PULSATILE BLOOD FLOW 



8 47 



the pressure gradient (47). Figure 10 demonstrates 

 this fact at the aortic valve where, during late systole 

 blood is flowing through the valve against a pressure 

 gradient. A similar finding has been shown for the 

 right ventricle (H. Okino, unpublished work). These 

 findings prove dynamically that the forward resistance 

 of the aortic and pulmonary valves is slight. Further, 

 the energy of external work of the ventricles is spent in 

 raising the blood pressure to sufficient level to acceler- 

 ate the blood into the aorta and pulmonary artery. 



Windkessel Model of the Arterial System 



This has been a concept of limited usefulness to 

 explain the form of the arterial pulses. It may be 

 represented by the analogue of figure 1 1 . The arterial 

 chamber is represented by the compliance (C), and 

 the peripheral resistance by the resistance term (R). 

 The basic relationship here, between pressure and 



'ihMMiM 0.5 sec mmmum 



IIIJiiiiMiillTiliiliiiiliWHki'liiliil^iiillliiHHill 



A P 



EMF 



F (tf C df + yiAP-RF L > dt 



fig. 9. Computer solution to blood flow in the ascending 

 aorta using the analogue computer of fig. 3. F em i = the flow 

 measured by the electromagnetic flowmeter. F t = computed 

 How. C(dP/dt) = the radial flow pattern derived from the time 

 differential of the aortic arch pressure P. 



flow, is F = C (dP/dt) + (i/R) P. When this electrical 

 model is experimentally pulsed by a current trans- 

 duced from the flow in the ascending aorta (F), the 

 voltage form (V) is obtained. By comparison, the 

 actual pressure pulse in the aortic arch (P) deviates 

 in several details from 1": 1) P has a superimposed 

 3 to 6 cps oscillation apparent from midsystole 

 throughout diastole, and 2) P has a more prominent 

 "incisura" marking aortic valve closure and a more 

 abrupt rise, often with an anacrotic wave. In addition, 

 the windkessel model fails to explain the changes in 

 form occurring along the arterial network. Detail 2 

 appears if the analogy is elaborated by the placement 

 of some restraint on the distensible element, i.e., 

 taking into consideration the friction in lateral 

 expansion of the arterial wall, as in equations 1 2 and 

 13. Detail / requires a concept of reflections or 

 resonant network filter as explained in the succeeding 

 paragraphs. Cope (7) has attempted new use of the 

 windkessel concept using empirical constants. 



Aortic Transformation of Flow and Pressure Pulses 



Figure 1 2 illustrates the changes in form and 

 magnitude of the flow pulses between the ascending 

 aorta and the abdominal aorta. The flow in the 

 descending thoracic aorta represents an intermediary 

 form and well illustrates the superimposition of a 

 prominent smooth 3 to 6 cps wave decreasing in 

 amplitude throughout diastole. This wave referred to 

 as the "resonant" wave frequently causes backflow in 

 diastole throughout the aorta and many of its 

 branches. Considered as a whole, the arterial system 

 is a low-pass filtered hydraulic supply, i.e., it is 

 designed to offer negligible impedance to steady flow 

 and frequencies up to 10 cps. There is normally one 

 frequency between 3 and 6 cps to which it offers 

 lowest impedance, and resonates at that frequency 

 with each beat of the heart. Early physiological 

 workers recognized this resonant system as analogous 

 to a low-frequency underdamped manometer system. 



Resonant-Network Model of the Arterial System 



This represents an improved concept to explain 

 the transformation of arterial pressures and flow 

 pulses. It is diagramed in figure 13. C\ roughly 

 represents the lumped compliance of the aortic arch 

 and its branches, and C 2 , the lumped compliance of 

 the abdominal aorta and its branches. L represents 

 the lumped inertance of the blood in the descending 

 aorta. F H represents the forcing function of the left 



