A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

Abstract

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D–0D fluid–structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier–Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier–Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta

Fluid dynamics of an idealized left ventricle: the extended Nitsche's method for the treatment of heart valves as mixed time varying boundary conditions

“…Several models have been formulated in this respect by considering the valves as immersed surfaces in the fluid problem either in a restricted area near the valves [31][32][33][34] or in full left heart models [35]. Several models have been formulated in this respect by considering the valves as immersed surfaces in the fluid problem either in a restricted area near the valves [31][32][33][34] or in full left heart models [35].…”

“…In describing the complex fluid dynamics in the LV, which includes asymmetric vortex structures allowing an efficient filling and a natural redirection towards the aorta, one of the most difficult aspects consists in accounting for the valves in a realistic and physiologically meaningful manner. Several models have been formulated in this respect by considering the valves as immersed surfaces in the fluid problem either in a restricted area near the valves [31][32][33][34] or in full left heart models [35]. In this context, our work focuses on the treatment of the valves as orifices of infinitesimal thickness located on the boundary of the LV domain, formulating a proper set of boundary conditions (BCs) for the Navier-Stokes equations that allows a simplified but realistic treatment of the mitral and aortic valves for the study of the LV fluid dynamics.…”

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

“…Current ways of performing personalization include estimation of fiber directions from imaging modalities such as diffusion MRI [178], as well as data assimilation of cardiac motion from imaging into electromechanics simulations through unscented Kalman filters [164,233]. Meanwhile, in the cardiac fluid dynamics community more and more advanced patient-specific valve models incorporating fluid-structure interaction are being developed [1,73,52,81,148,175,267], and may in the future be incorporated into full-heart computational models to study the joint effect of valve function and cardiac mechanics.…”

Using Discrete Multiphysics Modelling to Assess the Effect of Calcification on Hemodynamic and Mechanical Deformation of Aortic Valve

“…Computational fluid dynamics (CFD) was used to generate patient-specific aortic valve models from patient's medical images by [4] and [5]. Other studies focus [6][7][8][9][10] on investigating the stresses on the valve leaflets excluding the fluid flow behaviour in the model.…”