Wave intensity in the ascending aorta: effects of arterial occlusion

We examine the effects of arterial occlusion on the pressure, velocity and the reflected waves in the ascending aorta using wave intensity analysis. In 11 anaesthetised, open-chested dogs, snares were used to produce total arterial occlusion at 4 sites: the upper descending aorta at the level of the aortic valve (thoracic); the lower thoracic aorta at the level of the diaphragm (diaphragm); the abdominal aorta between the renal arteries (abdominal) and the left iliac artery, 2 cm downstream from the aorta iliac bifurcation (iliac). Pressure and flow in the ascending aorta were measured, and data were collected before and during the occlusion. During thoracic and diaphragm occlusions a significant increase in mean aortic pressure (46% and 23%) and in wave speed (25% and 10%) was observed, while mean flow rate decreased significantly (23% and 17%). Also, the reflected compression wave arrived significantly earlier (45% and 15%) and its peak intensity was significantly greater (257% and 125%), all compared with control. Aortic occlusion distal to the renal arteries, however, caused an indiscernible change in the pressure and velocity waveforms, and in the intensities and timing of the waves in the forward and backward directions. The measured pressure and velocity waveforms are the result of the interaction between the heart and the arterial system. The separated pressure, velocity and wave intensity are required to provide information about arterial hemodynamic such as the timing and magnitude of the forward and backward waves. The net wave intensity is simpler to calculate but provides information only about the predominant direction of the waves and can be misleading when forward and backward waves of comparable magnitudes are present simultaneously.     

Instantaneous blood flow, impedance and elastic properties computed in man from aortic pulse waves

A mathematical model of the pressure-flow relationship in the arterial circulation and its possible use in routine hemodynamics in man are described. The instantaneous blood flow velocity in the ascending aorta can be calculated from two pressure curves simultaneously recorded 5 cm apart. The mechanical aortic input impedance is computed from the recorded pressure and the calculated blood flow velocity curves. Projection of the pulse waves on a time-length plane leads to the determination of the pulse wave velocity and then an estimation of the elastic modulus of the aortic wall.     

Pulmonary vascular impedance and wave reflections in the hypoxic calf.

The alterations in pulsatile hemodynamics that occur during hypoxic pulmonary vasoconstriction have not been well characterized. Changes in oscillatory hemodynamics, however, may affect right ventricular-pulmonary vascular coupling and the dissipation of energy within the lung vasculature. To better define hypoxic pulsatile hemodynamics, we measured main pulmonary artery proximal and distal micromanometric pressures and ultrasonic flow in four open-chest calves during progressive hypoxia. Main pulmonary artery impedance and pressure transmission spectra were calculated using spectral analysis methods. Measured pressure and flow signals were separated in the time domain into forward and backward components. Hypoxia increased pulmonary blood pressure and resistance and produced multiple modifications in the impedance and pressure transmission spectra that indicated increased wave reflections and elasticity. The impedance and apparent phase velocity first-harmonic values were increased in amplitude, and the pressure transmission modulus plot showed an increased peak value. In addition, the impedance modulus plot demonstrated a rightward shift and increased oscillation in the mid- to high-frequency range. The time domain analysis also confirmed increased wave reflections and elasticity. Hypoxia produced large backward-traveling (reflected) pressure and flow waves. The initial portions of these waves arrived at the heart during systole, producing characteristic changes in the measured pressure and flow waveforms. With prolonged hypoxia, main pulmonary artery pulse wave velocity increased by 30%. Thus, hypoxia is associated with complex alterations in pulmonary artery elasticity and wave reflections that act to increase the oscillatory afterload of the right ventricle.     

