PULSATILE BLOOD FLOW 



84I 



appreciation should be had for the relationship be- 

 tween flow velocity, volume, and displacement. These 

 relationships may be expressed best by means of 

 calculus symbology, as follows: 



Displacement (cm) = / Velocity (cm/sec) dt 

 Jo 



Velocity (cm/sec) = / Acceleration (cm/sec 2 ), dt and 

 Jo 



Volume (cm 1 ) 



Flow (cm 3 /sec) 



= / Flow (cm 3 /sec) dt 

 Jo 



f 



Jo 



Volume acceleration (cm 3 /sec 2 ) dt 



For example, the cardiometer tracings during the 

 systolic ejection period may be said to be the negative 

 integral of flow through the aortic and pulmonary 

 valves, and the diastolic cardiometer tracing is the 

 integral of the flow through the A-V valves. Also, the 

 radial displacement of the arteries and veins may be 

 said to be the integral of the radial velocity of blood 

 flow within the lumen. 



Analogue computer techniques, useful in the study 

 of vascular hemodynamics (50), allow one to move 

 from volume to flow to acceleration by means of 

 integration, or the reverse, through differentiation. 

 Two types of integration are currently in use: /) the 

 true time integral which is an instantaneous sum of a 

 given function, beginning from any given time; and 

 2) damping or "meaning," an older usage of the word 

 which implies a mean value of a periodic function. 

 Damping may be accompished either mechanically or 

 electrically. The most practical way to perform this 

 mechanically in a pressure recording system is to 

 introduce compliance or resistance into the trans- 

 mitting system, e.g., by means of a bubble in the 

 gauge or a partial occlusion clamp on the catheter 

 tubing. Damping in an electrical system amounts to a 

 fully charged integrating circuit in which the rate of 

 current inflow into the integrator over one pulse 

 cycle equals the rate of current outflow. 



Resistance (R) 



This arises from the friction between shearing mole- 

 cules flowing through the segment. Expressed in 

 terms of the pressure difference (15) across the re- 

 sistance, AP R , in dynes per square centimeter 1 ; the 

 blood velocity, u, in centimeters per second; the cross- 

 sectional area, A, in square centimeters; and the flow 

 (F R = uA), in cubic centimeters per second, 



AP P AP R 



u-A 



F* 



(I) 



After Poiseuille, in terms of vessel dimensions, length 

 (/) in centimeters, radius (r) in centimeters, and blood 

 viscosity (77) in dynes • second per square centimeter, 



8t,1 



(2) 



The vessel wall also has a small resistance opposing 

 radial distention and collapse. The inverse of resist- 

 ance or conductance (1//?) is often a useful term. 

 The symbol for hydraulic and viscous resistance is 

 taken from electronics ( A/WV~). 



Inertance (L) 



This resides primarily as the mass of blood and 

 secondarily as the mass of the arterial wall. It is ex- 

 pressed in terms of acceleration (a), and attendant 

 pressure difference across the inertance, AP ; , , in 

 dynes per square centimeter. 



AP, 



AP, 



a- A dF, 



(3) 



L /dt 



where F L is the flow through the inertance, and 

 where L = m/A 2 , m is the mass of the blood in the seg- 

 ment of artery under consideration expressed in grams, 

 and A is the cross-sectional area in square centimeters. 

 In terms of vessel dimensions (55), / and r, in centi- 

 meters and blood density (p H ) in grams per cubic 

 centimeter, 



II. ELEMENTS OF VASCULAR HYDRAULICS 



The arterial system is a many-branched elastic 

 conduit for distribution of blood from the heart to all 

 body tissues. The caliber ranges from 35 mm for the 

 human aorta to 7 n for the capillaries. Over this wide 

 range each vascular segment may be described by 

 three fundamental physical properties: resistance, 

 inertance, and compliance. 



Pf, I 



(4) 



1 Pressure in dynes per square centimeter should be used 

 instead of the conventional pressure in millimeters of mercury. 

 The following expression is used to convert from millimeters of 

 mercury (h) to pressure in dynes per square centimeter (P) : 



P = 0.1 g pn e h = '3 2 3 X mm Hg 



where g is the acceleration of gravity in cm/sec 2 , and pn K is the 



