Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement
Introduction
In the cardiac system, the left ventricle (LV) is responsible for receiving oxygenated blood from the left atrium (LA) and pumping it into the human systemic circulation. The two heart valves associated with the LV, the aortic valve (AV) and the mitral valve (MV), work in coordination to ensure unidirectional flow through the cardiac system. On the left side of the heart, the higher pressure and associated increases in cyclic loading make the AV and MV more susceptible to cardiac diseases than the valves on the right side of the heart [1]. Valvular heart diseases [2] can severely deteriorate the normal function of these valves and fundamentally disrupt the cardiac hemodynamics. For patients with severe valvular diseases, heart valve replacement is one of the most viable intervention options, resulting in around 75,000 prosthetic implants in the United States and around 170,000 to 250,000 implants in the world annually [3], [4]. Recently, surgical bioprosthetic heart valves (BHVs), which are tri-radially symmetric devices that are designed to mimic the anatomy of the AV, have become the predominant choice for valve replacement operations [5]. Although the anatomies of the AV and MV are entirely different, it is a common practice to use the same BHV design (e.g. Medtronic Mosaic valve [6]) for both aortic and mitral valve replacements [7]. While the asymmetry of the native MV is believed to result in a circulatory flow pattern in the LV that aids in the washout of ventricular blood during systole [8], [9], the replacement of the native MV with a symmetric BHV may alter this flow pattern and negatively influence the cardiac hemodynamics [10], [11]. Furthermore, the clinical outcomes after combined aortic and mitral valve surgery are not well known [12]. In an effort to develop an improved understanding of these effects, this work proposes a computational fluid–structure interaction (FSI) framework for the simulation of the LV with both the AV and MV replaced with surgical BHVs.
The simulation of the intricate structures and function of the cardiac system requires suitable modeling and analysis methods that can accurately capture the physical complexity of this system. However, most of the previous LV simulations have utilized simplified assumptions regarding the LV geometry, deformation, or boundary conditions [13], [14], [15], [16], which significantly reduce the feasibility of effectively replicating the in-vivo cardiac motions or hemodynamics. In recent years, vascular simulations (i.e. simulations of blood flows inside the vessels connected to the heart) have reached a relatively mature state [17], [18], [19], [20], [21] with even clinical applications [22], [23], [24], [25]. At the same time, cardiac hemodynamics simulations (i.e. simulations of blood flows in the four chambers of the heart) still face many challenges, despite the advancements that have been made over the last decade [26], [27], [28], [29], [30]. Some of these challenges include obtaining the time-dependent large-scale heart-chamber deformation, resolving the complex hemodynamics, and considering their interactions with the structural mechanics of the heart valves [31]. As a result, realistic and robust numerical modeling of the cardiac system requires advanced FSI formulations and methodologies.
To approach the computational challenges of this complex system, traditional boundary-fitted methods for moving domain simulations, including the Arbitrary Lagrangian–Eulerian (ALE) [32], [33], [34] and Space–Time (ST) [35], [36], [37] methods, have been successfully applied to modeling the hemodynamics of wall-bounded biomedical problems [38], [39], [40], [41], [42]. However, for simulations that consider the geometries and motions of the heart valves, the large structural deformation of the valve leaflets can severely distort the boundary-fitted fluid elements if they are continuously deformed from a single reference configuration of the computational domain. Sophisticated mesh management algorithms are often required [43], [44], [45] to handle this type of problem. In addition, the heart valve experiences contact between the leaflets. Some existing specialized contact algorithms either impose a small distance to separate surfaces that would otherwise come into contact [46] or prescribe locations where the contact would occur [30], [47], [48]. While these assumptions are often sufficient for some idealized scenarios, they are inadequate for general valvular FSI simulations.
In light of these limitations for cardiac applications, immersogeometric analysis (IMGA) [49] was proposed as a geometrically flexible method to model and simulate heart valve FSI problems [50], [51], [52], [53], [54]. This novel method makes direct use of the CAD boundary representation (B-rep) of a complex design structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain [55], [56], [57], [58], [59]. This approach effectively deals with FSI problems involving structures with complex motion that leads to large deformations of the fluid domain, including changes of topology [60], [61]. Algorithms developed for structural contact and impact problems [62], [63] can also be directly adopted in the IMGA simulations. The variational formulation for immersogeometric FSI analysis was derived using a dynamic augmented Lagrangian (DAL) approach to weakly enforce kinematic and traction constraints [64], [65]. A hybrid ALE/IMGA methodology, in which a single computation combines both a boundary-fitted, deforming-mesh treatment of some fluid–structure interfaces and a non-boundary-fitted treatment of others, was also developed under the same framework [50]. A comprehensive review of IMGA and its recent developments and applications in heart valve simulations can be found in Hsu and Kamensky [66].
