METHODS OF MEASURING BLOOD FLOW 



1285 



flow from the relationship of these two variables in 

 the form of a thermal conductance coefficient : 



a (2) 



T c 



T sk 



where Q equals heat flow in (cal cm 2 sec), T c = core 

 temperature and T, k = skin temperature in °C. The 

 dimension of A is calories per square centimeter second 

 °C. The T c as measured does not always represent the 

 temperature of the arterial blood in the region under 

 study. Heat may be lost during the passage of blood 

 irom the core to the site of measurement. Hensel (50) 

 points out that, among other things, the special 

 geometry of the skin area, insulation, local metabo- 

 lism, and countercurrent heat exchange between 

 arteries and veins may modify k without changes of 

 blood flow. 



If it is possible to keep these variables constant, 

 relative changes in blood flow in skin areas can be 

 estimated by measuring k. Several methods are pro- 

 posed. The measuring device should avoid the "re- 

 action-error'' which would occur if calorimeter de- 

 vices are used with large heat capacities and 

 temperatures different from those of the skin (48). 

 However, it is necessary that the heat resistance of 

 the device be made much lower than that of the skin, 

 the resistance of which is determined by the blood 

 flow. 



A device (85) that fulfills the above conditions con- 

 sists of a cork plate 1 mm thick covered with two silver 

 plates with two thermojunctions. The unit is fixed 

 tightly on the skin. The temperature gradient meas- 

 ured between these plates is proportional to Q, the 

 heat flow from the skin. The temperature difference 

 T c — T, k is measured by connecting the skin thermo- 

 junction with a third junction placed in the mouth 

 or rectum. The quotient Q/(T C — T sk ) is measured 

 by a bridge circuit or by a ratiometer. Q can only be 

 measured if the thermal conductivity of the cork 

 plate is known. This value must be determined ex- 

 perimentally. Synchronous measurement of k and 

 blood flow of the finger with the venous occlusion 

 technique furnish a fairly good proportionality. This 

 was found at different room temperatures (15-30 C) 

 as well as at different skin and rectal temperatures. 

 Also, insulation of the arm did not influence the meas- 

 urements. It seems therefore that, according to Aschoff 

 and Wever's results, blood flow is the main factor 

 determining k. 



Vein 



Artery 



7 



50 



100 150 200 



fig. 7. Measurements with original Rein elements and 

 Aschoff and Wever ring-element. Figure shows effect on flow 

 readings when heating electrodes are placed at 90 and o° to 

 the thermojunctions. The compensating effect of a ring unit in 

 which the thermojunctions are fixed on silver rings surrounding 

 the vessel is shown to be effective for pulsations up to 1 20% of 

 mean flow. Abscissa = oscillations in percentage of mean flow. 

 Ordinate = thermostromuhr readings. [From Wever & Aschoff 

 (84)-] 



Flowmeters Based on the Measurement 

 of Thermal Conductivity 



In 1 92 1 the mathematician Carlslaw showed that 

 when a special source of heat is surrounded by an 

 infinitely extended mass of material a steady state is 

 approached in which the relation between heat pro- 

 duction, such as that generated electrically, and heat 

 loss is described by the equation: 



I Z R 



4vrATX 



(3) 



where / = electric current heating a filament with 

 the resistance R, r = radius of the sphere, T = tem- 

 perature of the sphere, and X = the thermal con- 

 ductivity constant. 



In application to our problem we have to consider 

 that X, because of the complexity of the tissue, is not 

 a simple constant but depends on several parameters 

 of the tissue under study (80), and most importantly 

 on blood flow. This dependence on flow provides the 

 basic principle for measurement with this type of 

 flowmeter. Experimental data (42) provided by meas- 

 urements of AT on living organs have shown that a 



