Waves In Elastic Tubes Research Articles

Hemodynamics and nonlinear acoustics: General approaches and solutions

Related problems of nonlinear acoustics and hemodynamics are discussed. Equations describing the propagation of pulse waves in elastic tubes taking into account the dependence of the cross-section, linear and nonlinear elasticity on the distance along the axis are obtained. It is shown that in narrowing tubes with their elasticity increasing shock fronts may be formed with the peak pressure increasing, and the peak speed decreasing. The analogous behavior was observed in experiments. The expression of the nonlinearity coefficient as a sum of the “geometrical” and “physical” nonlinearities having different signs is obtained. It is supposed that in a normally functioning system these nonlinearities compensate each other. The formation of the shock waves is the evidence of vascular pathology. It is shown that it is possible to restore the local heterogeneity of a vessel (the change of the cross-section or rigidity) on the basis of measurements of the reflected or transmitted wave. The principle of the action of the acoustic pump not containing mechanically moving parts is described.

Measurements of wave speed and reflected waves in elastic tubes and bifurcations

Wave intensity analysis is a time domain method for studying waves in elastic tubes. Testing the ability of the method to extract information from complex pressure and velocity waveforms such as those generated by a wave passing through a mismatched elastic bifurcation is the primary aim of this research. The analysis provides a means for separating forward and backward waves, but the separation requires knowledge of the wave speed. The PU-loop method is a technique for determining the wave speed from measurements of pressure and velocity, and investigating the relative accuracy of this method is another aim of this research. We generated a single semi-sinusoidal wave in long elastic tubes and measured pressure and velocity at the inlet, and pressure at the exit of the tubes. In our experiments, the results of the PU-loop and the traditional foot-to-foot methods for determining the wave speed are comparable and the difference is on the order of 2.9±0.8%. A single semi-sinusoidal wave running through a mismatched elastic bifurcation generated complicated pressure and velocity waveforms. By using wave intensity analysis we have decomposed the complex waveforms into simple information of the times and magnitudes of waves passing by the observation site. We conclude that wave intensity analysis and the PU-loop method combined, provide a convenient, time-based technique for analysing waves in elastic tubes.

Weakly Nonlinear Waves in Elastic Tubes Filled with a Layered Fluid

Weakly Nonlinear Waves in Elastic Tubes Filled with a Layered Fluid

Solitary waves in elastic tubes filled with a layered fluid

In this work, we studied the propagation of weakly non-linear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is studied. The governing equation is shown to be the perturbed Korteweg–de Vries (KdV) equation. A travelling wave type of solution for this evolution equation is sought and it is shown that the amplitude of the solitary wave for the perturbed KdV equation decays slowly with time.

The boundary layer approximation and nonlinear waves in elastic tubes

In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg–de Vries (KdV) and the Korteweg–de Vries–Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg–de Vries and viscous-Burgers equations.

Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures

The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid. The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture. The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity. Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change. The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated. The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations.

Experimental study of finite amplitude pulsatile pressure waves in elastic tubes

Abstract An experimental study of the propagation of pulsatile pressure waves in an elastic tube was made and results were compared to a theoretical analysis by Lou. The pressure waves were sinusoidally varying acting in a horizontal, longitudinally constrained tube containing water. The independent experimental parameters varied were the pressure wave frequency, pressure wave volume per cycle, static tube pressure and steady flow rate. The wave propagation speeds, measured by non-intrusive techniques, were found to be functions of the wave frequency and the phase angles of the wave elements as theoretically predicted by Lou.

Digital computer simulation of pulse wave transmission in arteries.

The transmission of pressure pulse waves in elastic tubes and arteries has been discussed by previous workers but the dependence of the viscoelastic parameters on frequency has not been taken into account in detail. In this paper pulse wave transmission in a model of an infinitely long viscoelastic tube containing a viscous fluid has been expressed in a simple mathematical form with the use of complex variables. The experimentally observed frequency dependence of viscoelastic parameters of canine arteries has been expressed analytically and incorporated in the simulation. The transmission of the pressure pulses over a small distance is simulated assuming uniform properties of the vessel wall over this interval. Some of the observed changes due to transmission are explained by the simulation, for example the gradual disappearance of the dichrotic notch from the thoracic aorta to the smaller arteries. The results on normal dogs are sufficiently encouraging to attempt simulation of the pulse wave transmission in arteries in pathological conditions.

Waves in Elastic Tubes: Velocity of the Pulse Wave in Large Arteries

An equation for waves in elastic tubes is developed and applied to cylindrical tubes with Hookian and with elastomeric walls. The former application yields the Moens-Korteweg formula, which has been found inadequate. The latter application leads to a rather complicated equation for the pulse-wave velocity. Values of pulse-wave velocities are computed for the thoracic aorta by means of the foregoing equation, and the results are compared with measured mean velocities for the entire aorta. Graphs and tables are given, so that a graphical analysis of this velocity equation can be applied to any large artery; and the method is illustrated by computing the pulse-wave velocity in the left common carotid. The relation l÷∫0lds/v, for the mean velocity over a tube of length l, is shown to be valid for the aorta and large arteries.