Parker KH (2017) The reservoir-wave model. Artery Research ??
This paper is based on the talk that I gave at the Arterial Hemodynamics: Past, Present and Future Symposium held at University College London last June. It will appear in a special issue of Artery Research based on that symposium. It is divided into three parts: a description of some recent work measuring the reservoir pressure at five different locations in the aorta in 40 'normal/ patients, an asymptotic analysis of the input impedance of the arterial tree in the limit of small frequency and some new results based on my recent work following the evolution of a single wave front introduced at the root of the aorta. The clinical measurements support the assumption that the reservoir pressure is uniform throughout the arterial tree (at least the aorta). The asymptotic analysis suggests that the low pressure component of the pressure waveform is similar to the reservoir pressure, it is uniform throughout the tree and it propagates into the tree at a rate determined by the wave speeds of the various arteries. The final part presents a novel way of looking at arterial hemodynamics and suggests that many of the complexities of arterial hemodynamics come directly from the complexity of the arterial tree. Probably the only practical result of this analysis is the suggestion that the diastolic fall-off of arterial pressure during diastole is actually the result of several exponentially decaying pressures that arise from different modes that characterise the propagation and reflection of the wave fronts in different parts of the arterial tree. This suggestion is extremely difficult to resolve experimentally because of the notoriously difficult mathematical problems in fitting multiple exponentials to data. The results, however, may help us to understand why we are still trying to explain arterial hemodynamics after more than a century of of effort.
Narayan O, Parker KH, Davies JE, Hughes AD, Meredith IT, Cameron JDclose (2017) Reservoir pressure analysis of aortic blood pressure: an in-vivo study at five locations in humans. Journal of Hypertension.
The reservoir and excess pressure waveforms are calculated from measurements made at 5 different sites down the aorta in 40 subjects. The results for each site and subject are ensemble averaged and the results are analysed using ICC (inter-class correlation). The results show that there is significant variation from site to site in the parameters that are fitted to the measured pressure waveform to calculate the reservoir pressure: the diastolic and systolic rate constants and the pressure asymptote for the diastolic pressure decay. However, the reservoir pressure waveform does not vary significantly from the ascending aorta to the aortic bifurcation. This is the first experimental verification of the assumption that the reservoir pressure is uniform throughout the large arteries, but delayed by the wave travel time from the root of the aorta. This is a significant result of the study and provides strong motivation for further tests of the reservoir-wave hypothesis I believe that this paper will be a landmark in the development of the reservoir pressure as a clinical tool.
Ntsinjana HN, Chung R, Ciliberti P, Muthurangu V, Schievano S, Marek J, Parker KH, Taylor AM, Biglino G (2017) Utility of Cardiovascular Magnetic Resonance-Derived Wave Intensity Analysis As a Marker of Ventricular Function in Children with Heart Failure and Normal Ejection Fraction. Frontiers of Pediatrics Vol: 5
Invasive studies are extremely difficult in children and so we have looked at using wave intensity analysis based on area and flow derived from MR images. The clinical application of these methods is in its infancy (no pun intended) and the results are encouraging. I once heard it said that adult cardiology is the study of the diseased heart and pediatric cardiology is the study of nature's mistakes. There is great potential in using wave intensity analysis to help us to understand the mechanical effects of these congenital malformations.
Baksi AJ, Davies JE, Hadjiloizou N, Baruah R, Unsworth B, Foale RA, Korolkova O, Siggers JH, Francis DP, Mayet J, Parker KH, Hughes AD (2016) Attenuation of reflected waves in man during retrograde propagation from femoral artery to proximal aorta, International Journal of Cardiology 202, 441-445, ISSN: 0167-5273
Most of the theory behind wave intensity analysis neglects the dissipation of the wave fronts as they propagate. The basic theory indicates that there will be dissipation if the fluid is viscous and there are ways to accommodate this effect mathematically. Unfortunately the analysis with dissipation is much more difficult and so we have tended to ignore it. This study is a timely reminder that real life is not ideal and that we may have to adapt our analysis to take dissipation into account. At the moment probably the best we can hope for is some way of determining from the measurements themselves if viscous effects are negligible. Ideally we should be looking at ways to incorporate these effects into our analysis.
Broyd CJ, Nijjer S, Sen S, Petraco R, Jones S, Al-Lamee R, Foin N, Al-Bustami M, Sethi A, Kaprielian R, Ramrakha P, Khan M, Malik IS, Francis DP, Parker K, Hughes AD, Mikhail GW, Mayet J, Davies JE (2016) Estimation of coronary wave intensity analysis using noninvasive techniques and its application to exercise physiology, American Journal of Physiology-Heart and Circulatory Physiology 310, H619-H627, ISSN: 0363-6135
Wide spread application of wave intensity analysis in medicine will probably depend on the development of non-invasive methods of measurement. Using echocardiographical methods to study wave intensity in the coronary arteries requires some virtuosity but the results are encouraging. The benefits of a non-invasive method are enormous and this paper may pave the way for future studies.
Li Y, Parker KH, Khir AW (2016) Using wave intensity analysis to determine local reflection coefficient in flexible tubes, Journal of Biomechanics 49, 2709-2717, ISSN: 0021-9290
This paper is based on Ye Li's PhD research looking at the determination of known reflection coefficients at the junction of elastic tubes with different properties using wave intensity analysis of the measured pressure and flow data. The most important finding is that there are 'near field' effects close to the reflection site that cause either over or under-estimation of the reflection coefficient depending on the conditions. The implications of this to in vivo wave intensity calculations are potentially very important but, as yet, totally unexplored.
Raphael CE, Cooper R, Parker KH, Collinson J, Vassiliou V, Pennell DJ, de Silva R, Hsu LY, Greve AM, Nijjer S, Broyd C, Ali A, Keegan J, Francis DP, Davies JE, Hughes AD, Arai A, Frenneaux M, Stables RH, Di Mario C, Prasad SK (2016) Mechanisms of Myocardial Ischemia in Hypertrophic Cardiomyopathy Insights From Wave Intensity Analysis and Magnetic Resonance, Journal of the American College of Cardiology 68, 1651-1660, ISSN: 0735-1097
It is very gratifying to be involved in work such as this that uses wave intensity analysis to help explain the mechanisms of ischemia in HCM patients. Wave intensity analysis of measurements from the coronary arteries show very different patterns of forward and backward waves in HCM patients and normal subjects and can be useful in differential diagnosis and possibly the assessment of the effect of treatment. I hope that this is the first of many clinical papers applying wave intensity analysis to many different conditions.
Raphael CE, Keegan J, Parker KH, Simpson R, Collinson J, Vassiliou V, Wage R, Drivas P, Strain S, Cooper R, de Silva R, Stables RH, Di Mario C, Frenneaux M, Pennell DJ, Davies JE, Hughes AD, Firmin D, Prasad SK (2016) Feasibility of cardiovascular magnetic resonance derived coronary wave intensity analysis, Journal of Cardiovascular Magnetic Resonance 18 ISSN: 1097-6647
Almost all of our previous work has been based on interventional measurements. Using non-invasive MR measurements is challenging for two reasons. The acquisition rate of MR data is relatively low making it difficult to derive information about the changes in pressure/area and flow with sufficient temporal resolution to be useful. Also it is currently impossible to measure pressure directly by MR and so it is necessary to use wave intensity based on area and flow (or to convert area measurements into pressure measurements by some appropriate calibration. I am still amazed that it is possible to measure flow rates in coronary arteries that are too small to be imaged but, because the flow is encoded by phase shifts in the signal it is possible to measure the mean phase shift in each voxel and hence the mean flow.
