Parameter Estimation for Linear Compartmental Models—A Sensitivity Analysis Approach

Linear compartmental models are useful, explanatory tools, that have been widely used to represent the dynamic behavior of complex biological systems. This paper addresses the problem of the numerical identification of such models, i.e., the estimation of the parameter values that will generate predictions closest to experimental observations. Traditional local optimization techniques find it difficult to arrive at satisfactory solutions to such a parameter estimation problem, especially when the number of parameters is large and/or few data are available from experiments. We present herewith a method based on a prior sensitivity analysis, which enables division of a large optimization problem into several smaller and simpler subproblems, on which only sensitive parameters are estimated, before the whole optimization problem is tackled from starting points that are already close to the optimum values. This method has been applied successfully to a linear 13-compartment, 21-parameter model describing the postprandial metabolism of dietary nitrogen in humans. The effectiveness of the method has been demonstrated using simulated and real data obtained in the intestine, blood and urine of healthy humans after the ingestion of a [15N]-labeled protein meal.