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

Abstract

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% stiffer 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.

Mechanical Stimulation of Bone Formation is Normal in the SAMP6 Mouse

“…First, we relied on estimated values of endocortical strain to equate the mechanical stimuli at the endocortical surfaces of SAMR1 and SAMP6 mice. It is not possible to directly measure endocortical strains, so we relied on periosteal data combined with finite element analysis to estimate the endocortical strains in our loading model [28]. It is possible that errors in these estimates may have led to differences in the level of stimuli applied to the different mouse strains.…”

“…The contact points were 1.8 mm diameter wooden dowels covered with a 2-mm thick rubber pads. In this setup, downward movement of the loading point produces tibial bending in the medial-lateral plane with tension on the medial surface [28]. (B) For sham bending, a single support point is placed opposite the loading point so that application of force does not produce bending of the tibia.…”

“…Periosteal bone formation was activated, but in the absence of bending there was no detectable endocortical response. Table 1 Compressive forces for in vivo tibial bending to produce estimated peak values of 1000 and 2000 με on endocortical surface of the tibial diaphysis in SAMR1 and SAMP6 mice [28]. Endocortical bone formation indices (mean ± SD) from mice subjected to tibial bending.…”

“…Values of applied force were chosen to produce a peak endocortical strain of either 1000 or 2000 microstrain (με) ( Table 1). Because endocortical strains cannot be measured directly, we estimated their values using periosteal strain data and engineering analysis, as described in detail previously [28]. Forces for the SAMP6 group were ~20% greater than for SAMR1 due to the greater moment of inertia of the SAMP6 tibia.…”

“…They were then dehydrated in ascending concentrations of ethanol (70-100%) and embedded in methylmethacrylate (Fisher) using standard procedures for undecalcified bone. Three consecutive transverse sections (100μm thickness) were cut from the mid-shaft of each tibia, 5 mm proximal from the distal tibiofibular junction (corresponding to the site of maximum bending strain [28]) using a saw microtome (Leica SP 1600). Sections were mounted on glass slides and viewed under UV excitation on a fluorescence equipped microscope (Leitz Orthoplan).…”