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

Abstract

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 ofthe 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 , and C,) 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 CR ranged between I .93 and 2.07 km/s (mean & SD.: 2.00 i 0.06 kmls) and the CL 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 ( u ) ranging from 0.14 to 0.32 (0.23 & 0.07). Young's modulus ( E ) from I5 to 22.8 GPa (19.9 I 2.5 GPa) and the shear modulus (C) from 7.6 to 8.9 GPa (8.4 k 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.

Simulation of the elastic behaviour of the human mandible: experimental validation and material parameter identification

“…Results were obtained which showed good agreement with previously reported values for human mandibular bone [3]. Further simulations with the calculated parameters matched the deformations which could be expected from clinical experience, giving further validation.…”

Biomechanics of the Canine Mandible During Bone Transport Distraction Osteogenesis

“…Mechanical properties for the cortical bone, regenerated bone, trabecular bone, dentin, BTRP device, and symphysis were not only evaluated but also assumed from several authors [12,[23][24][25] (Table 1). A previous study from the authors reported the mechanical properties of the regenerate dog cortical bone are not only heterogeneous, but also tend to be approximately transversely isotropic at a tissue level as opposed to control cortical bone that is orthotropic [26].…”

“…Isotropic elastic moduli of the dog trabecular bone were obtained from the ultrasonic test of the femora of eight dogs [25]. Poisson's Ratio in the trabecular bone was obtained from a 1 GHz acoustic microscope test [24]. The elastic properties for the dentin were obtained from a study that measured sound speed in bovine dentin and enamel [23].…”

Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

“…Equations (12) and (13) pertain to a pervious surface; in the case of impervious surface, the boundary conditions are the same as those of the pervious surface except the third and fourth equations of (12) and the third equation of (13) on fluid pressure; instead, here we have…”

“…These values are close to those of the experimental results. The values in the said study are detected at micrometer level [12]. These computations are based on the ( )-curve method, which involves surface acoustic waves (SAW) that are propagating along the surface of a specimen.…”