Numerical investigations of ultrasound wave propagating in long bones using a poroelastic model

Ultrasonic responses probed from an axial transmission test (ATT) may provide useful information about material and structural properties of cortical bone. For the mathematical modeling of ultrasonic wave propagation in long bones, most of studies assumed an (visco-)elastic behavior for cortical bone tissue by neglecting the interstitial pressure in the pores presented within this material. Here, a functionally graded anisotropic poroelastic model is proposed for describing the behavior of long bones in the ultrasonic frequency range. The simulation of time-domain wave propagation can efficiently be carried out by using a semi-analytical finite element method. The proposed model allows us investigate the influence of the presence of the pores, as well as their distribution in a bone layer on the speed of sound propagated in a cortical bone layer coupled with the marrow and the soft tissue. The effects of emitted signal’s frequency will also be examined.

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