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.

Deformations of the BHV from the FSI computation, colored by the maximum in-plane principal strain (MIPE) evaluated on the aortic side of the leaflet. 


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

  1. Wu MCH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks MS, Hsu M-C* (2018) An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valvesJournal of Biomechanics, 74:23–31.
  2. Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJR, Sacks MS, Hsu M-C* (2018) A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid–structure interaction analysisInternational Journal for Numerical Methods in Biomedical Engineering, 34:e2938.
  3. Hsu M-C*, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material modelsComputational Mechanics, 55:1211–1225(Web of Science Highly Cited Paper)
  4. Kamensky D, Hsu M-C*, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valvesComputer Methods in Applied Mechanics and Engineering, 284:1005–1053(Web of Science Highly Cited Paper) 
  5. Hsu M-C*, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid–structure interaction analysis of bioprosthetic heart valves: Significance of arterial wall deformationComputational Mechanics, 54:1055–1071(Web of Science Highly Cited Paper)
© Ming-Chen Hsu 2020