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Mathematical modeling of ultrasound in tissue engineering: From bioreactors to the cellular scale

Tobias M Louw, University of Nebraska - Lincoln


Tissue engineering seeks to provide a means to treat injuries that are beyond the body's natural ability to repair without the issues associated with allografts. Autologous cells are cultured in a bioreactor which controls the cellular environment (including mechanical stimulation) for optimal tissue growth. We investigate ultrasound as an effective means of mechanical stimulation by predicting the ultrasonic field in a bioreactor, as well as ultrasonic bioeffects at the cellular level. The Transfer Matrix Angular Spectrum Approach was found to be the most accurate and computationally efficient bioreactor model. Three critical factors influence experimental results: (1) the diameter of the tissue engineering scaffold greatly affects the ultrasonic field; (2) the position of the ultrasonic transducer and liquid level in the tissue culture well determines the maximum pressure amplitude in the bioreactor, but the pressure can be controlled by measuring the transducer input electrical impedance and manipulating the applied voltage; and (3) the position of pressure nodes are influenced by ultrasonic frequency and liquid level; this will affect the response of cells to applied ultrasound. On the cellular level, it was shown that chondrocytes respond to ultrasound with frequency dependence. A predicted resonance frequency near 5MHz matched experimental results showing maximum expression of load inducible genes at 5MHz. Mechanical stresses are concentrated near the nucleus at resonance, alluding to the possibility that the nucleus may directly sense ultrasonic stimulation. We postulate that ultrasound influences the transport of p-ERK to the nucleus or causes minor chromatin reorganization, leading to the observed frequency dependent gene expression. We linked in vitro ultrasonic stimulation to in vivo mechanical stimulation generated by natural movement. The chondrocyte's response to impact is under-damped, and the cell oscillates with a frequency close to the model predicted resonance. It appears that ultrasound applied close to the cell's resonant frequency effectively recreates the mechanical stimulation experienced by cells during natural movement. Ultrasonic bioreactors may therefore reproduce physiological conditions just as well as more complex bioreactors.

Subject Area

Biomedical engineering|Acoustics

Recommended Citation

Louw, Tobias M, "Mathematical modeling of ultrasound in tissue engineering: From bioreactors to the cellular scale" (2013). ETD collection for University of Nebraska - Lincoln. AAI3589769.