Mathematical model of the cardiovascular system under acceleration stress.

The pooling of blood in the lower part of the human body when it is subjected to longitudinal +Gz acceleration is one of the major reasons for cardiac insufficiency and the consequent impairment of certain important physiological functions. Headache, abdominal pain, change in heart rate, chest pain, impairment of vision, and hemorrhage are some of the manifestations of acceleration trauma. To predict the effects of time-dependent accelerations on the circulation, a mathematical model independent of assumptions extrapolated from normal G conditions must be considered. The model in the present study consists of a closed-loop hydrodynamic system comprising a heart pump, elastic tubes to represent the large arteries and veins, and a baroreceptor feedback mechanism to help to overcome cardiac insufficiency. The governing equations consist of the Navier-Stokes equations for fluid motion in the blood vessels, and equations of motion for time-dependent blood vessel deformation and ventricular contraction derived from nonlinear elasticity theory. In a numerical example, an experimentally measured deceleration profile is used and the calculated aortic flow is compared with the experimental values.