Ultrasonic Stimulation of Chondrocytes: Harmonic Analysis Elucidates Frequency Dependent Bioeffects

Therapeutic ultrasound has long been used to mediate the healing of fractures.  Recently, ultrasonics has been applied to bioreactors to enhance the properties of synthesized tissue.  It has been found that cartilaginous tissue in particular benefits from ultrasound stimulation, increasing cellular viability and the production of type II collagen in the extracellular matrix.  The exact mechanism responsible for the beneficial effects of ultrasound is as yet unknown, although many new theories are in development.  Focus has mostly been placed on cavitation effects, which would harm cells while increasing cellular membrane permeability. 

We provide an alternative theory based on harmonic acoustic analysis in which we investigate the gain and phase of the cellular and nucleic membrane in relation to the incident acoustic wave.  We model the cell using linear acoustic theory for fluids and solids.  An elegant solution is obtained by assuming harmonic time dependence and expanding the problem as an infinite series of Legendre polynomials.  The solution is both accurate and computationally inexpensive, allowing us to compare the effects of the acoustic wave over a wide range of frequencies.  This comparison reveals the fundamental resonance frequency of the cell as well as the associated phase shifts.  We hypothesize that the cell membrane wall thickness varies harmonically along with the flow of nutrients into and out of the cell.  Above the resonance frequency, this phase shift aids the flow of nutrients into the cell, while preventing nutrients from exiting.  This theory is validated by experimental results showing increased concentrations of nutrients in chondrocyte cells exposed to ultrasonic stimulation.