228 



Destructive Effects of High Intensity Ultrasound / 1 2. : 4 



where N is the cell concentration, t is time, and R is the rate constant 

 determining the probability of rupture per unit time. At lower fractions 

 of the original population remaining undamaged, this equation is not 

 always obeyed. The validity of Equation 1 is illustrated in Figure 4. 

 In integrated form, the preceding equation becomes 



In (N/N ) = Rt 



Thus, a plot of N against time permits calculating a value for R. The 

 value of R is a fragility in arbitrary units, provided both the ultrasonic 

 field and the suspending medium remain constant. 



1 1 1 



N = Number of Cells at t 

 A/ = Number of Cells aft=0 



20 30 40 50 60 



Exposure Time (min),i 



Figure 4. Log N/N vs t. These four curves illustrate the 

 linear dependence of log N/N on the exposure time t. The 

 four curves were obtained with different cells exposed to a 

 constant cavitating sonic field. 



The table on page 229 gives some typical values for relative fragili- 

 ties, normalized so that human red blood cells (rbc) are unity. Note 

 the wide range which represents the different properties of the surfaces 

 of different cells. The larger ones tend to be more fragile as measured 

 by this method, but there is no simple relationship between size and 

 fragility. 



Ultrasonic measurements of fragilities give results similar to other 

 types of measurements. For example, the fragility of red blood cells 

 can easily be measured by another method. This consists in suspending 

 the cells in NaCl solutions of various concentrations. As the concentra- 

 tion is lowered, the red blood cells swell and eventually burst (lyse). 