Su J, Manisty C, Parker KH, Simonsen U, Mellemkjaer S, Howard L, Hughes AD (2016) Wave intensity analysis in pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension, Journal of Human Hypertension 30, 647-648, ISSN: 0950-9240
This paper looks at the application of wave intensity analysis to the pulmonary circulation. I believe this is an area of great potential because relatively little is known about the hemodynamics of the pulmonary arteries. Pulmonary hypertension is a very dangerous condition and it is frequently difficult to differentiate between the many different causes of hypertension. The results of this work are very encouraging.
Clavica F, Parker KH, Khir AW, 2015, Wave intensity analysis in air-filled flexible vessels, Journal of Biomechanics 48, 687-694, ISSN: 0021-9290
Theoretically, wave intensity analysis should be valid for air-filled compliant vessels such as the airways. This was tested in vitro and we concluded that, although the wave speeds are much higher than in fluid-filled vessels, wave intensity analysis was applicable. Like all good research papers, the ultimate conclusion was that more research was needed to determine if it was applicable to the respiratory system.
Borlotti A, Park C, Parker KH, Khir AW, 2015, Reservoir and reservoir-less pressure effects on arterial waves in the canine aorta., Journal of Hypertension 33, 564-574, ISSN: 0263-6352
Since the reservoir-wave hypothesis assumes that the measured pressure in the aorta (P) is the sum of a reservoir pressure (Pr), which depends on the global compliance of the arteries, and the excess pressure (Pe), due to local waves, the wave intensity based on Pe must be less than the wave intensity based on P. We tested this using data measured in the dog and report the effect of using Pe on both the calculated wave speed and the magnitude of the wave intensity.
Biglino G, Ntsinjana H, Plymen C, Tann O, Giardini A, Derrick G, Parker KH, Tsang V, Schievano S, Taylor AM, 2014, Ventriculovascular interactions late after atrial and arterial repair of transposition of the great arteries, Journal of Thoracic and Cardiovascular Surgery, 148, 2627-2633, ISSN: 0022-5223
The aim of this study was to compare atrial switch and arterial switch operations for the repair of transposition of the great arteries (TGA), assessing cardiac function and ventriculoarterial (VA) coupling based on cardiac magnetic resonance (CMR) data. Using CMR-derived wave intensity analysis, this study provides a noninvasive comparison of the 2 systemic ventricles and evaluates the subclinical hemodynamic burden of these operations.
Borotti A, Li Y, Parker KH, Khir AW, 2014, Experimental evaluation of local wave speed in the presence of reflected waves, Journal of Biomechanics, 47, 87-95, ISSN: 0021-9290
We compared different methods for the determination of local wave speed in bench experiments and investigate their relative accuracy when reflections are present. Pressure (P), flow (Q) and diameter (D) were measured along a flexible tube far and close to a reflection site with either a positive or negative reflection coefficient. Wave speed was calculated using PU-loop, (lnD)U-loop, QA-loop, D(2)P-loop, sum of squares and characteristic impedance methods. Results were compared to the foot-to-foot method. We found that far from the reflections almost all methods give uniform results. Close to positive reflections the methods that rely on P and Q (or U) overestimate the wave speed value, while techniques based on D (or A) and Q (or U) underestimate it. On the contrary, close to negative reflections the methods that rely on P and Q (or U) underestimate the wave speed value, while techniques based on D (or A) and Q (or U) overestimate it. The D(2)P-loop does not seem to be affected by positive or negative reflections. Most of the methods currently used to determine local wave speed are affected by reflections, but the (lnD)U-loop remains the easiest technique to use in the clinic.
Clavica F, Parker KH, Khir AW, 2014, Wave intensity analysis in air-filled flexible vessels., Journal of Biomech, ISSN: 0021-9290
This work investigates the use of wave intensity analysis in the airways. Because air is much less dense than blood the wave speed in air-filled flexible vessels is large - close to the speed of sound. Simultaneous pressure (P) and velocity (U) measurements were made in a single tube and then in several flexible tubes connected in series. Wave speed was calculated using the foot-to-foot method (cf), which was used to separate analytically the measured P and U waveforms into their forward and backward components. Further, the data were used to calculate wave intensity, which was also separated into its forward and backward components. The results showed that the onsets and the nature of reflections (compression/expansion) derived with WIA, corresponded well to those anticipated using the theory of waves in liquid-filled elastic tubes. We suggest that WIA can provide relatively accurate information on reflections in air-filled flexible tubes, warranting further studies to explore the full potential of this technique in the respiratory system.
Davies JE, Lacy P, Tillin T, Collier D, Cruickshank JK, Francis DP, Malaweera A, Mayet J, Stanton A, Williams B, Parker KH, Thom SAM, Hughes AD, 2014, Excess Pressure Integral Predicts Cardiovascular Events Independent of Other Risk Factors in the Conduit Artery Functional Evaluation Substudy of Anglo-Scandinavian Cardiac Outcomes Trial, Hypertension, 64, 60-68, ISSN: 0194-911X
Excess pressure integral (XSPI), a new index of surplus work performed by the left ventricle, can be calculated from blood pressure waveforms and may indicate circulatory dysfunction. We investigated whether XSPI predicted future cardiovascular events and target organ damage in treated hypertensive individuals. Radial blood pressure waveforms were acquired by tonometry in 2069 individuals (aged, 63±8 years) in the Conduit Artery Functional Evaluation (CAFE) substudy of the Anglo-Scandinavian Cardiac Outcomes Trial (ASCOT). Measurements of left ventricular mass index (n=862) and common carotid artery intima media thickness (n=923) were also performed. XSPI and the integral of reservoir pressure were lower in people treated with amlodipine ± perindopril than in those treated with atenolol±bendroflumethiazide, although brachial systolic blood pressure was similar. A total of 134 cardiovascular events accrued during a median 3.4 years of follow-up; XSPI was a significant predictor of cardiovascular events after adjustment for age and sex, and this relationship was unaffected by adjustment for conventional cardiovascular risk factors or Framingham risk score. XSPI, central systolic blood pressure, central augmentation pressure, central pulse pressure, and integral of reservoir pressure were correlated with left ventricular mass index, but only XSPI, augmentation pressure, and central pulse pressure were associated positively with carotid artery intima media thickness. Associations between left ventricular mass index, XSPI, and integral of reservoir pressure and carotid artery intima media thickness and XSPI were unaffected by multivariable adjustment for other covariates. XSPI is a novel indicator of cardiovascular dysfunction and independently predicts cardiovascular events and targets organ damage in a prospective clinical trial. © 2014 American Heart Association, Inc.
Hametner B, Wassertheurer S, Hughes AD, Parker KH, Weber T, Eber B, 2014, Reservoir and excess pressures predict cardiovascular events in high-risk patients, International Journal of Cardiology, 171, 31-36, ISSN: 0167-5273
Background Analysis of the arterial pressure curve plays an increasing role in cardiovascular risk stratification. Measures of wave reflection and aortic stiffness have been identified as independent predictors of risk. Their determination is usually based on wave propagation models of the circulation. Another modeling approach relies on modified Windkessel models, where pressure curves can be divided into reservoir and excess pressure. Little is known of their prognostic value. Methods and results The aim of this study is to evaluate the predictive value of parameters gained from reservoir theory applied to aortic pressure curves in a cohort of high-risk patients. Furthermore the relation of these parameters to those from wave separation analysis is investigated. Central pressure curves from 674 patients with preserved ejection fraction, measured by radial tonometry and a validated transfer function, were analyzed. A high correlation between the amplitudes of backward traveling pressure waves and reservoir pressures was found (R = 0.97). Various parameters calculated from the reservoir and excess pressure waveforms predicted cardiovascular events in univariate Cox proportional hazards modeling. In a multivariate model including several other risk factors such as brachial blood pressure, the amplitude of reservoir pressure remained a significant predictor (HR = 1.37 per SD, p = 0.016). Conclusions Based on very different models, parameters from reservoir theory and wave separation analysis are closely related and can predict cardiovascular events to a similar extent. Although Windkessel models cannot describe all of the physiological properties of the arterial system, they can be useful to analyze its behavior and to predict cardiovascular events. © 2013 Elsevier Ireland Ltd.
