I 2 3 4 5 6 



fig. 15. Transfer function of the arteries computed by War- 

 ner (56). i/ n is equal to a resonant frequency. 



40 KS =4= 



1 H 



Olp 



005fJ 



Oil 



110*0 01 11) 



-nST^~ 



0005JJ 



=r=0SC 



fig. 16. Transmission line model of the arterial system, 

 showing the stacking of L-C transmission line segments. [From 

 van der Tweel (55).] 



compliance of the arch (C AA ), or 



dP 



Faa = F Broch + F 5lJbcl + F DTA + C AA — (15) 



figure 1 7 demonstrates this fact experimentally by 

 comparing a plot of the instantaneous sums of -F Br ach.> 

 F DTA ., F Subc i., and C AA (dP/dt) to F AA . The value of 

 C AA was adjusted arbitrarily. 



Abdominal Aorta and Its Terminal Branches 



By the time the pressure and flow pulses reach the 

 abdominal aorta, the highest frequency components 

 are so attenuated that the flow pulses are dominated 

 by a strong resonant wave superimposed on the mean 

 forward flow (fig. 18). The resonant flow wave in the 

 abdominal aorta is in phase with that in the de- 

 scending thoracic and the resonant pressure wave 

 [standing wave of Hamilton & Dow (21)] of the 

 abdominal aorta is 180 degrees out of phase with 



z 



= 5- 



in 

 a. 



u 



1- 



PULSATILE BLOOD FLOW 85 1 



125. 



Aortic Arch 

 Pressure (P) 

 100^3" 



\\ ^Flow Out of Aortic Arch 

 12 F 2 ,F 3 , F 4 , F 5 ) 



Flow into Aortic Arch (F,) 

 (Left Ventriculor Outflow) 



H 



5 sec 



0— V 



5—1 



5 — 



Aortic Arch Radial Flow (F 2 ) 



* — 



Flow out Arch Branches 



< S F 3 , F 4 , F 5 ) 

 Descending Thoracic Aorta Flow (F 3 ) 

 Brachiocephalic Artery Flow (F 4 ) 

 Subclavian Artery Flow (F 5 ) 



fig. 17. Distribution of blood flow in the aortic arch in a 

 manner analogous to KirchhofF's current law. It is shown that 

 the volumetric flow of blood into the arch of the aorta is equal 

 to the sum of the instantaneous flows into the subclavian artery, 

 brachiocephalic artery, descending thoracic aorta, and the 

 radial flow uptake in the aortic arch. The dotted line in the 

 lower section illustrates the branch outflows (not including 

 radial flow). 



that in the upper aorta (48). These phase relation- 

 ships are similar to those of the series resonant circuit 

 of figure 13. When the resonant flow wave reaches a 

 maximum moving down the aorta, the attending 

 pressure wave in the arch is falling most rapidly. 

 When the resonant flow wave reverses, and flows at 

 maximal rate headward in the aorta, the pressure 

 falls rapidly in the lower aorta while it rises rapidly 

 in the arch. There is a nodal area in the descending 

 thoracic aorta where the pressure wave is minimal 

 (2) and the flow wave is maximal. These findings 

 support the resonant-network model of the arterial 

 system. 



Figure 18 demonstrates the remarkable simul- 



