Optimal Control Theory Applied to a Difference Equation Model for Cardiopulmonary Resuscitation

Abstract

The techniques of optimal control are applied to a validated blood circulation model of cardiopulmonary resuscitation (CPR), consisting of a system of seven difference equations. In this system, the nonhomogeneous forcing term is the externally applied chest pressure acting as the "control". We seek to maximize the blood flow, as measured by the pressure differences between the thoracic aorta and the superior vena cava. The new aspect in this application is that the control values from the two previous time steps are used to calculate the pressures (state variables) at the current time step. We prove the existence and uniqueness of the optimal control and provide a new CPR strategy, with increased blood flow. The characterization of the optimal control is given in terms of the solutions of the circulation model and of the corresponding adjoint system. The numerical results show a significant increase in the blood flow as compared with standard CPR.

Near-optimal Waveforms for Improving Hemodynamic Effects during EDCPR

“…However, a study of CPR results shows that the outcome is partially determined by the deliverance push and blow, confirming the belief of Peter Safar [3]. Therefore, Charles F. Babbs and Eunok Jung et al researched the optimal waveforms for external chest and abdomen compression and decompression during CPR, and they discovered design principles underlying the optimal waveforms [3,4].…”

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