Christina and Ashraf W: Wave intensity analysis in the great arteries – What has been learnt during the last 25 years? Part 1.


Stroke volume ejection into the roots of the aorta and main pulmonary artery at every heart cycle gives rise to inextricably linked blood pressure and flow disturbances that propagate as waves along the flexible-walled vascular tree. The study of wave propagation in the circulation is gaining increasing clinical interest, as it can provide information about the physiological/pathophysiological mechanisms that integrate the various components of the cardiovascular system. Understanding these dynamic mechanisms allows for the derivation of markers that characterise the deterioration that occurs with disease or the improvement accomplished with therapeutic interventions. Such biomarkers provide valuable prognostic, diagnostic and treatment evaluation tools.

Wave intensity analysis (WIA) was introduced 25 years ago for the study of arterial wave travel1, 2. This analysis provides a method for the assessment of propagating waves and thereby of cardio-vascular interaction. The theoretical basis of WIA is founded on the solution of Euler’s one-dimensional equations of mass and momentum conservation in elastic tubes with Riemann’s method of characteristics3, 4. Unlike impedance-based methods, which assume that a waveform is synthesised by the superposition of sinusoidal wavetrains, WIA considers a waveform to be composed of the sequential addition of infinitesimal wavefronts1, 2, 5. WIA is a time-domain technique, with the results presented as a function of time, therefore enabling the association between wave intensity features and events during the cardiac cycle. It is outside the scope of this review to provide an extensive description of the method and the underpinning theory, but that material is available elsewhere1, 3, 6–8.

Briefly, WIA relies on the co-localised and simultaneous measurements of blood pressure (P) and flow velocity (U). Net wave intensity dI at any sampling interval is defined as:

dI = dP dU

where dP and dU denote the incremental differences in pressure and flow velocity, respectively, between successive sampling points. Therefore by definition dI is the power per unit area (W/m2) carried by a propagating wavefront1. With the dI profile constructed as a time series, the major peaks of the profile correspond to the dominant propagating waves over the course of the cardiac cycle. The area under a peak has units of J/m2 and characterises the energy per unit area transported by the wave. Based on standard convention, positive dI peaks correspond to waves propagating in the same direction as net blood flow (forward-traveling waves, originating from upstream) and negative dI peaks to waves propagating in the opposite direction (backward-traveling waves, originating from downstream). At any particular instant during the cardiac cycle, dI reveals the dominant direction of wave travel, which depends on the relative size and timing of the forward and backward wavefronts that pass from the measuring location.

Waves travel at speeds considerably higher than U. There is a variety of techniques available for the determination of wave speed (c), based on local measurements of P, U, vessel diameter (D) or analogous hemodynamic parameters9–17.

When wave speed is known, it is possible to decompose the changes in P and U as:

dP ±  =  1 2  (dP  ±  ρ c dU)

dU ±  =  1 2  (dU  ±   dP ρ c )

where ρ is the density of blood, and ‘+’ and ‘–’ indicate the forward and backward direction of the wave travel, respectively1.

The dI separated into forward (dI+) and backward (dI-) components can be written as dI ± = dp ± du ± , which, according to equations (2) and (3), yields:

dU ±  =  1 2  (dU  ±   dP ρ c )

Apart from their direction of travel, waves can be further categorized based on their nature, according to the blood pressure changes that accompany them. A compression wave is associated with an increase in pressure, and an expansion wave is associated with a decrease in pressure. Consequently, there are four possible types of waves: forward compression (FCW) and expansion (FEW) waves, and backward compression (BCW) and expansion (BEW) waves. A forward compression wave (FCW) causes flow acceleration, but a backward compression (BCW) wave causes flow deceleration. Conversely, a forward expansion wave (FEW) causes flow deceleration, whilst a backward expansion wave (BEW) causes flow acceleration.

As a consequence of the definition presented above, the value of wave intensity depends on the data acquisition frequency. This poses practical difficulties when a quantitative comparison needs to be made between data collected with different sampling frequencies. To overcome this difficulty, it has been proposed to substitute dP and dU with the corresponding time derivatives, dP/dt and dU/dt, respectively18. The resulting dI dimensions (W/(m2s2)) do not have the straightforward physical explanation facilitated by the original definition. However, the deviation between the original and the time-normalised wave intensity is essentially a scaling factor, with no difference in the physiological meaning or interpretation of the results7.

