing term. A simulation study is carried out to evaluate the performance of this approach in the context of estimation of kinetic constants in the three-compartment model used to analyze data from PET studies with fluoro-deoxyglucose (FDG). The results show that, over a range of realistic noise levels, the ridge regression procedure can be expected to reduce the root MSE of parameter estimates by 60%. This result is not found to be substantially dependent on the precise formulation of the penalty function used. Thus, the use of ridge regression for the estimation of kinetic parameters in PET studies is thus considered to be a promising tool.