Determining the finite elasticity reference state from a loaded configuration

Rajagopal, Vijay; Chung, Jae-Hoon; Bullivant, David; Nielsen, Poul M. F.; Nash, Martyn P.

doi:10.1002/nme.2045

Cited by 65 publications

(36 citation statements)

References 11 publications

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“…To estimate the stress at end-diastole and provide an appropriate stress/strain relationship for the myocardium under passive loading, it is important to identify the undeformed state of the heart. Using the techniques outlined in Nordsletten et al and Rajagopal et al [15,53], the undeformed state of the myocardium was estimated assuming a maximal applied pressure at end-diastole of 3 kPa. This undeformed configuration was used as the reference domain, s , in the ventricular simulations.…”

Section: Undeformed Myocardial Statementioning

confidence: 99%

Modelling left ventricular function under assist device support

McCormick

Nordsletten

Kay

et al. 2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYNumerical simulations provide a unique approach for investigating the impact of left ventricular assist devices (LVADs) on the pump function of the heart. To this end, the fictitious domain (FD) method was incorporated within a non-conforming coupled fluid-solid mechanics solver creating a model capable of capturing the full range of cardiac motion under LVAD support, including contact of the cannula with the ventricular wall. To demonstrate and verify the properties of the applied method, convergence studies were performed showing linear convergence for both a fluid only problem with an immersed rigid body, as well as a fluid-solid coupled problem with a fluid immersed rigid body interacting with the coupled elastic solid. The model was implemented on a left ventricular (LV) geometry constructed from human MRI data. Simulations were performed to compare LV function with an FD prescribed LVAD cannula and with a cannula applied as a Dirichlet boundary. Good agreement was observed between the simulations for myocardial deformation, major flow features and rates of energy transfer. Finally, an LV simulation was performed to bring the ventricular wall into contact with the cannula, demonstrating the applicability of the model to investigating LV function under LVAD support.

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Section: Undeformed Myocardial Statementioning

confidence: 99%

Modelling left ventricular function under assist device support

McCormick

Nordsletten

Kay

et al. 2011

Int. J. Numer. Meth. Biomed. Engng.

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“…28,29,37 We have also chosen to neglect the initial stress in the prone breast and approximate the unloaded state by reversing the load due to gravity. Other researchers have modeled the stress-free reference state by solving an iterative 27 or reverse problem, 26,27 which increases the complexity of the model. Another simplification was not to attempt to model any selfcontact between the breast and itself.…”

Section: Discussionmentioning

confidence: 99%

“…24 Some of these FE methods also model the stress-free reference state to account for the unknown distribution of the initially loaded state. 26,27 Our methodology is more aligned with earlier generation breast finite-element models, with a particular emphasis on ease of use and model robustness. Corresponding mammograms or compressed image data were not available for the bCT dataset used in our study.…”

Section: B Finite-element (Fe) Breast Modelsmentioning

confidence: 99%

“…Others have modeled the stress-free reference state by modeling the buoyance of the breast (physically or with a hydrostatic pressure) 20 or by solving an iterative 27 or reverse problem. 26,27 One G was applied in both the posterior and vertical directions to model the patient in a standing position, with the breast in contact with the detector. For an MLO view, the detector was set to a 45…”

Section: B2 Gravitymentioning

confidence: 99%

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Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation

Sturgeon

Kiarashi

et al. 2016

Med. Phys.

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Purpose: The authors are developing a series of computational breast phantoms based on breast CT data for imaging research. In this work, the authors develop a program that will allow a user to alter the phantoms to simulate the effect of gravity and compression of the breast (craniocaudal or mediolateral oblique) making the phantoms applicable to multimodality imaging. Methods: This application utilizes a template finite-element (FE) breast model that can be applied to their presegmented voxelized breast phantoms. The FE model is automatically fit to the geometry of a given breast phantom, and the material properties of each element are set based on the segmented voxels contained within the element. The loading and boundary conditions, which include gravity, are then assigned based on a user-defined position and compression. The effect of applying these loads to the breast is computed using a multistage contact analysis in FEBio, a freely available and well-validated FE software package specifically designed for biomedical applications. The resulting deformation of the breast is then applied to a boundary mesh representation of the phantom that can be used for simulating medical images. An efficient script performs the above actions seamlessly. The user only needs to specify which voxelized breast phantom to use, the compressed thickness, and orientation of the breast. Results: The authors utilized their FE application to simulate compressed states of the breast indicative of mammography and tomosynthesis. Gravity and compression were simulated on example phantoms and used to generate mammograms in the craniocaudal or mediolateral oblique views. The simulated mammograms show a high degree of realism illustrating the utility of the FE method in simulating imaging data of repositioned and compressed breasts. Conclusions: The breast phantoms and the compression software can become a useful resource to the breast imaging research community. These phantoms can then be used to evaluate and compare imaging modalities that involve different positioning and compression of the breast. C 2016 American Association of Physicists in Medicine. [http://dx

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“…Roughly speaking, the inverse problems deal with the determination of (bio)mechanical systems-with unknown material properties, geometry, sources or boundary conditions-from the responses to given excitations on their boundaries (e.g. Kavanagh & Clough 1971;Berzi et al 1994;Cailletaud & Pilvin 1994;Govindjee & Mihalic 1996;Delalleau et al 2006;Lei & Szeri 2006;Lu et al 2007;Rajagopal et al 2007). Often, inverse analysis is a convenient approach for use within the field of biomechanics and biomedical engineering, where one has little (or no) control of the geometry and/or the material properties in question.…”

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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Determining the finite elasticity reference state from a loaded configuration

Cited by 65 publications

References 11 publications

Modelling left ventricular function under assist device support

Modelling left ventricular function under assist device support

Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation

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

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