Finite element analysis of nonlinear orthotropic hyperelastic membranes

Kyriacou, S.K.; Schwab, Christoph; Humphrey, J. D.

doi:10.1007/s004660050146

Cited by 19 publications

(15 citation statements)

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“…More recently, Kyriacou and Humphrey applied a finite-element method to solve deformations of nonlinear, anisotropic, and hyperelastic membranes. 13 Their results showed that a rectangular inflated orthotropic membrane will bulge more along the less stiff (cross-fiber) direction, provided that the aspect ratio of the membrane is close to unity. Our results are consistent with these previous experimental and computational findings.…”

Section: Discussionmentioning

confidence: 96%

“…31 Variations on this problem examining fiber-reinforced hyperelastic membranous have observed an anisotropic deformation pattern. 13,23 The similarities of these classic mechanics problems to the biomechanics of the valve led us to hypothesize that the deformation of the anterior mitral leaflet under pressure loading is anisotropic and nonhomogeneous. Based on the results of previous studies, we expect that the cross-fiber stretch will be larger than the fiber stretch, and will increase with distance from the mitral annulus to the center of the mitral orifice.…”

Section: Introductionmentioning

confidence: 99%

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Nonhomogeneous Deformation in the Anterior Leaflet of the Mitral Valve

2004

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In the mitral valve, regional variations in structure and material properties combine to affect the biomechanics of the entire valve. Previous biaxial testing has shown that mitral valve leaflet tissue is highly extensible, and exhibits nonlinear, anisotropic material properties. In this study, experimental measurements of mitral valve leaflet deformation under quasi-static pressure loading were performed on isolated porcine hearts. Biplane video images of markers placed on the anterior leaflet surface were used to reconstruct the 3D position of the markers at several pressure levels over the physiological range. A least-squares finite-element method was used to fit parametric models to the markers and to calculate the deformation over the surface. The results showed that the leaflet deformations were anisotropic, exhibiting a large nonhomogeneous radial stretch and a small circumferential stretch. This information can be used to better understand how the valve deforms under physiological loading, and to help design treatments for valve problems, such as mitral regurgitation.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Nonhomogeneous Deformation in the Anterior Leaflet of the Mitral Valve

2004

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“…They are typically thin-walled and balloonlike in shape. On the basis of (idealized) axisymmetric lesions, Kyriacou, Schwab and Humphrey (1996) and Shah (1997), have developed fully nonlinear (materially and geometrically) finite element models with a Fung-type constitutive law. They investigated a range of (quasi-static) stress-strain behaviors from homogeneous and isotropic to heterogeneous and anisotropic.…”

Section: Finite Element Models In Vascular Solid Mechanicsmentioning

confidence: 99%

Computational Biomechanics of Soft Biological Tissue

Holzapfel

2004

Encyclopedia of Computational Mechanics

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Computational biomechanics of soft biological tissue is increasing our ability to address multidisciplinary problems of academic, industrial, and clinical importance. This article reviews parts of our current knowledge of the biomechanics of soft biological tissue, such as the arterial wall, the heart wall with the heart valves, and the ligament, as well as some of the available computational methods used to analyze them. The inherent complexities of the biological microstructure and function of the respective soft tissue are reviewed briefly, research effort related to the constitutive modeling catalogued, and a representative constitutive model for each considered soft tissue discussed in more detail. An account of residual stresses and biological processes such as growth and remodeling is provided. Finally, a few three‐dimensional finite element models that attempt to explain the integrated function of the respective soft tissue in terms of geometry, structure, and material properties are emphasized.

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“…Kyriacou et al, for example, presented a finite element code to analyze nonlinear orthotropic and hyper-elastic membranes in large deformation problems in 1996 [9]. The membrane strain energy is expressed in terms of the invariants of the Cauchy-Green strain tensor and the orthotropic properties are pre-defined in the "preferred directions".…”

Section: Introductionmentioning

confidence: 99%