In this paper a new technique is proposed to determine the acoustic properties as well as the thickness (and volume) of biological cells. Variations of thickness, density, acoustic wave velocity, stiffness, and attenuation coefficient of a living or dead cell are obtained by scanning the cell by an acoustic microscope. The distance between the cell and the microscope lens is varied and several voltage curves are thus obtained. These curves are then inverted by simplex optimization technique to obtain the cell parameters. The spatial resolution of the method is limited to the resolution of the scanning acoustic microscope. It allows to take advantage of the full range of frequencies and amplification of the microscope. Characteristic distributions of stiffness are exemplified with an endothelial cell in culture. The main part of the thin, lamellar cytoplasm has high stiffness, which drops close to the lamella/cell body transition region and only slightly increases again through the central part of the cell. Acoustic attenuation seems to be related to two factors, cytoplasm accumulation (in the lamellar parts) and scattering in the central part rich in organelles.

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In this paper, a mathematical formulation is presented to compute the V(z) of a tapering layered solid and applying this formulation to the determination of acoustic properties of biological cells and tissues. The formulation is adopted in the simplex inversion algorithm to obtain the acoustic properties of a tapering cell from its V(z) values. The influence of two parameters had been considered: The tapering angle and the presence of a thin liquid layer present between cells and the substratum to which they adhere. Up to a tapering angle less than 10 degrees, it can be safely neglected. However, if a larger angle is neglected, then the acoustic wave velocity in the cell is overestimated. Cell thickness estimation is not affected significantly when the tapering angle is ignored. The calculations of acoustic properties of cells are considerably influenced by the introduction of a thin fluid layer between the solid substratum and the overlying cell, neglecting the presence of at least a very thin layer (20-30 nm), in general, results in a considerable overestimation of sound velocity. The reliability of the data calculated from V(z) values was ascertained using an independent method to determine cell thickness by calculating it from the interference fringe pattern obtained with the reflection-interference light microscope. The shape of the glutaraldehyde-fixed cells was similar to fried eggs. The highest sound velocities were found close to the periphery of the dome-shaped cell center. In the very center and over most of the area of the thin periphery, sound velocity was close to that in saline.

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