The manner in which nonlinear behavior, such as the pressure-dependence of c and other elastic nonlinearities, affect WIA and wave propagation has also received some attention. However, the added value of nonlinear analysis is not unanimously endorsed. Some authors report substantial differences arising when nonlinearities are taken into account19–21. Others however state that the differences between the linear and nonlinear treatment of the one-dimensional equations result in quantitative discrepancies of less than 10% and therefore the linear treatment is sufficient for all practical and clinical purposes22, 23.

Foreseeing the added clinical value that would be imparted by the ability to derive local wave speed, wave intensity and wave separation from non-invasive measurements, equations analogous to those presented above but formulated using vessel diameter (D) and u (instead of P and U) have been recently presented and validated clinically in healthy middle-aged Europeans15, 24, 25. The clinical potential of this non-invasive technique is growing, as advances in ultrasound technology make possible the measurement of D and U at more locations and with higher accuracy. Measurements of D and U determined by cardiovascular magnetic resonance imaging (MRI) have been also used for the non-invasive determination of local wave speed and wave intensity in the human aorta26. A variation of the non-invasive WIA approach was subsequently presented, based on a vessel cross-sectional area (A) and U formulation of the fundamental equations (rather than D and U), and applied on high temporal resolution, phase-contrast MRI data derived from paediatric patients with single ventricle physiology27, 28.

Wave intensity wall analysis was developed for application in conjunction with speckle tracking echocardiography and uses the arterial wall deformation changes in the radial and longitudinal directions to derive approximate changes in P and U, respectively29, 30.

Figure 1:

Figure 1: Schematic representation of the major arteries and veins that will be discussed in terms of WIA in this review. PT: Pulmonary trunk; PA: pulmonary artery; PV: pulmonary vein; lA: left


This review will focus on the clinical usefulness of WIA, as established from in vivo and clinical studies, in the aorta, pulmonary arteries and pulmonary veins (Figure 1). The findings will be presented according to measuring site and are exclusively centred on P-u-based WIA derived from invasive measurements.

Aortic wave intensity

Numerous studies in the aorta have affirmed the reproducibility of the distinct pattern of three dominant wave intensity peaks that was first revealed in 1988, in a pioneering application of WIA in the human aorta2. Aortic wave intensity in health is typically characterised by the presence of waves mainly when the aortic valve is open, with little or no wave travel taking place during diastole (Figure 2). During systole, a FCW (FCWao) associated with a simultaneous upstroke in aortic pressure and flow velocity in early systole is followed by a BCW (BCWao) that coincides with rising aortic pressure and declining flow in mid-systole, and the wave sequence is concluded in late-systole by a FEW (FEWao) that is related to both decreasing aortic pressure and flow. A FCW (FCWao_2) associated with the brief increase in aortic pressure taking place during aortic valve closure (dicrotic notch) might be occasionally discerned in the aortic wave intensity profile as well.

Figure 2:

Figure 2: Diagrammatic representation of the aortic wave intensity profile derived from ascending aortic pressure and flow velocity measurements, for one cardiac cycle.


Aortic wave intensity in health

The FCWao is generated by the contraction of the left ventricle (LV) and is responsible for blood flow acceleration during early systolic ejection, by creating a pushing effect at the proximal end of the aorta1, 2, 31. The FEWao is generated as the rate of myocardial shortening is reduced, and, as it produces a pulling effect at the proximal end of the aorta, it is the main determinant of aortic blood flow deceleration during late systolic ejection and subsequent aortic valve closure. This was a revolutionary finding in the 1990s, that challenged the prevalent belief at that time that wave reflections from the periphery are the main mechanism of aortic flow deceleration1, 2, 31. The onset of the FEWao corresponds well with the time the LV long axis shortening begins to slow down (base and apex moving towards each other at a reduced pace)32. It has been shown theoretically that the peak of the FCWao depends on (max dP/dt)2 1/�c and the peak of the FEWao on �c(max(-dU/dt))2, where max dP/dt represents the maximum rate of LV pressure increase in early systole and max(-dU/dt) the maximum aortic flow deceleration in late systole18, 33, 34. These theoretical derivations consider the LV to be acting as a pressure generator in early systole and a flow generator in late systole.

