A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images

Flaig, Cyril; Arbenz, Peter

doi:10.1016/j.parco.2011.08.001

Cited by 71 publications

(57 citation statements)

References 9 publications

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“…A unit displacement was applied in each of the three spatial directions, and each of these three load cases were analysed separately. Micro-FE analyses were performed using the recently introduced octree-based FE-solver ParOSol [34].…”

Section: Micro-finite-element Modellingmentioning

confidence: 99%

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

Christen

Schulte

Zwahlen

et al. 2016

J. R. Soc. Interface.

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ResearchCite this article: Christen P et al. 2016 Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm. J. R. Soc. A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 mm and downscaled to 50, 61, 75, 82, 100, 125 and 150 mm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 mm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 mm, but that the dependency increases considerably at voxel sizes bigger than 82 mm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 mm, but that smaller voxel sizes would be advantageous.

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Section: Micro-finite-element Modellingmentioning

confidence: 99%

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

Christen

Schulte

Zwahlen

et al. 2016

J. R. Soc. Interface.

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“…Marrow elements were not included in the µFE models to reduce the computing time and avoid convergence issues due to a high contrast of their stiffness to the stiffness of bone. Linear µFE analyses were performed via the ParOSol solver (Flaig 2012) with three uniaxial and three shear load cases conducted under KUBCs and PMUBCs as described in a previous study (Pahr and Zysset 2008), leading to 1200…”

Section: Computation Of the Kubcs-and Pmubcs-based Stiffness Tensorsmentioning

confidence: 99%

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Daszkiewicz

Maquer

Zysset

2016

Biomech Model Mechanobiol

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word count: 249 Total word count: 3393Attachments: 5 figures and 2 tables + 1 figure and 4 tables in the appendices 2 Disclosure pageThe authors have no conflict of interest to report. AcknowledgmentsThe script manager Medtool (www.dr-pahr.at) was used to generate the µFE models, start the computations and analyse the results. The authors would like to thank Prof. Bert van Rietbergen for sharing the µCT data. Karol Daszkiewicz is supported by grants from the are also gratefully acknowledged. AbstractBoundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from µCT scans of femoral heads and vertebral bodies. They were converted into µFE models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs-and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors and model parameters ν0 (Poisson's ratio), E0 and µ0 (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on ν0. However, KUBCs-and PMUBCs-based E0 and µ0 respectively decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

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“…This allows to exploit the large amount of computing units available on a GPU compared to only a few cores of a CPU on a normal computer workstation. The analysis is performed with the dedicated micro-FE solver ParOSol [8] on the CPU. Boundary conditions are defined according to a bone loading estimation algorithm [9], providing physiological in vivo loading for this particular patient.…”

Section: Computational Implementationmentioning

confidence: 99%

Towards in silico prognosis using big data

Ohs

Keller

Blank

et al. 2016

Current Directions in Biomedical Engineering

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Clinical diagnosis and prognosis usually rely on few or even single measurements despite clinical big data being available. This limits the exploration of complex diseases such as adolescent idiopathic scoliosis (AIS) where the associated low bone mass remains unexplained. Observed low physical activity and increased RANKL/OPG, however, both indicate a mechanobiological cause. To deepen disease understanding, we propose an in silico prognosis approach using clinical big data, i.e. medical images, serum markers, questionnaires and live style data from mobile monitoring devices and explore the role of inadequate physical activity in a first AIS prototype. It employs a cellular automaton (CA) to represent the medical image, micro-finite element analysis to calculate loading, and a Boolean network to integrate the other biomarkers. Medical images of the distal tibia, physical activity scores, and vitamin D and PTH levels were integrated as measured clinically while the time development of bone density and RANKL/OPG was observed. Simulation of an AIS patient with normal physical activity and patient-specific vitamin D and PTH levels showed minor changes in bone density whereas the simulation of the same AIS patient but with reduced physical activity led to low density. Both showed unchanged RANKL/OPG and considerable cortical resorption. We conclude that our integrative in silico approach allows to account for a variety of clinical big data to study complex diseases.

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A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images

Cited by 71 publications

References 9 publications

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Towards in silico prognosis using big data

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