THE CIRCULATION AND CIRCULATION RESEARCH IN PERSPECTIVE 



in which rj, r-i, >'3, etc. represent regional or territorial 

 resistance in the different parallel circuits shown in 

 figure 2 (Wezler & Boger, 67). As an example of the 

 relation of parallel circuits to TPR, it has been esti- 

 mated that whereas the regional resistance of the 

 cerebral or coronarv circuits of dogs have magnitudes 

 of 18,000 dyne-sec per cm\ the TPR is very much 

 less in proportion, as the regional flow is less than 

 the total cardiac output. 



Dynamics of the Arterial System 



Since the distributing system accomplishes its 

 biological functions in a mechanical way, numerous 

 attempts have been made to express its dynamics by 

 mathematical formulations. A detailed exposition 

 and an evaluation of their present status is of course 

 excluded in an introductory chapter. The historical 

 fact may however be noted that mathematical treat- 

 ment of pressure waves in elastic tubes dates from the 

 early work of Euler (1775), Voung (1808), VV. E. 

 Weber (1866), Resal (1876), Moens (1878), and v. 

 Kries (1892). The interested reader may consult the 

 reviews by A. Miiller {45), H. Straub (58), A. Aperia 

 (i, 2), Wezler & Boger (67), Gomez (23), Wezler 

 & Sinn (69), Womersley (74), and W. Sinn (54). 

 A survey of such reviews reveals that, whereas there 

 is at present no consensus as to particulars, there is 

 agreement on general matheinatical formulations 

 which, for our purpose, can be translated into simple 

 language [see also (27, 59, 66)]. 



Pressure and flow in the arterial tree are main- 

 tained h\ the rhythmic action of the cardiac pump. 

 During each systole, the left ventricle ejects a definite 

 \olinne of blood into the aorta — about 60 to 100 

 ml in man — variously called the stroke volume, 

 systolic discharge, and pulse volume. The period of 

 ejection is very short; about 0.25 sec at normal heart 

 rate and less during cardiac acceleration. Moreover, 

 fully two-thirds of the stroke volume is displaced into 

 the aorta within about o. i sec, and very little during 

 the final 0.05 sec of systole. Since the aorta, at the 

 onset of ejection, is already distended under a pres- 

 sure of about 75 mm Hg, aortic uptake is accomplished 

 partly by accelerating the stationary blood column 

 and moving it ahead — kinetic energy — and partlv 

 by distending the elastic walls. The potential energy 

 thus stored in the elastic walls presses back on the 

 blood in accordance with Newton's third law of 

 motion and causes the rise of systolic pressure. In 

 short, the elasticitv coefFxient, which can be ex- 



pressed in dynes per cm=, is the basic determinant 

 of pulse pressure (67). 



The systolic elevation of pressure thus created in 

 the aorta is transmitted as a pressure wave through 

 the arterial tree at rates varying from 3 to 14 meters 

 per sec. However, as already intimated, the form of 

 the pulse pressure is altered in transmission by damp- 

 ing and by summation with reflected or standing 

 waves, and possibly by the unequal rates at which 

 harmonics of the pressure pulse are transmitted 

 [Peterson (48)]. 



In contrast to the high speed with which pressure 

 waves are propagated, the velocity with which blood 

 flows through the arterial tree ranges from 14 to 18 

 cm per sec. The reason for these differences may be 

 visualized by reference to figure i . As indicated by 

 the cross-hatched area, blood ejected during any 

 given systole is accommodated in the aorta and its 

 immediate branches. Blood already within this space 

 is displaced under pressure to a more distal segment 

 of the arterial tree as indicated by the black area. 

 This translocates blood to a third segment under 

 pressure, as indicated by the lined area. Thus whereas 

 the pressure wave may reach vessels in the feet within 

 0.2 to 0.3 sec, corpuscles ejected during any heart 

 beat do not arrive there until several more heart 

 beats have occurred. 



At the onset of diastole, the blood column reverses 

 momentarily during closure of the semilunar valves; 

 then it moves forward again as the elastic aortic 

 walls recoil slowly and reconvert the stored potential 

 energy into energy of flow. This buffering function 

 that maintains a constant flow through capillaries 

 was recognized by Borelli (1680) and by Hales (1733), 

 and was baptized as the Windkessel by E. H. Weber 

 (1834). Although, in a sense, the entire distributing 

 system aids in smoothing blood flow through the 

 capillaries, the aorta and its immediate branches 

 probably constitute the effective compression cham- 

 ber; the volume uptake of more peripheral branches 

 per mm Hg per unit length decreases rapidly, owing 

 to increasing stiffness of their walls [Remington (50)]. 



The elastic properties of the aortic walls are largely 

 due to the elastic fibers dispersed throughout the 

 intima, media, and adventitia. Their conformance 

 to Hooke's law probably explains the almost pro- 

 portional relationship between pulse pressure and 

 aortic uptake at ranges of end-diastolic pressure 

 between 40 and 100 mm Hg. Within these pressure 

 ranges the corrugated collagenous fibers merely 

 unfold and only act to stiffen the walls at end-diastolic 

 pressures above 100 mm Hg. The aortic walls also 



