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

Abnormal wave reflections and left ventricular hypertrophy late after coarctation of the aorta repair

Patients with repaired coarctation of the aorta are thought to have increased afterload due to abnormalities in vessel structure and function. We have developed a novel cardiovascular magnetic resonance protocol that allows assessment of central hemodynamics, including central aortic systolic blood pressure, resistance, total arterial compliance, pulse wave velocity, and wave reflections. The main study aims were to (1) characterize group differences in central aortic systolic blood pressure and peripheral systolic blood pressure, (2) comprehensively evaluate afterload (including wave reflections) in the 2 groups, and (3) identify possible biomarkers among covariates associated with elevated left ventricular mass (LVM). Fifty adult patients with repaired coarctation and 25 age- and sex-matched controls were recruited. Ascending aorta area and flow waveforms were obtained using a high temporal-resolution spiral phase-contrast cardiovascular magnetic resonance flow sequence. These data were used to derive central hemodynamics and to perform wave intensity analysis noninvasively. Covariates associated with LVM were assessed using multivariable linear regression analysis. There were no significant group differences (P≥0.1) in brachial systolic, mean, or diastolic BP. However central aortic systolic blood pressure was significantly higher in patients compared with controls (113 versus 107 mm Hg, P=0.002). Patients had reduced total arterial compliance, increased pulse wave velocity, and larger backward compression waves compared with controls. LVM index was significantly higher in patients than controls (72 versus 59 g/m(2), P<0.0005). The magnitude of the backward compression waves was independently associated with variation in LVM (P=0.01). Using a novel, noninvasive hemodynamic assessment, we have shown abnormal conduit vessel function after coarctation of the aorta repair, including abnormal wave reflections that are associated with elevated LVM

Analysis of local hemodynamics in central and peripheral arteries

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.To understand the function of the cardiovascular system, the propagation of waves in arteries has to be investigated, since they carry information which can be used for the prevention and diagnosis of cardiovascular diseases. The main goal of this thesis is to improve the understanding of wave propagation in central and peripheral arteries studying the local hemodynamics of the ascending aorta, the carotid artery and the femoral artery by analysing human, animal and in vitro data. Also, another aim is to introduce a technique for non-invasive determination of the local arterial distensibility, the wave speed, and wave intensities. Arterial hemodynamics is here studied using wave intensity analysis, a time domain technique based on pressure and velocity measurements that is derived from the 1D theory of wave propagation in elastic tubes. Also, variations of this technique were used, such as (i) the non-invasive wave intensity analysis that relies on diameter and velocity measurements and (ii) the reservoir-wave approach in which pressure is considered the sum of a pressure due to the elastic properties of the arteries and a pressure due to the travelling wave. To identify the correct analysis to describe the wave propagation in the ascending aorta using pressure and velocity measurements, the hemodynamics of the canine ascending aorta was studied invasively using the traditional wave intensity (or waveonly) analysis and the reservoir-wave approach in both control condition and during total aorta occlusions in order to provide clear reflection sites. The models produced a remarkably similar wave intensity curves, although the intensity magnitudes were different. The reservoir-wave model always yielded lower values for all hemodynamic parameters studied. Both models led to the conclusion that distal occlusions have little or no effect on hemodynamics in the ascending aorta. Since the ascending aorta is not an accessible vessel its examination in clinical routine is challenging. More superficial arteries, such as carotid, radial, brachial and femoral arteries, might be easier to examine, in particular using ultrasound equipment that is normally available in the clinic. These considerations led to the second study of this thesis that is the introduction of a new technique for the non-invasive determination of arterial distensibility, local wave speed and wave intensities to study arterial hemodynamics in humans. The technique relies only on diameter and velocity measurements that can be obtained using ultrasound. In particular, the technique was used for the first time to study the hemodynamic of the carotid and femoral arteries in a large population of healthy humans to investigate the changes with age and gender. The carotid artery was more affected by the aging process than the femoral artery, even in healthy subjects. Local wave speed, distensibility and hemodynamic wave intensity parameters (except the reflection index) had strong correlations with age at the carotid artery. The mechanical properties and hemodynamic parameters of the femoral artery were not significantly age-dependent, but local wave speed, distensibility and forward wave intensity were significantly gender-dependent. The findings of the first and second studies contributed to the design of the third study. The carotid artery is an elastic artery relatively close to the heart and thus the hemodynamics of this vessel is related to left ventricular function. For this reason, the carotid hemodynamics of the same healthy population was investigated for the first time using the reservoir-wave approach. Pressure and velocity measurements were separated into their reservoir and excess components and the effects of age and gender on these parameters were studied. It was found that in the carotid artery reservoir and excess components are strongly affected by the ageing process. From the above studies some questions about the hemodynamics of central arteries remained unsolved. For this reason it was decided to carry out in vitro experiments in a mock circulatory system to investigate the effects of variation of compliance and stroke volume on the reservoir and excess pressure components of the ascending aorta. This allows for the study of different physiological and pathological conditions, such as age, hypertension, atherosclerosis and ventricular dysfunction in relation to vascular compliance and stroke volume. The reservoir and excess components of the measured pressure wave were both significantly related to aortic compliance and stroke volume, but the reservoir pressure had a stronger relationship with aortic compliance compared with the excess pressure and its magnitude increased more significantly when the aorta became stiffer. Wave speeds, calculated using measured and excess pressures, followed the same pattern, but the one calculated using excess pressure was smaller than the other. Wave speed was strongly related to aortic compliance, but not to the change of stroke volume. In conclusion, the use of the wave-only and the reservoir-wave models led to different values of wave speed and intensities that can be explained considering the anatomy of the arterial system. Notably, elastic and muscular arteries are differently affected by age and gender. The hemodynamics of the carotid artery are strongly related to age also in healthy subjects. Pressure and flow velocity in the carotid artery can be separated into their reservoir and excess components. The new non-invasive technique based on diameter and velocity measurements could be relevant in clinical practice as a screening tool

