Software Verification of New Linear and Nonlinear Models of the Arterial System

Several new mathematical lumped models of the arterial system are developed. Constant, linear, quadratic, cubic, and exponential models for describing the arterial system compliance were derived. It is shown that all mathematical models developed, in general, have good agreement with the experimental data for different cases and different regimes. It was concluded from the simulation results using Simulink that for the normal pressure case, the lumped classical two-element Windkessel model performed rather well. For the hypertension case both the linear and quadratic compliance functions outperformed the Windkessel model for both systolic and diastolic regimes. They performed even better than the exponential compliance model in diastole, but considerably worse than the exponential compliance model in the systolic regime. For the vasodilator case, the cubic function arterial compliance model performs the best in both systolic and diastolic regimes, and the exponential arterial compliance function performs slightly better than the other models.