Ming-Chen Hsu
Assistant Professor
Mechanical Engineering, Iowa State University

Fluid–Structure Interaction Analysis of Bioprosthetic Heart Valves

The aim of this work is to develop a robust and accurate computational fluid–structure interaction (FSI) framework to simulate a tri-leaflet bioprosthetic heart valve (BHV) function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. We propose an immersogeometric method that directly analyzes a spline-based surface representation of the heart valve geometry immersed into a non-boundary-fitted discretization of the surrounding fluid domain. The variational formulation for immersogeometric FSI is derived using an augmented Lagrangian approach. The framework also includes a penalty-based dynamic contact algorithm for shell structures represented by isogeometric surfaces. A hybrid immersogeometric/arbitrary Lagrangian–Eulerian (ALE) methodology is also developed, which allows us to efficiently perform a computation that combines a boundary-fitted, deforming-mesh treatment of the artery with a non-boundary-fitted treatment of the leaflets. We simulate the coupling of the BHV, deforming artery and the surrounding blood flow under physiological conditions through an entire cardiac cycle, demonstrating the effectiveness of the proposed techniques in practical computations.

The importance of including arterial wall deformation in FSI simulation of heart valves is demonstrated by the comparison between rigid- (left) and elastic- (right) wall simulations. The rigid-wall results show large unphysical oscillation in the valve movement. The oscillation is much smaller when arterial wall elasticity is included, which has a compliance effect and can distend to absorb a fluid hammer impact and dissipate the initial kinetic energy to surrounding tissues and interstitial fluids.

A Framework for Designing Prosthetic Heart Valves using Immersogeometric FSI Analysis

Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. We developed a novel framework for designing BHVs using a parametric design platform and immersogeometric FSI analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid immersogeometric/ALE methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is carried out to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area (EOA) and the coaptation area (CA). Finally, the FSI simulation result of a design that balances EOA and CA reasonably well is presented.

References: Valvular FSI

14. Leveraging code generation for transparent immersogeometric fluid–structure interaction analysis on deforming domains. Engineering with Computers, accepted, 2023. https://doi.org/10.1007/s00366-022-01754-y [SharedIt]
13. Effects of membrane and flexural stiffnesses on aortic valve dynamics: identifying the mechanics of leaflet flutter in thinner biological tissues. Forces in Mechanics, 6:100053, 2022.
12. Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. Mechanics Research Communications, 112:103604, 2021.
11. Thinner biological tissues induce leaflet flutter in aortic heart valve replacements. Proceedings of the National Academy of Sciences, 117:19007–19016, 2020.
10. Heart valve isogeometric sequentially-coupled FSI analysis with the space–time topology change method. Computational Mechanics, 65:1167–1187, 2020. [SharedIt]
9. Immersogeometric fluid–structure interaction modeling and simulation of transcatheter aortic valve replacement. Computer Methods in Applied Mechanics and Engineering, 357:112556, 2019.
8. An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves. Journal of Biomechanics, 74:23–31, 2018.
7. A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid–structure interaction analysis. International Journal for Numerical Methods in Biomedical Engineering, 34:e2938, 2018.
6. Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid–thin structure interaction analysis, with application to heart valve modeling. Computers & Mathematics with Applications, 74:2068–2088, 2017.
5. Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines. Computer Methods in Applied Mechanics and Engineering, 314:408–472, 2017.
4. Stability and conservation properties of collocated constraints in immersogeometric fluid–thin structure interaction analysis. Communications in Computational Physics, 18:1147–1180, 2015.
3. Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Computational Mechanics, 55:1211–1225, 2015. [SharedIt]
2. An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves. Computer Methods in Applied Mechanics and Engineering, 284:1005–1053, 2015.
1. Fluid–structure interaction analysis of bioprosthetic heart valves: Significance of arterial wall deformation. Computational Mechanics, 54:1055–1071, 2014. [SharedIt]

References: Others

12. Benchtop characterization of the tricuspid valve leaflet pre-strains. Acta Biomaterialia, accepted, 2022. https://doi.org/10.1016/j.actbio.2022.08.046
11. An in-silico benchmark for the tricuspid heart valve – Geometry, finite element mesh, Abaqus simulation, and result data set. Data in Brief, 39:107664, 2021.
10. Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading. Journal of the Mechanical Behavior of Biomedical Materials, 123:104745, 2021.
9. Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves. Computer Methods in Applied Mechanics and Engineering, 384:113960, 2021.
8. Quantification of load-dependent changes in the collagen fiber architecture for the strut chordae tendineae-leaflet insertion of porcine atrioventricular heart valves. Biomechanics and Modeling in Mechanobiology, 20:223–241, 2021. [SharedIt]
7. A pilot in silico modeling-based study of the pathological effects on the biomechanical function of tricuspid valves. International Journal for Numerical Methods in Biomedical Engineering, 36:e3346, 2020.
6. Mechanics of porcine heart valves’ strut chordae tendineae investigated as a leaflet–chordae–papillary muscle entity. Annals of Biomedical Engineering, 48:1463–1474, 2020. [SharedIt]
5. A deep learning framework for design and analysis of surgical bioprosthetic heart valves. Scientific Reports, 9:18560, 2019.
4. Mechanics of the tricuspid valve—from clinical diagnosis/treatment, in vivo and in vitro investigations, to patient-specific biomechanical modeling. Bioengineering, 6:47, 2019.
3. A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves. Computer Methods in Applied Mechanics and Engineering, 330:522–546, 2018.
2. Computational methods for the aortic heart valve and its replacements. Expert Review of Medical Devices, 14:849–866, 2017.
1. Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials. Computer Methods in Applied Mechanics and Engineering, 291:280–303, 2015.