During this past grant year we have completed our initial efforts to develop sparse data estimation approaches for stochastic dynamic systems. For the case of multiple-output, multiple-input linear dynamic models with both model and measurement error terms modeled as Gaussian random processes, the joint likelihood of the observations is derived (as a function of the unknown model parameters) and maximized by direct nonlinear optimization. Assuming a continuous dynamic system formulation is used to describe the model under study, the corresponding equivalent discrete time formulation of the model is obtained. Using this equivalent discrete model formulation, the likelihood is defined (up to the unknown model parameters) by the mean and covariance for the vector of observations, both of which can be expressed analytically as functions of the model state matrices and the process and output error covariance matrices. Through Collaborative Project # 4, we recently used this estimation approach to model the cellular kinetics of the antiviral nucleoside analogs PMEA and PMPA. The experimental data from this study involved intracellular measurements of these phosphonate analogs and their mono- and diphosphate derivatives, obtained following systemic administration of the parent compounds in monkeys. Our estimation approach allowed us to decouple the (complicated) systemic disposition processes from the cellular events. The model developed for the metabolism of PMPA and PMEA in lymphoid has help to clarify several of the contradictory reports on the metabolism of these compounds observed in vitro.
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