Multi-level μ-Finite Element Analysis for Human Bone Structures

Arbenz, Peter; Lenthe, G. Harry van; Mennel, Uche; Müller, Ralph; Sala, Marzio

doi:10.1007/978-3-540-75755-9_30

Cited by 22 publications

(10 citation statements)

References 13 publications

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“…For planar graphs a PTAS [2] has been found, while for trees an optimum solution can be computed in O(n 2 ) time [6,7]. Our motivation to study the bisection problem comes from the need to parallelise a finite element computation of a human bone structure model in order to diagnose osteoporosis [1]. In such an application the aim is to distribute the data, modelled by the vertices (of a graph G), evenly onto a given number p corresponding closed curve of one of them both contains points belonging to the interior and to the exterior area into which the other cycle divides the plane.…”

Section: Comparing Optimal With Restricted Cutsmentioning

confidence: 99%

“…if β denotes its boundary then β ∩ P = ∅. If β only contains orthogonal lines 1 We will use calligraphic capital letters to denote areas in the plane such as polygons or 3 we refer to P as orthogonal. We call P simple if any two points in P lie on a closed curve in P which can be shrunk to a point without leaving P.…”

Section: Comparing Optimal With Restricted Cutsmentioning

confidence: 99%

See 1 more Smart Citation

Restricted Cuts for Bisections in Solid Grids: A Proof via Polygons

Feldmann

Das

Widmayer

2011

Graph-Theoretic Concepts in Computer Science

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Section: Comparing Optimal With Restricted Cutsmentioning

confidence: 99%

Section: Comparing Optimal With Restricted Cutsmentioning

confidence: 99%

Restricted Cuts for Bisections in Solid Grids: A Proof via Polygons

Feldmann

Das

Widmayer

2011

Graph-Theoretic Concepts in Computer Science

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“…Such models can be solved using dedicated numerical packages, especially designed for this kind of model. Compared to commercial FE solvers, such solvers typically are restricted to many simplifications regarding the models, but in return allow analyzing geometrically highly detailed models (Arbenz et al, 2007).…”

Section: Bone and Implant Geometrymentioning

confidence: 99%

Computational analyses of small endosseous implants in osteoporotic bone

Wirth

Müller²,

Lenthe³

2010

eCM

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For many years orthopedic implants were developed for patients with good bone stock. Recently it has become clear that these implants have a decreased performance when implanted in bone with low density, such as in osteoporosis. Reduced performance in osteoporotic bone is not unexpected because of the reduced quality of the peri-implant bone and the reduced bone-implant contact area. Nevertheless, the precise failure mechanisms are not well understood. Although experimental testing is considered the gold standard to determine implant fixation, it is hampered by many limitations. Computational models could potentially aid in obtaining a better understanding of implant fixation as they allow analyzing the mechanical interaction between implants and peri-implant tissues. This article provides a review of the existing finite element models of small endosseous implants in bone. The aim is to analyze the potential of such models to aid the understanding of implant failure mechanisms with the goal of improving implant performance in low quality bone.

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“…Systems of up to hundreds of millions of degrees of freedom have been solved on large scale computers within a couple of minutes [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

On Smoothing Surfaces in Voxel Based Finite Element Analysis of Trabecular Bone

Arbenz

Flaig

2008

Large-Scale Scientific Computing

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Abstract. The (micro-)finite element analysis based on three-dimensional computed tomography (CT) data of human bone takes place on complicated domains composed of often hundreds of millions of voxel elements. The finite element analysis is used to determine stresses and strains at the trabecular level of bone. It is even used to predict fracture of osteoporotic bone. However, the computed stresses can deteriorate at the jagged surface of the voxel model.There are algorithms known to smooth surfaces of voxel models. Smoothing however can distort the element geometries. In this study we investigate the effects of smoothing on the accuracy of the finite element solution, on the condition of the resulting system matrix, and on the effectiveness of the smoothed aggregation multigrid preconditioned conjugate gradient method.

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Multi-level μ-Finite Element Analysis for Human Bone Structures

Cited by 22 publications

References 13 publications

Restricted Cuts for Bisections in Solid Grids: A Proof via Polygons

Restricted Cuts for Bisections in Solid Grids: A Proof via Polygons

Computational analyses of small endosseous implants in osteoporotic bone

On Smoothing Surfaces in Voxel Based Finite Element Analysis of Trabecular Bone

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