Determination of Elastic Modulus in Mouse Bones Using a Nondestructive Micro-Indentation Technique Using Reference Point Indentation

Abstract

The determination of the elastic modulus of bone is important in studying the response of bone to loading and is determined using a destructive three-point bending method. Reference point indentation (RPI), with one cycle of indentation, offers a nondestructive alternative to determine the elastic modulus. While the elastic modulus could be determined using a nondestructive procedure for ex vivo experiments, for in vivo testing, the three-point bending technique may not be practical and hence RPI is viewed as a potential alternative and explored in this study. Using the RPI measurements, total indentation distance (TID), creep indentation distance, indentation force, and the unloading slope, we have developed a numerical analysis procedure using the Oliver-Pharr (O/P) method to estimate the indentation elastic modulus. Two methods were used to determine the area function: (1) Oliver-Pharr (O/P-based on a numerical procedure) and (2) geometric (based on the calculation of the projected area of indentation). The indentation moduli of polymethyl methacrylate (PMMA) calculated by the O/P (3.49-3.68 GPa) and geometric (3.33-3.49 GPa) methods were similar to values in literature (3.5-4 GPa). In a study using femurs from C57Bl/6 mice of different ages and genders, the three-point bending modulus was lower than the indentation modulus. In femurs from 4 to 5 months old TOPGAL mice, we found that the indentation modulus from the geometric (5.61 ± 1.25 GPa) and O/P (5.53 ± 1.27 GPa) methods was higher than the three-point bending modulus (5.28 ± 0.34 GPa). In females, the indentation modulus from the geometric (7.45 ± 0.86 GPa) and O/P (7.46 ± 0.92 GPa) methods was also higher than the three-point bending modulus (7.33 ± 1.13 GPa). We can conclude from this study that the RPI determined values are relatively close to three-point bending values.