Relationship between the blood-vessel coupling characteristics and the propagation of pulse waves

Abstract

Pulse waves cannot be understood simply as pressure waves (longitudinal waves) propagating in compressible blood fluid, nor as radially expanding-contracting displacement waves (transverse waves) propagating along solid blood vessels, but rather as complex waves with fluid-solid coupling and longitudinal wave-transverse wave coupling beyond ordinary imagination. Starting from a new approach to analyze the coupling constitutive relation, a series model is proposed, providing more information for traditional Chinese medicine (TCM) pulse diagnosis in terms of the “position, rate, shape and potential”. It is shown that the equivalent volumetric compression modulus Ks and the corresponding pulse wave propagation velocity cs of the coupling pulse wave system, mainly depend on two dimensionless parameters: the ratio of the blood modulus to the vessel modulus, Kb(p)/E(p) and the ratio of the diameter to the thickness, D(p)/h0, of thin-walled blood vessels, which may vary from person to person and from different pulse locations for the same person. The influences of them on the cs are quantitatively analyzed, showing that for human body the magnitude of Kb/E is in the order of 103 so that the magnitude of cs is in the order of 100–101 m/s to adapt to the human physio-biochemical reactions. By clinical invasive measurements, it is confirmed that the pulse volume transverse wave and the pulse pressure longitudinal wave are coupled and propagate at the same speed, and it is shown that the pulse wave is actually a “biological wave” with oxygenation and biochemical reactions on the wave front. Furthermore, the relations of the “pulse pressure amplification” with the nonlinear constitutive relation and with the load enhanced reflection at the bifurcation of blood vessels, as well as the Lewis’s hypothesis about the formation of dicrotic wave are discussed.