Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Harrison, Noel M.; McDonnell, Pat; Mullins, L.P.; Wilson, Niall; O’Mahoney, D.; McHugh, Peter E.

doi:10.1007/s10237-012-0394-7

Cited by 39 publications

(30 citation statements)

References 76 publications

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“…49 In a nonlinear mFEA incorporating damage, the strains at which damage forms in trabeculae were determined to be À 0.0116 (compression) and 0.0069 (tension) when the model was calibrated against compression tests of ovine trabecular bone. 50 The corresponding fracture strain estimates were double the damage strains, and so a failure strain between 0.02 and 0.007 appears reasonable. This range could not be achieved for the Renders et al 35 relationship when the failure volume was less than 10%.…”

Section: Discussionmentioning

confidence: 94%

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

Nyman¹,

Uppuganti²,

Makowski³

et al. 2015

BoneKEy Reports

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As in clinical studies, finite element analysis (FEA) developed from computed tomography (CT) images of bones are useful in pre-clinical rodent studies assessing treatment effects on vertebral body (VB) strength. Since strength predictions from microCT-derived FEAs (mFEA) have not been validated against experimental measurements of mouse VB strength, a parametric analysis exploring material and failure definitions was performed to determine whether elastic mFEAs with linear failure criteria could reasonably assess VB strength in two studies, treatment and genetic, with differences in bone volume fraction between the control and the experimental groups. VBs were scanned with a 12-mm voxel size, and voxels were directly converted to 8-node, hexahedral elements. The coefficient of determination or R 2 between predicted VB strength and experimental VB strength, as determined from compression tests, was 62.3% for the treatment study and 85.3% for the genetic study when using a homogenous tissue modulus (E t ) of 18 GPa for all elements, a failure volume of 2%, and an equivalent failure strain of 0.007. The difference between prediction and measurement (that is, error) increased when lowering the failure volume to 0.1% or increasing it to 4%. Using inhomogeneous tissue density-specific moduli improved the R 2 between predicted and experimental strength when compared with uniform E t ¼ 18 GPa. Also, the optimum failure volume is higher for the inhomogeneous than for the homogeneous material definition. Regardless of model assumptions, mFEA can assess differences in murine VB strength between experimental groups when the expected difference in strength is at least 20%.

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Section: Discussionmentioning

confidence: 94%

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

Nyman¹,

Uppuganti²,

Makowski³

et al. 2015

BoneKEy Reports

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“…The non-linear behaviour of microstructural trabecular bone models have also been modelled by reducing the elastic modulus of the trabecular material to 5% when critical principal strain is computed at a material point (Bayraktar et al 2004a;2004b;Niebur et al 2000;Guillén et al 2011;Verhulp et al 2008;Harrison et al 2012). Niebur et al (2000) based such criteria on macroscopic testing of cortical bone by Reilly and Burstein (1975).…”

Section: Discussionmentioning

confidence: 99%

“…Niebur et al (2000) based such criteria on macroscopic testing of cortical bone by Reilly and Burstein (1975). Under uniaxial compression Harrison et al (2012) incorporated material damage using the principal strain based criterion and fracture through element removal and cohesive forces in the trabecular microarchitecture. Also based on the testing of cortical bone specimens, Verhulp et al (2008) implemented the principal strain based criterion in addition to a perfectly-plastic VM plasticity formulation for the uniaxial compression testing of trabecular bone.…”

Section: Discussionmentioning

confidence: 99%

“…A number of studies have simulated non-linear trabecular behaviour by reducing the elastic modulus of the trabecular material when the principal strain at a material point exceeds a predefined value (Bayraktar et al 2004a;2004b;Niebur et al 2000;Guillén et al 2011;Verhulp et al 2008). Verhulp et al (2008) simulated uniaxial compression using μCT based trabecular geometry with a perfectly-7 plastic VM plasticity formulation, while Harrison et al (2012) simulated material damage and fracture in the trabecular microarchitecture, also under uniaxial compression. Apart from the studies of Niebur et al (2002) and Bayraktar et al (2004a), in which biaxial (triaxial stress) and axial-shear testing was simulated using the principal strain based modulus reduction model, none of these μCT studies has investigated the role of microstructural architecture in the multiaxial yielding of trabecular bone at the apparent level by considering loading configurations other than uniaxial compression.…”

Section: Introductionmentioning

confidence: 99%

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An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Kelly

Harrison

McDonnell

et al. 2012

Biomech Model Mechanobiol

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PublisherSpringer-Verlag AbstractInterbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using micro-computed tomography derived microstructural models, elucidating a mechanism of pressure dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress-strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress-strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure dependent yielding occurs.Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast the use of von Mises, Drucker-Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.

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“…Most of the studies reported in the literature adopted linear elastic constitutive law (Hara et al, 2002;Verhulp et al, 2006;Kim et al, 2007;Bevill and Keaveny, 2009;Wolfram et al, 2010;Vilayphiou et al, 2011;Torcasio et al, 2012;Gross et al, 2013;Harrison et al, 2013;Bauer et al, 2014) to assess elastic modulus at tissue level, to retrieve overall mechanical behavior at apparent level or finally to study the strain distribution. A number of non-linear models are reported in the literature, adopting both different constitutive law and failure criteria to try to replicate the force-displacement curve as experimentally measured at apparent level (Niebur et al, 2000;Bayraktar and Keaveny, 2004;Verhulp et al, 2008b;Sanyal et al, 2012;Wolfram et al, 2012;Harrison et al, 2013;Bauer et al, 2014;Baumann et al, 2016). However, there is lack of a clear consensus of the literature over which non-linear approach is the most suitable and reliable in identifying the overall failure in terms of both ultimate strain and loading curve.…”

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confidence: 99%

Trabecular Fracture Zone Might Not Be the Higher Strain Region of the Trabecular Framework

et al. 2018

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Trabecular bone fracture is a traumatic and localized event studied worldwide in order to predict it. During the years, researchers focused over the mechanical characterization of the trabecular tissue to understand its mechanics. Several studies pointed out the very local nature of the trabecular failure, finally identifying the fracture zone with the aim to study it separately. The complexity of the three-dimensional trabecular framework and the local nature of the fracture event do not allow the direct evaluation of a single trabecula's behavior within its natural environment. For this reason, micro-Finite Element Modeling has been seen as the best way to investigate this biomechanical issue. Mechanical strain analysis is adopted in the literature for the identification of micro fracture using criteria based on principal strains. However, it was never verified if the fracture zone is actually the zone where principal strains are concentrated. Here, we show how the maximum strain of the tissue might not be directly correlated to the fracture. In the present work, a previously validated technique was used to identify the fracture zone of 10 trabecular specimen mechanically tested in compression and scanned in micro-CT before and after the mechanical test. Before-compression datasets were used to develop 10 micro-FE models were the same boundary conditions of the mechanical test were reproduced. Our results show how the known linear behavior of the trabecular framework might not be directly related to the development of the fracture suggesting other non-linear phenomenon, like buckling or microdamage, as actual cause of the traumatic event. This result might have several implications both in micro-modeling and in clinical applications for the study of fracture related pathology, like osteoporosis.

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Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Cited by 39 publications

References 76 publications

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Trabecular Fracture Zone Might Not Be the Higher Strain Region of the Trabecular Framework

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