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HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



cylindrical tubes. The phenomenon of venous col- 

 lapse was inherent in the classical observations of 

 Harvey. It has remained a commonplace observation 

 in the use of the height above the heart at which super- 

 ficial veins collapse as a clinical estimate of central 

 venous pressure. Yet the hemodynamic significance of 

 venous collapse has been all too rarely appreciated. 



First, it is important to note that '"collapse" of 

 veins is not an all-or-none characteristic. Complete 

 collapse of the vein with obliteration of its lumen 

 represents an obstruction to blood flow which can 

 onlv exist on a transient basis. The collapse phenome- 

 non relates to the fact that the vein wall is not struc- 

 turally self-supporting. Energy is required to push 

 the vein walls out into a cylindrical configuration. 

 Any time that the intraluminal pressure becomes 

 equal to or less than the extravascular pressure, the 

 venous walls will tend to approximate each other in 

 an ellipsoidal cross section (73). 



This is best visualized by examining veins above 

 heart level. Hydrostatic forces will act to drain blood 

 from these veins and create a negative intraluminal 

 pressure. In addition, finite tissue pressures always 

 produce some degree of positive extravascular com- 

 pression. In the absence of blood flow, such a vessel 

 would remain completely collapsed. To preserve 

 flow in such a segment, intraluminal pressure must 

 be raised until it slightly exceeds the extravascular 

 pressure so as to open the collapsed vein. Intraluminal 

 pressure must further be elevated enough above 

 extravascular pressure to provide the necessary pres- 

 sure head to produce forward flow against the re- 

 sistance it confronts. However, since a slightly positive 

 transmural pressure will widen the collapsed lumen 

 and produce a marked fall in resistance, very little 

 pressure gradient is required to produce flow. There- 

 fore, the pressure measured in veins that are above 

 heart level will be essentially the same as the extra- 

 vascular tissue pressure, as originally emphasized by 

 Holt (51, 52, 80). It follows that such pressures have 

 no hemodynamic significance in the usual sense of 

 gradients along the vascular circuit, and they are in 

 no way specifically related to constriction or dila- 

 tion of the veins. 



A more rigorous statement of this relationship has 

 been clearly set forth in the exposition by Brecher 

 (11). The classical formulation of the Poiseuille law 

 for cylindrical tubes: 



resistance oc radius * 

 must be modified for collapsible tubes to the more 



complex expression: 



Rex 



2a 3 b 3 



in which R is resistance and a and b are the major 

 and minor axes of the ellipse. It should be noted that 

 in a cylinder where a = b, the second expression 

 reduces to the first. As an operational tool, this 

 formulation of resistance relationships is rarely of 

 practical value to the physiologist because the desired 

 dimensions are not accessible. Nevertheless, from a 

 theoretical standpoint it defines the fact that re- 

 sistance to flow will increase markedly as the vessel 

 progressively collapses to a flattened ellipse. 



The full import of this collapsibility resides in the 

 consequences it has upon the significant variables 

 determining blood flow. In a system of cylindrical 

 tubes, as represented by the arterial system, pressure 

 is normally maintained at homeostatic levels in the 

 arterial reservoir and, for any given vascular bed, 

 blood flow is controlled by resistance changes through 

 the activity of the vascular smooth muscle in the 

 arterial supply to that bed. To emphasize this point, 

 one might consider the pressure as essentially con- 

 stant (P a ) under a given situation and the significant 

 variables of flow (Q) and resistance (R a ) expressed as: 



6 = 4r x P„ 

 R„ 



In contrast, in any local venous bed, the flow is 

 obligate since in a steady state the veins must trans- 

 port the volume of blood delivered by arterial inflow. 

 Flow may therefore be considered constant and in 

 any venous segment resistance is controlled by the 

 local pressure (P,,) which, as outlined above, must 

 represent a small increment over the extravascular 

 pressure : 



Stated descriptively, in the venous system operating 

 under a state of partial collapse, local venous pressure 

 determines the cross section of the ellipse and thereby 

 adjusts resistance to accommodate the volume of 

 flow presented to the system. 



Extending this analysis further, in the arterial 

 system an increase in the reference pressure (P„) will 

 immediately lead to an equivalent increase in the 

 flow (neglecting factors of vessel elasticity and auto- 

 regulation). In the venous system, an increase in the 

 reference flow (Q.) will tend to increase pressures 

 slightly along the venous route. This will widen the 