Narayan O, Davies JE, Hughes AD, Dart AM, Parker KH, Reid C, Cameron JD, 2014, Central Aortic Reservoir-Wave Analysis Improves Prediction of Cardiovascular Events in Elderly Hypertensives, Hypertension, 65, ISSN: 0194-911X
Several morphological parameters based on the central aortic pressure waveform are proposed as cardiovascular risk markers, yet no study has definitively demonstrated the incremental value of any waveform parameter in addition to currently accepted biomarkers in elderly, hypertensive patients. The reservoir-wave concept combines elements of wave transmission and Windkessel models of arterial pressure generation, defining an excess pressure superimposed on a background reservoir pressure. The utility of pressure rate constants derived from reservoir-wave analysis in prediction of cardiovascular events is unknown. Carotid blood pressure waveforms were measured prerandomization in a subset of 838 patients in the Second Australian National Blood Pressure Study. Reservoir-wave analysis was performed and indices of arterial function, including the systolic and diastolic rate constants, were derived. Survival analysis was performed to determine the association between reservoir-wave parameters and cardiovascular events. The incremental utility of reservoir-wave parameters in addition to the Framingham Risk Score was assessed. Baseline values of the systolic rate constant were independently predictive of clinical outcome (hazard ratio, 0.33; 95% confidence interval, 0.13–0.82; P=0.016 for fatal and nonfatal stroke and myocardial infarction and hazard ratio, 0.38; 95% confidence interval, 0.20–0.74; P=0.004 for the composite end point, including all cardiovascular events). Addition of this parameter to the Framingham Risk Score was associated with an improvement in predictive accuracy for cardiovascular events as assessed by the integrated discrimination improvement and net reclassification improvement indices. This analysis demonstrates that baseline values of the systolic rate constant predict clinical outcomes in elderly patients with hypertension and incrementally improve prognostication of cardiovascular events.
Tyberg JV, Bouwmeester JC, Parker KH, Shrive NG, Wang J-J, 2014, The case for the reservoir-wave approach, International Journal of Cardiology, 172, 299-306, ISSN: 0167-5273
The Reservoir-Wave Approach is an alternative, time-domain approach to arterial hemodynamics that is based on the assertion that measured pressure and flow can be resolved into their volume-related (i.e., reservoir) and wave-related (i.e., excess) components. The change in reservoir pressure is assumed to be proportional to the difference between measured inflow and calculated outflow. Wave intensity analysis of the excess components yields a pattern of aortic wave propagation and reflection in the dog that is novel and physiologically plausible: waves are reflected positively from a site in the femoral circulation and negatively from a site below the diaphragm, where the total "daughter-vessel" cross-sectional area exceeds the "mother-vessel" area. With vasodilatation, the negative reflection is augmented and with vasoconstriction, it is virtually eliminated. On the other hand, conventional hemodynamic analysis has been shown to yield a paradoxical "forward-going backward wave" and the impedance minimum, previously assumed to be an indicator of the source of wave reflection according to quarter-wave-length theory, has been shown to be due to the reservoir component. Clinical studies employing the Reservoir-Wave Approach should be undertaken to verify experimental observations and, perhaps, to gain new diagnostic and therapeutic insights.
Hughes AD, Davies JE, Parker KH, 2013, The importance of wave reflection: a comparison of wave intensity analysis and separation of pressure into forward and backward components, 2013 35TH Annual International Conference of the Ieee Engineering in Medicine and Biology Society (EMBC), 229-232, ISSN: 1557-170X
Waves and wave reflections play an undoubted role in arterial hemodynamics. Wave intensity analysis and separation of pressure into forward and backward components can both be used to analyze wave phenomena in arteries, but result in different interpretations regarding the contribution of wave reflections to the aorta blood pressure waveform. We compare these approaches using pressure and flow measurements made in the human aorta and discuss why the interpretations might differ. © 2013 IEEE.
Hughes AD, Park C, Davies J, Francis D, Thom SAM, Mayet J, Parker KH, 2013, Limitations of Augmentation Index in the Assessment of Wave Reflection in Normotensive Healthy Individuals, PLOS One, 8, ISSN: 1932-6203
Objectives: Augmentation index (AIx) is widely used as a measure of wave reflection. We compared the relationship between AIx and age, height and sex with 'gold standard' measures of wave reflection derived from measurements of pressure and flow to establish how well AIx measures wave reflection. Materials and Methods: Measurements of carotid pressure and flow velocity were made in the carotid artery of 65 healthy normotensive individuals (age 21-78 yr; 43 male) and pulse wave analysis, wave intensity analysis and wave separation was performed; waveforms were classified into type A, B or C. AIx, the time of the first shoulder (Ts), wave reflection index (WRI) and the ratio of backward to forward pressure (Pb/Pf) were calculated. Results: AIx did not correlate with log WRI or Pb/Pf. When AIx was restricted to positive values AIx and log WRI were positively correlated (r = 0.33; p = 0.04). In contrast log WRI and Pb/Pf were closely correlated (r = 0.66; p<0.001). There was no correlation between the Ts and the timing of Pb or the reflected wave identified by wave intensity analysis. Wave intensity analysis showed that the morphology of type C waveforms (negative AIx) was principally due to a forward travelling (re-reflected) decompression wave in mid-systole. AIx correlated positively with age, inversely with height and was higher in women. In contrast log WRI and Pb/Pf showed negative associations with age, were unrelated to height and did not differ significantly by gender. Conclusions: AIx has serious limitations as a measure of wave reflection. Negative AIx values derived from Type C waves should not be used as estimates of wave reflection magnitude. © 2013 Hughes et al.