Using Acoustic Holography for Vibration Analysis

Disertační práce se zabývá bezkontaktní analýzou vibrací pomocí metod akustické holografie v blízkém poli. Akustická holografie v blízkém poli je experimentální metoda, která rekonstruuje akustické pole v těsné blízkosti povrchu vibrujícího předmětu na základě měření akustického tlaku nebo akustické rychlosti v určité vzdálenosti od zkoumaného předmětu. Konkrétní realizace této metody závisí na použitém výpočetním algoritmu. Vlastní práce je zaměřena zejména na rozbor algoritmů, které využívají k rekonstrukci zvukového pole v blízkosti vibrujícího objektu transformaci do domény vlnových čísel (prostorová transformace), kde probíhá vlastní výpočet. V úvodu práce je vysvětlena základní teorie metody akustické holografie v blízkém poli s popisem základních vlastností a dále rozborem konkrétních nejčastěji používaných algoritmům pro lokalizaci a charakterizaci zdroje zvuku a pro následnou vibrační analýzu. Stěžejní část práce se věnuje pokročilým metodám zpracování, které se snaží určitým způsobem optimalizovat přesnost predice zvukového pole v blízkosti vibrujícího předmětu v reálných podmínkách. Jde zejména o problematiku použitého měřicího systému s akustickými snímači, které nejsou ideální, a dále o možnost měření v prostorách s difúzním charakterem zvukového pole. Pro tento případ byla na základě literárního průzkumu optimalizována a ověřena metoda využívající dvouvrstvé mikrofonní pole, které umožňuje oddělení zvukových polí přicházejících z různých stran a tedy úspěšné měření v uzavřených prostorách např. kabin automobilů a letadel. Součástí práce byla také optimalizace, rozšíření a následné ověření algoritmů publikovaných v posledních letech pro měření v reálných podmínkách za použití běžně dostupných akustických snímačů.The main aim of the thesis is application of near-field acoustic holography for non-contact vibration analysis. Near-field acoustic holography is an experimental technique for reconstruction of sound field close to the surface of the vibrating object based on measurement of sound pressure or acoustic particle velocity in certain distance from the examined object. Practical realization of this method depends on used calculation procedure. The thesis is focused on analysis of acoustic holography algorithms with transformation into wavenumber domain (spatial transformation) where the reconstruction of the sound field near vibrating object is calculated. The introductory part of the thesis describes the theory of near-field acoustic holography with general characteristics and with analysis of most common algorithms used for localization and characterization of sound source and consequent vibration analysis. Principal part of the thesis deals with advanced processing methods where these methods try to optimize the accuracy of prediction of sound field near vibrating object in real environment. In this study, real measurement conditions represent the measurement system with non-ideal acoustic sensors and also areas with reverberant sound field. Based on literature study, there has been optimized and verified the new method which uses double layer microphone array to separate incoming and outgoing sound field, thus allows successful measurement in confined space e.g. cabins of cars and airplanes. Part of the thesis has been also focused on optimization, extension and successive experimental validation of selected classical algorithms published in last decade for possible measurement in real conditions and with common acoustic sensors.

Propagation and reflection of pulse waves in flexible tubes and relation to wall properties

