Modeling linear vibration of cell nucleus in low intensity ultrasound field.

Therapeutic ultrasound of low to medium intensity is known to induce alterations in structure and functioning of cells and tissues, both in vivo and in vitro. Such effects, including excitation or inhibition of action potentials, enhanced angiogenesis rate, increased membrane permeability and changes in molecular expression, cannot be attributed in many cases to rising temperatures or the presence of gas bubbles. This study attempts to find a possible alternative explanation for the cases where neither thermal effects nor cavitation mechanisms count. We focus our attention on the complex and dense structure of cell cytoplasm, looking for periodic separating forces and relative motion between intracellular elements, such as the nucleus, and the structure in which they are embedded. It is hypothesized that relative oscillatory displacements between intracellular elements of different densities might appear in cells in response to low intensity therapeutic ultrasound (LITUS). Those displacements might induce alterations in cell structure and functioning. A linear model is constructed and solved for a spherical object, representing a typical organelle such as the nucleus, within a homogenous viscoelastic medium that vibrates uniformly. The structure in which the object is embedded is described by four different rheologic models, including viscous fluid, elastic solid, and Voigt and Maxwell viscoelastic constructs. It is found that cyclic intracellular displacements comparable with and even larger than the mean thermal fluctuations may be obtained due to LITUS irradiation in conditions where the relative motion of organelles is dominated by elastic response, or where the effective viscosity of the cytoplasm is low. Resonance frequency at which intracellular vibration of maximal amplitude is obtained is found to lie within the low LITUS frequency range, i.e., tens to hundreds of kHz. Local intracellular strain on the order of 0.5% is found for 1 microm organelle in 10 microm cell under typical LITUS settings. It is suggested that fatigue-like, cumulative effect underlie the transfer of the intracellular strain into biologic alterations.