THICKNESS OF WALLS 287 



Sections of the ventricles at different points show that the 

 ventricular walls vary in thickness at different parts. For 

 instance in the left ventricle the apex, in the fully dilated ventricle, 

 has, by far, the thinnest wall. As presumably the pressure in the 

 chamber is constant over the whole wall area at any moment, some 

 other factor must be found to account for this diminution in 

 thickness. From the purely physical study of the shape assumed 

 by elastic- walled cavities the conclusion has been drawn that 

 where an elastic membrane is subjected to internal pressure, its 

 shape will be determined by the law of distribution of radial 

 pressure. With a given shape and size of body, equilibrium is 

 maintained by altering the thickness (resistance to pressure) of 

 the wall so that where curvature is least the wall is thickest and vice 

 versa. The apex of the heart is the portion with the greatest 

 curvature. 



To take a very simple example : if an elastic band is stretched between 

 two points on a flat surface it will exert no pressure on any part of the 

 underlying surface. But if it is stretched over a curved surface, e.g. a 

 cylinder, it will exercise a downward pressure depending on the radius of 

 the cylinder. A flat surface may be considered as equivalent to a curved 

 surface of infinite radius. As the numerical value of the radius is decreased, 

 i.e. as the curvature is increased, the pressure exerted by the band will 

 increase. In mathematical form p = T/R, i.e. Pressure per unit of surface 

 = Tension of band divided by Kadius of curvature. 



Where there are curvatures in two dimensions, e.g. a sphere, 



2T 



the two pressure effects are additive, i.e. p= -. 



H 



The ventricles are roughly egg-shaped, i.e. they have radii in 

 two dimensions and of unequal length. The pressure will there- 

 fore be equal to the sum of these, i.e. p = T/R+T/R 1 . 



We have seen reason to correlate thickness with pressure. 



We may therefore say that thickness of wall varies inversely 

 with the radius of curvature. This gives the formula 



t(l/R+llR 1 )=C, 



where 2=thickness of the walls and C a constant. 



The wall of the apex of the heart has the largest mean curvature 

 (R is least and, therefore, t is least). 



Similar reasoning may be applied to the consideration of the 

 thickness of the walls of the blood vessels. The pressure (P) 

 within the vessel is balanced by (1) the elastic tension of the wall 

 (T) divided by the radius of curvature (R), and (2) by the pressure 



