13: i / Mechanical Resonances of Biological Cells 



235 



One might wonder why surface modes of resonance were referred to 

 above as the basis for the characteristic frequencies for cellular dis- 

 ruption. Far more work has been done with pulsating bubbles in which 

 the surface remains spherical than with bubble surface modes of vibration. 

 However, all calculations show that any pulsating modes for biological 

 cells (or any resonance dependent on the wavelength of sound in the 

 suspending medium) should occur at much higher frequencies than those 

 observed with cavitating sound fields. Accordingly, the characteristic 



Thin Membrane; Seat of 

 Interfacial Tension, T. 



Cell Cortex; a Cel- 

 like Material with 

 sSAear Modulus, \l. 



Figure I. The interfacial-tension model (a) and rigid-shell 

 model (b) . These two models of the surface of a biological cell 

 are essentially different in that (a) presupposes that the cell 

 wall lacks any rigidity or shear modulus whereas, by contrast 

 (b) includes the rigidity of the outer cell layers but ignores any 

 interfacial tension which may be present. Both disregard 

 the contributions of the intracellular structure to the forces 

 determining the cell shape. 



frequencies seem to represent some other resonance of the biological cell 

 such as surface vibrations. 



Sections 2 and 3 deal with the mathematical development of two 

 simple models of biological cells, both of which make resonances reason- 

 able in the observed frequency ranges. These are illustrated in Figure 1 . 

 The first model treats the cell as if it were a sphere surrounded by a 

 membrane possessing an interfacial tension but no rigidity. The 

 internal viscosity of the cell is ignored in this first approximation. This 

 model has been used to describe the results of centrifuge studies on cells, 

 shape-distortion studies, and so forth. Because the model has proved 

 useful for static studies, it seemed a promising one for dynamic studies 

 such as observations of surface modes of resonances. 



The second model also treats the cell as a fluid-filled sphere with 

 negligible internal viscosity. However, it assigns a rigidity to the cell 

 cortex, or outer layers. In both models, the cells are considered, then, 

 to be spheres filled with one ideal, incompressible liquid and surrounded 

 by another. Clearly, no biological cell fits this description. Thus, the 



