The Velocity of the Pulse Wave in Man. 



299 



Moreover, the velocity of the hlood in the aorta, and to some degree in any 

 artery, varies considerably at different moments of the cardiac cycle ; such 

 differences will cause one part of the pulse wave to be transmitted with a 

 greater velocity than another, and so will lead to a certain modification in the 

 apparent form of the wave. In the absence of definite knowledge of the 

 velocity of the blood in any given case it is not possible to make any 

 allowance for it ; it is necessary, however, to bear in mind that it may, under 

 certain circumstances, appreciably — though not considerably — affect the 

 velocity and modify the form of the transmitted wave. 



Considered in its full complexity the theory of the transmission of the pulse 

 wave is difficult. There are, however, two factors which allow us to simplify 

 it : (a) the distance over which the wave travels is relatively short ; (V) the 

 wave form, owing to the elastic nature of all the tissues producing it, shows no 

 very sharp discontinuities or changes of curvature. In consequence of (b), in 

 the analysis of the wave into a system of simple harmonic waves, the shorter 

 wave-lengths are relatively unimportant, and it is the transmission of these 

 waves which would have required the more complicated treatment. With 

 the help of Mr. E. A. Milne, of Trinity College, Cambridge, a fuller theory of 

 the wave transmission has been worked out ; it is unnecessary to give this 

 theory at length, but it may be stated that, with the type of wave occurring 

 in arteries, and within the limits of experimental error, the formula given by 

 Moens(7) in 1878 is sufficiently accurate for our purpose. We will consider 

 the meaning and application of this formula. 



If v be the velocity of the front of the pulse wave, y the radius of the 

 artery at the end of diastole, c the thickness of the arterial wall, E the 

 modulus of elasticity of the artery for lateral expansion, and p the density of 

 the blood, the following relation holds : 



Assuming that p is constant, and equal (say) to 1*055, this formula contains 

 three variable factors, on which the value of v depends, viz., E, c and y. In 

 this form the expression is of little value, since E, c and y vary from artery 

 to artery, and none of them express any easily measurable factor. By a 

 simple transformation, however, a formula may be obtained which throws 

 much light upon the mechanics of the circulation. A small rise hp in 

 pressure may be shown to cause a small increase, By = y 2 hpj¥x, in the radius 

 y of the artery, or a small increase, hV = 'liry^hp/'Kc, in its volume V per 

 unit length. Hence 2?//Ec = dY/Vdp, from which 



v = x /(V/[pdV/dp]). 



In this equation p is measured in dynes per square centimetre, and v in 