Sen S, Asrress KN, Nijjer S, Petraco R, Malik IS, Foale RA, Mikhail GW, Foin N, Broyd C, Hadjiloizou N, Sethi A, Al-Bustami M, Hackett D, Khan MA, Khawaja MZ, Baker CS, Bellamy M, Parker KH, Hughes AD, Francis DP, Mayet J, Di Mario C, Escaned J, Redwood S, Davies JE, 2013, Diagnostic Classification of the Instantaneous Wave-Free Ratio Is Equivalent to Fractional Flow Reserve and Is Not Improved With Adenosine Administration, Journal of the American College of Cardiology, 61, 1409-1420, ISSN: 0735-1097
Objectives: This study sought to determine if adenosine administration is required for the pressure-only assessment of coronary stenoses. Background: The instantaneous wave-free ratio (iFR) is a vasodilator-free pressure-only measure of the hemodynamic severity of a coronary stenosis comparable to fractional flow reserve (FFR) in diagnostic categorization. In this study, we used hyperemic stenosis resistance (HSR), a combined pressure-and-flow index, as an arbiter to determine when iFR and FFR disagree which index is most representative of the hemodynamic significance of the stenosis. We then test whether administering adenosine significantly improves diagnostic performance of iFR. Methods: In 51 vessels, intracoronary pressure and flow velocity was measured distal to the stenosis at rest and during adenosine-mediated hyperemia. The iFR (at rest and during adenosine administration [iFRa]), FFR, HSR, baseline, and hyperemic microvascular resistance were calculated using automated algorithms. Results: When iFR and FFR disagreed (4 cases, or 7.7% of the study population), HSR agreed with iFR in 50% of cases and with FFR in 50% of cases. Differences in magnitude of microvascular resistance did not influence diagnostic categorization; iFR, iFRa, and FFR had equally good diagnostic agreement with HSR (receiver-operating characteristic area under the curve 0.93 iFR vs. 0.94 iFRa and 0.96 FFR, p = 0.48). Conclusions: iFR and FFR had equivalent agreement with classification of coronary stenosis severity by HSR. Further reduction in resistance by the administration of adenosine did not improve diagnostic categorization, indicating that iFR can be used as an adenosine-free alternative to FFR. (Classification Accuracy of Pressure-Only Ratios Against Indices Using Flow Study [CLARIFY]; NCT01118481) © 2013 American College of Cardiology Foundation.
Biglino G, Steeden JA, Baker C, Schievano S, Taylor AM, Parker KH, Muthurangu V, 2012, A non-invasive clinical application of wave intensity analysis based on ultrahigh temporal resolution phase-contrast cardiovascular magnetic resonance, Journal of Cardiovascular Magnetic Resonance, 14, ISSN: 1097-6647
Wave intensity analysis, traditionally derived from pressure and velocity data, can be formulated using velocity and area. Flow-velocity and area can both be derived from high-resolution phase-contrast cardiovascular magnetic resonance (PC-CMR). In this study, very high temporal resolution PC-CMR data is processed using an integrated and semi-automatic technique to derive wave intensity.
Davies JE, Alastruey J, Francis DP, Hadjiloizou N, Whinnett ZI, Manisty CH, Aguado-Sierra J, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J, 2012, Attenuation of Wave Reflection by Wave Entrapment Creates a "Horizon Effect" in the Human Aorta, Hypertension, 60, 778-+, ISSN: 0194-911X
Wave reflection is thought to be important in the augmentation of blood pressure. However, identification of distal reflections sites remains unclear. One possible explanation for this is that wave reflection is predominately determined by an amalgamation of multiple proximal small reflections rather than large discrete reflections originating from the distal peripheries. In 19 subjects (age, 35-73 years), sensor-tipped intra-arterial wires were used to measure pressure and Doppler velocity at 10-cm intervals along the aorta, starting at the aortic root. Incident and reflected waves were identified and timings and magnitudes quantified using wave intensity analysis. Mean wave speed increased along the length of the aorta (proximal, 6.8±0.9 m/s; distal, 10.7±1.5 m/s). The incident wave was tracked moving along the aorta, taking 55±4 ms to travel from the aortic root to the distal aorta. However, the timing to the refection site distance did not differ between proximal and distal aortic measurement sites (proximal aorta, 48±5 ms versus distal aorta, 42±4 ms; P=0.3). We performed a second analysis using aortic waveforms in a nonlinear model of pulse-wave propagation. This demonstrated very similar results to those observed in vivo and also an exponential attenuation in reflection magnitude. There is no single dominant refection site in or near the distal aorta. Rather, there are multiple reflection sites along the aorta, for which the contributions are attenuated with distance. We hypothesize that rereflection of reflected waves leads to wave entrapment, preventing distal waves being seen in the proximal aorta. © 2012 American Heart Association, Inc.
Davies JE, Sen S, Broyd C, Hadjiloizou N, Baksi J, Francis DP, Parker KH, Hughes AD, Foale RA, Chukwuemeka A, Casula R, Malik IS, Mikhail GW, Mayet J, 2012, Response to Letter Regarding Article, "Arterial Pulse Wave Dynamics After Percutaneous Aortic Valve Replacement: Fall in Coronary Diastolic Suction With Increasing Heart Rate as a Basis for Angina Symptoms in Aortic Stenosis", Circulation, 125, E613-E613, ISSN: 0009-7322
Parker KH, Alastruey J, Stan GB (2012) Arterial reservoir-excess pressure and ventricular work., Med Biol Eng Comput 50, 419-424. [pdf]
The conservation of mass in an arterial network and the calculus of variations are used to show that the reservoir pressure waveform results in the minimal hydraulic work by the left ventricle to provide a given volume flow rate. The analysis is highly mathematical but the results are very interesting. Although it may be impossible to realise these optimal conditions physiologically, the reservoir pressure may be a useful benchmark for evaluating the 'efficiency' of clinically measured pressure waveforms.
:Sen S, Escaned J, Malik IS, Mikhail GW, Foale RA, Mila R, Tarkin J, Petraco R, Broyd C, Jabbour R, Sethi A, Baker CS, Bellamy M, Al-Bustami M, Hackett D, Khan M, Lefroy D, Parker KH, Hughes AD, Francis DP, Di Mario C, Mayet J, Davies JE (2012) Development and validation of a new adenosine-independent index of stenosis severity from coronary wave-intensity analysis: results of the ADVISE (ADenosine Vasodilator Independent Stenosis Evaluation) study. J Am Coll Cardiol 59 1392-1402. [pdf]
The iFR (Instantaneous Wave-free Ratio) is described and the results of a study looking at the iFR and FFR in approximately 130 stenosed coronary arteries are reported. The iFR is a measure of the functional effect of a coronary stenosis which is measured during the period in diastole when the coronary arteries are virtually free of waves. The results ore very interesting, particularly because the measurement is made without inducing hyperaemia by adenosine, as in the measurement of the FFR. This means that the iFR can be measured beat by beat and can follow the acute changes induced by stenting or other interventions. This is a very exciting application of wave intensity analysis to clinical measurements.
Davies JE, Sen S, Broyd C, Hadjiloizou N, Baksi J, Francis DP, Foale RA, Parker KH, Hughes AD, Chukwuemeka A, Casula R, Malik IS, Mikhail GW, Mayet J (2011) Arterial pulse wave dynamics after percutaneous aortic valve replacement: fall in coronary diastolic suction with increasing heart rate as a basis for angina symptoms in aortic stenosis. Circulation 124 1565-1572. [pdf]
Wave intensity analysis is used to assess haemodynamic changes in the coronary arteries after percutaneous aortic valve replacement. During aortic stenosis, it is found that the coronary reserve is impaired with the diastolic suction wave decreases as heart rate is increased by pacing. After valve repair, the coronary reserve rapidly recovers its normal pattern with an increasing diastolic suction wave as pacing is increased. This may explain the presence of angina in aortic stenosis and its relief after valve repair. This paper is an excellent example of the use of wave intensity analysis to reveal arterial dynamics.
:Alastruey J, Khir AW, Matthys KS, Segers P, Sherwin SJ, Verdonck PR, Parker KH, Peiro J (2011) Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements. J Biomech 44, 2250-2258, ISSN:0021-9290. [pdf]
The ability of a numerical 1-D wave model of arterial dynamics to predict pressure and flow in the arterial network is tested by comparing numerical and experimental results for an in vitro model of the 55 largest human arteries. The experimental model is made from silicone rubber and the dimensions and physical properties of the vessels are measured accurately. The numerical model is run using these properties and the numerical and experimental pressure and flow waveforms are compared. Overall, the comparison gives us confidence to use the numerical model for in vivo data where the physical properties of the arteries are less well known. There is little about wave intesity analysis per se in this paper, but since the theory underlying the numerical model is identical to the theory underlying wave intensity analysis, the results are interesting from the point of view of wave intensity analysis.
