The fabric dependence of the orthotropic elastic constants of cancellous bone

Turner, Charles H.; Cowin, Stephen C.; Rho, Jae-Young; Ashman, Richard; Rice, Janet C.

doi:10.1016/0021-9290(90)90048-8

Cited by 292 publications

(194 citation statements)

References 21 publications

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“…In most of these studies, relationships were determined by correlating Young's moduli and Poisson ratios, measured from compression tests, with the results of the surfacebased mean intercept length (MIL) fabric measure for a large number of cubic bone specimens. 4,7,8,25,27 Relationships found in these studies were generally accurate with squared correlation coefficients of R 2 Ͼ 0.72, but these were incomplete, because only a subset of the nine orthotropic elastic constants could be predicted. Moreover, the relationships found were not the same in the studies.…”

Section: Introductionmentioning

confidence: 83%

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

Kabel

Rietbergen

Odgaard

et al. 1999

Bone

167

107

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The hypothesis that trabecular morphology can predict the elastic properties of cancellous bone has only partly been verified and no predictive analytical model is currently available. Such models are becoming increasingly relevant as the resolution levels of three-dimensional scanning techniques approach the size of trabeculae. This study took advantage of micro-finite-element methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. Numerical analysis was based on high-resolution three-dimensional computer reconstructions of cancellous bone specimens from which the complete elastic characteristics and trabecular morphology, represented by three different fabric measures (the mean intercept length and two volume-based ones), were calculated. Each fabric measure was analyzed individually using the tensorial relationships derived by Cowin (Mech Mater 4:137-147; 1985). Models for both stiffness and compliance entries were developed. The models based on stiffness entries could explain 93.4%-95.6% of the variance, whereas those based on compliance entries could explain 89.2%-89.4%. When using the former model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star volume distribution), with 23% less remaining variance. The high correlations found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtain considerably better estimates of bone quality in vivo compared with the rough two-dimensional density measurements used today. (Bone 25:481-486; 1999) © 1999 by Elsevier Science Inc. All rights reserved.

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Section: Introductionmentioning

confidence: 83%

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

Kabel

Rietbergen

Odgaard

et al. 1999

Bone

167

107

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“…It lias bcen claimed that voliune-based methods, such as SVD, predict mechanical properties better than surfacebased methods [27,33]. Tlie degree of anisotropy lias bcen reported, using tlie m a n intercept lcngtli (MIL) nietliod, to liave a mean value of 1.62 for human cancellous bone [I?], 1.73 for bovine and 1.54 for liuman proxiiiial tibial samples [32], and 1.55 for sperm whale vertebral cancellous bone [27]. Odgaard et al [27] reported, using the SVD method, a mean value of 10.25 (range 2.20-1 6.97) for sperm whale vertebral cancellous bone.…”

Section: Discussionmentioning

confidence: 99%

Age‐related variations in the microstructure of human tibial cancellous bone

Ding

Odgaard

Linde

et al. 2002

Journal Orthopaedic Research

167

129

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A thorough understanding of the microstructure of cancellous bone is crucial for diagnosis, prophylaxis, and treatment of agerelated skeletal diseases. Until now, little has been known about age-related variations in the microstructure of peripheral cancellous bone. This study quantified age-related changes in the tliree-dimensioiial (3D) microstructure of huiiian tibial cancellous bone. One hundred and sixty cylindricul cnncellous bone specimens were produced from 40 normal proxinial tibiae froiii 40 donors, aged 16-85 years. These speciiiiciis were micro-computed tomography (inicro-CT) scanned, and microstructural propei-tics werc dctcrinincd. The specimens were h e n tested in compression to obtain Young's iiioduliis.The degree of anisotropy, mean marrow space volume, and bone surface-to-volume ratio increased significantly with age. Bone volunie fraction, mean trabecular volume, and bone surface density decreased significantly with age. Connectivity did not have a general relationship with age. Bone voltiine fraction together with anisotropy best predicted Young's modiilus. Age-related changes in the microstructural properties had the same trends for both iiiedial and lateral condyles of the tibia. The observed increase of anisotropy and constant connectivity suggest a bone remodeling mechanism that may reorient trabecular volume orientation in aging tibial cancellous bone. The aging trabeculae align more strongly to the priinary direction -parallel to the tibial longitudinal loading axis. 0 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved. liitroductioiiTlie incidence of age-related skeletal diseases, such as osteoartlirosis [ 171 and osteoporosis [ 19,301 has increased in the past two decades, as a result of an increase in tlie elderly population and a change in lifestyle. These diseases are major health care problems in t e r m of socio-econoinic costs. A tlioi-ougli understanding of agerelated changes in tlie microstructure of caticellous bone is crucial for diagnosis, prophylaxis, a i d treatmcnt of these age-related skeletal diseases, and for the design, fixation and durability of joint prostheses.Previous investigations 011 the microstructure of cancellous bone have demonslrated significant agere la ted changes i ii ca ~icellous bone micros t r tic t u ra 1 parameters, such as bone volume fraction and bone [I ,29,3 1,341. but one study includes femoral cancellous bone [20]. However, tlie method used in this latter study [10] has been recognized to bc subject to serious limitations [9,24]. Therefore, no gencrnl coticlusions for age-related variations in the microstructure of human peripheral cancellous bone are available.

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“…The experimental procedure for the surface area orientation measurement of cancellous bone is described by Whitehouse (1974), Whitehouse and Dyson (1974), Harrigan and Mann (1984), and Turner et al (1987Turner et al ( , 1990. The work of these authors, and Odgaard (1997Odgaard ( , 2001), Odgaard et al (1997), van Rietbergen et al (1996, Matsuura et al (2008) and others, has shown that the fabric tensor is a good measure of the structural anisotropy in cancellous bone tissue (Cowin, 1997).…”

Section: Fabric Dependence Of Tensors Appearing In the Poroelastmentioning

confidence: 99%

“…Therefore, acquired signals were filtered out using bandpass filters with a frequency bandwidth of 0.5 6 0.25 MHz for the fast wave and a frequency bandwidth of 1.6 6 0.6 MHz for the slow wave. The fabric tensor describing the microarchitecture on each sample was measured using the mean intercept length as described in Whitehouse (1974), Whitehouse and Dyson (1974), Harrigan and Mann (1984), and Turner et al (1987Turner et al ( , 1990. The phase angles h, u were determined as the relative orientation of the principal axes of fabric in respect to the measurement directions A, B, and C of the cube samples.…”

Section: E Comparison Between Experimental Measurements and Theoretimentioning

confidence: 99%

Fabric dependence of quasi-waves in anisotropic porous media

Cardoso

Cowin

2011

The Journal of the Acoustical Society of America

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Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor-a quantitative stereological measure of the degree of structural anisotropy of bone-into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.

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The fabric dependence of the orthotropic elastic constants of cancellous bone

Cited by 292 publications

References 21 publications

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

Age‐related variations in the microstructure of human tibial cancellous bone

Fabric dependence of quasi-waves in anisotropic porous media

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