In contrast to the FCWao and FEWao which are both of LV origin, the BCWao originates distally as the FCWao is reflected at multiple sites of impedance mismatch along the arterial tree (e.g. bifurcations and locations of change in arterial structure). Thus, the BCWao is in fact an accumulated reflected wave that is largely determined by vascular properties35, 36. The BCWao produces a pushing effect in the distal aorta, causing aortic pressure rise upon its arrival at the proximal aorta. The arrival time of the BCWao at the aortic root has been found to be closely related to the time of the inflection point on the systolic aortic pressure upstroke (conventionally thought to signify the arrival of the reflected pressure pulse from the periphery). Also, the magnitude of the BCW showed good agreement with the augmentation index, according to a study conducted in elderly patients with atherosclerosis. The results of the study suggested that the BCWao provides an alternative means for the assessment of wave reflections, a key phenomenon in cardiovascular research37. The importance of wave reflections stems not only from their link to systolic aortic pressure augmentation and consequent hypertension risk, but also from the information they may contain about vascular properties and changes resulting from age, disease or pharmacological interventions. Interestingly, the arrival time of the BCWao at the aortic root in healthy dogs has been found to coincide with the time that the LV minor axis shortening begins to slow down (septum and free wall moving towards each other at a reduced pace), posing a question about whether the BCWao does in fact affect LV wall movement speed and thus LV mechanical function32.

Even though the presence and impact of arterial wave reflections are not doubted, the long-lasting belief that the reflection site lies at a fixed location in the periphery is questioned by recent findings35. It might seem straightforward to use aortic wave speed and the time delay between onsets of FCWao and BCWao, as observed at a certain measuring location, for estimating the distance to the reflection site, and thereby map it anatomically. However, in vivo studies that involved the progressive movement of the measuring location along the aorta without interfering with the vasculature35 or, oppositely, maintained the measuring location unchanged while well-defined reflection sites were introduced sequentially through total aortic occlusions along the aorta36, found a “horizon effect”. The summated BCWao that arrived at the measuring location was not affected in timing or magnitude by contributions from remote reflections (beyond the “horizon”), indicating that the BCWao is the result of reflections occurring near the measuring location rather than the result of reflections at a fixed anatomical location35, 36.

Administration of cardioactive and vasoactive agents for the pharmacological manipulation of certain cardiac or vascular mechanisms, and study of the subsequent changes in the aortic wave intensity parameters can provide advanced insight into the dynamics of ventricular-arterial interaction during the cardiac cycle. Dobutamine (positive inotropic effect), propranolol (negative inotropic effect), methoxamine (vasoconstrictor) and nitroglycerin (vasodilator) have been tested in this context in healthy animals6, 33, 38. The size of the FCWao was reduced with propranolol and increased with dobutamine, with no concurrent changes in the FEWao. This outcome was consistent with the affect these two agents are known to have on cardiac contractility and thus on max dP/dt33; as mentioned above, max dP/dt is a determinant of the FCWao but not of the FEWao34. Additional observations on the effect of dobutamine have been described by other investigators38. Methoxamine also reduced preferentially the size of the FCWao, a result ascribed primarily to increased afterload6, 33. Nitroglycerine caused a decrease in both FCWao and FEWao, which was attributed to reduced venous LV filling or preload, and to reduction in wave speed, respectively33.

Aortic wave intensity in disease and intervention

In the surgical setting, the effect of abdominal aortic clamping on wave travel was investigated in patients undergoing peripheral vascular reconstruction surgery39. An increase in the energy carried by the BCWao arriving at the aortic root and evidence of a subsequent rise in LV hydraulic work, presumably triggered by the rise in afterload produced by the BCWao, led to the postulation that the intra-operative impairment of LV function known to occur in this patient population could have been caused by an increase in oxygen demand that was not met by increased supply and thereby provoked ischemia39. Aortic malformations, such as an abdominal aneurysm40 and coarctation41, have been modelled computationally in the adult circulation and the results revealed a disturbed backward wave intensity pattern in the ascending aorta and the aortic arch, respectively, compared to health.

Aortic WIA during counterpulsation has revealed the presence of additional backward-travelling aortic waves during diastole42–44. The energies of these waves are correlated to conventional hemodynamic parameters used for the assessment of counterpulsation benefit.

The reservoir-wave approach

The separation of the P and U waveforms into their forward and backward components using WIA1 appears to have included two conceptual difficulties. Firstly, the separation exhibits diastolic self-cancelling pressure and flow waves, a phenomenon that is physiologically highly unlikely to occur. The other difficulty is that the separation considers that the measured P is solely due to traveling waves, and does not take into account the pressure changes generated due to the storage during systole and gradual release during diastole of blood volume into the elastic aortic wall.

