Objective: To apply the mathematical techniques of optimal control theory (OCT) to a validated model of the human circulation during cardiopulmonary resuscitation (CPR), so as to discover improved waveforms for chest compression and decompression that maximize the systemic perfusion pressure (SPP). Methods: The human circulatory system is represented by seven difference equations, which describe the pressure changes in systemic vascular compartments caused by chest compression. The forcing term is the intrathoracic pressure generated by the external chest compression, which is taken as the “control” variable for the system. The optimum waveform of this forcing pressure as a function of time, determined from OCT, maximizes the calculated SPP between the thoracic aorta and the superior vena cava over a period of 13.3 sec of continuous chest compression under clinically realistic conditions. Results: The optimal waveform included both compression and decompression of the chest to the maximum allowable extent. Compression-decompression waveforms were rectangular in shape. The frequency of optimal compression-decompression was 90/min. The duty cycle (compression duration / cycle time) was 40 percent. The SPP for the optimum control waveform was 36 mmHg vs. 25 mmHg for standard CPR. Conclusions: OCT suggests that both compression and decompression of the chest are needed for best hemodynamics during CPR.


This is the author-accepted manuscript of Eunok Jung, Suzanne, Lenhart, Vladimir Protopopescu, and Charles F. Babbs, Optimal control theory applied to a difference equation model for cardiopulmonary resuscitation, Mathematical Models and Methods in Applied Sciences, Vol. 15, No. 10, 1519-1531, 2005.
Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, Volume 15, Issue 10, 2005, 1519-1531 DOI 10.1142/S0218202505000856 © World Scientific Publishing Company Mathematical Models and Methods in Applied Sciences


ACD-CPR, Cardiopump®, decompression, duty cycle, impedance, heart arrest, hemodynamics

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