Estimation of the distribution of low-intensity ultrasound mechanical index as a parameter affecting the proliferation of spermatogonia stem cells in vitro

Considering the use of physical and mechanical stimulation, such as low-intensity ultrasound for proliferation and differentiation of stem cells, it is essential to understand the physical and acoustical mechanisms of acoustic waves in vitro. Mechanical index is used for quantifying acoustic cavitation and the relationship between acoustic pressure and the frequency. In this study, modeling of the mechanical index was applied to provide treatment protocol and to understand the effective physical processes on reproducibility of stem cells. Due to low intensity of ultrasound, Rayleigh integral model has been used for acoustic pressure computation. The acoustic pressure and mechanical index equations are modeled and solved to estimate optimal mechanical index for 28, 40, 150 kHz and 1 MHz frequencies. This model are solved in different intensities and distances from transducer in cylindrical coordinates. Based on the results of the mechanical index, regions with threshold mechanical index of 0.7 were identified for extracting of radiation arrangement to cell medium. Acoustic pressure distribution along the axial and radial was extracted. In order to validate the results of the modeling, the acoustic pressure in the water and near field depth was measured by a piston hydrophone. Results of modeling and experiments show that the model is consistent well to experimental results with 0.91 and 0.90 correlation of coefficient (p < 0.05) for 1 MHz and 40 kHz. Low-intensity ultrasound with 0.40 mechanical index is more effective on enhancing the proliferation rate of the spermatogonia stem cells during the seven days of culture. In contrast, higher mechanical index has a harmful effect on the spermatogonial stem cells. Thus, considering cavitation threshold of different materials is necessary to find effective mechanical index ranges on proliferation for the used frequencies. This acoustic propagation model and ultrasound mechanical index assessments can be used with acceptable accuracy, for the extraction special arrangement of acoustic exposure used in biological conditions in vitro. This model provides proper treatment planning in vitro and in vivo by estimating the cavitation phenomenon.