842 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



The symbol for inertance is that for electrical induc- 

 tance (13£R5T~"). Because inertance is defined in terms 

 of volumetric acceleration, the larger the cross section 

 of the vessel lumen, the smaller is the inertance in 

 a vessel of given length. 



-'ffOTffWW^ 



) 



Compliance (C) 



Compliance is a property of the arterial wall 

 arising from its distensibility and chiefly residing in the 

 elastic fibers. The contribution of smooth muscle and 

 fibrous tissue has not been determined. It is expressed 

 in terms of blood volume (V) in the segment and the 

 attending pressure difference across the vascular wall 

 AP C . 



AP C AP C J 



(5) 



where F r is the flow into the compliance, or in terms of 

 dimensions (22) length (/), radius (r), wall thickness 

 (0), and the modulus of elasticity (£) : 



C° 



2irr- 

 Eo-l 



(6) 



The symbol for compliance is that of electrical 

 capacitance ( — I 1 — ). 



Axial Flow 



In a segment of rigid pipe axial flow is analogous to 

 the current in the diagram of figure 1 . Where AP axia i 

 = p l — P 2 , AP a at any instant in time will be equal 

 to the sum of the pressure differences due to the R and 

 L components. Thus : 



A P. 



axial 



= AP, 



*■ AP 

 Rtsislono r " r Inertanca 



(7) 



(Any pressure gradient resulting from gravity 

 cancels if the pressures are referred to the same level.) 

 Substituting from equations 1 and 3, and considering 

 F R = F L = F, 



AP=RF+L 



dF 

 dt 



(8) 



integrating with respect to time we have 



F-j-f(AP -RF)dt (9) 



This equation may be solved continuously by an 

 analogue computer and has some practical applica- 



density of mercury at the existing experimental conditions in 

 g/cm 3 . 



fig. I. Electrical analogue of axial flow and pressure in a 

 rigid tube. 



i 



Fr I 



J' 



fic. 2. Electrical analogue of radial How in an elastic tube. 



tion in the ascending aorta (12, 13). The procedure 

 is to subtract P> from Pi to obtain i\P, and then to 

 subtract RF from AP and integrate the result. If 

 j/L is known or is chosen arbitrarily, R may then be 

 adjusted until F achieves some known boundary 

 condition such as F = o during diastole. Figure 3.Z? 

 graphically illustrates the procedure. If accurate 

 values for vessel dimensions, blood density, and 

 viscosity are available to calculate L and R, the 

 result can be obtained in terms of actual flow in 

 cubic centimeters per second, otherwise the answer 

 only yields the velocity in centimeters per second. 



Radial Flow 



In a visco-elastic artery, radial flow is analogous to 

 the current in the diagram of figure 2. 



4Pm*m"A%*AIk 



(10) 



where AP ra diai represents the pressure difference across 

 the arterial wall (P T \ — P r2 ). Substituting from equa- 

 tions 1 and 5, where F r = F c = F R , 



AP,'7-fFdt + RF 



(II) 



and differentiating, 



