Intracellular temperature distribution produced by ultrasound

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Abstract
The steady-state temperature profile of a biological cell exposed to ultrasound was calculated by solving the time-independent driven heat flow equation. Concentric spheres [3] with different thermal conductivities and acoustic absorption coefficients, immersed in a nonabsorbing infinite medium, were used to represent each cell in a dilute aqueous suspension exposed to ultrasound. The inner sphere represented the nucleus, the middle shell the cytoplasm and the outer shell the plasma membrane. Using representative radii, absorption coefficients and thermal conductivities a steady-state temperature rise of 0.13 mK at the cell center was calculated for frequency 1 MHz and intensity 1 W/cm2. Two forms of temperature (T) dependence on distance (r) from sphere center were calculated: T = D -Er2 and T = G + (F/r), where D, E, F and G are constants which are determined by the intensity, sphere radii, thermal conductivities and absorption coefficients. The inner sphere had form 1 dependence, the shells had both types of dependence and the outside medium had form dependence. Variation of the absorption and conductivity parameters indicated a stronger dependence of temperature on absorption coefficients than on thermal conductivities. Temperature rises greater than 1.degree. were not obtained unless the intensity, absorption coefficient or the inverse of the conductivity was increased by 4 orders-of-magnitude above the representative values used to calculate the 0.13 mK temperature rise.

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