Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe fluid-structure interaction models of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employ a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. We develop both an idealized model of the root with three-fold symmetry of the aortic sinuses and valve leaflets, and a more realistic model that accounts for the differences in the sizes of the left, right, and noncoronary sinuses and corresponding valve cusps. As in earlier work, we use fiber-based models of the valve leaflets, but this study extends earlier IB models of the aortic root by employing incompressible hyperelastic models of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backwards displacement method that determines the unloaded configurations of the root models. Our models yield realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations demonstrate that IB models of the aortic valve are able to produce essentially grid-converged dynamics at practical grid spacings for the high-Reynolds number flows of the aortic root

Magnitude and return time of the reflected wave: the effects of large artery stiffness and aortic geometry

Background: Increased large artery stiffness is a major determinant of systolic pressure and indicator of cardiovascular events. The reflected wave, its arrival time (return time) and magnitude, contributes to systolic pressure, and is a supposed indicator of aortic stiffness. With aortic stiffening, the return time is assumed to decrease inversely with PWV as 2L/PWV, where L is the aortic length. However, several studies reported that the inflection point of aortic pressure, a surrogate of return time, varies little with aortic stiffness. Methods: We studied the effects of aortic stiffness on wave reflection in an anatomically accurate arterial model. Return time is time difference of forward, P-f, and backward, P-b, pressure. Return time, inflection and shoulder points, augmentation index, and reflection magnitude (P-b/P-f) were calculated by standard rules. Results: Peripheral resistance does not affect reflection directly, but only through pressure (stiffness) changes. Magnitude of reflected waves depend about equally on aortic geometry (taper, branches) and distal aortic reflection. Therefore, relations of augmentation index and reflection magnitude with stiffness are nonlinear and complex; augmentation index is most sensitive to stiffness. Between PWV 6 and 12 m/s, representing ages of 20-80 years, return time and inflection and shoulder points change differently with stiffness and PWV cannot be derived from them. Pulse pressure is strongly dependent on aortic stiffness. Taper changes return time by a factor 2, but has little effect on reflection magnitude, augmentation index, and inflection point. Conclusion: Accurate quantitative information on arterial stiffness cannot be obtained from reflection parameters. The augmentation index is most sensitive to stiffness change