Biomechanical Modeling of Refractive Corneal Surgery

Alastrué, V.; Calvo, Begoña; Peña, Estefanía; Doblaré, M.

doi:10.1115/1.2132368

Cited by 139 publications

(125 citation statements)

References 28 publications

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“…Exactly the same constitutive model was used in Alastrué et al (2006) and Lanchares et al (2008) for analysing surgical procedures such as photorefractive keratectomy and limbal relaxing incisions, and for analysing the palpation of the cornea (Niroomandi et al 2008). …”

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

Constitutive modelling of arteries

2010

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This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thickwalled circular cylindrical tube in order to illustrate its extension-inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

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Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

Constitutive modelling of arteries

2010

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“…However, the whole eye model may not be efficient because it is highly time consuming and not economical for development and analysis. Alastrue et al (5) analyzed the corneal model with the limbus constrained against displacement. Anderson et al (23) compared the deformation pattern of the entire eye model to the rigid cornea-limbus boundary.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Recently, the use of computational models based on the finite element method has proven to be an effective way for studying corneal mechanics and related diseases (2,6,(11)(12) . These models have been successful in predicting the pre-and postoperative response to eye surgery for myopia, hyperopia, as tigma tism, and keratoconus (5,(13)(14)(15)(16) . The finite element method (FEM) is a numerical technique to obtain approximate solutions for partial differential equations involving physical, thermal, chemical, and other phenomena.…”

Section: Introductionmentioning

confidence: 99%

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Finite element modelling of cornea mechanics: a review

Nejad

Foster

Gongal

2014

Arquivos Brasileiros De Oftalmologia

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The cornea is a transparent tissue in front of the eye that refracts light and facilitates vision. A slight change in the geometry of the cornea remarkably affects the optical power. Because of this sensitivity, biomechanical study of the cornea can reveal much about its performance and function. In vivo and in vitro studies have been conducted to investigate the mechanics of the cornea and determine its characteristics. Numerical techniques such as the finite element method (FEM) have been extensively implemented as effective and noninvasive methods for analyzing corneal mechanics and possible disorders. This article reviews the use of FEM for assessing the mechanical behavior of the cornea. Different applications of FEM in corneal disease studies, surgical predictions, impact simulations, and clinical applications have been reviewed. Some suggestions for the future of this type of modeling in the area of corneal mechanics are also discussed.

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“…Several continuum modelling approaches to describe the anisotropic material properties of soft biological tissues have been suggested in the literature; see, for instance, Almeida & Spilker (1998), the contributions in Cowin & Humphrey (2000), Alastrué et al (2007) and Menzel & Steinmann (2001) for a comparison of two different modelling approaches. While phenomenological formulations are used to consider individual fibre families to be perfectly aligned with pre-defined directions, recent investigations additionally account for the dispersion of fibres; see Gasser et al (2006) for a formulation based on generalized structural tensors and Marquez (2006) in view of experimental investigations to identify the orientation of fibre distributions.…”

Section: Introductionmentioning

confidence: 99%

A microsphere-based remodelling formulation for anisotropic biological tissues

Menzel

Waffenschmidt

2009

Phil. Trans. R. Soc. A.

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Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material's anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

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Biomechanical Modeling of Refractive Corneal Surgery

Cited by 139 publications

References 28 publications

Constitutive modelling of arteries

Constitutive modelling of arteries

Finite element modelling of cornea mechanics: a review

A microsphere-based remodelling formulation for anisotropic biological tissues

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