Wave propagation in a model of the arterial circulation

The propagation of the arterial pulse wave in the large systemic arteries has been calculated using a linearised method of characteristics analysis to follow the waves generated by the heart. The model includes anatomical and physiological data for the 55 largest arteries adjusted so that the bifurcating tree of arteries is well matched for forward travelling waves. The peripheral arteries in the model are terminated by resistance elements which are adjusted to produce a physiologically reasonable distribution of mean blood flow. In the model, the pressure and velocity wave generated by the contraction of the left ventricle propagates to the periphery where it is reflected. These reflected waves are re-reflected by each of the bifurcations that they encounter and a very complex pattern of waves is generated. The results of the calculations exhibit many of the features of the systemic arteries, including the increase of the pulse pressure with distance away from the heart as well as the initial decrease and then the large increase in the magnitude of back flow during late systole going from the ascending aorta to the abdominal aorta to the arteries of the leg. The model is then used to study the effects of the reflection or absorption of waves by the heart and the mechanisms leading to the incisura are investigated. Calculations are carried out with the total occlusion of different arterial segments in order to model experiments in which the effects of the occlusion of different arteries on pressure and flow in the ascending aorta were measured. Finally, the effects of changes in peripheral resistance on pressure and velocity waveforms are also studied. We conclude from these calculations that the complex pattern of wave propagation in the large arteries may be the most important determinant of arterial haemodynamics.     

High frequency characteristics of the arterial system

Pressure, flow and diameter were measured in the abdominal aorta of five anesthetized dogs during normal heart beats and heart beats with a superimposed impulse (generated by rapidly injecting a small volume of saline into the system). From Fourier analysis it was found that the impulse enhanced the amplitudes of the higher harmonics so that frequencies up to 80 Hz could be studied. Both the input impedance and apparent phase velocity above 20 Hz were independent of frequency and their average values were designated as characteristic impedance and true phase velocity. Average characteristic impedance for all five animals was 2.0 +/- 0.1 X 10(8) Nsm-5 and average phase velocity was 8.3 +/- 0.6 ms-1. Phase velocities calculated from characteristic impedance (1.76-2.39 X 10(8) Nsm-5) and from the slope of the pressure-diameter relation (0.102-0.25 X 10(-8) Nm-3) were similar to the true phase velocity as defined above (6.79-9.85 ms-1). It may be concluded that the input impedance converges to characteristic impedance and apparent phase velocity converges to phase velocity for high frequencies.     

Resolving the time lag between pressure and flow for the determination of local wave speed in elastic tubes and arteries

It is well established that wave speed can be determined using the initial linear part of the pressure–velocity loop (PU-loop). However, the frequency response of most flow measuring devices is usually slower than that of solid-state pressure transducers; making flow waveforms lagging in time behind pressure waveforms. If this lag, which is traditionally determined by eye, is not corrected prior to the analysis, the PU-loop method may provide inaccurate wave speeds. The main aim of this work is therefore to introduce an objective technique to establish the value of this lag.The new technique relies on the linearity between pressure and velocity in the absence of reflections, and determines the highest correlation factor between pressure and velocity in the range of minimum pressure to maximum velocity. We shifted the flow waveform backwards in time steps equal to the sampling interval, and the time shift associated with the highest correlation indicates the correct time lag of the flow waveform. We first tested the new technique in vitro using a uniform latex tube and compared the results to those established using the traditional by eye method, whilst varying the filter setting of the flowmeter. Then we applied the new technique to pressure and flow measured in the ascending aorta of anaesthetised open-chested dogs.We found the time lag between pressure and velocity calculated by the new technique in good agreement with that determined by eye in vitro and that increasing the filtering power generated greater delay between the measured pressure and flow. The results obtained in vivo using the new technique were also in good agreement with those determined by eye. We therefore conclude that the new technique provides a convenient and objective way of correcting the lag and can reliably align pressure and flow.     

Aortic reflection coefficients and their association with global indexes of wave reflection in healthy controls and patients with Marfan's syndrome

