11:3/ The Absorption of Electromagnetic and Ultrasonic Energy 



211 



alternating field, the molecule must reverse its polarization each half 

 cycle. 2 Above the relaxation frequency the electric field changes so fast 

 that the molecular polarization no longer follows it. The larger the 

 molecule, the lower the relaxation frequency. The dielectric constant 

 and resistivity of the molecules drop fairly abruptly from higher values 

 below the relaxation frequency to lower values above the relaxation 

 frequency. Proteins have relaxation frequencies in the range of mega- 

 cycles apparently without effect on the lumped parameters of tissues. 



1,000- 



5 400 



3 



8 



10 



4 5 6/ 

 log f (cps) 



Figure 3. Resistivity of muscle as a function of frequency. 

 Note the similarity of the relaxation regions for Figures 2 and 3. 

 After H. P. Schwan and C. F. Kay, "Conductivity of Living 

 Tissues," Annals of the New York Academy of Sciences 65: 1007 

 (1957). 



Small molecules such as those of water exhibit similar relaxations in the 

 region of 10 10 cps, giving rise to region y in Figures 3 and 4. The low 

 frequency relaxation, in region a, must represent the behavior of some 

 part of the cell that is large compared to a protein molecule. 



The frequency dependence of the resistivity and dielectric constants of 

 many different types of tissues are all similar. These are also similar to 

 that of blood. The resistivity of blood, particularly at low frequencies, 

 is lower than that of most other tissues, owing to its high water content. 

 The values for muscle, liver, spleen, pancreas, lung, and kidney are all 

 very similar, except that below 10 5 cps they are higher than that for 

 blood. Exceptions to the preceding general pattern are brain tissue, 

 fat tissue, and bone. The last, with its high content of calcium phos- 

 phate crystals, is very different from soft tissues. Its impedance is 



2 For small molecules with a permanent dipole moment, this implies an actual 

 physical rotation. For small molecules without a permanent dipole moment, and for 

 all large molecules, this change involves a rearrangement of the electron orbitals and 

 of the atomic spacings within the molecule. 



