A mathematical high time resolution model of the arterial system under extracorporeal circulation

The purpose of the following study was to establish a computer-generated model of the hemodynamic effects of pulsatile extracorporal perfusion describing flow and pressure parameters in the body for any given input flow patterns.

The human arterial tree was delineated according to a 128-branch model encompassing bifurcations and linear physical properties of the arterial walls. The distribution of flow and pressure waves was calculated based on a refined 3-element windkessel model. Autoregulatory mechanisms of brain and kidneys were implemented.

By providing a simulated, "pump-generated" flow curve as the input signal to the system, the model was able to create and display flow and pressure curves at a high time resolution in each part of the systemic circulation including reflection phenomena throughout any observation period chosen. The hemodynamic effects of different pump-flow patterns, age, variations in hematocrit, hypothermia and occlusion of arterial branches, like the renal artery, could be simulated.

In an attempt to get closer to a mathematically based regulation of heart-lung machines, this model of computer generated extracorporeal circulation provides an initial step. Ongoing research is required for implementation of metabolic conditions and continuous approximation of the model of the real physiologic or pathologic situation.