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Mathematical model of the cardiovascular system under acceleration stress
Insights
This study models blood circulation during Gz acceleration, simulating cardiac insufficiency and physiological effects. The mathematical model accurately predicts aortic flow, aiding in understanding acceleration trauma.
Area of Science:
- Cardiovascular Physiology
- Biomechanical Engineering
- Mathematical Modeling
Background:
- Longitudinal +Gz acceleration causes blood pooling, leading to cardiac insufficiency and physiological impairment.
- Symptoms of acceleration trauma include headache, abdominal pain, altered heart rate, vision impairment, and hemorrhage.
Purpose of the Study:
- To develop a predictive mathematical model for time-dependent accelerations on circulation.
- To create a model independent of assumptions from normal G conditions.
Main Methods:
- A closed-loop hydrodynamic system model was developed, including a heart pump, elastic vessels, and a baroreceptor feedback mechanism.
- Governing equations involved Navier-Stokes equations for fluid dynamics and nonlinear elasticity for vessel/ventricular dynamics.
Main Results:
- The model successfully simulated the effects of Gz acceleration on the cardiovascular system.
- Numerical examples using experimental deceleration profiles showed calculated aortic flow comparable to experimental values.
Conclusions:
- The developed mathematical model provides a robust framework for predicting circulatory responses to acceleration.
- This model can help mitigate cardiac insufficiency and physiological impairments during Gz acceleration exposure.
Abstract:
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.