The reservoir-wave model appears to resolve these two difficulties, as it essentially assumes that the measured P consists of the reservoir pressure due to the blood volume stored into the aorta (Pr) and an excess pressure associated with wave propagation (Pexcess)45, 46. Simultaneous measurements of aortic pressure and LV outflow are required for the separation of these two pressure components. The reservoir-wave model does not produce self-cancelling waves; Pr follows the diastolic exponential decay of P, and Pexcess follows closely the shape of the flow waveform. The reservoir-wave approach has more recently been extended to calculate Pr from measured pressure alone at an arbitrary location in the arteries, without the need to measure LV outflow47. The mechanics underlying the reservoir and excess pressures calculated with the two approaches described above have been investigated theoretically and computationally48.

When using the reservoir-wave approach, wave intensity can be calculated with Pexcess and U instead of P and U. Although the shape of the separated curves derived with classical and reservoir-wave WIA is very similar, the intensity of both aortic forward and backward waves is always smaller with the reservoir-wave approach49. It has been reported that in the proximal human aorta, peak P- when using the reservoir-wave model accounts for ~6% , whereas it would account for ~30% of total pressure using the classical approach50. Analogous findings, comprising a reduction of the BCWao with the reservoir-wave approach during dramatic physiological manipulations, such as aortic occlusion, have also been reported49. Comparable results about the BCWao are described based on computational and ovine data51.

Other physiological questions, such as LV filling dynamics52, wave propagation and reflection in the canine aorta53, alterations in wave reflection with administration of vasodilators and vasoconstrictors in the canine circulation54, wave propagation in the venous circulation55 and the effect of ageing on Pr56 have also been investigated with reservoir-wave WIA46.

Pulmonary artery wave intensity

Pulmonary wave intensity in the adult circulation

The wave intensity pattern observed in the main pulmonary artery of healthy animals is qualitatively similar to the typical aortic pattern. An early-systolic FCW (FCWpulm) is generated by the contraction of the RV and exerts a pushing effect at the proximal end of the pulmonary trunk (PT), while a late-systolic FEW (FEWpulm) is produced as the rate of RV contraction begins to decelerate, and with the pulling effect it causes at the proximal end of the PT, it is instrumental in pulmonary blood flow reversal, similarly to the FEWao in the aorta57–59. However, the reflection of the FCWpulm that appears in mid-systole is in fact a BEW (BEWpulm), which tends to aid RV ejection by creating a pulling effect downstream of the PT57, 58. Although it has been recently advocated that the anatomical site of an “open-end” type reflector that could give rise to such a BEWpulm is not fixed throughout the cardiac cycle57, it is nonetheless likely located at the proximal portion of the pulmonary tree and gives rise to negative reflections as a result of the immediate and extensive branching of the pulmonary arteries, and the ensuing marked increase in cross-sectional area57, 58. A late-systolic BCW that could be the “closed-end” type reflection of the FCWpulm at the terminal arterioles, is also occasionally observed57.

Human studies have not been performed in the pulmonary artery, however a study related to asthma research was conducted in dogs with hypoxia-induced pulmonary vasoconstriction59. An enhanced vasodilatory effect of inhalation of nitric oxide (NO) in He, rather than NO in N2, was associated with a reduction in the size of the FCWpulm, potentially indicative of the decreased demand for RV contractility for the maintenance of cardiac output59. A concurrent drop in wave speed could also be associated with the observed FCWpulm reduction.

Pulmonary wave intensity in the foetal circulation

WIA has been extensively used in studying foetal lamb circulatory physiology. In the foetus, the PT arises from the base of the right ventricle and branches into what is essentially a trifurcation constituted by the left and right pulmonary artery (PA) and the ductus arteriosus (DA). Each PA branches immediately and extensively to form the pulmonary vascular bed, while the DA provides a direct connection between the PT and the descending aorta. Because of its ability to track the origin of propagating waves, WIA is uniquely suited to probe the ventricular-vascular interactions that take place at this junction and that overall result in distinctly different blood flow profiles at each of the daughter and parent vessels involved in the trifurcation60–62.

