PROcEED: Probabilistic reverse dosimetry approaches for estimating exposure distributions.

Unlabelled: As increasing amounts of biomonitoring survey data become available, a new discipline focused on converting such data into estimates of chemical exposures has developed. Reverse dosimetry uses a pharmacokinetic model along with measured biomarker concentrations to determine the plausible exposure concentrations-- a critical step to incorporate ground-truthing experimental data into a distribution of probable exposures that reduces model uncertainty and variability. At the population level, probabilistic reverse dosimetry can utilize a distribution of measured biomarker concentrations to identify the most likely exposure concentrations (or intake doses) experienced by the study participants.

Comparison of Optimal Design Methods in Inverse Problems.

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times.

Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations.

A Mathematical Model for the First-Pass Dynamics of Antibiotics Acting on the Cardiovascular System.

We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.