Algorithms for Fluid–Structure Interaction

Abstract

The human body presents several fluid-structure interaction (FSI) problems, such as the operation of the heart and its valves, motion of blood cells in the circulation, peristaltic contractions in the gut, vibration of vocal cords, operation of the lungs during breathing, contraction of the urinary bladder, and a host of others. Modeling such problems and devising computational techniques to solve the governing equations is an increasingly popular and powerful way to understand the behavior of these systems in the healthy and pathological states. Fluid-structure interaction problems in different organ systems can present different challenges. In the presence of blood (i.e., in the cardiovascular system), FSI problems are plagued by numerical stiffness arising from added mass effects, while such constraints are absent in the presence of air (as in the respiratory and voice systems). In addition, at large scales, fluid inertia can play a significant role, leading to unsteady, transitional, and weakly turbulent flows. At small scales (as in blood cells), viscous effects assume importance. This chapter provides a survey of some of the important issues that arise in the cardiovascular system when FSI problems are tackled. Three primary techniques are discussed, viz., the immersed boundary approach, the immersed interface approach, and the sharp interface approach. The suitability of these approaches to specific problems is addressed and example calculations are shown to illustrate the state of the art of FSI in the cardiovascular system.

Patient-specific bicuspid valve dynamics: Overview of methods and challenges

“…While non-invasive imaging modalities make patient-specific modeling a realistic possibility for future clinical use, the process of segmenting images and turning the resulting geometry into a body-fitted or geometrically descriptive mesh for computational analysis is quite time-consuming, and often a major bottleneck in performing such analyses (Dumont et al, 2004; Vigmostad and Udaykumar, 2011). Several groups have developed valuable tools which make segmentation of medical images simpler, and help expedite the meshing process (Steinman et al, 2003; Antiga et al, 2008; Taylor and Steinman, 2010).…”

Dynamics of Flow in a Mechanical Heart Valve: The Role of Leaflet Inertia and Leaflet Compliance

“…5, we plot a schematic of the shape of the bottom side of the leaflet during valve closure and opening when £=500. As it was expected [12,14], the leaflet has a convex curvature during opening, and it preserves this type of curvature until the moment of the maximum opening angle. On the other hand, as the fluid decelerates and the valve closes, the leaflet has a concave curvature.…”

“…Thus, £=500 corresponds to G= 11,940 Pa. According to the work of Vigmostad et al [14], a physiological value for the shear modulus is G = 5520 Pa. Thus, in the present work, the leaflet has a shear modulus, which is twice as large as the physiological value, but it is more compliant than the one used in the work of De Hart et al [12,13] (G=1.5X 10* Pa and G=30,000 Pa, respectively).…”

“…Although they used a coarse mesh, due to memory and CPU-time limitations, their findings were in agreement with experimental results. Recently, Vigmostad et al [14] examined the work of De Hart et al [12] by modeling the leaflet as a flexible rod, which was not allowed to rotate about the point of support. Their findings are in qualitative agreement with the results of De Hart et al as they used a high-resolution mesh and a more compliant leaflet.…”

Computational Mitral Valve Evaluation and Potential Clinical Applications

“…This algorithm strongly couples the interface between the solid and the fluid using sub-iterations between partitioned solvers towards a robust and stable solutions for both solid and fluid. At the interface, an immersed interface-like approach 90,91 has been employed to incorporate the moving leaflets on the fluid as a source term in the momentum equation.…”