Wang J-J, Shrive NG, Parker KH, Hughes AD, Tyberg JV (2011) Wave Propagation and Reflection in the Canine Aorta: Analysis Using a Reservoir-Wave Approach. Can J Cardiol 27 ISSN:0828-282X. [pdf]
Pressure and velocity waveforms measured along the aorta of dogs are analysed using the reservoir/excess ressure. By tracking significant features of the separated forward and backward excess pressure, it is possible to determine the wave tracks of the principle waves identified by wave intensity analysis; the foot of the initial forward compression wave and its reflection from two distinct sites in the arterial tree, and the forward expansion wave at the end of systole. The results are very convincing and give a good indication of the complexity of the wave patterns in the normal arterial system. This is one of the best examples of the ability of wave intensity analysis to reveal the intricacies of arterial haemodynamics.
:Waters SL, Alastruey J, Beard DA, Bovendeerd PHM, Davies PF, Jayaraman G, Jensen OE, Lee J, Parker KH, Popel AS, Secomb TW, Siebes M, Sherwin SJ, Shipley RJ, Smith NP, van de Vosse FN (2011) Theoretical models for coronary vascular biomechanics: Progress & challenges, Prog in Biophys & Molec Biol 104 49-76, ISSN:0079-6107. [pdf]
This article presents an overview of theoretical modelling of coronary haemodynamics resulting from a meeting of the cardiac physionome project. It is very wide-ranging and represents the diverse opinons of many experts in the field. Wave intensity analysis is discussed only briefly but seeing it relative the the 'big picture' is informative.
:Manisty C, Mayet J, Tapp RJ, Parker KH, Sever P, Poulter NR, Thom SA, Hughes AD, ASCOT Investigators (2010) Wave reflection predicts cardiovascular events in hypertensive individuals independent of blood pressure and other cardiovascular risk factors: an ASCOT (Anglo-Scandinavian Cardiac Outcome Trial) substudy. J Am Coll Cardiol 56, 24-30. [pdf]
Wave intensity analysis was used to separate the forward and backward pressure waveforms in patients participating in a prospective study of different hypertensive drugs (a sub-study within the ASCOT trial). Several parameters were studied and it was found that the ratio of the peak backward pressure to the peak forward pressure was the best, and statistically significant, predictor of cardiac events. This study lays the foundations for the incorporation of wave intensity analysis in the clinical assessment of the cardiovascular system.
Davies JE, Baksi J, Francis DP, Hadjiloizou N, Whinnett ZI, Manisty CH, Aguado-Sierra J, Foale RA, Malik IS, Tyberg JV, Parker KH, Mayet J, Hughes AD (2010) The arterial reservoir pressure increases with aging and is the major determinant of the aortic augmentation index. Am J Physiol Heart Circ Physiol 298 H580-H586. [pdf]
This is the first paper applying the reservoir/wave hypothesis to clinical data. The results are interesting and significant. The reservoir pressure is found to be the major component of the measured pressure waveform and is the dominant contributor to the augmentation pressure and hence the augmentation index AIx, which could have major implications in the understanding of the clinical implications of AIx. Probably the most important result of this work is the observation that the magnitude of the backward reflections is significantly smaller after the effect of the reservoir pressure is taken into account. This seems to call for a reevaluation of many of the current models of arterial mechanics.
Baksi AJ, Treibel TA, Davies JE, Hadjiloizou N, Foale RA, Parker KH, Francis DP, Mayet J, Hughes AD (2009) A meta-analysis of the mechanism of blood pressure change with aging. J Am Coll Cardiol 54 2087-2092. [pdf]
Baksi AJ, Treibel TA, Davies JE, Hadjiloizou N, Foale RA, Parker KH, Francis DP, Mayet J, Hughes AD (2010) Changes in the Central Arterial Pressure Pulse With Aging Reply. J Am Coll Cardiol 55 2183-2184, ISSN:0735-1097.
This meta-study of all published papers reporting the timing of reflected waves in the central aorta reveal that all reflected waves were found to return before the end of systole. The correlation of return time with age revealed a small decrease with age, but backward extrapolation of the linear regression line indicated that the reflected wave would appear at the end of systole at the age of -221 years. This ludicrous result highlights the wide-spread observation that the reflected wave in the proximal aorta is always observed during mid-systole. This is contrary to widely-held views about the mechanics of the observed changes in the shape of the aortic pressure waveform with age. It is an important paper for wave intensity analysis because it underlines the need for a fuller, more detailed analysis of arterial waves.
Manisty CH, Zambanini A, Parker KH, Davies JE, Francis DP, Mayet J, Thom SAMcG, Hughes AD, Anglo-Scandinavian Cardiac Outcome Trial Investigators (2009) Differences in the magnitude of wave reflection account for differential effects of amlodipine - versus atenolol-based regimens on central blood pressure: an Anglo-Scandinavian cardiac outcome trial substudy. Hypertension 54, 724 - 730, ISSN: 1524-4563. [pdf]
This paper shows the potential of wave intensity analysis in the interpretation of clinical data. The ASCOT study indicated significant differences in cardiac outcomes of two drug regimes that produced the same reduction in blood pressure but could not explain the mechanisms causing the difference.
Alastruey J, Parker KH, Peiro J, Sherwin SJ (2009) Analysing the pattern of pulse waves in arterial networks: a time-domain study, J Eng Math 64, 331 - 351, ISSN: 0022-0833. [pdf]
One of the benefits of describing waves in the arteries using successive wavefronts is that it is possible to follow individual waves as they reflect and rereflect within the arterial system. This paper describes a way of determining these wave paths. The results show the complexity of the wave patterns, but suggests ways of dealing with the complexity.
Aguado-Sierra J, Davies JE, Hadjiloizou N, Francis D, Mayet J, Hughes AD, Parker KH (2008) Reservoir-wave separation and wave intensity analysis applied to carotid arteries: a hybrid 1D model to understand haemodynamics. Conf Proc IEEE Eng Med Biol Soc 2008, 1381 - 1384, ISSN: 1557-170X. [pdf]
This paper looks at the application of wave intensity analysis to the interpretation of measurements made in the carotid arteries. The emphasis is on the separation of the measured waveforms into reservoir and wave pressures and the subsequent separation of the wave pressure into forward and backward waves.
Tyberg JV, Davies JE, Wang ZB, Whitelaw WA, Flewitt JA, Shrive NG, Francis DP, Hughes AD, Parker KH, Wang J-J (2009) Wave intensity analysis and the development of the reservoir-wave approach. Med Biol Eng Comput 47, 221 - 232, ISSN: 0140-0118. [pdf]
This is probably the best starting point for understanding the reservoir-wave hypothesis for the interpretation of arterial pressure waveforms. In the absence of a good theoretical derivation of the two pressures, the legitimacy of the separation must be judged by its practical results. This paper describes both the ad hoc reasoning behind the hypothesis and gives a number of examples of its efficacy in the interpretation of experimental measurements.
Wang J, Shrive NG, Parker KH, Tyberg JV (2009) "Wave" as defined by wave intensity analysis. Med Biol Eng Comput 47, 189 - 195, ISSN: 0140-0118. [pdf]
An excellent introduction to waves from the point of view of wave intensity analysis. Most of the waves that we experience, sound waves, light waves, surface waves on the ocean, etc., have the form of sinusoidal wavetrains. This, however, is not the only way to think about waves and this paper described the extension of ideas developed in gas dynamics to the arteries. All of the ideas are illustrated by experimental results.
