844 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



X, and X c depend on the frequency (v) as follows: 



/ 



Xj2iryL 



X C 2wvC 



The impedance to blood flow through L and C 

 elements will therefore be expected to be frequency 

 dependent, and may be termed hydraulic reactance 

 in contradistinction to resistance which is not fre- 

 quency dependent. Hydraulic impedance may r be 

 expressed as dP/dF, i.e., the rate of change of pressure 

 with respect to simultaneous rate of change of flow. 

 On a pressure-flow diagram, impedance would be 

 represented by the tangent to the curve at any given 

 time. 



Flow Source Versus Pressure Source 



The impedance or "stiffness" of the flow source 

 and pressure source may be expected to influence the 

 response of a vascular segment. For example, a small 

 branch, such as a renal artery arising directly from 

 the aorta, is fed by a stiff pressure source, inasmuch as 

 great changes in renal vascular impedance encoun- 

 tered within extreme physiological ranges have no 

 effect on the abdominal aorta pressure. 



On the other hand, the left ventricle without 

 external controls behaves as a flow source because 

 relatively great changes in systemic arterial imped- 

 ances (viz., aortic stenosis, hypertension, vasodila- 

 tion) cause small changes in the cardiac output. On 

 a beat-to-beat basis, therefore, the left ventricle may 

 be considered to be a stiff flow source or volume pump, 

 and the response of the arterial system is greatly 

 influenced by this fact. The performance of the left 

 ventricle as a volume pump is illustrated in figure 5. 

 The carotid sinus feedback loop tends to make the 

 heart rate and strength of contraction vary inversely 

 with the arterial pressure, but requires several beats 

 for its correcting action. Hormonal negative feedback 

 loops also act on the heart to cause it to perform as a 

 stiff pressure source, but act even more slowly than 

 the reflexes. 



The Analogy Approach 



This is: a) to diagram an electrical network model 

 of specific segments of the arterial system based on 

 qualitative facts available from physiology by identi- 

 fying blood pressure and blood flow with electrical 

 voltage and current; b) to test the model against 

 conditions in an experimental animal by pulsing a 

 direct analogue or an analogue computer with 

 electrical voltage or current transduced from the 



100 

 80 

 60 



8 







+ 100 



+ 50 





 -50 



BLOOD PRESSURE 



5 



AORTIC BLOOD 

 FLOW 



AP 

 (LV.P-A.A.P) 



0.5 sec 



fig. 5. Response of the dog's left ventricle to sudden increase 

 in outflow resistance caused by partial occlusion of the as- 

 cending aorta. — ■ — Control; moderate obstruction; 



■ • • • severe obstruction. 



blood pressure or flow. The computer is programmed 

 to solve the equation of the electrical network, but in 

 this case in terms of pressure and flow instead of 

 voltage and current. Several general considerations 

 of the analogue approach are available (32, 34, 54, 

 60). 



Considerations of this section approach the vascular 

 system from the standpoint of a transient response as 

 distinguished from the usual use of steady-state 

 oscillation in which the harmonic content must be 

 known to reach a solution (20, 26, 51, 61, 62). The 

 transient response method has the advantage of 

 giving an instantaneous solution while in addition 

 each term of the equation has physiological meaning. 

 To regard the arterial pulse as a steady-state oscilla- 

 tion is to fail to recognize the input pulse and the 

 response of the vessels as two independent phenomena 



