Modulus Of Trabeculae Research Articles

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Determination of Bone Trabeculae Modulus—An Ultrasonic Scanning and MicroCT (μCT) Imaging Combination Approach

To date, there is no method to measure non-destructively the modulus of trabeculae within cancellous bone, whilst retaining its structural integrity. In this study ultrasonic scanning, coupled with microCT imaging, is employed to determine trabeculae modulus along the three major anatomical axes non-destructively. The proposed method allows cancellous bone specimens to remain intact, for possible use in subsequent studies. Volume rendering of the microCT images allows three-dimensional visualization of cancellous bone specimens to be tested. This facilitates trabeculae selection and accurate measurement of distance traveled by the ultrasonic wave, thus yielding a good degree of confidence in the acoustic velocity measured. For all the three principal anatomical directions, the measured acoustic speeds ranged from 2,115 to 3,077 m/s, giving an average of 2,505 m/s. Average wave velocities in the superior–inferior, medial–lateral and anterior–posterior anatomical directions were found to be 2,295, 2,469 and 2,754 m/s, respectively; the differences corresponding to the three directions do not appear to be significant. Subsequently, the modulus was then determined using elastic wave propagation theory.

Young's modulus of trabecular and cortical bone material: Ultrasonic and microtensile measurements

An ultrasonic technique and microtensile testing were used to determine the Young's modulus of individual trabeculae and micro-specimens of cortical bone cut to similar size as individual trabeculae. The average trabecular Young's modulus measured ultrasonically and mechanically was 14.8 GPa (S.D. 1.4) and 10.4 (S.D. 3.5) and the average Young's modulus of microspecimens of cortical bone measured ultrasonically and mechanically was 20.7 GPa (S.D. 1.9) and 18.6 GPa (S.D. 3.5). With either testing technique the mean trabecular Young's modulus was found to be significantly less than that of cortical bone ( p<0.0001). However, the specimens were dried before microtensile testing so Young's modulus values may have been greater than those of trabeculae in vivo. Using Young's modulus measurements obtained from 450 cubes of cancellous bone and 256 cubes of cortical bone, Wolff's hypothesis that cortical bone is simply dense cancellous bone was tested. A multiple regression analysis that controlled for group membership showed that Young's modulus of cortical bone cannot be extrapolated from the Young's modulus vs density relationship for cancellous bone, yet the Young's modulus of trabeculae can be predicted by extrapolation from the relationship between Young's modulus vs density of the cancellous bone. These results suggest that when considered mechanically, cortical and trabecular bone are not the same material.