Stress estimation in different bone layers subject to therapeutic ultrasound in an intelligent bone system

Physiological effects caused by power ultrasound radiation are of therapeutic benefits for fracture healing. However, these effects are hard to detect with current instrumentations. The aim of this paper is to analyze the behavior of bone subject to therapeutic ultrasound and provide data reference for an intelligent bone ultrasonic system. In this paper, we adopted a 3-D finite element method as a virtual measurement tool to study the acoustic-radiation-induced stress fields inside and on the surface of bone. The equivalent long bone model was built and the soft tissue was involved by establishing coupling connections with bone surface points. The ultrasound radiation was generated by a 2-MHz excitation and was applied on the surface of soft tissue. In this paper, we first defined six paths in different bone layers to quantitatively study the longitudinal stress distribution and examined the concentration center positions and width with sliding windows. Then, the circumferential stress evolution from relaxation fields to concentration fields was investigated by computing the stress fields on cross sections. Analytical dispersion curves were measured to characterize the guided wave modes. The results show that the middle bone tissue has a higher mean stress (2027.7 Pa) than the surface (763.3 Pa) and the outer bone layer (1898.1 Pa), and the stress distribution of the middle layer is less disturbed (coefficient of variation = 39.8 %). Also, on cross section of the concentration zones, periodical fields with a distance of half-wavelength are obtained. From 0.2 to 2 MHz, the acoustic intensity grows proportionally with excitation amplitude.