Mathematical Modeling of Ultrasound in Regenerative Medicine: From the Cellular Scale to the Macroscale

As articular cartilage is avascular with limited ability for self-repair, osteoarthritis and other cartilage injuries are biomedical burdens. Thus we investigated low-intensity ultrasound in cartilage restoration. We completed the following objectives: 1) described the deformation pattern of chondrocytes in an acoustic field; 2) identified frequency sensitive mechanism(s) involved in ultrasound induced cartilage restoration; 3) investigated the nonlinear effects of cellular interaction with an acoustic field; 4) identified the in vivo chondrocyte resonant frequency; and 5) investigated the extent of ultrasound propagation through the joint space. To elucidate underlying mechanisms in ultrasound induced bioeffects, we first showed that low-intensity ultrasound applied at resonance induces deformation equivalent to that applied at 1MHz and significantly higher intensities (170kPa). The stored mechanical energy as a result of this deformation was maximized at resonance and the energy density in the nucleus was twice as high as in the cytoplasm. A mechanochemical model that linked the mechanical stimulation of ultrasound and the increased mechanical energy density in the nucleus to the downstream targets of the ERK pathway showed that ultrasound stimulation induces frequency dependent gene expression as a result of altered rates of transcription factors binding to chromatin. The bifurcation behavior of the cell when it is excited near resonance showed multiplicity. At positive detuning the mechanical energy coupled to the cell is small, it is higher at resonance but significantly higher at sub-resonant frequencies in the multiplicity range. Thus, there exists an optimal range of frequencies for ultrasound treatment where mechanical energy coupling is maximized. As the resonant frequency is highly dependent on the mass and stiffness, we identified the resonant frequency of an in vivo chondrocyte in healthy and osteoarthritic conditions to be in the range of 3.5-4.1 MHz. We investigated the extent of ultrasound propagation through the rabbit knee joint space and the sheep elbow space and coupled these experimental results with computer simulations of the joint spaces. The joint space leads to high attenuation thus the aid of computational models can assist clinicians in determining the effectiveness of ultrasound on patient specific cartilage restoration and optimal transducer positioning