Early return of reflected pressure waves increases the load on central arteries and may increase the risk of aortic rupture in patients with Marfan's syndrome (MFS). To assess whether wave reflection is elevated in MFS, we used ultrasound and MRI to measure central pressure and flow waveforms in 26 patients (13-54 yr of age) and 26 age- and gender-matched controls. Aortic systolic and diastolic cross-sectional areas were measured at the ascending and descending aorta (AA and DA), diaphragm (DIA), and lower abdominal aorta (AB). From these measurements, local characteristic impedance (Z(0-xx)) and local reflection coefficients (Gamma(xx-yy)) were calculated. Calculated global wave reflection indexes were the augmentation index (AIx) and the ratio of backward to forward pressure wave (P(b)/P(f)). The aorta was wider in MFS patients at AA (P < 0.01) and DA (P < 0.01). Aortic pulse wave velocity was 42 cm/s higher in MFS patients (P < 0.05). Z(0-xx) was not different between groups, except at DA, where it was lower in MFS patients. In controls, Gamma(AA-DA) was 0.31 +/- 0.08, Gamma(DA-DIA) was 0.00 +/- 0.11, and Gamma(DIA-AB) was 0.31 +/- 0.16. Mean values of Gamma(xx-yy) were not different between MFS patients and controls. In controls, aging diminished Gamma(AA-DA) but increased Gamma(DIA-AB). Clear age-related patterns were absent in MFS patients. AIx or P(b)/P(f) was not higher in MFS patients than in controls. There were indications for enhanced wave reflection in young MFS patients. Our data demonstrated that the major determinants of AIx were pulse wave velocity and the effective length of the arterial system and, to a lesser degree, HR and P(b)/P(f).     

Wave intensity analysis of left ventricular filling

Wave intensity analysis (WIA) is a powerful technique to study pressure and flow velocity waves in the time domain in vascular networks. The method is based on the analysis of energy transported by the wave through computation of the wave intensity dI = dPdU, where dP and dU denote pressure and flow velocity changes per time interval, respectively. In this study we propose an analytical modification to the WIA so that it can be used to study waves in conditions of time varying elastic properties, such as the left ventricle (LV) during diastole. The approach is first analytically elaborated for a one-dimensional elastic tube-model of the left ventricle with a time-dependent pressure-area relationship. Data obtained with a validated quasi-three dimensional axi-symmetrical model of the left ventricle are employed to demonstrate this new approach. Along the base-apex axis close to the base wave intensity curves are obtained, both using the standard method and the newly proposed modified method. The main difference between the standard and modified wave intensity pattern occurs immediately after the opening of the mitral valve. Where the standard WIA shows a backward expansion wave, the modified analysis shows a forward compression wave. The proposed modification needs to be taken into account when studying left ventricular relaxation, as it affects the wave type.     

Determination of wave speed and wave separation in the arteries using diameter and velocity

The determination of arterial wave speed and the separation of the forward and backward waves have been established using simultaneous measurements of pressure (P) and velocity (U). In this work, we present a novel algorithm for the determination of local wave speed and the separation of waves using the simultaneous measurements of diameter (D) and U. The theoretical basis of this work is the solution of the 1D equations of flow in elastic tubes. A relationship between D and U is derived, from which, local wave speed can be determined; C=±0.5(dU_±/d ln D_±). When only unidirectional waves are present, this relationship describes a linear relationship between ln D and U. Therefore, constructing a ln DU-loop should result in a straight line in the early part of the cycle when it is most probable that waves are running in the forward direction. Using this knowledge of wave speed, it is also possible to derive a set of equations to separate the forward and backward waves from the measured D and U waveforms. Once the forward and backward waveforms of D and U are established, we can calculate the energy carried by the forward and backward waves, in a similar way to that of wave intensity analysis. In this paper, we test the new algorithm in vitro and present results from data measured in the carotid artery of human and the ascending aorta of canine. We conclude that the new technique can be reproduced in vitro, and in different vessels of different species, in vivo. The new algorithm is easy to use to determine wave speed and separate D and U waveforms into their forward and backward directions. Using this technique has the merits of utilising noninvasive measurements, which would be useful in the clinical setting.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

Influence of the distensibility of large arteries on the longitudinal impedance: application for the development of non-invasive techniques to the diagnosis of arterial diseases

Background

This study shows that the arterial longitudinal impedance constitutes a hemodynamic parameter of interest for performance characterization of large arteries in normal condition as well as in pathological situations. For this purpose, we solved the Navier?CStokes equations for an incompressible flow using the finite element analysis method and the Arbitrary Lagrangian Eulerian (ALE) formulation. The mathematical model assumes a two-dimensional flow and takes into account the nonlinear terms in the equations of fluid motion that express the convective acceleration, as well as the nonlinear deformation of the arterial wall. Several numerical simulations of the blood flow in large vessels have been performed to study the propagation along an arterial vessel of a pressure gradient pulse and a rate flow pulse. These simulations include various deformations of the wall artery leading to parietal displacements ranging from 0 (rigid wall) to 15% (very elastic wall) in order to consider physiological and pathological cases.