Parker KH (2009) An introduction to wave intensity analysis. Med Biol Eng Comput 47, 175 - 188, ISSN: 0140-0118. [pdf]
This paper is the origin and a shortened version of this web site. Having been asked by the editor to write an introduction, I got a bit carried away and was told that I would have to shorten my original draft to about one third of its length for it to be published. Rather than discarding the excised material I decided to 'author'* these web pages, which then took on a life of their own.
Parker KH (2009) A brief history of arterial wave mechanics. MEed Biol Eng Comput 47, 111 - 118, ISSN: 0140-0118. [pdf]
I have always been interested in the origins of arterial haemodynamics and enjoyed writing this short history. Not being an historian, I had to rely on secondary sources for most of the information that is included. Since I believe that the way forward is often found by looking backward, I hope that it spurs others into digging deeper into the history of our subject. It is a very rewarding activity and, who knows, scholarship may some day come back into favour as an activity in universities.
Hughes AD, Parker KH (2009) Forward and backward waves in the arterial system: impedance or wave intensity analysis? Med Biol Eng Comput 47, 207 - 210, ISSN: 1741-0444. [pdf]
This paper was written to demonstrate that wave intensity and impedance analysis have more in common than is sometimes appreciated. Although there are differences, both approaches share the basic physics. The separation of measured waveforms into their forward and backward components was originally done in the context of impedance analysis. We wanted to show that despite their different approaches their results can be identical.
Alastruey J, Sherwin, SJ, Parker KH, Rubens DD (2009) Placental transfusion insult in the predisposition for SIDS: A mathematical study. Early Human Development 85, 455-459. [pdf]
Alastruey J, Sherwin SJ, Parker KH, Rubens DD (2010) Reply to 'cord clamp insult may predispose to SIDS'. Early Hum Dev 86.
This study was motivated by the observation of a correlation between the results of newborn hearing tests and the incidence of SIDS (sudden infant death syndrome). A 1-D numerical model was used to analyse the propagation of a pressure wave generated by placental transfusion during birth into the carotid arteries of the fetus. It was postulated that this wave could cause differential damage to the left and right ear because of the different arterial connectivity of the right and left carotids. The results are not conclusive, but they do contribute to the discussion of the hypothesis.
Alastruey J, Parker KH, Peiro J, Sherwin SJ (2008) Lumped parameter outflow models for 1-D blood flow simulations: Effect on pulse waves and parameter estimation, Commun Comput Phys 4 317 - 336, ISSN: 1815-2406. [pdf]
One of the most promising developments in computational fluid mechanics, as well as other areas of physics, is the multi-scale approach to problems. Full calculation of fine-scale structure can be practically impossible even if the detailed physics and boundary conditions are known. Using simpler models based on larger scales is probably the way forward. The integration of multi-scale information, however, is not straightforward and this paper looks at the problem in the particular case of arterial mechanics.
Hadjiloizou N, Davies JE, Malik IS, Aguado-Sierra J, Willson K, Foale RA, Parker KH, Hughes AD, Francis DP, Mayet J (2008) Differences in cardiac microcirculatory wave patterns between the proximal left mainstem and proximal right coronary artery. Am J Physiol Heart Circ Physiol 295, H1198 - H1205, ISSN: 0363-6135. [pdf]
This paper is one of our first forays into coronary artery mechanics. I believe that wave intensity analysis provides information that may be essential in understanding this extremely complex but equally rewarding area,
Davies JE, Parker KH, Francis DP, Hughes AD, Mayet J (2008) What is the role of the aorta in directing coronary blood flow? Heart 94, 1545 - 1547, ISSN: 1355-6037.
Davies JE, Parker KH, Francis DP, Hughes AD, Mayet J (2009) What is the role of the aorta in directing coronary blood flow? Reply. Heart 95 937 - 938, ISSN: 1355-6037,
This brief paper was written to explain wave intensity to cardiologists interested in flow in coronary arteries. It stimulated several responses and our reply.
Aguado-Sierra J, Alastruey J, Wang J-J, Hadjiloizou N, Davies J, Parker KH (2008) Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries. Proc Inst Mech Eng [H], 222, 403-416, ISSN: 0954-4119. [pdf]
Previous work on the reservoir pressure has relied upon simultaneous measurement of pressure and flow at the root of the aorta. This is not practical in many clinical situations and so we have developed an algorithm for calculating the reservoir pressure using only the pressure measured at an arbitrary point in the arterial system.
Alastruey J, Moore SM, Parker KH, David T, Peiro J, Sherwin SJ (2008) Reduced modelling of blood flow in the cerebral circulation: Coupling 1-D, 0-D and cerebral auto-regulation models, Int J Numer Meth Fl, 56, 1061-1067, ISSN: 0271-2091. [pdf]
Our 1-D model of waves has been coupled to a model of cerebral auto-regulation to predict cerebral flow after various changes in conditions.
Wang JJ, Shrive NG, Parker KH, Tyberg JV. (2008) Effects of vasoconstriction and vasodilatation on LV and segmental circulatory energetics. Am J Physiol Heart Circ Physiol 294, H1216-H1225, ISSN: 0363-6135. [Epub ahead of print]
The implications of the reservoir-wave hypothesis to the energetics of the left side of the cardiovascular system.
Aguado-Sierra J, Hadjilizou N, Davies JE, Francis, D, Mayet, J, Parker, KH. (2007) Pressure reservoir-wave separation applied to the coronary arterial data. Conf Proc IEEE Eng Med Biol Soc, 1, 2693 - 2696, ISSN: 1557-170X [pdf]
A short conference paper describing an early algorithm for the calculation of the reservoir pressure from measured pressure waveforms.
Alastruey J, Parker KH, Peiro J, Byrd SM, Sherwin SJ. (2007) Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows, J Biomech, 40, 1794 - 1805, ISSN: 0021-9290 [pdf]
The application of our 1-D modelling program to the large arteries of the cerebral circulation. Because of the difficulty in accessing these vessels, numerical modelling can play a particularly important role in understanding cerebral haemodynamics.
Curtis SL, Zambanini A, Mayet J, Thom SAM, Foale R, Parker KH, Hughes AD. (2007) Reduced systolic wave generation and increased peripheral wave reflection in chronic heart failure, Am J Physiol-Heart C 293, H557 - H562, ISSN: 0363-6135 [pdf]
A study of the changes in the pattern of wave intensity in patients with chronic heart failure. The methods used were non-invasive and entailed synchronisation of ensemble averaged pressure and velocity waveforms.
Davies JE, Hadjiloizou N, Leibovich D, Malaweera A, Whinnett ZI, Manisty CH, Francis DP, Aguado-Sierra J, Foale RA, Malik IS, Parker KH, Mayet J, Hughes, AD. (2007) Importance of the aortic reservoir in determining the shape of the arterial pressure waveform - The forgotten lessons of Frank. Artery Res. 1, 40-45. [pdf]
A short conference paper describing an early algorithm for the calculation of the reservoir pressure from measured pressure waveforms.
A study of left ventricular filling in open-chest dogs, looking at the effect of separating the pressure signal into its reservoir and wave components.
Matthys KS, Alastruey J, Peiro J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ. (2007) Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements., J Biomech 40, 3476 - 3486, ISSN: 0021-9290 [pdf]
A validation of the numerical modelling through the comparison of numerical predictions and measurements on a bench-top model of the large arteries.
