Numerical simulations of electric fields in bone induced by an ultrasound wave using a piezoelectric finite-difference time-domain method

Numerical simulations of the piezoelectric effect of bone under ultrasound irradiation were attempted to perform using a three-dimensional (3D) elastic finite-difference time-domain (FDTD) method with piezoelectric constitutive equations (PE-FDTD method). The electric fields in a human femur induced by an ultrasound burst wave at 1 MHz, which was radiated perpendicular to the bone axis, were simulated by the PE-FDTD method. Two sets of the piezoelectric parameters were used to investigate the effect of the piezoelectric anisotropy. The spatial distribution of the electric field in the axial direction of the bone could strongly depend on the piezoelectric anisotropy and was not necessarily similar to the distribution of the normal stress in the same direction. Moreover, the comparison between the simulated results for the normal and fractured bone models showed that the electric field could change by the fracture.