Measurement of material elastic constants of trabecular bone: A micromechanical analytic study using a 1 GHz acoustic microscope

The propagation speed (C) of surface acoustic waves (SAW), e.g. Rayleigh (R-waves) and longitudinal lateral waves (L-waves), the latter being the surface manifestation of the longitudinal waves, strongly reflect mechanical properties of materials. In view of an increasing interest in ultrasonic methodology in the field of bone biomechanics, we tested the hypothesis that both R- and L-waves can be excited in trabecular bone using an acoustic microscope at 1 GHz and that their speeds (C_R and C_L) can be extracted from V(z)-curves, i.e. plots of lens output voltage as a function of the lens focal point position with respect to the specimen surface. In accordance with V(z)-curves theoretically synthesized on the basis of incident field theory, experimental curves for canine femoral trabecular bone showed evidence of both R- and L-waves in almost all regions of recording. The measured C_R ranged between 1.93 and 2.07 km/s (mean ± SD.: 2.00 ± 0.06 km/s) and the C_L ranged between 2.33 and 4.33 km/s (3.37 ± 0.61 km/s). Knowledge of both speeds allowed computation of a number of material constants by means of simple theory of elasticity and assumptions of the material density. We found values of Poisson ratio (v) ranging from 0.14 to 0.32 (0.23 ± 0.07), Young's modulus (E) from 15 to 22.8 GPa (19.9 ± 2.5 GPa) and the shear modulus (G) from 7.6 to 8.9 GPa (8.4 ± 0.5 GPa). Anisotropy in the trabecular bone material was clearly detected at the micrometer level. In conclusion, the V(z)-curve method was successfully used to determine the distribution of material elastic constants of trabecular bone with micrometer resolution.