Determination of wave speed and distensibility of flexible tubes using diameter and velocity

It is well accepted that wave speed is one of the key factors describing wave propagation in arteries. Local wave speed is directly related to the mechanical properties of the arterial wall and is widely used to determine the arterial distensibility . Several methods have been proposed for determining wave speed in arteries, such as foot-to-foot and PU-loop methods. In this paper, we suggest a new method for the determination of wave speed and wall distensibility, using noninvasive measurements. The theoretical foundation of this method is based on the 1-D conservation of mass and momentum equations of flow in flexible tubes. We simultaneously measured pressure, diameter and velocity at the same site, sequentially along silicon and latex tubes which are 1 m in length and of different diameters. We compared the results of the new method, ln(D)U-loop, with those determined by the PU-loop method. Wave speeds determined by both methods are comparable, although wave speeds determined by the new technique are slightly smaller than those determined by PU-loop method. We also compared distensibility calculated by the new method with those calculated using the traditional method (Dt), Dt = 3DdP/AdA, where A and dA are the cross sectional area and its change respectively, and dP is the change in pressure. The results of both methods are in agreement. We conclude that the new technique has the advantage of using only noninvasive parameters which is of clinical relevance

A new approach to investigate wave dissipation in viscoelastic tubes: Application of wave intensity analysis

Wave dissipation in elastic and viscoelastic medium has been investigated extensively in the frequency domain. The aim of this study is to examine the pattern of wave dissipation in the time-domain using wave intensity analysis. A single semi-sinusoidal pulse was generated in 8 mm and 16 mm diameter tubes; each is of 200 cm in length. Pressure and flow measurements were taken at intervals of 5 cm along the tube. In order to examine the effect of the wall mechanical properties on wave dissipation, we also modified the wall of the 16 mm tube; a thread of strong cotton was wound with a pitch of approximately 30deg around the circumference of the tube in the longitudinal direction. The separated forward pressure, wave intensity and wave energy were calculated using wave intensity analysis. The amplitudes of the forward pressure wave, wave intensity and wave energy dissipated exponentially with distance. In the 8 mm diameter tube, the dissipation of forward pressure, wave intensity and wave energy were greater than those in 16 mm tube. For the same sized of tube, there was no significant difference in the dissipation of forward pressure, wave intensity and wave energy between the modified and normal wall tubes. It is concluded that the size of tube has a significant effect on the wave dissipation but the mechanical properties of the wall do not have a discernable effect on wave dissipatio

Automating the determination of wave speed using the pu-loop method

The PU-loop (pressure-velocity loop) is a method for determining wave speed and relies on the linear relationship between the pressure and velocity in the absence of reflected waves. This linearity of the PU-loop during early systole, which is directly related to wave speed, has always been established by eye. This paper presents a new technique that establishes this linearity and thus determining wave speed online. Pressure and flow were measured in the ascending aorta of 11 anesthetised dogs. The slope of the PU-loop, indicating wave speed was determined by eye and by using the new technique. The difference between the slopes of the two methods is in the order of 3%. The new technique is convenient and allows for the online assessment of wave speed, which could be used as a bedside tool for the assessment of arterial compliance

Determination of wave intensity in flexible tubes using measured diameter and velocity

Wave intensity (WI) is a hemodynamics index, which is the product of changes in pressure and velocity across the wave-front. Wave Intensity Analysis, which is a time domain technique allows for the separation of running waves into their forward and backward directions and traditionally uses the measured pressure and velocity waveforms. However, due to the possible difficulty in obtaining reliable pressure waveforms non-invasively, investigating the use of wall displacement instead of pressure signals in calculating WI may have clinical merits. In this paper, we developed an algorithm in which we use the measured diameter of flexible tube's wall and flow velocity to separate the velocity waveform into its forward and backward directions. The new algorithm is also used to separate wave intensity into its forward and backward directions. In vitro experiments were carried out in two sized flexible tubes, 12 mm and 16 mm in diameters, each is of 2 m in length. Pressure, velocity and diameter were taken at three measuring sites. A semi-sinusoidal wave was generated using a piston pump, which ejected 40 cc water into each tube. The results show that separated wave intensity into the forward and backward directions of the new algorithm using the measured diameter and velocity are almost identical in shape to those traditionally using the measured pressure and velocity. We conclude that the new algorithm presented in this work, could have clinical advantages since the required information can be obtained non-invasively

