Biot Theory-based Finite Element Modeling of Continuous Ultrasound Propagation Through Microscale Articular Cartilage

Abstract

Abstract Low-intensity ultrasound has shown promise in promoting the healing and regeneration of cartilage degraded by osteoarthritis. In this study, a 2-D finite element method (FEM) model was developed for solving the Biot theory equations governing the propagation of continuous ultrasound through cartilage. Specifically, we compute the ultrasound-induced dilatations and displacements in microscale cartilage that is represented as consisting of four zones, namely the chondrocyte cell and its nucleus, the pericellular matrix (PCM) that forms a layer around the chondrocyte, and the extracellular matrix (ECM). The chondrocyte–PCM complex, referred to as the chondron, is embedded in the ECM. We model multiple cartilage configurations wherein the ECM layer contains chondrons along the depth, as well as laterally. The top surface of ECM layer is subjected to specified amplitude and frequency of continuous ultrasound. The resulting wave propagation is modeled by numerically solving the 2-D Biot equations for seven frequencies in the 0.5~MHz to 5~MHz range. It is seen that ultrasound is attenuated in the ECM and the attenuation increases monotonically with frequency. In contrast, manyfold augmentation of ultrasound amplitudes is observed inside the cytoplasm and nucleus of the chondrocyte. Chondrocytes act as a major sink of ultrasound energy, thereby reducing the depthwise propagation of ultrasound fluctuations. Regions of high dilatations and displacements were found at the ECM–PCM interface, PCM–chondrocyte interace, as well as in the cytoplasm and nucleus.