A Mathematical Cardiovascular Model with Pulsatile and Non-pulsatile Components

In this study, two existing mathematical cardiovascular models, a non-pulsatile global model and a simplified pulsatile left heart model were investigated, modified and combined. A global lumped compartment cardiovascular model was developed that could predict the pressures in the systemic and pulmonary circulation, and specifically the pulsatile pressures in the the finger arteries where real-time measurements can be obtained. Linking the the average flow with a pulsatile flow is the main difficulty. The left ventricle is assumed to be the source of pulse waves in the system. Modifications were made in the ventricular elastance to model the variations of the stiffness of heart muscles during stress or exercise state. The systemic aorta compartment is added to indicate pressure changes detected by the baroreceptors acting as a control mechanism in the system. Parameters were estimated to simulate an average normal blood pressures during rest and exercise conditions. Introduction In Kappel and Peer (1993) [4], a cardiovascular mathematical model has been developed for the response of the system to a short term submaximal workload. It is based on the four compartment model by Grodin’s mechanical part of the cardiovascular system. It considers all the essential subsystems such as systemic and pulmonary circulation, left and right ventricles, baroreceptor loop, etc. Included in the model are the basic mechanisms such as Starling’s law of the heart, the Bowditch effect and autoregulation in the peripheral regions. The basic control autoregulatory mechanisms were constructed assuming that the regulation is optimal with respect to a cost criterion. The model provided a satisfactory description of the overall reaction of the cardiovascular-respiratory system under a constant ergometric workload imposed on a test person on a bicycle-ergometer. Further studies have been done to include the respiratory system, see Timischl (1998) [13]. The model was also extended and used to describe the response of the cardiovascular-respiratory system under orthostatic stress condition, see for