PHYSICAL EQUILIBRIA OF HEART AND VESSELS 



97 



the equilibrium radius Ri and tlie elastic tension 

 represented by ARi. Suppose that due to the de- 

 velopment of an active tension the vessel constricts 

 to radius R-i. The total tension, elastic plus active, 

 must be represented by the ordinate BR-i. Yet, since 

 the stretch has decreased, the elastic tension has 

 diminished from ARi to CRo. Therefore the intercept 

 BC, between the Laplacian line at B and the elastic 

 line at C, must represent the amount of the active 

 tension required to produce this diminution of the 

 radius from Ri to ^2, ie., the two tensions T^ and 

 Tr are represented by the two parts BC and CR^ 

 of the ordinate erected at /?■.• In this way we can 

 predict how much decrease in radius of the vessel 

 will result from increasing the active tension by a 

 given amount, e.g., a tension of a magnitude repre- 

 sented by DE will reduce the radius almost to the 

 unstretched value. Thus a very small increase over 

 that required to constrict from Ri to Ro will reduce 

 the radius a great deal more. Since DE is the ma.xi- 

 mum intercept, once the radius has approached the 

 unstretched radius Ro, no more active tension will 

 be required to reduce the vessel to zero radius, i.e., 

 to close it altogether (unless some new force, not 

 represented in this diagram, intervenes). 



15. THE CRITICAL CLOSING ACTIVE TENSION 



We therefore conclude that if the transmural 

 pressure is kept constant, and the active tension 

 (vasomotor tone) is progressively increased, a critical 

 value of this tension (represented by DE) could 

 result in complete closure of the vessel. For a higher 

 transmural pressure the straight line (Laplacian 

 line) would have a steeper slope. The same con- 

 clusion would be reached, but the "critical closing 

 active tension" would be greater. The term "critical" 

 is used because an instability appears at this critical 

 point. If, then, the transmural pressure remained 

 constant, and the active tension (vasomotor tone) 

 progressively increased, we would predict that 

 "spasm," or "critical closure" of the vessel would 

 result at a certain level of that vasomotor tone. 



16. THE CRITICAL CLOSING PRESSURE 



The same conclusion is reached, though more 

 directly in terms of the existence 01 a "critical closing 

 pressure" rather than a "critical closing active ten- 

 sion," by using the diagram of figure 16. Here the 



sum of the active and elastic tensions is plotted in 

 the curve, rather than the elastic tension alone, as 

 it was in figure 15. A constant amount of active 

 tension (corresponding to a constant degree of 

 vasomotor tone) has been added to raise the "elastic 

 line" 01 figure 1 3 by the same amount for all radii. 

 The Laplacian line for transmural pressure Pi in- 

 tersects the curve at two points. Of the.se, the upper 

 point of intersection represents a stable equilibrium, 

 the lower a completely unstable equilibrium of no 

 real significance. >s^ow imagine a progressive de- 

 crease in the transmural pressure P to ^2, Pz, etc. 

 The slope of the Laplacian line will have to be 

 progressively reduced. When a critical pressure 

 (P3) is reached, the line will touch (be tangent to) 

 the curve. The point of contact of this tangent will 

 represent a real equilibrium, which will be stable 

 for increases in radius, but unstable for decreases in 

 radius. (This is the sort of unilateral stability of a 

 particle on the very edge of a table.) The Laplace 

 line for any pressure less than this critical pressure 

 will have no intersection with the curve at any point. 

 This means that no equilibrium is possible with 

 transmural pressures less than this critical value. 

 The prediction can therefore be made that if vascular 

 beds are in a state of constrictor tone, i.e., the walls 

 of the arterioles have an active tension, independent 

 of stretch, there would be a tendency to complete 

 closure if the transmural pressure dropped below a 

 "critical closing pressure." 



17. THE CRITICAL CLOSING PRESSURE AS AN INDEX 

 OF VASOMOTOR TONE 



This critical closing pressure would increase, the 

 greater the degree of vasomotor tone, i.e., the greater 

 the active tension. This is because, on figure 16, 

 the curve will be raised if the active tension is in- 

 creased, so the slope of the tangent will be also in- 

 creased. It is obvious from the diagram that the 

 tangent will touch the curve at a point very close 

 to the unstretched radius ro, of the vessel, since this 

 is where the curve begins to increase in slope. Thus, 

 to a close appro.ximation, the critical closing pressure 



(CCP) 



CCP = — 



(22) 



This is the basis for the use of the CCP of a vascular 

 bed as an index of vasomotor tone, in terms of T^. 

 It has the advantage over the use of the resistance to 