The foetal PT wave intensity profile is characterised by the same FCWpulm and FEWpulm that are encountered in the adult PT63, 64. Notwithstanding, often the FCWpulm presents a second, mid-systolic peak that might be related to the structural immaturity of the foetal myocardium and the resulting poor coordination between LV and RV systolic function65. In addition, the presence of a prominent mid-systolic BCW (BCWpulm_foet_PT) has been observed in the foetal PT and temporally associated with the onset of the characteristic mid-systolic plateau in PT blood flow 63. Due to the elimination of the BCWpulm_foet_PT upon ligation of the PT proximal to the DA, and taking into consideration the inferred origin of this wave based on wave speed and timing, the BCWpulm_foet_PT was attributed to the reflection of the FCWpulm at the distal pulmonary vasculature63. The latter was presumed to be acting as a “closed-end” type reflection site in the foetus due to the high vascular resistance of the fluid-filled lungs63. Furthermore, it was observed that the magnitude of the BCWpulm_foet_PT is larger than that of the foetal and adult BCWao and also that the BCW (BCWpulm_foet_PA) of the left PA exceeds in magnitude the FCWpulm. These findings indicated that the BCWpulm_foet_PT cannot be accounted for solely by reflections, but most likely mid-systolic impulsive vasoconstriction of the pulmonary microcirculation during each cardiac cycle contributes to its generation64. WIA performed in the beats surrounding an ectopic beat, showed that there is a close relationship between the BCWpulm_foet_PA and the preceding FCWpulm on a beat-to-beat basis, with matching transient potentiation in both waves after an ectopic beat. This relationship highlighted the possible role of the BCWpulm_foet_PA in the regulation of PA and PT hemodynamics66. This wave is also transmitted into the DA as a FCW (FCWpulm_foet_DA) and is responsible for augmentation in DA mid-systolic blood flow, a mechanism that supports foetal right-to-left flow at a period in the cardiac cycle where PT and PA flows are decreasing67. The comparative assessment of foetal PT and ascending aortic pressure and flow velocity profiles indicated that the higher mean pressure routinely observed in the PT is entirely due to systolic differences65. WIA investigation revealed that these differences were because of a larger FCWpulm than FCWao and a larger BCWpulm_foet_PT than BCWao, signifying that both ventricular and vascular components are responsible for the augmentation of foetal systolic PT pressure65.

Pulmonary vein wave intensity

The aetiology of bi-phasic antegrade systolic flow in the pulmonary veins (PVs) has been explored with WIA, in order to establish whether it is predominantly driven by left- or right-sided cardiac events68. In patients undergoing elective coronary artery bypass surgery, an early-systolic downstream-originating BEW (BEWpulm_vein) was indicative of suction of blood by the LA as the basis of the first peak in systolic PV flow, while the second peak was temporally associated with a late-systolic upstream-originating FCW (FCWpulm_vein) that actively pushed blood towards the LA68. The generation of the FCWpulm_vein has been attributed to the propagation of the FCWpulm across the pulmonary microvascular bed and subsequent transmission to the PVs68, but mathematical modelling has shown that a contribution from reflected waves cannot be discounted69.

The late-diastolic retrograde flow observed in the PVs has also been studied with WIA70. It was shown that as the LA contracts, it generates a FCW (FCWLA) that travels towards the LV and also a BCW (BCWLA) that travels towards the PVs70. The FCWLA tends to accelerate flow into the LV, but gets partially reflected at the mitral orifice, giving rise to a second BCW in the LA (BCWLA_2). Both BCWLA and BCWLA_2, once transmitted into the PVs, tend to decelerate PV flow in late diastole. The size of the reflected wave was augmented as LV stiffness was acutely increased, and resulted in higher retrograde flow through the PVs70.


Introduced approximately 25 years ago, WIA has proven to be a very useful tool in investigating a wide range of physiological and clinical questions. The technique has a number of features that make it particularly suited to studying ventricular-arterial coupling. The analysis and results are presented in the time domain, where linking WIA features and events during the cardiac cycle is intuitive. WIA also allows for the separation of P, U and wave intensity into their forward and backward components, which originate from upstream and downstream, respectively. Even with the recent introduction of the reservoir-wave approach, WIA remains a useful tool, whether being calculated using the wave pressure or the measured pressure. In this article we reviewed the use of WIA in the great arteries and veins, and in Part II we will review its use in other arterial vessels and in the ventricles.



Parker KH, Jones CJH (1990) Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics. Journal of Biomedical Engineering. 112: 322–326


Parker KH, Jones CJH, Dawson JR et al 1988 What Stops the Flow of Blood from the Heart? Heart and Vessels. 4: 241–245


Parker KH (2009) An introduction to wave intensity analysis. Med Biol Eng Comput. 47: 175–88


Parker KH (2009) A brief history of arterial wave mechanics. Med Biol Eng Comput. 47: 111–8


Wang JJ, Shrive NG, Parker KH et al 2009 “Wave” as defined by wave intensity analysis. Med Biol Eng Comput. 47: 189–95


Hughes AD, Parker KH, Davies JE (2008) Waves in arteries: A review of wave intensity analysis in the systemic and coronary circulations. Artery Research. 2: 51–59


Jones CJH, Sugawara M, Avies RH et al 1994 Arterial Wave Intensity: Physical Meaning and Physiological Significance, in “Recent Progress in Cardiovascular Mechanics”,. H. Hosoda, et al. Editors,Harwood Academic Publishers: Chur, Switzerland.p. 129–148.


