Theoretically proposed optimal frequency for ultrasound induced cartilage restoration

Background Matching the frequency of the driving force to that of the system’s natural frequency of vibration results in greater amplitude response. Thus we hypothesize that applying ultrasound at the chondrocyte’s resonant frequency will result in greater deformation than applying similar ultrasound power at a frequency outside of the resonant bandwidth. Based on this resonant hypothesis, our group previously confirmed theoretically and experimentally that ultrasound stimulation of suspended chondrocytes at resonance (5 MHz) maximized gene expression of load inducible genes. However, this study was based on suspended chondrocytes. The resonant frequency of a chondrocyte does not only depend on the cell mass and intracellular stiffness, but also on the mechanical properties of the surrounding medium. An in vivo chondrocyte’s environment differs whether it be a blood clot (following microfracture), a hydrogel or the pericellular and extracellular matrices of the natural cartilage. All have distinct structures and compositions leading to different resonant frequencies. In this study, we present two theoretical models, the first model to understand the effects of the resonant frequency on the cellular deformation and the second to identify the optimal frequency range for clinical applications of ultrasound to enhance cartilage restoration.