CHAPTER 6 



Physical principles of circulatory phenomena: 

 the physical equilibria of the heart and 

 blood vessels 



ALAN C BURTON Del^artment of Biophysics, Universitt of Western Ontario, London, Ontario, Canada 



CHAPTER CONTENTS 



Importance of the Size of the Vessels 



Importance of the DistensibiUty of Blood Vessels: Transmural 



Pressures 

 Forces Concerned With the Equilibrium of the Blood Vessel 



Wall 

 The Distending Force 

 The Constricting Force 

 Equilibrium Between These Forces: The Law of Laplace 

 Equilibrium for the Longitudinal Tension 

 Modification of the Law of Laplace for Thick -Walled Vessels 

 Nature of the Tension in the Wall, Elastic and Active Tensions 

 Total Tension in the Wall of Different Vessels 

 Elastic Tension in the Wall 



The Reason for the Shape of Elastic Diagrams of Blood Vessels 

 Graphic Method for the Equilibrium Under Elastic Tension 



Alone 

 The Phenomenon of •'Blowout" 

 Equilibrium Under Active Tension Alone 

 Equilibrium Under Elastic Tension Plus Active Tension 

 The Critical Closing Active Tension 

 The Critical Closing Pressure 



The Critical Closing Pressure as an Index of Vasomotor Tone 

 The Fundamental Instability of Vessels Under Constrictor 



Tone: The Stabilizing Role of Elastic Tissue and Sensi- 

 tivity of Control 

 Experimental Verilication of the Theory of Critical Closing 



Pressures and Critical Closing Active Tensions 

 Which Vessels Close at the Critical Pressure? 

 Minimum Values of Critical Closing Pressure: Residua! Critical 



Closing Pressure 

 Physiological Range of Critical Closing Pressures 

 Application of the Law of Laplace to the Heart 

 Measurement of Active Tension in Vascular Smooth Muscle 

 Appendix 

 Pressure Gradient Through the Vessel Wall 



Active Tension Only in the Wall 

 Purely Elastic Artery 



I . IMPORTANCE OF THE SIZE OF THE VESSELS 



THE BLOOD VESSELS of the \ascular bed include a very 

 wide range of size, thickness of wall, and number of 

 vessels that are "in parallel" as well as "in series" 

 with each other. The mean pressure of the blood 

 within these various vessels also ranges from o\'er 

 loo mm Hg in the aorta to values near zero in the 

 large veins. Figure i schematically illustrates this 

 wide variety in dimensions of the blood vessels (6), 

 and in the composition of their walls as to the four 

 main tissues, endothelium, elastin, collagenous and 

 smooth muscle fibers. Since these different tissue 

 elements have very different physical properties, we 

 have a right to e.xpect that this great \ariety of com- 

 position and size has a physiological importance. 



The system of blood vessels has, of course, the 

 function of distribution of blood to the different parts 

 of the body, in amounts related to the needs of the 

 various tissues and organs. The distribution will be 

 determined by the relative "resistance to flow" of the 

 various routes through which the driving pressure 

 difference, between aorta and vena cava, may propel 

 the blood. The law of Poiseuille relates to flow of 

 simple fluids through rigid pipes. The modifications 

 of the law when it is applied to the flow of blood 



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