11:5/ The Absorption of Electromagnetic and Ultrasonic Energy 



215 



hemoglobin is similar to that due to the plasma proteins. Absorption 

 by proteins represents the major part of the ultrasonic absorption in 

 blood. A much smaller effect can be observed in dilute suspensions of 

 blood cells, which may be attributed to the motion of the liquid relative 

 to the cells. The absorption coefficient for whole blood is about 0.2 

 db/cm at 1 mc, or in other units about 0.03 db per wavelength. The 

 second figure is correct within a factor of two throughout the frequency 

 range 0.7 to 10 mc; that is to say, the absorption per wavelength increases 

 only very slowly with increasing frequency. The graphs in Figure 4 

 show this variation. Figure 5 shows the variation of the absorption 

 per wavelength over a greater frequency range. 



This slow increase is extremely difficult to understand. All simple 

 theories indicate that the absorption per wavelength should be pro- 

 portional to the frequency. The failure of the simple theories is 



^ 10 



7 

 5 



x 



Q- 



3 



2- 



i.O 

 0.7 

 = 0.5 



b 



°- 0.3 

 c 



5 0.2 



§■ 



I 0.1 



-S? 



J3 



S 7 



vt Red Cells (90 vol.%) 

 °» Plasma 



vo Carstensen, Li, Schwan, 1953 

 » • Gramberg, 1956 



I I L_i ''''I 



5 7 



5 7 



10" l J J I0 Q c J J ' 10° L J J ' 10' 



Frequency (cps) 



Figure 5. Ultrasonic absorption of red blood cells and plasma 

 from 30 kc to 10 mc. Note that the absorption per wave- 

 length changes only fivefold when the frequency changes three 

 hundredfold. (To convert nepers to db, multiply by 8.7.) 

 After E. L. Carstensen, with permission. 



"explained" by saying that relaxations occur and that, as a result, the 

 protein molecules no longer move as a whole at higher frequencies, or 

 else somehow parts of the molecules become free to slip back and forth 

 past other parts. Even on this model, the absorption per wavelength 

 should be approximately independent of frequency only in a very- 

 narrow frequency region. Instead, the absorption depends only slightly 

 on the frequency over the entire range from 0.3 to 20 mc (that is, almost 

 a 100: 1 ratio or about six octaves). It is still possible to explain away 



