Control studies of the cardiopulmonary systems

Chappell, Paul H (1979) Control studies of the cardiopulmonary systems. University of Southampton, Doctoral Thesis.

Abstract

This thesis is concerned with the mathematical modelling of the respiratory and circulatory systems. Equations have been written for the mechanical properties of the two systems and for pulmonary gas exchange. The model equations are dynamic and are represented in state space form. In particular the thesis contains equations for the mechanical coupling between the two systems. Numerical solutions of the system equations have been obtained, and show the effects of changes in parameter values, such as tidal volume, on the circulatory system during artificial ventilation of the lungs. Criterion functions have been formulated which contain squared volume and work terms. Minimisation of these functions using dynamic programming techniques and system equations produce muscle pressures which are exponential functions of time. It is considered that the respiratory and cardiac muscles behave as pumps which are optimally controlled. Model equations for the circulatory system also include equations for the coronary vasculature. Starlings Law of the heart has been investigated and simulated results show good agreement with those of Starling.

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