Numerical Simulation of Ultrasonic Backscattering During Fracture Healing Using Numerical Models Based on Scanning Acoustic Microscopy Images

Abstract

Quantitative ultrasound has been used as a monitoring means of osteoporosis and fracture healing by several research groups worldwide applying experimental and computational techniques. However, fracture healing is a complex biological process and an interdisciplinary knowledge is required to fully comprehend the pathways of bone regeneration and gene expression as well as the structural and material changes occurring at different healing stages. Over the last decade, the incorporation of computational tools and the illustration of bone microstructure and material properties at different hierarchical levels using micro-computed tomography and scanning acoustic microscopy (SAM) have paved the way for the investigation of complex wave propagation phenomena which cannot be observed via traditional experimental procedures. In this study, we use the boundary element method to perform simulations of ultrasound propagation at successive bone healing stages. Bone healing is simulated as a three stage process and numerical models are established based on SAM images derived from week 3, week 6 and week 9 after the osteotomy. Callus is considered as a two-dimensional medium and its composite nature is integrated in the models via the combination of SAM images and an iterative effective medium approximation. We use a plane wave excitation at 1 MHz to investigate the interaction with cortical and callus tissues. The scattering amplitude variation is calculated in the backward and forward direction, as well. It was found that the scattering amplitude derived from appropriate directions and excitation frequencies could convey significant quantitative information for the evaluation of fracture healing.