STUDIES ON THE ARTERIAL PULSE WAVES

1. NOTES ON THE MECHANICAL ANALYSIS OF ARTERIAL PULSE WAVE

抄録

In this note, the writer made an attempt to generalize the so-called “Windkesselmodel” into a model of high elasticity with stress relaxation and tried to unify the view-points based on the theory of elasticity and hydrodynamical point of view. The results obtained were summarized as follows; 1) Based on the fact that Frank's equation for Windkesselmodel [1], and Maxwells equation [6] can be said, from the standpoint of fomality, to be identical to each other, and that Maxwell's equation is a special case of Boltzman's equation [7], the modified Boltzman's equation [9] is assumed to be reducable to [6] under an appropriate after effect function. Then we have equations [16, 17, 18] for the propagation of wave in the medium of high elasticity, which coincides with hydrodynamical equation [4].
2) Solving under appropriate initial and boundary conditions, it can be shown that propagation velocity of instantaneous change of pressure and that of flow velocity accompanying it are √γ/ρ as given by Frank, while under stationary condition transmission velocity differs from Frank's, depending on the peripheral and frictional resistance. For actual pulsative changes in the arterial system caused by heart cycles, it seems improbable that a stationary state as a whole can exist, hence the changes of pressure and velocity must propagate with same velocity along arteries.
3) This conclusion, as a matter of course, does not contradict with the es tablishment of Hamilton's standing wave, but concerns only with the beginings of these pulsative changes. Therefore the question, whether the pattern of pressure pulse wave coincides with that of velocity pulse wave, remains entirely undetermined.