Bleasdale RA, Parker KH, Jones CJH (2003) Chasing the wave. Unfashionable but important new concepts in arterial wave travel. American Journal of Physiology Heart and Circulatory Physiology. 284: H1879–1885


Khir AW, O’Brien AB, Gibbs JSR et al 2001 Determination of Wave Speed and Wave Separation in the Arteries. Journal of Biomechanics. 34: 1145–1155


Harada A, Okada T, Niki K et al 2002 On-line noninvasive one-point measurements of pulse wave velocity. Heart and Vessels. 17: 61–8


Rabben SI, Stergiopulos N, Hellevik LR et al 2004 An ultrasound-based method for determining pulse wave velocity in superficial arteries. J Biomech. 37: 1615–22


Davies JE, Whinnett ZI, Francis DP et al 2006 Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans. American Journal of Physiology Heart and Circulatory Physiology. 290: H878–885


Aguado-Sierra J, Parker KH, Davies JE et al 2006 Arterial pulse wave velocity in coronary arteries. Conf Proc IEEE Eng Med Biol Soc. 1: 867–70


Kolyva C, Spaan JA, Piek JJ et al 2008 Windkesselness of coronary arteries hampers assessment of human coronary wave speed by single-point technique. Am J Physiol Heart Circ Physiol 295: H482–90


Feng J, Khir AW (2010) Determination of wave speed and wave separation in the arteries using diameter and velocity. Journal of Biomechanics. 43: 455–62


Mynard JP, Davidson MR, Penny DJ et al 2011 Robustness of the P-U and lnD-U loop wave speed estimation methods: effects of the diastolic pressure decay and vessel wall non-linearities. Conf Proc IEEE Eng Med Biol Soc. 2011: 6446–9


Alastruey J (2011) Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed. Journal of Biomechanics. 44: 885–91


Ramsey MW, Sugawara M (1997) Arterial wave intensity and ventriculoarterial interaction. Heart Vessels Suppl. 12: 128–34


Jones CJ, Parker KH, Hughes R et al 1992 Nonlinearity of human arterial pulse wave transmission. J Biomech Eng 114: 10–4


Mynard J, Penny DJ, Smolich JJ (2008) Wave intensity amplification and attenuation in non-linear flow: implications for the calculation of local reflection coefficients. Journal of Biomechanics. 41: 3314–21


Mynard JP, Davidson MR, Penny DJ et al 2012 Non-linear separation of pressure, velocity and wave intensity into forward and backward components. Medical and Biological Engineering and Computing. 50: 641–8


Pythoud F, Stergiopulos N, Bertram CD et al 1996 Effects of friction and nonlinearities on the separation of arterial waves into their forward and backward components. Journal of Biomechanics. 29: 1419–1423


Pythoud F, Stergiopulos N, Meister JJ (1996) Separation of arterial pressure waves into their forward and backward running components. Journal of Biomechanical Engineering. 118: 295–301


Borlotti A, Khir AW, Rietzschel ER et al 2012 Noninvasive determination of local pulse wave velocity and wave intensity: changes with age and gender in the carotid and femoral arteries of healthy human. J Appl Physiol. (1985); 113: 727–35


Li Y, Khir AW (2011) Experimental validation of non-invasive and fluid density independent methods for the determination of local wave speed and arrival time of reflected wave. Journal of Biomechanics. 44: 1393–9


Li Y, Borlotti A, Hickson SS et al 2010 Using magnetic resonance imaging measurements for the determination of local wave speed and arrival time of reflected waves in human ascending aorta. Conf Proc IEEE Eng Med Biol Soc. 2010: 5153–6


Biglino G, Steeden JA, Baker C et al 2012 A non-invasive clinical application of wave intensity analysis based on ultrahigh temporal resolution phase-contrast cardiovascular magnetic resonance. J Cardiovasc Magn Reson. 14: 57


Biglino G, Schievano S, Steeden JA et al 2012 Reduced ascending aorta distensibility relates to adverse ventricular mechanics in patients with hypoplastic left heart syndrome: noninvasive study using wave intensity analysis. Journal of Thoracic and Cardiovascular Surgery. 144: 1307–13


