External tissue support and fluid–structure simulation in blood flows

Abstract

The objective of this work is to address the formulation of an adequate model of the external tissue environment when studying a portion of the arterial tree with fluid-structure interaction. Whereas much work has already been accomplished concerning flow and pressure boundary conditions associated with truncations in the fluid domain, very few studies take into account the tissues surrounding the region of interest to derive adequate boundary conditions for the solid domain. In this paper, we propose to model the effect of external tissues by introducing viscoelastic support conditions along the artery wall, with two-possibly distributed-parameters that can be adjusted to mimic the response of various physiological tissues. In order to illustrate the versatility and effectiveness of our approach, we apply this strategy to perform patient-specific modeling of thoracic aortae based on clinical data, in two different cases and using a distinct fluid-structure interaction methodology for each, namely an Arbitrary Lagrangian-Eulerian (ALE) approach with prescribed inlet motion in the first case and the coupled momentum method in the second case. In both cases, the resulting simulations are quantitatively assessed by detailed comparisons with dynamic image sequences, and the model results are shown to be in very good adequacy with the data.

Reduced Numerical Approximation of Reduced Fluid-Structure Interaction Problems With Applications in Hemodynamics

“…The RFSI model as presented in Colciago et al [1] is an unsteady Navier-Stokes model set on a fixed domain with generalized Robin boundary conditions (For similar models see e.g., [21][22][23][24] Although the RFSI model lives in a fixed domain, it is necessary to define an auxiliary variable which stands for the displacement of the arterial wall d s,h . Using a backward Euler finite difference method for the time derivatives, the fully discrete weak formulation of the RFSI problem is written as follows:…”

“…Unfortunately, this is not possible when considering problem (2). The generalized boundary condition applied on Ŵ derives from a structural model which solution is driven by the pressure condition set on the external boundary in the structural model (see [1,22]). If we solve the reduced system not taking into account the pressure variable, we cannot recover the velocity on the boundary Ŵ and the output functionals that depends on these values (e.g., wall shear stress).…”

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

“…However, Crosetto et al 10 show that for 3-D FSI problems the elastic behavior of external tissues support on the outer arterial wall can be handled by enforcing a Robin boundary condition on Γ 0 S,ext . This approach has been further extended in Moireau et al 30 to include also the viscoelastic response of the tissues, such that the resulting Robin boundary condition for the 3-D FSI problem reads…”

“…In particular, at the best of our knowledge, evidences of the benefit of such a more complex model with respect to simplified problems, e.g., stand-alone 3-D FSI simulations, has been neither directly investigated nor quantified by numerical comparisons in real cardiovascular problems. Moreover, most of the patient-specific cardiovascular applications in the literature does not make use of networks of 1-D arteries to account for the systemic circulation, which instead is condensed by using lumped parameters models directly coupled with the inlets/outlets of the 3-D geometries of the patients (see, e.g., Baretta et al 2 and Moireau et al 30 ).…”

“…In this regard, it is essential to account for the correct boundary data on the the solid wall geometries. This problem has been already addressed by Crosetto et al 10 and Moireau et al 30 for the external surface of the arterial wall, where Robin boundary conditions have been successfully used to account for the elastic and viscoelastic responses of the external tissues. Nevertheless, the values of the empiric tissue parameters appearing at the boundaries is rather difficult to estimate, and neither calibration procedures nor sensitivity analysis to show the effect of the variation of the parameters on the main quantities of interest were provided.…”