One-dimensional modelling of pulse wave propagation in human airway bifurcations in space-time variables

Airflow in the respiratory system is complicated as it goes through various regions with different geometries and mechanical properties. Three-dimensional (3-D) simulations are typically limited to local areas of the system because of their high computational cost. On the other hand, the one-dimensional (1-D) equations of flow in compliant tubes offer a good compromise between accuracy and computational cost when a global assessment of airflow in the system is required. The aim of the current study is to apply the 1-D formulation in space and time variables to study the propagation of a pulse wave in human airways; first in a simple system composed of just one bifurcation, trachea-main bronchi, according to the symmetrical Weibel model. Then extending the system to include a further generation, the bronchi branches. Pulse waveforms carry information about the functionality and morphology of the respiratory system and the 1-D modelling, in terms of space and time variables, represents an innovative approach for respiratory response interpretation. 1-D modelling in space-time variables has been extensively applied to simulate blood pressure and flow in the cardiovascular system. This work represents the first attempt to apply this formulation to study pulse waveforms in the human bronchial tree

Vascular device interaction with the endothelium

Copyright @ 2008 Elsevier. This is the post-print version of the article.Cerebral stents and Intra Aortic Balloon Pumps (IABP) are examples of mechanical devices that are inserted into arteries to restore flows to clinically healthy states. The stent and the IABP ‘correct’ the arterial flow by static dilation and by cyclical occlusion respectively. As this presentation shows, these functions are effectively modelled by current engineering practice. As interventions however, by their very nature they involve physical contact between a non-biological structure and the sensitive endothelial surface. The possible damage to the endothelium is not currently well addressed and we also consider this issue. Cerebral stents generally have two primary clinical objectives: to mechanically dilate a stenosed artery and to have minimal detrimental impact upon local blood flow characteristics. These objectives are well served at the arterial scale as these devices are evidently effective in opening up diseased arteries and restoring vital flows. However, at the near-wall micro-scale the picture is less satisfactory, as thin stent wires apply stresses to the endothelium and glycocalyx and the local flow is disturbed rather than being ideally streamlined. This causes further interaction with this endothelium topography. Wall Shear Stress (WSS) is the measure commonly used to indicate the interaction between fluid and wall but it is a broad brush approach that loses fidelity close to the wall. We will present simulation results of blood flow through a stented cerebral saccular aneurysm under these limitations of WSS. The Intra Aortic Balloon Pump (IABP) is a widely used temporary cardiac assist device. The balloon is usually inserted from the iliac artery, advanced in the aorta until it reaches the desired position; with its base just above the renal bifurcation and the tip approximately 10cm away from the aortic valve. The balloon is inflated and deflated every- (1:1), every other- (1:2) or every second (1:3) cardiac cycle. Balloon inflation, which takes place during early diastole, causes an increase in the pressure of the aortic root which leads to an increase in coronary flow. Balloon deflation which takes place during late diastole achieves one of the main IABP therapeutic effects by reducing left ventricular afterload. Unavoidably, the balloon contacts the inner wall of the aorta with every inflation/deflation cycle. This repeated event and possible contact with atherosclerotic plaque have been reported to be responsible for balloon rupture. However, there has not been a methodical study to investigate the mechanical effects of balloon-wall interaction. For example, during inflation the balloon approaches the endothelium as it displaces a volume of blood proximally and distally. This squeezing process generates shear stresses, which hasn't yet been quantified. Similarly, when the balloon moves away from the endothelium during deflation, it generates micro pressure differences that may impose stretching (pulling) stresses on the endothelium cells. Both of the above cases indicate that a very high spatial resolution is required in order to fully understand the process of interaction between device and endothelium, and to interpret the effects at the cellular level

