Inverse Finite Element Characterization of Nonlinear Hyperelastic Membranes

Kyriacou, S.K.; Shah, Aamir S.; Humphrey, Jay D.

doi:10.1115/1.2787301

Cited by 39 publications

(20 citation statements)

References 20 publications

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“…They proposed the nonlinear theory of elastic membranes as an appropriate theoretical framework for saccular aneurysms. Later studies by Kyriacou et al (1997) and Seshaiyer et al (2001) and Seshaiyer and Humphrey (2003) found that the Fung-type anisotropic hyperelastic model described the experimental results well and reported the estimated material parameters. and Shah et al (1998) performed nonlinear finite element analysis on membrane models of idealized axisymmetric saccular aneurysms and investigated the influence of lesion shape on the wall stress distribution.…”

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confidence: 86%

“…Recently, Ma et al (2007) introduced patientspecific geometry reconstructed from computed tomography angiography (CTA) images into finite element models of cerebral aneurysms. They also employed the anisotropic nonlinear constitutive model reported for ICA tissues (Seshaiyer et al 2001;Seshaiyer and Humphrey 2003;Kyriacou et al 1997), making their work a significant step forward towards predicting the wall stress in realistic aneurysms.…”

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confidence: 99%

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Inverse method of stress analysis for cerebral aneurysms

Zhou

Raghavan

2007

Biomech Model Mechanobiol

130

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We present a method for predicting the wall stress in a class of cerebral aneurysms. The method hinges on an inverse formulation of the elastostatic equilibrium problem; it takes as the input a deformed configuration and the corresponding pressure, and predicts the wall stress in the given deformed state. For a membrane structure, the inverse formulation possesses a remarkable feature, that is, it can practically determine the wall tension without accurate knowledge of the wall elastic properties. In this paper, we present a finite element formulation for the inverse membrane problem and perform material sensitivity studies on idealized lesions and an image-based cerebral aneurysm model.

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confidence: 86%

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confidence: 99%

Inverse method of stress analysis for cerebral aneurysms

Zhou

Raghavan

2007

Biomech Model Mechanobiol

130

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“…The approach of an inverse analysis has also been used in several previous works in order to determine parameters pertaining to the material behaviour of isotropic and/or homogeneous structures (Berzi et al 1994;Kyriacou et al 1997;Cohen et al 1998;Soulhat et al 1999;Huang et al 2003;Lu et al 2007, in press). A notable limitation with all these approaches is, however, that several materials are in fact both inhomogeneous and anisotropic.…”

Section: Discussion and Summarymentioning

confidence: 99%

“…Cartilage and intervertebral discs, for example, are two collagenous soft tissues that have been examined by inverse analysis (Laible et al 1994;Cohen et al 1998;Soulhat et al 1999;Huang et al 2003), and aneurysmal arterial tissue has also been analysed by the use of inverse methods (Lu et al 2007, in press). In addition, Kyriacou et al (1997) show that the material behaviour of neoHookean membranes can be characterized by employing the inverse finiteelement (FE) method. However, soft biological tissues are inhomogeneous.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis

Kroon

Holzapfel

2008

Proc. R. Soc. A.

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A new method is proposed for estimating the elastic properties of the inhomogeneous and anisotropic structure of saccular cerebral aneurysms by inverse analysis. The aneurysm is modelled as a membrane and the constitutive response of each individual layer of the passive tissue is characterized by a transversely isotropic strain energy function of exponential type. The collagen fibres in the aneurysm wall are assumed to govern the mechanical response. Four parameters characterize the constitutive behaviour of the tissue: two initial stiffnesses of the collagen fabric in the two in-plane principal directions, one parameter describing the degree of nonlinearity that the collagen fibres exhibit and the other structural parameter, i.e. the angle which defines the orientation of the collagen fibres. The parameter describing the fibre nonlinearity is assumed to be constant, while all others are assumed to vary continuously over the aneurysm surface. Two model aneurysms, with the same initial geometry, boundary and loading conditions, constitutive behaviour and finite-element discretization, are defined: a 'reference model' with known distributions of material and structural properties and an 'estimation model' whose properties are to be estimated. An error function is defined quantifying the deviations between the deformations from the reference and the estimation models. The error function is minimized with respect to the unknown parameters in the estimation model, and in this way the reference parameter distributions are re-established. In order to achieve a robust parameter estimation, a novel element partition method is employed. The accordance between the estimated and the reference distributions is satisfactory. The deviations of the maximum stress distributions between the two models are below 1%. Consequently, the wall stresses in the cerebral aneurysm estimated by inverse analysis are accurate enough to facilitate the assessment of the risk of aneurysm rupture.

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“…ABAQUS [11] is used for the FEM and the Marquardt algorithm [12] is used for the nonlinear regression. We should note that the first part, the contraction, provides a mapping that may be used in itself as a rather simple image normalization map.…”

Section: Normalization Of the Imagementioning

confidence: 99%

A biomechanical model of soft tissue deformation, with applications to non-rigid registration of brain images with tumor pathology

Kyriacou

Davatzikos

1998

Lecture Notes in Computer Science

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Abstract.The finite element method is applied to the biomechanics of brain tissue deformation. Emphasis is given to the deformations induced by the growth of tumors, and to the deformable registration of anatomical atlases with patient images. A uniform contraction of the tumor is first used to obtain an estimate of the shape of the brain prior to the growth of the tumor. A subsequent nonlinear regression method is used to improve on the above estimate. The resulting deformation mapping is finally applied to an atlas, yielding the registration of the atlas with the tumor-deformed anatomy. A preliminary 2D implementation that includes inhomogeneity and a nonlinear elastic material model is tested on simulated data as well as a patient image. The long-term scope of this work is its application to surgical planning systems.

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Inverse Finite Element Characterization of Nonlinear Hyperelastic Membranes

Cited by 39 publications

References 20 publications

Inverse method of stress analysis for cerebral aneurysms

Inverse method of stress analysis for cerebral aneurysms

Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis

A biomechanical model of soft tissue deformation, with applications to non-rigid registration of brain images with tumor pathology

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