Mathematical modeling of aortic valve dynamics during systole

- Mathematical modeling of aortic valve dynamics is given.
- The effects of sinus vortices are included.
- The effects of variable vascular resistance are included.
- Aortic valve opening-closing phases are captured.

We have derived a mathematical model describing aortic valve dynamics and blood flow during systole. The model presents a realistic coupling between aortic valve dynamics, sinus vortex local pressure, and variations in the systemic vascular resistance. The coupling is introduced by using Hill׳s classical semi-spherical vortex model and an aortic pressure-area compliance constitutive relationship. The effects of introducing aortic sinus eddy vortices and variable systemic vascular resistance on overall valve opening-closing dynamics, left ventricular pressure, aortic pressure, blood flow rate, and aortic orifice area are examined. In addition, the strength of the sinus vortex is coupled explicitly to the valve opening angle, and implicitly to the aortic orifice area in order to predict how vortex strength varies during the four descriptive phases of aortic valve motion (fast-opening, fully-opening, slow-closing, and fast-closing). Our results compare favorably with experimental observations and the model reproduces well-known phenomena corresponding to aortic valve function such as the dicrotic notch and retrograde flow at end systole. By invoking a more complete set of physical phenomena, this new model will enable representation of pathophysiological conditions such as aortic valve stenosis or insufficiency, making it possible to predict their integrated effects on cardiac load and systemic hemodynamics.