Verified Solution and Propagation of Uncertainty in Physiological Models

We demonstrate here a method for the verified solution of nonlinear ODE models in physiology, computing rigorous bounds on the trajectories of the state variables, based on the ranges of the uncertain parameters. We also demonstrate an approach for the propagation of uncertain probability distributions in one or more model parameters and/or initial conditions. Assuming an uncertain probability distribution (p-box) for each parameter and/or initial condition of interest, we propagate these distributions through the dynamic model to the state variables. As a result, we obtain a p-box describing the probability distribution for each state variable at times of interest. As test problems, we use two physiological models. The first model simulates the metabolism of glucose in diabetic patients. The second is a simulation of long-term starvation that models the human body over time given uncertain metabolic rates. In both problems, comparisons are made with results obtained from Monte Carlo analysis.