In this work, based on the different types of deformation present in the LV and BHV subproblems, we formulate an FSI framework in which the LV is treated with a boundary-fitted, deforming-mesh ALE approach and the BHVs are treated with a non-boundary-fitted IMGA approach. Within this hybrid ALE/IMGA concept, a variety of advanced technologies are seamlessly integrated, including geometry modeling [67], fluid dynamics [68], structural mechanics [69], [70], and structural contact/impact [71]. Such a versatile technology is well suited for the multiscale, multiphysics modeling environment of cardiac flows. The detailed geometry and deformation information for the LV are obtained over the complete cardiac cycle from a separate cardiac biomechanics simulation, which is based on the technology proposed in Krishnamurthy et al. [72], and used as an input to the cardiac FSI simulation. A high-quality fluid domain finite element mesh is created and deformed in time in a boundary-fitted fashion following the endocardial surface information obtained from the biomechanics simulation of the LV. Using the corresponding annulus information, we construct two BHVs, one attached to the aortic annulus and one to the mitral annulus, and immerse them into the background LV fluid meshes. These two distinct approaches are integrated within our hybrid ALE/IMGA framework to solve for the complex hemodynamics of the LV coupled to the structural mechanics of the BHVs. Particular emphasis is placed on understanding the alteration in the left ventricular hemodynamic pattern that may result from these valve replacements.
This paper is organized as follows. In Section 2, we present the main constituents of the hybrid ALE/IMGA framework for solving the cardiac and valvular FSI problem. Section 3 details the techniques for obtaining the LV geometry and its time-dependent motion over a complete cardiac cycle, and the problem setup of the ventricular FSI simulation. The results are presented in Section 4, in which we demonstrate and discuss the LV flow pattern after bioprosthetic aortic and mitral valve replacement. Finally, we draw conclusion and motivate future research in Section 5.
Section snippets
Fluid–structure interaction methodology
In this section, we present the main constituents of the hybrid ALE/IMGA FSI framework for simulating cardiac problems. We start with the discussion of the DAL FSI framework. We then provide a comprehensive overview on the numerical formulations for all the subproblems in the FSI system. Finally, we demonstrate how the numerical ingredients are integrated together within the ALE/IMGA framework.
Ventricular fluid–structure interaction simulation
In this section, we present the implementation details for simulating blood flow inside an LV model in which the native AV and MV are replaced with BHVs. Based on the LV motion obtained from a cardiac biomechanics simulation, we use an interactive geometry framework [67] to construct the fluid mesh and BHV models, and specify the boundary conditions of the FSI problem in a complete cardiac cycle.
FSI simulation results
The FSI simulation is carried out for four cardiac cycles in order to achieve a statistically periodic steady state. To evaluate the variations between cycles, the volumetric flow rate entering the mitral inflow tract is monitored and compared between the third and fourth cycles. The L2-norm of flow rate difference between the two cycles is below 3% of the L2-norm of fourth-cycle flow rate. All the results presented in this section are based on the fourth cycle. Several snapshots of the BHV
Conclusions
This study focuses on using advanced hybrid ALE/IMGA modeling and simulation to better understand the hemodynamics in the LV with BHV implants. The structures and kinematics of the BHVs are expected to have a significant influence on the LV hemodynamics. However, the computational challenges presented by such a complex application pose a substantial obstacle for numerical investigations that use classical methods. Such challenges include large-scale structural deformations, as well as
Declaration of Competing Interest
The authors declare no conflict of interest.
Acknowledgments
E.L. Johnson, M.S. Sacks, and M.-C. Hsu were partially supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under award numbers R01HL129077 and R01HL142504. A. Krishnamurthy was partially supported by the same institute under award number R01HL131753 and by the National Science Foundation under award number 1750865. All this support is gratefully acknowledged. We also thank the Texas Advanced Computing Center (TACC) at The University of Texas at Austin
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