The parameter identification problem attempts to find parameter values that cause the solution of a predictive model to match data. In this work, parameters in cardiovascular and respiratory models are identified. This work’s main contribution is in its application of gradient based optimization techniques and insight into methods to identify parameters that can be estimated given subject specific data.
The models presented in this paper are lumped compartment models of the cardiovascular and respiratory systems. Lumped compartment models treat the cardiovascular and respiratory systems as collections of interconnected compartments transporting blood and exchanging oxygen and carbon dioxide. Using these compartments, a system of ordinary differential equations (ODE) is generated that incorporates several physiological parameters representing vascular resistances, compliances, and tissue metabolic rates. The solution to this ODE system is used to predict cerebral blood flow, systemic arterial blood pressure, and expired carbon dioxide partial pressures, which are then compared to subject data.
Minimizing the two-norm difference between between the result of the predictive model and the experimental data is a non-linear least squares problem. Although the least squares problem is overdetermined, the data do not contain enough information to determine all model parameters. A combination of sensitivity analysis, expert knowledge, and subset selection techniques reduce the number of model parameters estimated.