Bjallmark A, Larsson M, Nowak J et al 2011 Effects of hemodialysis on the cardiovascular system: quantitative analysis using wave intensity wall analysis and tissue velocity imaging. Heart and Vessels. 26: 289–97


Larsson M, Bjallmark A, Lind B et al 2009 Wave intensity wall analysis: a novel noninvasive method to measure wave intensity. Heart and Vessels. 24: 357–65


Jones CJ, Sugawara M (1993) “Wavefronts” in the aorta--implications for the mechanisms of left ventricular ejection and aortic valve closure. Cardiovascular Research. 27: 1902–5


Page CM, Khir AW, Hughes AD et al 2010 Normal asynchrony of left ventricular long and short axes: their relationship with aortic hemodynamics. International Journal of Cardiology. 142: 166–71


Jones CJH, Sugawara M, Kondoh Y et al 2002 Compression and Expansion Wavefront Travel in Canine Ascending Aortic Flow: Wave Intensity Analysis. Heart and Vessels. 16: 91–98


Niki K, Sugawara M, Uchida K et al 1999 A noninvasive method of measuring wave intensity, a new hemodynamic index: application to the carotid artery in patients with mitral regurgitation before and after surgery. Heart and Vessels. 14: 263–71


Davies JE, Alastruey J, Francis DP et al 2012 Attenuation of wave reflection by wave entrapment creates a “horizon effect” in the human aorta. Hypertension. 60: 778–85


Khir AW, Parker KH (2005) Wave Intensity in the Ascending Aorta: Effects of Arterial Occlusion. Journal of Biomechanics. 38: 647–655


Koh TW, Pepper JR, DeSouza AC et al 1998 Analysis of Wave Reflections in the Arterial System Using Wave Intensity: A Novel Method for Predicting the Timing and Amplitude of Reflected Waves. Heart and Vessels. 13: 103–113


Penny DJ, Mynard JP, Smolich JJ (2008) Aortic wave intensity analysis of ventricular-vascular interaction during incremental dobutamine infusion in adult sheep. Am J Physiol Heart Circ Physiol. 294: H481–9


Khir AW, Henein MY, Koh T et al 2001 Arterial Waves in Humans During Peripheral Vascular Surgery. Clinical Science. 101: 749–757


Swillens A, Lanoye L, De Backer J et al 2008 Effect of an Abdominal Aortic Aneurysm on Wave Reflection in the Aorta. 55: 1602–11


van den Wijngaard JP, Siebes M, Westerhof BE (2009) Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation. Med Biol Eng Comput. 47: 211–20


Kolyva C, Pantalos GM, Giridharan GA et al 2009 Discerning aortic waves during intra-aortic balloon pumping and their relation to benefits of counterpulsation in humans. J Appl Physiol. 107: 1497–503


Lu PJ, Yang CF, Wu MY et al 2011 Wave energy patterns of counterpulsation: a novel approach with wave intensity analysis. Journal of Thoracic and Cardiovascular Surgery. 142: 1205–13


Lu PJ, Yang CF, Wu MY et al 2012 Wave intensity analysis of para-aortic counterpulsation. American Journal of Physiology Heart and Circulatory Physiology. 302: H1481–91


Wang J Jr., O’Brien AB, Shrive NG et al 2003 Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol. 284: H1358–1368


Parker KH (2013) Arterial reservoir pressure, subservient to the McDonald lecture, Artery 13. Artery Research (in press)


Aguado-Sierra J, Alastruey J, Wang JJ et al 2008 Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries. Proc Inst Mech Eng H. 222: 403–16


Alastruey J (2010) On the mechanics underlying the reservoir-excess separation in systemic arteries and their implications for pulse wave analysis. Cardiovasc Eng. 10: 176–89


Borlotti A, Khir A (2011) Wave speed and intensity in the canine aorta: analysis with and without the Windkessel-wave system. Conf Proc IEEE Eng Med Biol Soc. 2011; 219–22


Tyberg JV, Davies JE, Wang Z et al 2009 Wave intensity analysis and the development of the reservoir-wave approach. Med Biol Eng Comput. 47: 221–32


Mynard JP, Penny DJ, Davidson MR et al 2012 The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study. Journal of Hypertension. 30: 734–43


Flewitt JA, Hobson TN, Wang J Jr. et al 2007 Wave intensity analysis of left ventricular filling: application of windkessel theory. Am J Physiol Heart Circ Physiol. 292: H2817–2823


