Computational modeling of mechanical anisotropy in the cornea and sclera

Pinsky, Peter M.; Heide, D. van der; Chernyak, Dimitri

doi:10.1016/j.jcrs.2004.10.048

Cited by 195 publications

(181 citation statements)

References 9 publications

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“…An initial global study of the error as a function of {α, β, µ} showed insensitivity to µ and consequently µ was set to 10.0kP a (the same order of magnitude as cited in [69] for human corneas). (See [76] for a complete sensitivity analysis of the QLV framework).…”

Section: Resultsmentioning

confidence: 99%

“…Following [69], the fibril strain-energy function, W f ibrils , is determined by integrating contributions of individual fibrils w f ibril…”

Section: Methodsmentioning

confidence: 99%

“…However, very few previous investigations have explicitly characterized the viscoelastic response, the notable exception being the study [64]. Moreover, while fiber-matrix models have been developed to describe corneal anisotropy [68,69], there do not to appear to be any viscoelastic cornea models.…”

Section: Introductionmentioning

confidence: 99%

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The mechanics of soft biological composites.

Nguyen

Grazier²,

Boyce³

et al. 2007

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Biological tissues are uniquely structured materials with technologically appealing properties. Soft tissues such as skin, are constructed from a composite of strong fibrils and fluid-like matrix components. This was the first coordinated experimental/modeling project at Sandia or in the open literature to consider the mechanics of micromechanically-based anisotropy and viscoelasticity of soft biological tissues. We have exploited and applied Sandia's expertise in experimentation and mechanics modeling to better elucidate the behavior of collagen fibril-reinforced soft tissues.The purpose of this project was to provide a detailed understanding of the deformation of ocular tissues, specifically the highly structured skin-like tissue in the cornea. This discovery improved our knowledge of soft/complex materials testing and modeling. It also provided insight into the way that cornea tissue is bio-engineered such that under physiologically-relevant conditions it has a unique set of properties which enhance functionality. These results also provide insight into how non-phsyiologic loading conditions, such as corrective surgeries, may push the cornea outside of its natural design window, resulting in unexpected non-linear responses. Furthermore, this project created a clearer understanding of the mechanics of soft tissues that could lead to bio-inspired materials, such as highly supple and impact resistant body armor, and improve our design of human-machine interfaces, such as micro-electricalmechanical (MEMS) based prosthetics. Through this study,

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Section: Resultsmentioning

confidence: 99%

“…Following [69], the fibril strain-energy function, W f ibrils , is determined by integrating contributions of individual fibrils w f ibril…”

Section: Methodsmentioning

confidence: 99%

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The mechanics of soft biological composites.

Nguyen

Grazier²,

Boyce³

et al. 2007

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“…The method allows the use of a black box structural solver if the finite element code is able to update the initial stress tensor field with each iteration [19]. A similar approach of prestressing was used earlier by Pinsky et al to include the internal stress state in the cornea under the presence of the full intraocular pressure load through a fixed point iteration instead of increasing the pressure incrementally [20].…”

Section: Existing Solution Methods and Limitationsmentioning

confidence: 99%

Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry andin vivostress incorporation

Bols

Degroote

Trachet³

et al. 2013

ESAIM: M2AN

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Abstract.In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasiNewton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.Mathematics Subject Classification. 65D18, 74L15, 49Q10, 65N21, 90C53.

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“…The factor in parenthesis is the pull-back of the fluid pressure through the motion to the reference configuration. For anisotropic porous materials, examples of the strain energy density function W can be found in Gasser et al (2006) and Pinsky et al (2005). The relationship between the total Cauchy stress tensor in equation (6) and the second Piola-Kirchhoff stress tensor in equation (7) is given by…”

mentioning

confidence: 99%

A nonlinear macroscopic multi-phasic model for describing interactions between solid, fluid and ionic species in biological tissue materials

Pinsky

2010

Philosophical Magazine

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To cite this version:Long-Yuan Li, Peter Pinsky. A nonlinear macroscopic multi-phasic model for describing interactions between solid, fluid and ionic species in biological tissue materials. Philosophical Magazine, Taylor Francis, 2010, 91 (2) Abstract -This paper presents a nonlinear, macroscopic multi-phasic model for describing the interactions between solid, fluid, and ionic species taking place in porous materials. Governing equations are derived based on the nonlinear theories of solid mechanics, linear flow theory of Newtonian fluids, and theory of irreversible thermodynamics for the transport of ions and ionic solutions. The model shows that the transport coupling between ions and ionic solution exists only when the porous material has a membrane-like feature which could be inside the material or on the material boundaries. Otherwise, the coupling occurs only between the solid and fluid phases and the transport of ionic species will have no effect on the macroscopic stresses, strains and displacements of the porous material. As an application of the present multi-phasic model, a numerical example of the human cornea under the shock of NaCl hypertonic solution applied to its endothelial surface is presented. This is a typical example of how ionic transport induces swelling in biological tissues. The results obtained from the present multi-phasic model demonstrate that the mechanical properties of the tissue have important influence on the swelling of the cornea. Without taking into account this influence, the predicted swelling may be exaggerated.

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Computational modeling of mechanical anisotropy in the cornea and sclera

Abstract: The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.

Cited by 195 publications

References 9 publications

The mechanics of soft biological composites.

The mechanics of soft biological composites.

Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry andin vivostress incorporation

A nonlinear macroscopic multi-phasic model for describing interactions between solid, fluid and ionic species in biological tissue materials

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