Wave intensity analysis: A novel non-invasive method for determining arterial wave transmission

Wave intensity analysis is a novel technique for assessing wavelet transmission in the cardiovascular system. Using this tool, we have developed non-invasive techniques to study wave transmission in both central & peripheral arteries in man. The aim of this study was to determine the reproducibility of various haemodynamic measures in the carotid, brachial and radial arteries. 12 treated hypertensive men underwent applanation tonometry and pulsed Doppler ultrasound studies of the carotid, brachial and radial arteries on 2 occasions. Coefficients of variation for the local wave speed, cardiac compression wave intensity and main reflected wave intensity ranged between 3.7-6.6%, 8.2-11.4% and 12.5-19.6% respectively. We conclude that non-invasive methods used for wave intensity analysis are reproducible & provide additional information regarding the complex phenomenon of arterial wave transmission in man

Simultaneous determination of wave speed and arrival time of reflected waves using the pressure-velocity loop

This is the post print version of the article. The official published version can be found at the link below.In a previous paper we demonstrated that the linear portion of the pressure–velocity loop (PU-loop) corresponding to early systole could be used to calculate the local wave speed. In this paper we extend this work to show that determination of the time at which the PU-loop first deviates from linearity provides a convenient way to determine the arrival time of reflected waves (Tr). We also present a new technique using the PU-loop that allows for the determination of wave speed and Tr simultaneously. We measured pressure and flow in elastic tubes of different diameters, where a strong reflection site existed at known distances away form the measurement site. We also measured pressure and flow in the ascending aorta of 11 anaesthetised dogs where a strong reflection site was produced through total arterial occlusion at four different sites. Wave speed was determined from the initial slope of the PU-loop and Tr was determined using a new algorithm that detects the sampling point at which the initial linear part of the PU-loop deviates from linearity. The results of the new technique for detecting Tr were comparable to those determined using the foot-to-foot and wave intensity analysis methods. In elastic tubes Tr detected using the new algorithm was almost identical to that detected using wave intensity analysis and foot-to-foot methods with a maximum difference of 2%. Tr detected using the PU-loop in vivo highly correlated with that detected using wave intensity analysis (r 2 = 0.83, P < 0.001). We conclude that the new technique described in this paper offers a convenient and objective method for detecting Tr, and allows for the dynamic determination of wave speed and Tr, simultaneously

Impact of Tapering of Arterial Vessels on Blood Pressure, Pulse Wave Velocity, and Wave Intensity Analysis using 1-Dimensional Computational Model

© 2020 Brunel University London. The angle of arterial tapering increases with ageing, and the geometrical changes of the aorta may cause an increase in central arterial pressure and stiffness. The impact of tapering has been primarily studied using frequency-domain transmission line theories. In this work, we revisit the problem of tapering and investigate its effect on blood pressure and pulse wave velocity (PWV) using a time-domain analysis with a 1D computational model. First, tapering is modelled as a stepwise reduction in diameter and compared with results from a continuously tapered segment. Next, we studied wave reflections in a combination of stepwise diameter reduction of straight vessels and bifurcations, then repeated the experiments with decreasing the length to physiological values. As the model's segments became shorter in length, wave reflections and re-reflections resulted in waves overlapping in time. We extended our work by examining the effect of increasing the tapering angle on blood pressure and wave intensity in physiological models: a model of the thoracic aorta and a model of upper thoracic and descending aorta connected to the iliac bifurcation. Vessels tapering inherently changed the ratio between the inlet and outlet cross-sectional areas, increasing the vessel resistance and reducing the compliance compared with non-tapered vessels. These variables influence peak and pulse pressure. In addition, it is well established that pulse wave velocity increases in an ageing arterial tree. This work provides confirmation that tapering induces reflections and offers an additional explanation to the observation of increased peak pressure and decreased diastolic pressure distally in the arterial tree

Towards the non-invasive determination of arterial wall distensible properties: new approach using old formulae

Addenbrook’s Hospital; Brunel University London