Wang JJ, Shrive NG, Parker KH et al 2011 Wave propagation and reflection in the canine aorta: analysis using a reservoir-wave approach. Canadian Journal of Cardiology. 27:389e1–10


Wang JJ, Bouwmeester JC, Belenkie I et al 2013 Alterations in aortic wave reflection with vasodilation and vasoconstriction in anaesthetized dogs. Canadian Journal of Cardiology. 29: 243–53


Wang JJ, Flewitt JA, Shrive NG et al 2005 The systemic venous circulation - waves propagating on a Windkessel: Relation of arterial and venous Windkessels to the systemic vascular resistance. American Journal of Physiology Heart and Circulatory Physiology. 00494.2005


Davies JE, Baksi J, Francis DP et al 2010 The arterial reservoir pressure increases with aging and is the major determinant of the aortic augmentation index. American Journal of Physiology Heart and Circulatory Physiology. 298: H580–6


Dwyer N, Yong AC, Kilpatrick D (2012) Variable open-end wave reflection in the pulmonary arteries of anesthetized sheep. J Physiol Sci. 62: 21–8


Hollander EH, Wang J Jr., Dobson GM et al 2001 Negative wave reflections in pulmonary arteries. American Journal of Physiology Heart and Circulatory Physiology. 281: H895–902


Nie M, Kobayashi H, Sugawara M et al 2001 Helium inhalation enhances vasodilator effect of inhaled nitric oxide on pulmonary vessels in hypoxic dogs. American Journal of Physiology Heart and Circulatory Physiology. 280: H1875–81


Smolich JJ, Mynard JP, Penny DJ (2011) Pulmonary trunk, ductus arteriosus, and pulmonary arterial phasic blood flow interactions during systole and diastole in the fetus. Journal of Applied Physiology. 110: 1362–73


Smolich JJ, Penny DJ, Mynard JP (2012) Enhanced central and conduit pulmonary arterial reservoir function offsets reduced ductal systolic outflow during constriction of the fetal ductus arteriosus. American Journal of Physiology Regulatory, Integrative and Comparative Physiology. 302: R175–83


Smolich JJ, Penny DJ, Mynard JP (2012) Increased right ventricular output and central pulmonary reservoir function support rise in pulmonary blood flow during adenosine infusion in the ovine fetus. American Journal of Physiology Regulatory, Integrative and Comparative Physiology. 302: R1450–7


Grant DA, Hollander E, Skuza EM et al 1999 Interactions between the right ventricle and pulmonary vasculature in the fetus. Journal of Applied Physiology. 87: 1637–43


Smolich JJ, Mynard JP, Penny DJ (2008) Simultaneous pulmonary trunk and pulmonary arterial wave intensity analysis in fetal lambs: evidence for cyclical, midsystolic pulmonary vasoconstriction. American Journal of Physiology Regulatory, Integrative and Comparative Physiology. 294: R1554–62


Smolich JJ, Mynard JP, Penny DJ (2010) Wave intensity analysis of right ventricular and pulmonary vascular contributions to higher pulmonary than aortic blood pressure in fetal lambs. American Journal of Physiology Heart and Circulatory Physiology. 299: H890–7


Smolich JJ, Mynard JP, Penny DJ (2009) Dynamic characterization and hemodynamic effects of pulmonary waves in fetal lambs using cardiac extrasystoles and beat-by-beat wave intensity analysis. American Journal of Physiology Regulatory, Integrative and Comparative Physiology. 297: R428–36


Smolich JJ, Mynard JP, Penny DJ (2009) Ductus arteriosus wave intensity analysis in fetal lambs: midsystolic ductal flow augmentation is due to antegrade pulmonary arterial wave transmission. American Journal of Physiology Regulatory, Integrative and Comparative Physiology. 297: R1171–9


Smiseth OA, Thompson CR, Lohavanichbutr K et al (1999) The Pulmonary Venous Systolic Flow Pulse-Its Origin and Relationship to Left Atrial Pressure. Journal of the American College of Cardiology. 34: 802–809


Hellevik LR, Segers P, Stergiopulos N et al (1999) Mechanism of pulmonary venous pressure and flow waves. Heart and Vessels. 14: 67–71


Hobson TN, Flewitt JA, Belenkie I et al (2007) Wave intensity analysis of left atrial mechanics and energetics in anesthetized dogs. American Journal of Physiology Heart and Circulatory Physiology. 292: H1533–40

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