A cylindrical-bubble model for the response of plant-tissue gas bodies to ultrasound

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Abstract
Many plant tissues contain gas in intercellular channels (gas bodies) which pulsate when insonated at megahertz frequencies, thus causing perturbations in nearby cells. Certain long, narrow gas bodies may be approximated acoustically by cylindrical gas bubbles with added stiffness due to the cell walls bounding the gas. Typical gas bodies in Elodea leaves and Vicia faba roots have four and three walls, respectively, which are about 0.5 μm thick and 6 μm wide. The Young’s modulus of the wall material is estimated to be 1010 dyn/cm2, and the walls are subject to a tensile stress of about 104 dyn/cm. Theoretical expressions for the effective stiffness and mass and the radiation, viscous, and thermal damping constants are obtained for free cylindrical bubbles and gas bodies. A 6‐μm diam cylindrical bubble is expected to be resonant at 0.3 MHz with a total damping constant of 0.33. A four‐walled gas body with 6 μm wide sides is expected to be resonant at 3 MHz, with a total damping constant of 0.48. In a typical plant tissue, significant gas‐body activation and intracellular perturbation are expected over the range 0.6–12 MHz, making such tissues useful subjects for the study of the biological effects of ultrasound at these medically relevant frequencies.