Finite element analysis of the mouse tibia: Estimating endocortical strain during three-point bending in SAMP6 osteoporotic mice

To support future studies of tibial bending in a murine model of senile osteoporosis (SAMP6), we sought to determine the relationship between applied external bending force and peak endocortical strain in the tibiae of SAMP6 and control SAMR1 mice. The lower hindlimbs of mice were loaded by three-point bending in the lateral-medial plane with a support length of 10 mm. Force-periosteal strain relations were first determined using standard strain gauge methods. Finite-element analysis (FEA) models of the tibia-fibula were generated based on microcomputed tomography images. After choosing appropriate boundary conditions, FEA predictions of periosteal strains were within 15% of measured values. FEA revealed a narrow (3-4 mm) region of the central tibia with well-developed bending strains (tension medially, compression laterally); outside this region, we observed high shear strains. Both the strain gauge data and the finite-element simulations indicated that the tibia of the SAMP6 mouse was 20-25% suffer than the SAMR1 tibia, consistent with a larger moment of inertia and higher cortical bone modulus. Thus, higher levels of force are required to produce the same target values of strain in the SAMP6 tibia. The ratio of periosteal to endocortical strain in the region of interest was similar for the two mouse strains (1.5-1.6). Based on these ratios, we scaled the strain gauge data to estimate the force-endocortical strain relations for the two mouse strains. In conclusion, FEA, with supporting strain gauge measurements, has provided unique insight regarding the strain environment throughout the tibia during three-point bending in mice.