Parameter estimation in distributed models of blood-tissue exchange: a Monte Carlo strategy to assess precision

Distributed parameter models of blood-tissue exchange are increasingly used to interpret multiple tracer dilution data in regional kinetic studies. To derive a measure of the precision with which the model parameters are estimated is therefore of paramount importance. The standard approach to deriving precision of estimates does not take into account the fact that some of the model parameters are fixed. Thus, the precision of parameter estimates is not realistic and, in all likelihood, it is overestimated. The aim of this study is to describe a Monte Carlo method devised to obtain a theoretically sound measure of the precision of estimates, which takes into account both measurement error and the uncertainty associated with the fixed parameters. The fixed parameter values are taken from a probability distribution. By letting the fixed parameters vary according to their distribution, a large number of synthetic datasets is generated. Noise is then added. Estimating the parameters in each of these synthetic datasets allows the derivation of a Monte Carlo mean and standard deviation, which provides a realistic measure of precision. The methodology is illustrated for a simulated data case study dealing with the estimation of the capillary permeability-surface area product in a two tracer experiment.