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

Abstract

Mechanical properties of cancellous bone is of increasing interest due to its involvement in aging pathologies and oncology. Characterization of fragile bone tissue is challenging and available methodologies include quasi-static compressive tests of small size specimens, ultrasound and indentation techniques. We hypothesized that modal analysis of flexure beams could be a complementary methodology to obtain Young modulus. The sampling methodology was adapted such that the uniqueness of the linear dynamic response was available 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 small beam-like specimens in canine distal femurs. X-ray microtomography confirmed the microarchitecture preservation, the homogeneity and the isotropy at the specimen scale to derive effective properties. 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 collection site. Experimental tests were rapid and reproducible and our preliminary results were in good agreement with literature data. In conclusion, beam modal analysis could be considered for exploring mechanical properties of fragile and scarce biological tissues.

Keywords: Bone mechanics; Cancellous bone; Canine bone; Modal analysis; Theoretical and experimental approach.