Results

The results show significant changes of the rate flow and the pressure gradient wave as a function of aosc, the relative variation in the radius of the artery over a cardiac cycle. These changes are notable beyond a critical value of aosc equal to 0.05. This critical value is also found in the evolution of the longitudinal impedance. So, above a variation of radius of 5%, the convective acceleration, created by the fluid-wall interactions, have an influence on the flow detectable on the longitudinal impedance.

Conclusions

The interpretation of the evolution of the longitudinal impedance shows that it could be a mean to test the performance of large arteries and can contribute to the diagnosis of parietal lesions of large arteries. For a blood vessel with a wall displacement higher than 5% similar to those of large arteries like the aorta, the longitudinal impedance is substantially greater than that obtained in the absence of wall displacement. This study also explains the effects of convective acceleration, on the shape of the decline of the pressure gradient wave and shows that they should not be neglected when the variation in radius is greater than 5%.     

Systems engineering analysis of aortic root blood pressure

This paper describes the aortic blood pressure as a function of aortic blood flow and the parameters of the blood and circulatory system. The method of performance involves the analogue of a multi-branched electrical to hydraulic transmission line applying graphical convolution to the blood flow-transform impedance relationship resulting in a theoretical pressure curve for the infinite aorta. The difference between the single pressure pulse and the computed adjusted infinite aorta pressure curve is described as the reflected wave. This reflected wave is then shown to be of reasonable configuration in time and velocity. The blood pressure is thus finally described completely by the physical parameters of the blood and the circulatory system and the blood flow.     

Inflation waves induced by axial acceleration of the aorta

The phenomenon of high-amplitude inflation waves resulting from a sharp axial acceleration of the aorta, as may occur in road accidents, is investigated theoretically. The aorta is modeled as an axisymmetric tapered membranic shell (tube) made of an incompressible, nonlinear viscoelastic material with cylindrical orthotropy. It is filled with an inviscid, incompressible fluid whose flow is considered as quasi-one dimensional along the tube axis. The equations of motion of the tube and of the fluid are solved numerically, by using a two-step explicit scheme, for several axial acceleration profiles. The solutions shows that an inflation wave is generated and it propagates in opposite direction to that of the acceleration. The wall stresses, deformations and their time derivatives as well as fluid velocity and pressure are determined along the tube at different time intervals. Peak axial and circumferential stresses are high, with the latter far exceeding the former. These stresses may cause rupture of the aorta.     

CFD analysis of the human airways under impedance-based boundary conditions: application to healthy,diseased and stented trachea

A computational fluid dynamics model of a healthy, a stenotic and a post-operatory stented human trachea was developed to study the respiration under physiological boundary conditions. For this, outflow pressure waveforms were computed from patient-specific spirometries by means of a method that allows to compute the peripheral impedance of the truncated bronchial generation, modelling the lungs as fractal networks. Intratracheal flow pattern was analysed under different scenarios. First, results obtained using different outflow conditions were compared for the healthy trachea in order to assess the importance of using impedance-based conditions. The resulted intratracheal pressures were affected by the different boundary conditions, while the resulted velocity field was unaffected. Impedance conditions were finally applied to the diseased and the stented trachea. The proposed impedance method represents an attractive tool to compute physiological pressure conditions that are not possible to extract in vivo. This method can be applied to healthy, pre- and post-operatory tracheas showing the possibility of predicting, through numerical simulation, the flow and the pressure field before and after surgery.     

