Large-scale Bayesian parameter estimation for a three-compartment cardiac metabolism model during ischemia

Abstract

The estimation of a large number of parameters in metabolic systems from few measurements is a difficult and important problem. A three-compartment model of the cellular cardiac metabolism depends on a large number of parameters, many of which are nonphysical. The model consists of a large system of stiff nonlinear ordinary differential equations that describe the dynamics of the concentrations in the three compartments during ischemia. The data are limited to measured concentrations at few observation times, thus making the inverse problem severely under-determined and ill-posed. The problem is modelled in a Bayesian framework where we relate the unknown parameters to the data through conditional probability density functions. This setting allows us to import necessary a priori knowledge about the model into the estimation process to guide us towards a meaningful solution. The methods for the parameter estimation combine numerical methods for unconstrained optimization and Monte Carlo-based statistical sampling techniques.