A Quasi-linear Viscoelastic Constitutive Equation for the Brain: Application to Hydrocephalus

Drapaca, Corina S.; Tenti, G.; Rohlf, Katrin; Sivaloganathan, S.

doi:10.1007/s10659-006-9071-3

Cited by 45 publications

(22 citation statements)

References 39 publications

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“…For surgical applications one can argue that the relaxation constant of tissues such as arteries is low compared to the surgeons actions, making viscoelasticity a less important feature. In brain tissue however, viscoelasticity is a pronounced phenomenon which should for example be modelled by using timedependent coefficients in the Mooney-Rivlin model, as suggested Miller (2005), or by using the QLV-theory with a box-shaped spectrum as a tissue frequency response, described by Drapaca et al (2006). When accurately modelling biomechanical behaviour of ligament or tendons during loading, incorporation of damage, heterogeneity, anisotropy and viscoelasticity are all important, for which the model described by Natali et al (2003Natali et al ( , 2005 is the most complete.…”

Section: Discussionmentioning

confidence: 99%

“…The most common and widely used nonlinear viscoelastic model is the quasi-linear viscoelastic model (QLV-model) of Fung (1993) (Provenzano et al 2002;Drapaca et al 2006). It accounts for elastic nonlinearity of the stress -strain behaviour by factorising the relaxation function Gðx; tÞ into a function of time and a function of strain:…”

Section: Linear Vs Nonlinear Viscoelasticitymentioning

confidence: 99%

“…. Drapaca et al (2006) uses a box-shaped spectrum as a tissue frequency response which leads to the following formula in the time domain:…”

Section: Linear Vs Nonlinear Viscoelasticitymentioning

confidence: 99%

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Soft tissue modelling for applications in virtual surgery and surgical robotics

Famaey

Sloten

2008

Computer Methods in Biomechanics and Biomedical Engineering

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Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided. The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.

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Section: Discussionmentioning

confidence: 99%

Section: Linear Vs Nonlinear Viscoelasticitymentioning

confidence: 99%

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Soft tissue modelling for applications in virtual surgery and surgical robotics

Famaey

Sloten

2008

Computer Methods in Biomechanics and Biomedical Engineering

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“…Then, according to (24), the first Piola-Kirchhoff stress T for incompressible materials under uniaxial deformation can be determined as…”

Section: Uniaxial Test For Incompressible Hyperelastic Materialsmentioning

confidence: 99%

“…This limitation has to be kept in mind when modelling viscoelastic biological tissues with the approaches listed in this paper. However, the results of the hyperelastic modelling could be easily incorporated into more sophisticated models, including the effects of viscosity, anisotropy and others [24,36,61,[71][72][73].…”

Section: Lungmentioning

confidence: 99%

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Wex

Arndt

Stoll

et al. 2015

Biomedical Engineering / Biomedizinische Technik

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Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

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Measurement of the nonlinear mechanical properties of a poly(vinyl alcohol) sponge under longitudinal and circumferential loading

Karimi

Navidbakhsh

2013

J of Applied Polymer Sci

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Poly(vinyl alcohol) sponges (P‐sponges) have been used as a potential implant material for the replacement and repair of soft tissues, including cartilage, liver, and kidney. However, the application of P‐sponges as tissue replacement materials is almost entirely bounded because of a lack of sufficient mechanical properties. In this study, we characterized the mechanical properties of a fabricated poly(vinyl alcohol) sponge (P‐sponge) under a series of longitudinal and circumferential uniaxial loadings. The nonlinear mechanical behavior of the P‐sponge was also computationally investigated with hyperelastic strain energy density functions, that is, the Ogden, Yeoh, Mooney–Rivlin, and Neo‐Hookean models. A hyperelastic constitutive model was selected to best fit the axial behavior of the sponge. The results reveal that the Young's modulus and maximum stress of the P‐sponge in the longitudinal direction were 16 and 17% greater than that in the circumferential direction, respectively. The Yeoh model, in addition, was selected to represent the nonlinear behavior of the poly(vinyl alcohol) material and could be used in future biomechanical simulations of the soft tissues. These results can be used to understand the mechanical properties of spongy materials in different loading directions. In addition, they have implications for ophthalmic and plastic surgeries and wound healing and tissue engineering purposes. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40257.

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A Quasi-linear Viscoelastic Constitutive Equation for the Brain: Application to Hydrocephalus

Cited by 45 publications

References 39 publications

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling for applications in virtual surgery and surgical robotics

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Measurement of the nonlinear mechanical properties of a poly(vinyl alcohol) sponge under longitudinal and circumferential loading

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