Takaaki Asada

One-Dimensional Model for Propagation of a Pressure Wave in a Model of the Human Arterial Network: Comparison of Theoretical and Experimental Results

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.

Noninvasive assessment of arterial stiffness by pulse wave analysis

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 _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 (R² = 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 (R² = 0.48) and CAVI (R² = 0.71). Therefore, this new method has potential for diagnosing arterial stiffness.

Simple Analysis of the Pulse Wave for Blood Vessel Evaluation

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.

Experimental study on the pressure and pulse wave propagation in viscoelastic vessel tubes-effects of liquid viscosity and tube stiffness

A pulse wave is the displacement wave which arises because of ejection of blood from the heart and reflection at vascular bed and distal point. The investigation of pressure waves leads to understanding the propagation characteristics of a pulse wave. To investigate the pulse wave behavior, an experimental study was performed using an artificial polymer tube and viscous liquid. A polyurethane tube and glycerin solution were used to simulate a blood vessel and blood, respectively. In the case of the 40 wt% glycerin solution, which corresponds to the viscosity of ordinary blood, the attenuation coefficient of a pressure wave in the tube decreased from 4.3 to 1.6 dB/m because of the tube stiffness (Young¿s modulus: 60 to 200 kPa). When the viscosity of liquid increased from approximately 4 to 10 mPa·s (the range of human blood viscosity) in the stiff tube, the attenuation coefficient of the pressure wave changed from 1.6 to 3.2 dB/m. The hardening of the blood vessel caused by aging and the increase of blood viscosity caused by illness possibly have opposite effects on the intravascular pressure wave. The effect of the viscosity of a liquid on the amplitude of a pressure wave was then considered using a phantom simulating human blood vessels. As a result, in the typical range of blood viscosity, the amplitude ratio of the waves obtained by the experiments with water and glycerin solution became 1:0.83. In comparison with clinical data, this value is much smaller than that seen from blood vessel hardening. Thus, it can be concluded that the blood viscosity seldom affects the attenuation of a pulse wave.

Experimental Study on the Pulse Wave Propagation in a Human Artery Model

A pulse wave is composed of incident and reflected waves. Since the attenuation of the reflected wave changes markedly owing to arterial stiffness, analyzing this wave is useful for evaluating an artery. In our previous study, we proposed an estimation method for the reflected wave. However, because the actual path and reflection point of the reflected wave are unknown, it is unclear which artery contributes the reflected wave. We then attempted to investigate the reflection point and concerning artery using a human artery model. This model has four bifurcations using viscoelastic tubes, constructed with an aorta and femoral, subclavian, radial, and left carotid arteries. The details of the model are similar to those of an actual human artery. We measured the inner pressure and flow velocity using this model, and investigated the reflection point. Finally and consequently, the reflection point was estimated to be the end of the carotid artery. The estimated reflected wave was then considered to propagate in the carotid artery.

Simple and noninvasive analysis of the pulse wave for blood vessel evaluation

The pulse wave is a good indicator to evaluate the viscoelastic properties of blood vessels. The wave is composed of an incident wave and a reflected wave. Since the reflected wave is generated by the reflection of the incident wave at the peripheral artery after propagating long distance along blood vessels, the characteristics of that wave depend remarkably on arterial stiffness. Therefore, the evaluation of arterial stiffness may be possible from the analysis of this reflected wave. In this study, we propose a simple and noninvasive technique to estimate the reflected wave from the pulse wave observed at common carotid artery, making use of a commercial piezoelectric transducer and an ultrasonic diagnostic equipment. First, we estimated the incident wave from the blood flow velocity waveform. Then, the reflected wave was obtained by subtracting the incident wave from the pulse wave. As a result, the maximum values of the reflected wave increased with advancing age. This result was in good agreement with the increasing elasticity of blood vessels due to age.

1D model for propagation of pulse wave in an arterial network: Comparative study of theory and experiment

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to the arterial stiffness. However, the pulse wave consists of two components, incident wave and multi-reflected 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 build a 1D numerical simulation model of pulse wave propagating in distensible tubes. To evaluate the applicability of the model, theoretical estimations were compared with experimental results. Experiments: Two basic distensible tubes, a straight tube and a single bifurcation tube, and a simple arterial network with four bifurcations were constructed. A pulse flow was input into these models using a controlled pump and then pressure waves and flow velocity were measured. Modelization: A 1D governing equations were formulated from the Navier-Stokes equations and continuity equation. Under the same configuration as for experiments, the governing equations were computed using MacCormack scheme. Consequently, theoretical waves of each case fit with experimental ones. The sum of squared differences between the theoretical and experimental waves for each case was less than 10%. This proves the usefulness of our modelization for understanding the phenomenon of pulse propagation in the human arterial network.

Stable Parametric Amplification Using Elastic Microcapsules Placed in Silicone Rubber

To realize a stable parametric amplification, elastic polymer microcapsules are applied instead of microscopic gas bubbles. Small quantities of the microcapsules are compounded with the silicone rubber, and the mixture is formed into a cylindrical shape as a sample of a nonlinear device. The device is located on the sound-field where the finite amplitude sounds of two near frequencies are trasmitting. It is experimentally observed that the strong nonlinear vibration of the spatially fixed microcapsules generates a stable difference-frequency sound with high efficiency and wide frequency range.

Ultrasound radiation from a three-layer thermoacoustic transformation device

A thermophone is a thermoacoustic transducer, which generates sound via time-varying Joule heating of an electrically conductive layer, which leads to expansion and contraction of a small pocket of air near the surface of the film. In this work, a 10-μm-thick Ag-Pd conductive film was coupled with heat-insulating and heat-releasing layers to fabricate a three-layer thermophone for generating ultrasound. The heat-insulating layer was 47 μm thick, and was made of glass. The heat-releasing layer was 594 μm thick, and was made of 94% alumina. Because of the simple sound-generation mechanism, which does not require mechanical moving parts, the Ag-Pd conductive film on the glass substrate can produce ultrasound radiation with broadband frequency characteristics, where exiting commercial electrode materials were used. We also demonstrate that the measured directivity patterns are in good agreement with theoretical predictions, assuming a rectangular diaphragm with the same size as the metallic film.

Effect of Viscoelasticity of Vessel Walls on Pulse Wave

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.