• Eunok Jung, Charles F Babbs, Suzanne Lenhart, and Vladimir A Protopopescu.
• Department of Mathematics, Konkuk University, Seoul, Republic of Korea.
• Acad Emerg Med. 2006 Jul 1;13(7):715-21.

ObjectivesTo 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 coronary perfusion pressure (CPP).MethodsThe human circulatory system is represented by seven difference equations that describe the pressure changes in systemic vascular compartments that are caused by chest compression. The forcing term is the intrathoracic pressure that is 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, is that which maximizes the calculated CPP between the thoracic aorta and the superior vena cava over a period of 13.3 seconds of continuous chest compression.ResultsThe 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 that was found by OCT was 90 per minute. The optimal duty cycle (compression duration per cycle time) was 40%. The CPP for the optimum control waveform was 36 mm Hg vs. 25 mm Hg for standard CPR.ConclusionsOptimal control theory suggests that both compression and decompression of the chest are needed for best hemodynamics during CPR.

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