Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor

Harrigan, Timothy P.; Mann, Robert W.

doi:10.1007/bf00540446

Cited by 554 publications

(318 citation statements)

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“…The degree of trabecular connectivity, measured by Conn.D, also provides valuable information, since loss of connectivity has substantial impact on structural integrity and results in elevated fracture risk (4,9,27). DA is a measure of directional variation of a structure, calculated from a ratio of maximum to minimum eigenvalues of the mean intercept length tensor (7,10,26). Though not directly correlated with the mechanical properties of bone, DA provides insight into the directional dependence of bone strength (4,10).…”

Section: Introductionmentioning

confidence: 99%

“…DA is a measure of directional variation of a structure, calculated from a ratio of maximum to minimum eigenvalues of the mean intercept length tensor (7,10,26). Though not directly correlated with the mechanical properties of bone, DA provides insight into the directional dependence of bone strength (4,10). With age, trabecular bone is known to become more rod-like (6), with connectivity being lost by disruption of thin horizontal trabeculae, and increasingly anisotropic (24).…”

Section: Introductionmentioning

confidence: 99%

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Resolution Dependence of the Non-metric Trabecular Structure Indices

Sode¹,

Burghardt²,

Nissenson³

et al. 2008

Bone

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Non-metric indices of topological features of trabecular bone structure, such as structure model index (SMI), connectivity density (Conn.D), and degree of anisotropy (DA), provide unique information relevant to bone quality. With recent technological advancement, in vivo assessment of these indices may be possible from images acquired using high-resolution imaging techniques such as highresolution peripheral quantitative computed tomography (HR-pQCT). However, more detailed investigation of the dependence of non-metric indices on spatial resolution is needed to determine their applicability.The purpose of this study was to determine whether these three non-metric indices are affected by the spatial resolution of CT images. First, the SMI, Conn.D, and DA were calculated for trabecular bone specimens with varying plate-like and rod-like structures from resampled μCT images across a range of spatial resolutions and compared to the reference values. To account for differences in size across different species and anatomical sites, the results are reported in normalized resolution units. Next, the impact of resolution on the non-metric indices for cores of human distal tibia trabecular bone from clinical HR-pQCT images was evaluated to determine the applicability of the non-metric indices to in vivo imaging.We found that the non-metric indices of trabecular bone structure were affected by spatial resolution of CT images. Particularly, the SMI deviated from the high-resolution μCT reference value depending on the structure type, whether plate-like or rod-like. Both Conn.D and DA were underestimated in the images obtained at an in vivo resolution. It is not trivial to determine absolute threshold for validity of these non-metric indices without considering a specific study design (e.g. relative resolution, the size of the treatment effect to detect, and specimen type). The results of this study provide an upper bound for the accuracy of the non-metric indices under limited resolution scenarios.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resolution Dependence of the Non-metric Trabecular Structure Indices

Sode¹,

Burghardt²,

Nissenson³

et al. 2008

Bone

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“…Parameters quantifying 3D connectivity [24,28], 3D anisotropy [29], and 3D irregularity [17,30] can be extracted from 3D images. These methods have been used to characterize cancellous bone from different sites [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Relationship between compressive properties of human os calcis cancellous bone and microarchitecture assessed from 2D and 3D synchrotron microtomography

Follet

Bruyère-Garnier

Peyrin

et al. 2005

Bone

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The aim of this study was to determine the contribution of 2D and 3D microarchitectural characteristics in the assessment of the mechanical strength of os calcis cancellous bone. A sample of cancellous bone was removed in a medio-lateral direction from the posterior body of calcaneus, taken at autopsy in 17 subjects aged 61-91 years. The sample was first used for the assessment of morphological parameters from 2D morphometry and 3D synchrotron microtomography (ACT) (spatial resolution = 10 Am). The 2D morphometry was obtained from three slices extracted from the 3D ACT images. Very good concordance was shown between 3D ACT slices and the corresponding physical histologic slices. In 2D, the standard histomorphometric parameters, fractal dimension, mean intercept length, and connectivity were computed. In 3D, histomorphometric parameters were computed using both the 3D mean intercept length method and model-independent techniques. The 3D fractal dimension and the 3D connectivity, assessed by Euler density, were also evaluated. The cubic samples were subjected to elastic compressive tests in three orthogonal directions (X, Y, Z) close to the main natural trabecular network directions. A test was performed until collapse of trabecular network in the main direction (Z). The mechanical properties were significantly correlated to most morphological parameters resulting from 2D and 3D analysis. In 2D, the correlation between the mechanical strength and bone volume/tissue volume was not significantly improved by adding structural parameters or connectivity parameter (nodes number/tissue volume). In 3D, one architectural parameter (the trabecular thickness, Tb.Th) permitted to improve the estimation of the compressive strength from the bone volume/tissue volume alone. However, this improvement was minor since the correlation with the BV/TV alone was high (r = 0.96). In conclusion, which is in agreement with the statistic's rules, we found, in this study, that the determination of the os calcis bone compressive strength using the 3D bone volume fraction cannot be improved by adding 3D architectural parameters.

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“…Fabric can be evaluated, for example, by mean-intercept length (MIL) measurements ( Harrigan and Mann, 1984;Whitehouse, 1974). For trabecular bone it was found that the MIL fits well to an ellipsoid, which has three planes of symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…finding, it was proposed that trabecular bone architecture exhibits orthotropic material behavior (Ashman et a l 1984;Cowin and Mehrabadi, 1989;Harrigan and Mann, 1984;Snyder et ai.t 1989;Whitehouse, 1974). The nine orthotropic elastic coefficients in a coordinate system aligned with the fabric axes can be determined from nine elastic coefficients measured by compression tests or ultrasound experiments in the specimens' coordinate system, using a coordinate transformation (Cowin et al, 1991).…”

Section: Introductionmentioning

confidence: 99%

Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

Rietbergen

Odgaard

Kabel

et al. 1996

Journal of Biomechanics

181

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Abstract-A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric measurements. The method uses high-resolution computer reconstructions of trabecular bone specimens as input for large-scale FE-analyses to determine all the 21 elastic coefficients in the overall stiffness matrix of the specimen, using a direct mechanics approach. An optimization procedure is then used to find the coordinate transformation that yields the best orthotropic representation of this matrix. The method is illustrated here relative to two trabecular bone specimens. The techniques developed here can be used to obtain a complete characterization of the mechanical properties of trabecular architecture. With the development of in vivo reconstruction techniques, even in vivo measurements will be possible.

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Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor

Cited by 554 publications

References 3 publications

Resolution Dependence of the Non-metric Trabecular Structure Indices

Resolution Dependence of the Non-metric Trabecular Structure Indices

Relationship between compressive properties of human os calcis cancellous bone and microarchitecture assessed from 2D and 3D synchrotron microtomography

Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

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