Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.

A pulse wave is considered to be a good indicator to evaluate the viscoelastic properties of blood vessels. The wave is composed of an incident wave and a reflected wave. The evaluation of blood vessels may be possible from the analysis of this reflected wave, because the reflected wave propagates to the peripheral artery. We propose a simple method of estimating the reflected wave from the pulse wave observed at common carotid artery, making use of a commercial piezoelectric transducer. First, we estimate the incident wave from the observed blood flow velocity. Then, the reflected wave is estimated by subtracting the incident wave from the observed pulse wave. The amplitudes of the reflected wave obtained in senior subjects were larger than those of junior subjects. This result is in good agreement with the common point of view about the vessel wall, that the attenuation during pulse wave propagation is usually small in elderly people.

The pulse wave comes from the displacement of surface skin and is composed of incident and reflected waves. Since the properties of the reflected wave change considerably owing to the viscoelasticity of the vessel walls, the analysis of the reflected wave is considered to be useful for evaluating arterial stiffness; thereby, appropriate estimation of the incident wave is important for separating the pulse wave. Here, the incident wave is generated by a forward wave, which is the intravascular pressure caused by blood flow. In the former analysis, we assumed the blood vessel as an elastic tube and estimated the forward wave from the blood flow velocity waveform. In this study, we used a viscoelastic model to estimate a more appropriate forward wave. In this estimation, we used viscoelastic properties similar to those of bovine aorta, human aorta, or human artery. The estimated forward waves showed that the difference in the viscous properties of vessel walls causes minimal changes in the forward waves, which were also similar to that estimated using the elastic model. The result tells us that the elastic model is acceptable and useful for the estimation of forward wave, incident wave, and reflected wave, which enables the simple evaluation of the viscoelastic properties of vessel walls. #

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Pulse wave evaluation is an effective method for arteriosclerosis screening. The pulse wave comprises two displacement components, the incident wave ε(i)(t) and the reflected wave ε(r)(t). Because the amplitude of the reflected wave changes markedly with arterial stiffness, analysis of this wave is useful for evaluation of such stiffness. In this paper, a noninvasive method for extracting the reflected component from a pulse wave is proposed. First, the pulse wave ε(i)(t) + ε(r)(t) and blood flow velocity u(i)(t) - u(r)(t) were measured at the common carotid artery. A new approach is used to estimate the displacement wave ε(i)(t) -ε(r)(t), in which a transform of the conservation of mass, an elastic tube model, and a Voigt model for a viscoelastic body are applied to blood flow velocity data. Twice the amplitude of the reflected wave [TARW; 2ε(r)(t)] was obtained by subtracting the amplitude of the calculated displacement wave from that of the observed pulse wave. This method was applied to subjects aged from their 20s to 60s to evaluate differences in the reflected component. The results indicate moderate correlation between age and TARW (R(2) = 0.65). To evaluate the validity of this method for screening arterial stiffness, we compared TARW with existing diagnostic indices pulse wave velocity (PWV) and cardio-ankle vascular index (CAVI). TARW was moderately correlated with PWV (R(2) = 0.48) and CAVI (R(2) = 0.71). Therefore, this new method has potential for diagnosing arterial stiffness.