Piezoelectric finite-difference time-domain simulations of piezoelectric signal generated in cancellous bone by ultrasound irradiation

Abstract

Bone formation can be driven by mechanical loads applied to the bone. By taking advantage of this mechanism, the accelerated healing of bone fracture using low-intensity pulsed ultrasound (LIPUS) has been medically practiced. Bone can behave as a piezoelectric material, and the piezoelectric effects are considered to accompany the bone formation. However, the piezoelectric properties in bone, particularly in cancellous bone with a porous structure, at ultrasound frequencies are too complex to easily clarify. In such a case, numerical simulations can be helpful because they enable visualization in the "black box." Numerical simulations by an elastic finite-difference time-domain (FDTD) method have been widely performed to investigate ultrasound behaviors in bone. In this study, the elastic FDTD method with piezoelectric constitutive equations (PE-FDTD method) was used to simulate the piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation. The cubic cancellous bone model was reconstructed from the x-ray microtomographic image. The piezoelectric signal waveforms when an ultrasound burst wave was irradiated in three orthogonal directions were calculated, together with the ultrasound signal waveforms propagated through cancellous bone. From the calculated results, the effect of the trabecular orientation was investigated.