Model Constraints

A typical situation in PET modeling problems is that a simple model with few parameters is often not adequate to describe the tissue concentration curve. However, a more complex model that does adequately describe the data frequently produces parameter estimates that have large uncertainties (standard errors). Specifically, a simple one-compartment, two-parameter model is often insufficient, whereas a two-compartment, four-parameter model is "better" by various statistically significant measures. A number of authors have dealt with this conflict by applying constraints. These entail specifying exact values for certain parameters or defining relationships between the parameters that must be met. In either case, the effect is to reduce the number of parameters that must be determined from the model. If the constraints are accurate (or reasonably so), then the sensitivity of the model data to the remaining parameters is increased and the uncertainty in their estimation is reduced. Often the constraint equations use a priori values for physiological constants based on the presumed interpretation of the model parameters in terms of Michaelis-Menten parameters [90-92]. Alternatively, some parameters may be constrained based on measurements made in other regions [93]. For example, a common approach for receptor-binding tracers is first to analyze a reference region known to have little or no specific binding to determine parameters associated with the magnitude of nonspecific binding. Then, regions with specific binding are analyzed with nonspecific-binding rate constants constrained to equal those estimated in the reference region [81, 94]. Alternatively, additional studies can be performed to aid the estimation process by constraining parameters to be common to the analysis of both studies. For receptor-binding tracers, a study with an inactive enantiomer can be used to determine parameters of nonspecific binding [95,96]. In addition, paired studies with high and low specific activity injections and/or displacement can be performed and analyzed simultaneously with some parameters shared in the models for the two studies [97,98].

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