FDTD simulation of induced potentials in bone by ultrasound irradiation

Abstract

Low Intensity Pulsed Ultrasound (LIPUS) can shorten the healing time of fractures by irradiating low-power ultrasound. However, the full mechanism of bone fracture healing is still unknown. One possible mechanism is the ultrasonically induced electrical potential due to the weak piezoelectricity of bone. There are several studies reporting the acceleration of fracture healing due to electrical stimulation. In this study, the piezoelectric finite-difference time-domain (PE-FDTD) method, which is an elastic FDTD method with piezoelectric constitutive equations in the stress-charge form, was used to consider the induced electrical potentials. Simulations were performed with a heterogeneous digital model of the human radius created from the 3 D CT data. Assuming a fracture at the distal part of the radius, ultrasound in the MHz range entered bone perpendicular to the bone axis. The guided longitudinal waves first propagated along the pseudo-piped shape bone, followed by the weak shear and surface waves. However, the intensity of the electric field in the bone increased owing to the shear wave. Shear wave seems a key factor to understand the ultrasonically induced electrical potentials in bone.