Using wave intensity analysis to determine local reflection coefficient in flexible tubes

The contribution of upper and lower body arterial vessels to the aortic root reflections: A one-dimensional computational study

BACKGROUND AND OBJECTIVES

Reflections measured at the aortic root are of physiological and clinical interest and thought to be composed of the superimposed reflections arriving from the upper and lower parts of the circulatory system. However, the specific contribution of each region to the overall reflection measurement has not been thoroughly examined. This study aims to elucidate the relative contribution of reflected waves arising from the upper and lower human body vasculature to those observed at the aortic root.

METHODS

We utilised a one-dimensional (1D) computational model of wave propagation to study reflections in an arterial model that included 37 largest arteries. A narrow Gaussian-shaped pulse was introduced to the arterial model from five distal locations: carotid, brachial, radial, renal, and anterior tibial. The propagation of each pulse towards the ascending aorta was computationally tracked. We calculated the reflected pressure and wave intensity at the ascending aorta in each case. The results are presented as a ratio of the initial pulse.

RESULTS

The findings of this study indicates that pressure pulses originated at the lower body can hardly be observed, while those originated from the upper body account for the largest portion of reflected waves seen at the ascending aorta.

CONCLUSIONS

Our study validates the findings of earlier studies, which demonstrated that human arterial bifurcations have a significantly lower reflection coefficient in the forward direction as compared to the backward direction. The results of this study underscore the need for further in-vivo investigations to provide a deeper understanding of the nature and characteristics of reflections observed in the ascending aorta, which can inform the development of effective strategies for the management of arterial diseases.

Arterial wave dynamics preservation upon orthostatic stress: a modelling perspective

Pressure-flow travelling waves are a key topic for understanding arterial haemodynamics. However, wave transmission and reflection processes induced by body posture changes have not been thoroughly explored yet. Current in vivo research has shown that the amount of wave reflection detected at a central level (ascending aorta, aortic arch) decreases during tilting to the upright position, despite the widely proved stiffening of the cardiovascular system. It is known that the arterial system is optimized when in the supine position, i.e. propagation of direct waves is enabled and reflected waves are trapped, protecting the heart; however, it is not known whether this is preserved with postural changes. To shed light on these aspects, we propose a multi-scale modelling approach to inquire into posture-induced arterial wave dynamics elicited by simulated head-up tilting. In spite of remarkable adaptation of the human vasculature following posture changes, our analysis shows that, upon tilting from supine to upright: (i) vessel lumens at arterial bifurcations remain well matched in the forward direction, (ii) wave reflection at central level is reduced due to the backward propagation of weakened pressure waves produced by cerebral autoregulation, and (iii) backward wave trapping is preserved.

A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

The aim of this work is to study the behavior of reflection of a longitudinal wave at a free surface of dissipative half-space under the effects of compressive initial stresses. When a longitudinal wave is incident on the free surface of an elastic dissipative half-space, two damped waves (Primarywaves and secondary waves are reflected. Among of these waves, P-waves are affected by compressional initial stresses. The governing equation and corresponding closed-form solutions are derived based on Biot’s incremental deformation theory. The equations of motion are solved analytically and the influence of initial stress parameter on the reflection coefficient of P-wave incidents at the free surface of dissipative half-space is studied in detail. Numerical computations are performed for actual Earth crust and the results analyzing the incident of longitudinal waves are discussed and presented graphically. The analytical solutions and numerical results reveal that the compressive initial stress parameter has notable effects on the reflection coefficient of longitudinal wave incidents on the free surface of dissipative medium. In addition, it has been observed that the presence of compressive initial stresses increases the phase velocity of the longitudinal waves. To the authors’ best knowledge, effects of compressive initial stresses on the reflection coefficients of the incident longitudinal wave on a free surface of dissipative half-space have not been studied before. Since the actual Earth is subject to initial stresses due to different resources, understanding the influences of compressive initial stresses on the reflection coefficient of a longitudinal wave helps seismologists and earthquake engineers to get accurate results of the reflection coefficients of seismic waves propagation in the Earth. Thus, the present study would be useful for seismology and earthquake engineering fields and further study about the nature of seismic waves.

The speed, reflection and intensity of waves propagating in flexible tubes with aneurysm and stenosis: Experimental investigation

A localized stenosis or aneurysm is a discontinuity that presents the pulse wave produced by the contracting heart with a reflection site. However, neither wave speed (c) in these discontinuities nor the size of reflection in relation to the size of the discontinuity has been adequately studied before. Therefore, the aim of this work is to study the propagation of waves traversing flexible tubes in the presence of aneurysm and stenosis in vitro. We manufactured different sized four stenosis and four aneurysm silicone sections, connected one at a time to a flexible ‘mother’ tube, at the inlet of which a single semi-sinusoidal wave was generated. Pressure and velocity were measured simultaneously 25 cm downstream the inlet of the respective mother tube. The wave speed was measured using the PU-loop method in the mother tube and within each discontinuity using the foot-to-foot technique. The stenosis and aneurysm dimensions and c were used to determine the reflection coefficient (R) at each discontinuity. Wave intensity analysis was used to determine the size of the reflected wave. The reflection coefficient increased with the increase and decrease in the size of the aneurysm and stenosis, respectively. c increased and decreased within stenosis and aneurysms, respectively, compared to that of the mother tube. Stenosis and aneurysm induced backward compression and expansion waves, respectively; the size of which was related to the size of the reflection coefficient at each discontinuity, increases with smaller stenosis and larger aneurysms. Wave speed is inversely proportional to the size of the discontinuity, exponentially increases with smaller stenosis and aneurysms and always higher in the stenosis. The size of the compression and expansion reflected wave depends on the size of R, increases with larger aneurysms and smaller stenosis.

Boundary waves in a microfluidic device as a model for intramural periarterial drainage

The failure to clear amyloid-Beta from an aging brain leads to its accumulation within the walls of arteries and potentially to Alzheimer's disease. However, the clearance mechanism through the intramural periarterial pathway is not well understood. We previously proposed a hydrodynamic reverse transport model for the cerebral arterial basement membrane pathway. In our model, solute transport results from fluidic forcing driven by the superposition of forward and reverse propagating boundary waves. The aim of this study is to experimentally validate this hydrodynamic reverse transport mechanism in a microfluidic device where reverse transport in a rectangular conduit is driven by applying waveforms along its boundaries. Our results support our theory that while the superimposed boundary waves propagate in the forward direction, a reverse flow in the rectangular conduit can be induced by boundary wave reflections. We quantified the fluid transport velocity and direction under various boundary conditions and analyzed numerical simulations that support our experimental findings. We identified a set of boundary wave parameters that achieved reverse transport, which could be responsible for intramural periarterial drainage of cerebral metabolic waste.