  This paper presents a new method for modeling the mechanics of the aortic
valve, and simulates its interaction with blood. As much as possible, the model
construction is based on first principles, but such that the model is
consistent with experimental observations. We require that tension in the
leaflets must support a pressure, then derive a system of partial differential
equations governing its mechanical equilibrium. The solution to these
differential equations is referred to as the predicted loaded configuration; it
includes the loaded leaflet geometry, fiber orientations and tensions needed to
support the prescribed load. From this configuration, we derive a reference
configuration and constitutive law. In fluid-structure interaction simulations
with the immersed boundary method, the model seals reliably under physiological
pressures, and opens freely over multiple cardiac cycles. Further, model
closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting
the unique features of this model construction, we conduct experiments on
reference configurations, constitutive laws, and gross morphology. These
experiments suggest the following conclusions, which are directly applicable to
the design of prosthetic aortic valves. (i) The loaded geometry, tensions and
tangent moduli primarily determine model function. (ii) Alterations to the
reference configuration have little effect if the predicted loaded
configuration is identical. (iii) The leaflets must have sufficiently nonlinear
material response to function over a variety of pressures. (iv) Valve
performance is highly sensitive to free edge length and leaflet height. For
future use, our aortic valve modeling framework offers flexibility in
patient-specific models of cardiac flow.