Wave reflection effects in the central circulation of American alligators (Alligator mississippiensis): what the heart sees

A large central compliance is thought to dominate the hemodynamics of all vertebrates except birds and mammals. Yet large crocodilians may adumbrate the avian and mammalian condition and set the stage for significant wave transmission (reflection) effects, with potentially detrimental impacts on cardiac performance. To investigate whether crocodilians exhibit wave reflection effects, pressures and flows were recorded from the right aorta, carotid artery, and femoral artery of six adult, anesthetized American alligators (Alligator mississippiensis) during control conditions and after experimentally induced vasodilation and constriction. Hallmarks of wave reflection phenomena were observed, including marked differences between the measured profiles for flow and pressure, peaking of the femoral pressure pulse, and a diastolic wave in the right aortic pressure profile. Pulse wave velocity and peripheral input impedance increased with progressive constriction, and thus changes in both the timing and magnitude of reflections accounted for the altered reflection effects. Resolution of pressure and flow waves into incident and reflected components showed substantial reflection effects within the right aorta, with reflection coefficients at the first harmonic approaching 0.3 when constricted. Material properties measured from isolated segments of blood vessels revealed a major reflection site at the periphery and, surprisingly, at the junction of the truncus and right aorta. Thus, while our results clearly show that significant wave reflection phenomena are not restricted to birds and mammals, they also suggest that rather than cope with potential negative impacts of reflections, the crocodilian heart simply avoids them because of a large impedance mismatch at the truncus.     

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.     

A novel servo-control system that imposes desired aortic input impedance on in situ rat heart

To clarify the pathophysiological role of dynamic arterial properties in cardiovascular diseases, we attempted to develop a new control system that imposes desired aortic impedance on in situ rat left ventricle. In 38 anesthetized open-chest rats, ascending aortic pressure and flow waveforms were continuously sampled (1,000 Hz). Desired flow waveforms were calculated from measured aortic pressure waveforms and target impedance. To minimize the difference between measured and desired aortic flow waveforms, the computer generated commands to the servo-pump, connected to a side branch of the aorta. By iterating the process, we could successfully control aortic impedance in such a way as to manipulate compliance and characteristic impedance between 60 and 160% of their respective native values. The error between desired and measured aortic flow waveforms was 70 +/- 34 microl/s (root mean square; 4.4 +/- 1.4% of peak flow), indicating reasonable accuracy in controlling aortic impedance. This system enables us to examine the importance of dynamic arterial properties independently of other hemodynamic and neurohumoral factors in physiological and clinical settings.     

Effects of periodic accelerations on blood flow in arteries

This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.     

Significance of the contribution of aerobic and anaerobic components to several distance running performances in female athletes

To assess the most important determinant for successful distance running (800 m, 1500 m and 3000 m events) in female athletes, measurements of several anaerobic indices were made (peak power, mean power) using the Wingate anaerobic test (WAnT), and aerobic indices such as oxygen uptake (VO2) or running velocity (v) at lactate threshold (LT), VO2 or v at onset of blood lactate accumulation (OBLA), running economy (RE), and maximal oxygen uptake were determined using the incremental treadmill test. The RE was represented by a VO2 value measured at 240 m.min-1 of a standard treadmill velocity. A stepwise multiple regression analysis (SAS stepwise procedure) combined the best features of forward inclusion and backward elimination to determine the most important factors in predicting the performance of running these distances as dependent variables. The stepwise procedure showed that the blood lactate variables such as LT and/or OBLA are highly correlated with, and contributed to predicting performance running 800 m-3000 m, whereas the anaerobic component was related only to running 800 m. In conclusion, blood lactate variables account for a large part of the variation in distance running performance in female as in male runners. The component of the anaerobic system which can be measured by the WAnT was shown to contribute to performance in running 800 m, but not in longer distances.     

Turbulence in the canine ascending aorta and the blood pressure.

Turbulent velocity fluctuations were measured and analyzed in the canine ascending aorta using a hot-film anemometer. Blood flow rate and temperature were stabilized using a special bypass technique. Blood pressure was elevated by Methoxamine infusion. Turbulence components were extracted from measured data using an ensemble averaging technique. Turbulence intensity correlated best with blood flow rate although the variance was relatively large, especially when the blood flow velocity was high. When pooled data were grouped into subclasses using peak aortic flow velocity as the criteria, turbulence intensity correlated well with aortic systolic blood pressure in each of the subclasses. Spectral bandwidth correlated with aortic pressure in the same manner. In summary, turbulence in the aorta developed when blood pressure was high. Both an increase of turbulence intensity and an widening of turbulence spectra may be ascribed to a stiffening of the aortic wall due to an elevation of blood pressure.