A deep neural network-enhanced multi-scale coupled model of patient-specific acoustic wave propagation for mechanotransduction stimulation of healthy and osteoarthritic knee articular cartilage

Abstract This study presents a multi-scale computational framework to quantify how externally applied acoustic waves propagate through the knee joint and induce mechanotransductive strain at the level of the chondrocyte nucleus. Patient-specific knee geometries ( n = 8) were used to simulate acoustic wave transmission through layered tissues, while a representative volume element modelled the coupled solid–shell–acoustic behaviour of the chondrocyte, pericellular matrix, and extracellular matrix. Modal and frequency–response analyses identified the spheroidal s 3 mode as the dominant contributor to nuclear deformation. Strain amplification was found to occur within defined frequency bands rather than at a single frequency, with healthy patients exhibiting a broader mid-frequency amplification region (50–170 kHz) and diseased patients showing a shifted low-frequency (30–85 kHz) dominance due to hypertrophy and altered stiffness. Macro-to-micro coupling demonstrated that, despite anatomical variability, consistent transmissibility trends were preserved across patients, with ideal frequencies for healthy and OA patients. Time-explicit simulations comparing linear and nonlinear acoustic formulations revealed negligible harmonic generation at the applied pressure levels, indicating that linear acoustics adequately describe propagation within the mechanotransductive strain range considered. Overall, the results demonstrate that cartilage stimulation is frequency-band dependent and disease-sensitive, and they provide a mechanistically grounded basis for optimizing ultrasound excitation parameters based on cellular-scale mechanics rather than empirical frequency selection.