This thesis was submitted for the degree of Docter of Philosophy and awarded by Brunel University.The wall properties of the arteries play an important role in cardiovascular function. Stiffness of large artery is predictive of cardiovascular events. To understand the function of the cardiovascular system, special attention should be paid to the understanding of pulse wave propagation, because pulse waves carry information of the cardiovascular function, and provide information which can be useful for the prevention and diagnosis of diseases. This thesis presents a series of in vitro experimental studies of wave propagation, wave reflection and determination of mechanical properties of flexible vessels. In this thesis, several studies have been included: 1) applied and compared foot-to-foot, PU-loop and lnDU-loop methods for determination of wave speed in flexible tubes and calf aortas; 2) investigated the variation of local wave speed determined by PU-loop with proximity to the reflection site; 3) investigated using wave intensity analysis (WIA) as the analytical technique to determine the reflection coefficient; 4) developed a new technique which based on one-point simultaneous measurements of diameter and velocity to determine the mechanical properties of flexible tubes and calf aortas. In the first study, it is found wave speeds determined by PU-loop and lnDU-loop methods are very similar, and smaller than those determined by foot-to-foot method. The timing of arrival time of reflected wave based on diameter and velocity technique highly agreed with the corresponding timing based on pressure and velocity technique. The shapes of forward and backward non-invasive wave intensities based on diameter and velocity are very similar with the corresponding shapes based on pressure and velocity. Although the density term is not part of the equation, the lnDU-loop method for determining local wave speed is sensitive to the fluid density. In the second study, it is found wave speed measured by PU-loop is varied with proximity to the reflection site. The closer the measurement site to the reflection site, the greater the effect upon measured wave speed; a positive reflection caused an increase in measured wave speed; a negative reflection caused a decrease in measured wave speed. Correction iteration process was also considered to correct the affected measured wave speed. In the third study, it is found, reflection coefficient determined by pressure, square roots of wave intensity and wave energy are very close, but they are different from reflection coefficient determined by wave intensity and wave energy. Due to wave dissipation, the closer the measurement site to the reflection site, the greater is the value of the local reflection coefficient. The local reflection coefficient near the reflection site determined by wave intensity and wave energy are very close to the theoretical value of reflection coefficient. In the last study I found that distensibility determined by the new technique which utilising lnDU-loop is in agreement with that determined from the pressure and area which obtained from tensile test in flexible tubes; distensibility determined by the new technique is similar to those determined in the static and dynamic distensibility tests in calf aortas; Young’s modulus determined by the new technique are in agreement with that those determined by tensile tests in both flexible tubes and calf aortas. In conclusion, wave speed determined by PU-loop and lnDU-loop methods are very similar, the new technique lnDU-loop provides an integrated noninvasive system for studying wave propagation; wave speed determined by PU-loop is affected by the reflection, the closer the measurement site to the reflection site, the greater the change in measured wave speed; WIA could be used to determine local reflection coefficient when the measurement site is close to the reflection site; the new technique using measurements of diameter and velocity at one point for determination of mechanical properties of arterial wall could potentially be non-invasive and hence may have advantage in the clinical setting

Wave propagation in flexible tubes

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Wave dissipation was previously investigated intensively in the frequency domain, in which the dissipation of waves is described as attenuation of pressure pulse decay with respect to the frequency or harmonics. In this thesis, wave dissipation, including decay of pressure pulse, peak of wave intensity and wave energy, is investigated in the time domain using wave intensity analysis (WIA). Wave intensity analysis benefits to this research in several aspects including: 1) WIA allows for wave dissipation investigated in the time domain; 2) WIA does not make any assumptions about the tube's wall non-linearity and the analysis takes into account the effects of the vessel's wall viscoelastic properties, convective, frictional effects and fluid viscosity; 3) WIA offers a technique (separation) to study wave dissipation in one direction whilst taking into account the effect of reflections from the opposite direction; 4) The physical meaning of wave intensity provides a convenient method to study the dissipation of energy carried by the waves along flexible tubes. In this research, it is found that the degree of dissipation in flexible tube were not only affected by the mechanical properties of the wall property and viscosity of liquid but also by the other factors including initial pressure and pumping speed of piston as well as direction of wave in relation to direction of flow. Also an new technique to separate waves into forward and backward directions only using diameter and velocity might potentially be used to separate the waves in both directions non-invasively based on the non-invasive measurement of diameter (wall movement) available

Fluid-structure interaction simulation of pulse propagation in arteries : numerical pitfalls and hemodynamic impact of a local stiffening

When simulating the propagation of a pressure pulse in arteries, the discretization parameters (i.e. the time step size and the grid size) need to be chosen carefully in order to avoid a decrease in amplitude of the traveling wave due to numerical dissipation. In this paper the effect of numerical dissipation is examined using a numerical fluid-structure interaction (FSI) model of the pulse propagation in an artery. More insight in the influence of the temporal and spatial resolution of the wave on the results of these simulations is gained using an analytical study in which the scalar linear one-dimensional transport equation is considered. Although this model does not take into account the full complexity of the problem under consideration, the results can be used as a guidance for the selection of the numerical parameters. Furthermore, this analysis illustrates the difference in accuracy that can be obtained using a second-order implicit time integration scheme instead of a first-order scheme. The results from the analytical and numerical studies are subsequently used to determine the settings necessary to obtain a grid and time step converged simulation of the wave propagation and reflection in a simplified model of an aorta with repaired aortic coarctation. This FSI model allows to study the hemodynamic impact of a stiff segment and demonstrates that the presence of a stiff segment has an important impact on a short pressure pulse, but has almost no influence on a physiological pressure pulse. This phenomenon is explained by analyzing the reflections induced by the stiff segment