Identification of effective elastic modulus using modal analysis : application to canine cancellous bone

Abstract

Mechanical properties of cancellous bone play a role in osteoporosis and fracture induction, bone tumor microenvironment, fracture healing and implant fixation. Most characterization methods used to identify cancellous bone Young modulus are compressive tests, which are known to comprise significant limitations especially when they are performed on small size specimens. We hypothesized that modal analysis of straight beams could be proposed as an alternative methodology to obtain effective elastic properties. Theoretical key-points were provided to determine the elastic modulus from natural frequencies and mode shapes. In a first step, the methodology was validated using a synthetic bone model as control. Then, water-jet cutting allowed collecting fourteen regular beam-like specimens in specific zones of canine distal femurs. X-ray microtomography confirmed the preservation of tissue microarchitecture and homogeneity. The first natural frequency in clamped-free boundary conditions was used to obtain mean values of Young modulus, which ranged from 210 MPa to 280 MPa depending on the specimen’s collection site. This was in good agreement with literature data obtained with uniaxial compressive tests. Experimental tests were rapid and reproducible, non-destructive and did not depend on scale factor. Therefore, beam modal analysis can be a compelling methodology for exploring mechanical properties of fragile and scarce biological tissues.