Aguado-Sierra J, Parker KH, Davies JE, Francis D, Hughes AD, Mayet J. (2006) Arterial pulse wave velocity in coronary arteries., Conf Proc IEEE Eng Med Biol Soc 1, 867 - 870, ISSN: 1557-170X [pdf]
The application of the sum of squares method for calculation wave speed in coronary arteries.
Alastruey, J, Parker, KH, Peiro, J, Sherwin, SJ. (2006) Can the modified Allen''s test always detect sufficient collateral flow in the hand? A computational study. Comput Methods Biomech Biomed Engin, 9, 353 - 361, ISSN: 1025-5842 [pdf]
The use of our 1-D modelling program to calculate pressure and flow waveforms in the vessels of the arm. The main interest in this work was to study the effects of anastomoses on wave intensity analysis. Backward wavefronts in the radial artery can arise both from reflections and from the conduction of forward waves in the ulnar artery through the palmar arch.
Davies JE, Whinnett ZI, Francis DP, Manisty CH, Aguado-Sierra J, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. (2006) Evidence of a dominant backward-propagating "suction" wave responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy, Circulation 113, 1768 - 1778, ISSN: 0009-7322 [pdf] [editorial]
The use of wave intensity analysis to study the filling of the left ventricle. The role of suction in early diastolic filling is an oft debated question.
Wang JJ, Flewitt JA, Shrive NG, Parker KH, Tyberg JV. (2006) Systemic venous circulation. Waves propagating on a windkessel: relation of arterial and venous windkessels to systemic vascular resistance, Am J Physiol Heart Circ Physiol 290, H154 - H162 [pdf]
The application of wave intensity analysis to the venous system. The reservoir-wave hypothesis seems to be very important in venous haemodynamics.
Davies JE, Whinnett ZI, Francis DP, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. (2005) Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans., Am J Physiol Heart Circ Physiol 290, H878 - H885, ISSN: 0363-6135 [pdf]
A study of the ability of the PU-loop to determine local wave speed in the human aorta. Comparisons are made between PU-loop and foot-to-foot measurements.
Khir AW, Parker KH, (2005) Wave intensity in the ascending aorta: effects of arterial occlusion, J Biomech 38, 647 - 655, ISSN: 0021-9290 [pdf]
A repeat of the classic experiments by Westerhof in 1970 studying the effect of complete occlusion at different sites in the canine aorta, using wave intensity analysis.
Khir AW, Price S, Hale C, Young DA, Parker KH, Pepper JR. (2005) Intra-aortic balloon pumping: Does posture matter?, Artif Organs 29, 36 - 40, ISSN: 0160-564X [pdf]
A study of the mechanics of the intra-aortic balloon pump. Wave intensity analysis is not used directly, but the concept of wavefronts is used in the interpretation of the experimental results.
Wang ZB, Jalali F, Sun YH, Wang JJ, Parker KH, Tyberg JV. (2005) Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis, Am J Physiol-Heart C 288, H1641 - H1651, ISSN: 0363-6135 [pdf]
The use of wave intensity analysis to explore the question of diastolic suction in the early filling of the canine left ventricle.
Zambanini A, Cunningham SL, Parker KH, Khir AW, Thom SAM, Hughes AD. (2005) Wave-energy patterns in carotid, brachial, and radial arteries: a noninvasive approach using wave-intensity analysis, Am J Physiol-Heart Circ 289, H270 - H276, ISSN: 0363-6135 [pdf]
Wave intensity analysis applied to non-invasive measurements of pressure by applanar tonometry and velocity by Doppler ultrasound in human peripheral arteries.
Hollander EH, Dobson GM, Wang JJ, Parker KH, Tyberg JV. (2004) Direct and series transmission of left atrial pressure perturbations to the pulmonary artery: a study using wave-intensity analysis, Am J Physiol-Heart C 286, H267 - H275, ISSN: 0363-6135
The use of wave intensity analysis to study the 'cross-talk' between the left atrium and the pulmonary artery in dogs.
Khir AW, Zambanini A, Parker KH. (2004) Local and regional wave speed in the aorta: effects of arterial occlusion, Med Eng Phys 26, 23 - 29, ISSN: 1350-4533 [pdf]
Aortic wave speed is measured using the PU-loop method. The effects of aortic occlusion and its attendant effects on arterial pressure are examined.
Sun YH, Anderson TJ, Parker KH, Tyberg JV. (2004) Effects of left ventricular contractility and coronary vascular resistance on coronary dynamics, Am J Physiol-Heart C 286, H1590 - H1595, ISSN: 0363-6135 [pdf]
The first application of wave intensity analysis to the study of coronary arteries. Measurements in the canine coronary arteries were studied using wave intensity analysis.
Wang JJ, Parker KH, (2004) Wave propagation in a model of the arterial circulation, J Biomech 37, 457 - 470, ISSN: 0021-9290 [pdf]
Chronologically the first theoretical paper using a model based on the method of characteristics and wave intensity analysis. This work was part of J-J Wang's PhD thesis (1997).
Bleasdale RA, Parker KH, Jones CJH. (2003) Chasing the wave. Unfashionable but important new concepts in arterial wave travel, Am J Physiol-Heart C 284, H1879 - H1885, ISSN: 0363-6135 [pdf]"
A review of wave intensity analysis and how it could affect clinical thinking.
Franke VE, Parker KH, Wee LY, Fisk NM, Sherwin SJ. (2003) Time domain computational modelling of 1D arterial networks in monochorionic placentas, ESAIM-Math Model Num 37, 557 - 580, ISSN: 0764-583X [pdf]
The application of our 1-D modelling program to flow in the placenta of single placenta identical twins. Twin-twin transfusion syndrome is a serious problem with these pregnancies and the modelling can provide useful predictions about the effect of different anastomoses.
Khir AW, Price S, Henein MY, Parker KH, Pepper JR. (2003) Intra-aortic balloon pumping: effects on left ventricular diastolic function, Eur J Cardio-Thorac 24, 277 - 282, ISSN: 1010-7940 [pdf]
A study of the effect of intra-aortic balloon pumping on the filling of the left ventricle in humans.
Sherwin SJ, Franke VE, Peiro J, Parker KH. (2003) One-dimensional modelling of a vascular network in space-time variables, J Eng Math 47, 217 - 250, ISSN: 0022-0833 [pdf]
The development of a 1-D computer program to model arterial wave travel using the method of characteristics.
Wang JJ, O'Brien AB, Shrive NG, Parker KH, Tyberg JV. (2003) Time-domain representation of ventricular-arterial coupling as a windkessel and wave system, Am J Physiol-Heart C 284, H1358 - H1368, ISSN: 0363-6135 [pdf]
The introduction of the reservoir-wave hypothesis. Simultaneous measurements of pressure and velocity in the canine ascending aorta are analysed to show the efficacy of the hypothesis in understanding arterial haemodynamics.
Jones CJH, Sugawara M, Kondoh Y, Uchida K, Parker KH. (2002) Compression and expansion wavefront travel in canine ascending aortic flow: wave intensity analysis, Heart Vessels 16, 91 - 98, ISSN: 0910-8327
Early studies of wave intensity patterns in the canine ascending aorta. The effects of nitrates and methoxamine on aortic waves is explored.
