Stabilizing Control for a Pulsatile Cardiovascular Mathematical Model

In this paper, we develop a pulsatile model for the cardiovascular system which describes the reaction of this system to a submaximal constant workload imposed on a person at a bicycle ergometer test after a period of rest. Furthermore, the model should allow to use measurements for the pulsatile pressure in fingertips which provide information on the diastolic and the systolic pressure for parameter estimation. Based on the assumption that the baroreceptor loop is the essential control loop in this case, we design a stabilizing feedback control for the pulsatile model which is obtained by solving a linear-quadratic regulator problem for the linearization of a non-pulsatile counterpart of the pulsatile model. We also investigate the behavior of the model with respect to changes in the weight of the term in the cost functional for the linear-quadratic regulator problem which penalizes the deviation of the momentary pressure in the aorta from the pressure at the stationary situation which should be obtained.