234 Mechanical Resonances of Biological Cells /1 3 : I 



friction in metals and polymers. It appears reasonable that if similar 

 resonances occurred for biological cells, these resonances could be an 

 indication of the physical properties of the cells. 



The previous chapter referred to the existence of certain characteristic 

 frequencies at which cells are more easily destroyed than at other fre- 

 quencies. At a characteristic frequency, the relative rate at which a 

 given type of cell is destroyed is greatly increased. Optical studies have 

 also shown distortions in the shape of cells exposed to ultrasonic vibra- 

 tions; these distortions occur to a greater extent at a lower ultrasonic 

 pressure at certain frequencies characteristic of the geometry of the cell. 

 The accompanying table shows the sizes and the characteristic frequencies 

 of various strains of paramecia. Other studies have shown similar 

 effects for red blood cells and for single cell types of algae. It is easiest 

 to interpret these as due to mechanical resonances involving the cell 

 surfaces. Similar surface resonances have been demonstrated and 

 studied for air bubbles suspended in water and for rain drops. 



TABLE I 

 Optimum Frequency versus Size 



In this chapter, the mathematical theory for surface resonances of 

 biological cells is discussed. It forms a link between cell models and the 

 experiments demonstrating characteristic frequencies. In this chapter, 

 the typical approach of the mathematical physicist is followed. First, 

 very simple models are analyzed, then the conclusions are modified to 

 fit more complex models which come closer to the physical form of the 

 particular type of biological cells involved. 



It was noted in the introduction that an attempt had been made to 

 limit the level of mathematics necessary to understand this text but that 

 a few chapters demonstrated that biophysics does use more advanced 

 mathematical techniques where needed. The reader with an aversion 

 to mathematical treatments is advised to omit the rest of the chapter. 

 Those whose mathematics does not extend beyond calculus will find it 

 necessary to accept several statements and conclusions on faith but 

 should find most of the chapter understandable. 



