METHODS OF MEASURING BLOOD FLOW 



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diaphragm 

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fig. 1 7. Schematic diagram of different 

 arrangements of bristle and pendulum flow- 

 meters, a: Bristle in the proper sense, b: Stiff 

 needle with flexible origin (short flat spring or 

 similar), c: Stiff needle the fulcrum of which is 

 formed by a diaphragm, d: Similar to a or b t 

 with a body at the tip. e: Similar to c, with a 

 body at the tip. /.• Coaxial compact cylinder, 

 held by one or two springs. The types a, b, c 

 are now commonly called "bristles," the 

 types d, e, f: "pendulums." [Redrawn and 

 modified from Taylor (127).] 



flow pulses, it is said to indicate mean flow faithfully, 

 irrespective of whether the flow is steady or pulsatile, 

 provided no phases of essential backflow occur. Its 

 resistance to blood flow is relatively high. The small 

 model causes pressure drops of about 5, 1 3, 30, and 50 

 mm Hg at flow rates of 1, 2, 3, and 4 liters per min, 

 respectively. The pressure drops caused by the large 

 model are lower. Heparinization of the dogs is, of 

 course, necessary. Some alteration of the pulse wave 

 and hemolysis might be caused by the instrument. 



BRISTLE AND PENDULUM FLOWMETERS 



When a body is immersed in a streaming fluid, it 

 represents an obstacle to the flow. The force exerted 

 on the body by the streaming fluid is due partly to 

 friction and partly to mass inertia of the fluid. Ac- 

 cording to Frank (40), this force F is given approxi- 

 mately by the formula: 



F'V + Cf* ( ' 0) 



where v = velocity of the fluid acting on the body; C\ 

 and C2 = coefficients which depend on the viscosity 

 and density, respectively, of the fluid, on the size and 

 shape of the body, and on the local distribution of 

 velocities; C\ v = frictional term; C« v 2 = inertia term. 

 Sometimes, another approximation is used: 



F -" Cv* 



(II) 



where, in case of blood, the exponent k is found to be 

 between 1.2 and 2.0. As will be discussed below, theo- 

 retical estimation of the coefficients and of the expo- 

 nent is impossible except under very simple conditions, 



so that an empirical determination is usually neces- 

 sary. 



If the body is held in its position by an elastic device, 

 it will undergo some displacement due to the force F, 

 and thus the degree of displacement can be taken as a 

 measure of that force. Since the force is related to the 

 fluid velocity, according to equation 10 or 11, the 

 registration of the displacements by mechanical, 

 optical, electrical, or other means represents a con- 

 tinuous recording of the flow. For the construction 

 of such devices, the following requirements should be 

 taken into account: a) The resistance to flow produced 

 by the obstacle must be so small that the flow is not 

 significantly influenced, b) Where pulsatile flow is to 

 be recorded, the natural frequency of the elastically 

 suspended body must be much greater than the 

 highest significant frequency. If this condition is ful- 

 filled, the displacements of the body will be very small. 

 c) As far as possible a fixed relationship should be ob- 

 tained between force and displacement on the one 

 hand and average flow velocity on the other, inde- 

 pendently of the velocity profile. This will be discussed 

 below. 



The body itself can be in the form of a rod or 

 needle set perpendicularly to the direction of flow. 

 This needle is usually attached at its origin to the end 

 of a side tube while its tip remains free and reaches the 

 axis of the main tube as shown in figure 1 7<j to c . In 

 some devices, the needle is longer. If the origin is 

 totally fixed whereas the needle itself is flexible, it 

 will be called a bristle in the proper sense (fig. ija). 

 In most cases the needle is rigid, but is allowed to 

 move about a fulcrum (fig. 176 and c). While this 

 type physically represents a pendulum, it is now usu- 

 ally called a bristle, too. The common characteristic 



