PULSATILE BLOOD FLOW 



843 



F = C 



dAP r 

 dt 



R 



dF 

 dt 



(12) 



or rearranging equation 1 1 



w [ Ap r-~rf Fdt ] <"> 



Since measurements of pressure and vessel diameter 

 are very similar, friction within the arterial wall and 

 radial inertance are apparently quite small, although 

 in the final analysis, as clearly indicated by Peterson 

 (35), one must consider acceleration along with dis- 

 tensibility and friction. 



When the total flow (F T ) in an elastic pipe is con- 

 sidered, both radial and axial flow equations must be 

 combined as follows for instantaneous flow: F T = 

 !'„,,,, 1 + F Tmiial , and, from equations 9 and 12, 



V J rf( AP o- R al r a)dt+ (14) 



In analogue computer language this equation is 

 solved as in figure 3. Patel et al. (33) have found 

 negligible degrees of inertiance and resistance in the 

 pulmonary artery wall. 



A more complete hydraulic diagram of an arterial 

 segment may be well shown as in figure 4. L, , Ri , 

 and C'i represent its most important elements, with 

 R 2 and R 3 representing radial and axial resistance, 

 and C-i representing axial compliance. The complete 

 arterial system may be viewed as a continuous linkage 

 of such segments, each branch and segment having 

 quantitative differences in magnitude of the individual 

 physical elements. At the same time, the physical 

 elements of any segment or group of segments may be 

 described by over-all "lumping" of the elements. 



The arterial system is not a passive network because 

 the elements may be influenced by the nervous 

 system, endocrine system, metabolic processes in the 

 wall, and changes in the physical properties of the 

 blood. In addition, the values of the elements are 

 nonlinear functions of pressure, vascular dimensions, 

 velocity profile and many other influences. In spite of 

 these complications, much can be learned by linear 

 analysis of the pressure and flow pulses at various 



fig. 3. Analogue computer diagram for solution of the equa- 

 tion of liquid flow in an clastic tube. P, and ft represent the 

 lateral pressures from two stream points. AP is the independent 

 variable (AP = P l - ft). 



U R, 



L, 



-VWA 



R, 



fig. 4. Elaborate electrical analogy of a vascular segment. 



points within the arterial network studied under 

 reasonably steady-state conditions. 



Hydraulic Impedance 



This is the concept of total opposition to pulsating 

 and constant flow. Drawing on the electrical symbol- 

 ogy, we have Z, X L , A' c , and X R , where Z represents 

 the total impedance, and A' L , X c , and X R equal the 

 inertial, compliant, and resistive impedances. X R is the 

 opposition to flow, X L is the opposition to change in 

 flow, and A'c is the opposition to change in volume. Both 



