A three-dimensional analysis of a bioprosthetic heart valve

Black, Martin M.; Howard, I. C.; Huang, Xu; Patterson, E. A.

doi:10.1016/0021-9290(91)90304-6

Cited by 72 publications

(46 citation statements)

References 7 publications

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“…Finite element stress analyses of BHV suggests that high exural stresses during valve opening and high tensile stresses during valve closure are associated with failure locations (Hamid et al, 1986;Black et al, 1991;Krucinski et al, 1993). Their accuracy, however, is limited by the use of simplistic isotropic material approximations, since in reality lea¯ets are anisotropic biocomposite materials (Sacks and Chuong, 1998).…”

Section: Introductionmentioning

confidence: 99%

A structural constitutive model for chemically treated planar tissues under biaxial loading

Sacks

2000

Computational Mechanics

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Chemically treated, biologically derived soft collagenous tissues are used extensively in medical devices. To enable prosthesis design through computational methods, physically realistic constitutive models are required. In the present study, a structural approach was utilized that incorporated experimentally measured angular distribution of collagen ®bers. Using biaxial mechanical data from our previous study (Annals of Biomedical Engineering, vol. 26(5), pp. 892±902, 1998), the effective ®ber and matrix stress±strain responses were predicted. The agreement with the experimental data supported the assumption that the mechanical effects of chemical treatment are equivalent to the addition of an isotropic elastic matrix. An important utility of this model is its ability to separate the effects of chemical treatment on the ®bers and matrix. Applications of this approach include utilization in the design of novel chemical treatments that produce speci®c mechanical responses, the study of fatigue damage, and ®nite element implementation for tissue engineering scaffold design.

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Section: Introductionmentioning

confidence: 99%

A structural constitutive model for chemically treated planar tissues under biaxial loading

Sacks

2000

Computational Mechanics

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“…3a. Other models added anisotropic (Kunzelman et al 1993) and nonlinear (Black et al 1991;Howard et al 2003) material descriptions. As with the static case, the dynamic solid-phase case is presently being used with advanced material models and relevant experimental work (Kim et al 2006(Kim et al , 2008, whose simulation results are shown in Fig.…”

Section: Organ-scalementioning

confidence: 99%

“…For these elements, a separate and equally significant effort has been made toward creating a theoretical framework for using shells to model large deformations in general (Dvorkin et al 1995;Betsch et al 1996;Basar and Kintzel 2003;Chapelle et al 2004;Sze et al 2004;Weinberg and Kaazempur-Mofrad 2006) and developing tools for handling complex material models (Klinkel and Govindjee 2002). Bioprosthetic valves have been modeled with shells having aligned-fiber models (Black et al 1991;Carmody et al 2004). Shell models have also been implemented for mitral valve leaflet tissue (Prot et al 2007), including the effect of changes in thickness (Weinberg and Kaazempur-Mofrad 2006).…”

Section: Tissue-scalementioning

confidence: 99%

On the multiscale modeling of heart valve biomechanics in health and disease

Weinberg

Shahmirzadi

Mofrad

2010

Biomech Model Mechanobiol

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Theoretical models of the human heart valves are useful tools for understanding and characterizing the dynamics of healthy and diseased valves. Enabled by advances in numerical modeling and in a range of disciplines within experimental biomechanics, recent models of the heart valves have become increasingly comprehensive and accurate. In this paper, we first review the fundamentals of native heart valve physiology, composition and mechanics in health and disease. We will then furnish an overview of the development of theoretical and experimental methods in modeling heart valve biomechanics over the past three decades. Next, we will emphasize the necessity of using multiscale modeling approaches in order to provide a comprehensive description of heart valve biomechanics able to capture general heart valve behavior. Finally, we will offer an outlook for the future of valve multiscale modeling, the potential directions for further developments and the challenges involved.

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“…Attempts to design more durable prostheses would benefit from understanding the stresses that drive this degradation process. Computational methods of structural analysis have yielded some insights into the mechanics of prosthetic valves and the organs they are modeled after [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], but such approaches typically approximate the effect of the fluid crudely, as a uniform pressure applied to each of the valve leaflets. The goal of studies on computational heart valve FSI, such as those cited earlier, is to account for the effect of the fluid more accurately.…”

Section: Introductionmentioning

confidence: 99%

Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis

Kamensky

Evans

Hsu

2015

Commun. Comput. Phys.

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The purpose of this study is to enhance the stability properties of our recently-developed numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, T.J.R. Hughes, "An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves", Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005-1053] for immersing spline-based representations of shell structures into unsteady viscous incompressible flows. In the cited work, we formulated the fluid-structure interaction (FSI) problem using an augmented Lagrangian to enforce kinematic constraints. We discretized this Lagrangian as a set of collocated constraints, at quadrature points of the surface integration rule for the immersed interface. Because the density of quadrature points is not controlled relative to the fluid discretization, the resulting semi-discrete problem may be over-constrained. Semi-implicit time integration circumvents this difficulty in the fully-discrete scheme. If this time-stepping algorithm is applied to fluid-structure systems that approach steady solutions, though, we find that spatially-oscillating modes of the Lagrange multiplier field can grow over time. In the present work, we stabilize the semi-implicit integration scheme to prevent potential divergence of the multiplier field as time goes to infinity. This stabilized time integration may also be applied in pseudo-time within each time step, giving rise to a fully implicit solution method. We discuss the theoretical implications of this stabilization scheme for several simplified model problems, then demonstrate its practical efficacy through numerical examples. In the cited work, we formulated the fluid-structure interaction (FSI) problem using an augmented Lagrangian to enforce kinematic constraints. We discretized this Lagrangian as a set of collocated constraints, at quadrature points of the surface integration rule for the immersed interface. Because the density of quadrature points is not controlled relative to the fluid discretization, the resulting semi-discrete problem may be over-constrained. Semi-implicit time integration circumvents this difficulty in the fully-discrete scheme. If this time-stepping algorithm is applied to fluid-structure systems that approach steady solutions, though, we find that spatially-oscillating modes of the Lagrange multiplier field can grow over time. In the present work, we stabilize the semi-implicit integration scheme to prevent potential divergence of the multiplier field as time goes to infinity. This stabilized time integration may also be applied in pseudo-time within each time step, giving rise to a fully implicit solution method. We discuss the theoretical implications of this stabilization scheme for several simplified model problems, then demonstrate its practical efficacy through numerical examples.

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A three-dimensional analysis of a bioprosthetic heart valve

Cited by 72 publications

References 7 publications

A structural constitutive model for chemically treated planar tissues under biaxial loading

A structural constitutive model for chemically treated planar tissues under biaxial loading

On the multiscale modeling of heart valve biomechanics in health and disease

Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis

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