Adaptive diffuse domain approach for calculating mechanically induced deformation of trabecular bone

Aland, Sebastian; Landsberg, Christoph; Müller, R; Stenger, Florian; Bobeth, M.; Langheinrich, AC; Voigt, Axel

doi:10.1080/10255842.2012.654606

Cited by 14 publications

(8 citation statements)

References 19 publications

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“…AMDiS is freely available for research and teaching purposes and can be downloaded at http://www.amdis-fem.org. The software has been used for a wide range of problems, from elasticity in bones [50] to multiphase flows with nanoparticles [51].…”

Section: Amdismentioning

confidence: 99%

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Aland

Boden

Hahn³

et al. 2013

Numerical Methods in Fluids

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SUMMARYA pressure‐driven flow of elongated bullet‐shaped bubbles in a narrow channel is known as Taylor flow or bubble‐train flow. This process is of relevance in various applications of chemical engineering. In this paper, we describe a typical simplified experimental setting, with surface tension, density and viscosity as prescribed input parameters. We compare a sharp‐interface model based on a moving grid aligned with the bubble boundary (ALE coordinates) and a diffuse‐interface model where the bubble shape is implicitly given by a phase‐field function. Four independent implementations based on the two modeling approaches are introduced and described briefly. Besides the simulation of the bubble shapes, we compare some resulting quantities such as pressure difference and film widths within the implementations and to existing analytical and experimental results. The simulations were conducted in 2D and 3D (rotationally symmetric). Good accordance of the results indicate the applicability and the usability of all approaches. Differences between the models and their implementations are visible but in no contradiction to theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Amdismentioning

confidence: 99%

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Aland

Boden

Hahn³

et al. 2013

Numerical Methods in Fluids

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“…Later, in [48] and [49] alternate derivations of diffuse-domain methods for such problems were presented. Diffuse-domain methods have been applied to a wide variety of problems that arise, for example, in biology (e.g., [42,50,51,52,53,54,55,56,57,58]), in fluid dynamics (e.g., [59,60,61,62,63]) and in materials science (e.g., [64,55,65,66,67]), just to name a few, and have been implemented using a wide spectrum of methods including in-house finitedifference, finite-element and pseudo-spectral algorithms and software packages such as Matlab, AMDiS [68], MRAG [69], and BSAM [70].…”

Section: Introductionmentioning

confidence: 99%

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

Guo

Lowengrub

2020

Journal of Computational Physics

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The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a larger, regular domain. The original PDE is reformulated using a smoothed characteristic function of the complex domain and source terms are introduced to approximate the boundary conditions. The reformulated equation, which is independent of the dimension and domain geometry, can be solved by standard numerical methods and the same solver can be used for any domain geometry. A challenge is making the method higher-order accurate. For Dirichlet boundary conditions, which we focus on here, current implementations demonstrate a wide range in their accuracy but generally the methods yield at best first order accuracy in , the parameter that characterizes the width of the region over which the characteristic function is smoothed. Typically, ∝ h, the grid size. Here, we analyze the diffuse-domain PDEs using matched asymptotic expansions and explain the observed behaviors. Our analysis also identifies simple modifications to the diffuse-domain PDEs that yield higher-order accuracy in , e.g., O( 2 ) in the L 2 norm and O( p ) with 1.5 ≤ p ≤ 2 in the L ∞ norm. Our analytic results are confirmed numerically in stationary and moving domains where the level set method is used to capture the dynamics of the domain boundary and to construct the smoothed characteristic function.

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“…By comparing the computational stiffness k with the experimental stiffness, an effective microscopic Young's modulus of the bone tissue can be extracted. The FEA was done with parallel in-house software [19,34,35] using the library PETSc [36].…”

Section: Finite-element Analysismentioning

confidence: 99%

Analysis of microscopic bone properties in an osteoporotic sheep model: a combined biomechanics, FE and ToF-SIMS study

Müller

Henß

Kampschulte

et al. 2019

J. R. Soc. Interface.

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The present study deals with the characterization of bone quality in a sheep model of postmenopausal osteoporosis. Sheep were sham operated ( n = 7), ovariectomized ( n = 6), ovariectomized and treated with deficient diet ( n = 8) or ovariectomized, treated with deficient diet and glucocorticoid injections ( n = 7). The focus of the study is on the microscopic properties at tissue level. Microscopic mechanical properties of osteoporotic bone were evaluated by a combination of biomechanical testing and mathematical modelling. Sample stiffness and strength were determined by compression tests and finite-element analysis of stress states was conducted. From this, an averaged microscopic Young’s modulus at tissue level was determined. Trabecular structure as well as mineral and collagen distribution in samples of sheep vertebrae were analysed by micro-computed tomography and time-of-flight secondary ion mass spectrometry. In the osteoporotic sheep model, a disturbed fibril structure in the triple treated group was observed, but bone loss only occurred in form of reduced trabecular number and thickness and cortical decline, while quality of the residual bone was preserved. The preserved bone tissue properties in the osteoporotic sheep model allowed for an estimation of bone strength which behaves similar to the human case.

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Adaptive diffuse domain approach for calculating mechanically induced deformation of trabecular bone

Cited by 14 publications

References 19 publications

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

Analysis of microscopic bone properties in an osteoporotic sheep model: a combined biomechanics, FE and ToF-SIMS study

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