“Optimal Control applied to a CPR model with chest and abdominal pressures”

Abstract

Techniques of optimal control are applied to a blood circulation model of cardiopulmonary resuscitation (CPR), which is described by a nonlinear system of seven difference equations. The variables are the pressures in the seven components of the model, namely: abdominal aorta, inferior vena cava, carotid arteries, jugular veins, thoracic aorta, right heart and superior vena cava, and thoracic pump (pulmonary vasculature and left heart). Forcing terms, representing chest and abdominal pressures, act as controls. The controls at two previous time steps give input to the seven pressure components at the current time step, which is a novel feature from the control viewpoint. We seek to maximize the blood flow, as measured by the systemic perfusion pressure, i.e., the pressure difference between the thoracic aorta and the right heart, summed over all the time steps. In principle, an increase in the blood flow would result in an increase of the surviving rates of the CPR procedure. By applying optimal control methods, we characterize the optimal waveforms for external chest and abdominal compression/decompression in terms of the original model coupled with corresponding adjoint equations. Numerical results for several scenarios are given, calculated using an iterative method. The optimal waveforms confirm the positive effects of active decompression and interposed abdominal compression.