Accuracy of beam theory for estimating bone tissue modulus and yield stress from 3-point bending tests on rat femora

Mechanical analysis of animal long bones often makes use of beam theory to estimate tissue properties from bending tests. An earlier study (van Lenthe et al., 2008) found that beam theory leads to a considerable underestimation of the Young's modulus of mice femora. However, we hypothesized that beam theory might still be an accurate tool for the determination of bone strength from experimental data. The first goal was to test this hypothesis, along with checking if the underestimation of the tissue modulus is also valid for rat femurs. The second goal was to investigate if micro-FE and beam theory would yield similar increases in Young's moduli and yield stress during aging. Twelve rat femurs (12 and 16 weeks old) were scanned using micro-CT and subjected to a three-point bending test from which the bending stiffness and the yield force were obtained. The Young's modulus and yield stress then were calculated by regressing the experimental results with results obtained from beam theory and micro-FE analysis based on the micro-CT scans. It was found that bone strength calculated using beam theory overestimated that calculated from micro-FE by 8.0%. The Young's modulus did not significantly differ. When comparing age groups, similar increases in tissue modulus and yield strength were found for beam theory and micro-FE, with significant differences only for the micro-FE yield stress. We concluded that the use of beam theory to calculate bone yield strength from 3-point bending test results of rat femurs leads to its overprediction.