208 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 3 



In general, all of the terms R, X, a, and e vary with frequency. Studies 

 of their variation should be interpretable in terms of the molecular 

 structure of cells and cell membranes. Such interpretations could 

 either support or refute a given molecular model. The electrical con- 

 stants are obtained, in general, by measuring the electrical impedance of 

 suspensions of cells and of aggregates of cells organized into tissues. The 

 success and limitations of this approach are discussed in the next section. 



3. Biological Impedance 



The membranes of most cells act as insulators at low frequencies. 

 Thus, if one suspends cells in a saline solution, most of the current will 

 flow around the cells. The electrical current must then follow a longer 

 path than in the absence of the cells. In terms of electrical impedance, 

 the resistance (or resistivity) will be higher for the suspension than for 

 the pure suspending medium. The difference in these two resistivities 

 can be used to find the volume of the cell. 



For tissues, likewise, the low frequency impedance is a measure of the 

 free space between the cells. It is interesting that this impedance is 

 about the same for skeletal muscle, liver, and cardiac muscle. The 

 resistivity p is about 900 ohm -cm, dropping slowly as the frequency 

 increases from 1 cps to 1 ,000 cps. Blood, with fewer formed elements, 

 has a much higher conductivity (that is, lower resistivity), whereas fatty 

 tissues and bones have lower conductivities in this low frequency region. 



Between 1 kc and 100 kc, the impedance of a suspension of single cells 

 drops quite sharply to a lower value. For a suspension of single cells of 

 simple geometry in a saline solution, one can solve exactly the equations 

 describing the flow of current. A first approximation is to assume the 

 cell is a spherical homogeneous conductor surrounded by a noncon- 

 ducting (lipid) layer as shown in Figure 1 . This fits the impedance data 

 in a qualitative fashion. The lipid layer acts as a capacitor in series 

 with the cell interior. At low frequencies, the impedance of the 

 capacitor (that is, the lipid shell) 



Z -J- 



is very high because the frequency co appears in the denominator. 

 Hence, little current can enter the cells, which then appear to be 

 insulators. At higher frequencies, Z c becomes negligible and current 

 can readily pass into the cell interior. At such frequencies, the im- 

 pedance of the suspension will be less than it is at lower frequencies. 

 A better quantitative fitting of the theory to the experiment can be 



