title: Tissue modulus calculated from beam theory is biased by bone size and geometry: implications for the use of three-point bending tests to determine bone tissue modulus.
abstract: Current practice to determine bone tissue modulus of murine cortical bone is to estimate it from three-point bending tests, using Euler-Bernoulli beam theory. However, murine femora are not perfect beams; hence, results can be inaccurate. Our aim was to assess the accuracy of beam theory, which we tested for two commonly used inbred strains of mice, C57BL/6 (B6) and C3H/He (C3H). We measured the three-dimensional structure of male and female B6 and C3H femora (N=20/group) by means of micro-computed tomography. For each femur five micro-finite element (micro-FE) models were created that simulated three-point bending tests with varying distances between the supports. Tissue modulus was calculated from beam theory using micro-FE results. The accuracy of beam theory was assessed by comparing the beam theory-derived moduli with the modulus as used in the micro-FE analyses. An additional set of fresh-frozen femora (10 B6 and 12 C3H) was biomechanically tested and subjected to the same micro-FE analyses. These combined experimental-computational analyses enabled an unbiased assessment of specimen-specific tissue modulus. We found that by using beam theory, tissue modulus was underestimated for all femora. Femoral geometry and size had strong effects on beam theory-derived tissue moduli. Owing to their relatively thin cortex, underestimation was markedly higher for B6 than for C3H. Underestimation was dependent on support width in a strain-specific manner. From our combined experimental-computational approach we calculated tissue moduli of 12.0+/-1.3 GPa and 13.4+/-2.1 GPa for B6 and C3H, respectively. We conclude that tissue moduli in murine femora are strongly underestimated when calculated from beam theory. Using image-based micro-FE analyses we could precisely quantify this underestimation. We showed that previously reported murine inbred strain-specific differences in tissue modulus are largely an effect of geometric differences, not accounted for by beam theory. We suggest a re-evaluation of the tissue properties obtained from three-point bending tests, especially in mouse genetics.
authors.affiliation: Institute for Biomechanics, ETH Zürich, Zürich, Switzerland. harry.vanlenthe@mech.kuleuven.be
authors.forename: G Harry
authors.initials: GH
authors.lastname: van Lenthe
authors.forename: Romain
authors.initials: R
authors.lastname: Voide
authors.forename: Steven K
authors.initials: SK
authors.lastname: Boyd
authors.forename: Ralph
authors.initials: R
authors.lastname: Müller
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D001842:Bone and Bones / Q000033:anatomy & histology* / Q000502:physiology; D005269:Femur / Q000033:anatomy & histology* / Q000502:physiology; D051379:Mice; D008953:Models, Anatomic; D008954:Models, Biological