Khir AW, Parker KH. (2002) Measurements of wave speed and reflected waves in elastic tubes and bifurcations, J Biomech 35, 775 - 783, ISSN: 0021-9290 [pdf]
Testing wave intensity analysis in-vitro. Waves in latex tubes and bifurcations are studied using simultaneous pressure and flow measurements and wave intensity analysis.
Khir AW, Parker KH, (2002) Erratum to "Measurements of wave speed and reflected waves in elastic tubes and bifurcations", J Biomech 35, 1149 - 1150, ISSN: 0021-9290 [pdf]
A correction to a previous paper.
Zambanini A, Khir AW, Byrd SM, Parker KH, Thom SAM, Hughes AD. (2002) Wave intensity analysis: a novel non-invasive method for determining arterial wave transmission. Comp in Cardiol 29, 717-720 [pdf]
A description of non-invasive measurement of wave intensity in the carotid, brachial and radial arteries using applanar tonometry and Doppler ultrasound.
Hollander EH, Wang JJ, Dobson GM, Parker KH, Tyberg JV. (2001) Negative wave reflections in pulmonary arteries, Am J Physiol-Heart C 281, H895 - H902, ISSN: 0363-6135 [pdf]
The first application of wave intensity analysis to the pulmonary artery. The results of measurements in the canine pulmonary artery revealed a reflected expansion wave early in systole.
Khir AW, O'Brien A, Gibbs JSR, Parker KH. (2001) Determination of wave speed and wave separation in the arteries, J Biomech 34, 1145 - 1155, ISSN: 0021-9290 [pdf]
The introduction of the PU-loop method for determining local wave speed. The method is applied to human and canine data from various sources.
Khir AW, Henein MY, Koh T, Das SK, Parker KH, Gibson DG. (2001) Arterial waves in humans during peripheral vascular surgery, Clin Sci 101, 749 - 757, ISSN: 0143-5221 [pdf]
The application of wave intensity analysis to the study of waves in human peripheral arteries. The data were taken during surgery.
Wang JJ, Parker KH, Tyberg JV. (2001) Left ventricular wave speed, J Appl Physiol 91, 2531 - 2536, ISSN: 8750-7587 [pdf]
A study of the applicability of wave analysis to the left ventricle. The data are used to deduce the effective wave speed of the ventricle.
Sun YH, Anderson TJ, Parker KH, Tyberg JV. (2000) Wave-intensity analysis: a new approach to coronary hemodynamics, J Appl Physiol 89, 1636 - 1644, ISSN: 8750-7587 [pdf]
The first application of wave intensity analysis to the study of coronary arteries. Data were measured in the dog and wave intensity analysis is applied to better understand the complex effects of myocardial contraction on the intra-myocardial blood vessels.
Koh TW, Pepper JR, DeSouza AC, Parker KH. (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 Vessels 13, 103 - 113, ISSN: 0910-8327
A demonstration of the use of wave intensity analysis to determine the time of arrival of reflected waves in the human aorta. The data were obtained during surgery.
Macrae JM, Sun YH, Isaac DL, Dobson GM, Cheng CP, Little WC, Parker KH, Tyberg JV. (1997) Wave-intensity analysis: a new approach to left ventricular filling dynamics, Heart Vessels 12, 53 - 59.
The first application of wave intensity analysis to the filling of the left ventricle. Studies in the canine heart suggested that suction plays an important role in the early filling of the ventricle.
Jones CJ, Parker KH, Hughes R, Sheridan DJ. (1992) Nonlinearity of human arterial pulse wave transmission., J Biomech Eng 114, 10 - 14, ISSN: 0148-0731
A study of non-linear effects in human aortic wave mechanics. The data were obtained using a dual pressure and EM flow catheter in humans undergoing catheterisation.
Parker, KH, Jones, CJ, (1990) Forward and backward running waves in the arteries: analysis using the method of characteristics., J Biomech Eng 112, 322 - 326, ISSN: 0148-0731 [pdf]
Our first paper on the full derivation of wave intensity analysis. The emphasis is on the method although there are some examples of its application to measured data.
Parker KH, Jones CJ, Dawson JR, Gibson, DG. (1988) What stops the flow of blood from the heart?, Heart Vessels 4, 241 - 245, ISSN: 0910-8327 [pdf]
The first paper on wave intensity analysis. At the time we still thought that reflections from the periphery were the primary cause of the stopping of aortic flow rather than forward expansion wavefronts generated by the relaxing left ventricle.
Davies J, Parker KH, Francis DP, Hughes AD, Mayet J (2009) Heart, 2009, Vol: 95, Pages: 937 - 938, ISSN: 1468-201X.
Ieng SME, Davies JER, Francis DP, Parker KH, Mayet J, Hughes AD (2008) Evidence of a ''common'' reservoir pressure transmitted along the length of the aorta which is the predominate determinate of arterial pressure in humans, J Hum Hypertens 22, 734 - 734, ISSN: 0950-9240.
Davies JER, Whinnett ZI, Hadjiloizou N, Aguado-Sierra J, Parker KH, Francis DP, Hughes AD, Mayet J (2008) Evidence of augmentation of systolic coronary blood flow by retrograde wave reflection travelling-back from the proximal aorta, J Hum Hypertens 22, 718 - 719, ISSN: 0950-9240.
Davies JE, Whinnett ZI, Hadjiloizou N, Manisty CH, Hughes AD, Parker KH, Francis DP, Mayet J (2008) Microcirculatory-originating pressure predominantly determines coronary blood flow in humans: Evaluation using wave intensity analysis. Heart 94, A121, ISSN: 1355-6037.
Malaweera ASN, Davies JE, Hadjiloizou N, Manisty CH, Aguado-Sierra J, Zambanini A, Mayet J, Francis DP, Parker KH, Hughes AD (2008) Peripheral pulsatile arterial pressure is determined by the central reservoir, which is similar across different arterial sites, Heart 94, A114-A115, ISSN: 1355-6037.
Hughes AD, Davies JE, Francis D, Mayet J, Parker KH (2008) Peripheral augmentation index and wave reflection in the radial artery, Hypertension, 51, E45-E46, ISSN: 0194-911X.
Davies JE, Hadjiloizou N, Manisty CH, Whinnett ZI, Francis DP, Parker KH, Mayet J, Hughes AD (2008) Evidence to support the role of the aortic reservoir via a direct mechanism in determination of the pressure waveform with ageing, J Am Coll Cardiol, 51, A339-A339, ISSN: 0735-1097.
Davies JE, Francis DP, Manisty CH, Hadjiloizou N, Aguado-Sierra J, Malik IS, Foale RA, Hughes AD, Parker KH, Mayet J. (2007) A unifying explanation of the aortic pulse waveform in humans, J Am Coll Cardiol 49, 397A - 398A, ISSN: 0735-1097
Malaweera A, Davies JE, Hadjiloizou N, Manisty C, Zambanini A, Aguado-Sierra J, Thom SA, Parker KH, Francis DP, Mayet J, Hughes AD. Pulsatile arterial pressure is predominantly determined by the aortic reservoir, which can be determined non-invasively from peripheral measurement sites, J Hum Hypertens, 2007, 21, 849 - 850, ISSN: 0950-9240
Davies JE, Francis DP, Hadjiloizou N, Manisty CH, Aguado-Sierra J, Foale RA, Parker KH, Mayet J, Hughes AD. Changes in arterial reservoir function, not wave reflection, account for the effect of ageing on pressure augmentation in the proximal aorta, J Hum Hypertens, 2007, 21, 848 - 848, ISSN: 0950-9240
Wang JJ, Parker KH, Shrive NG, Tyberg JV. Predicting a reflection site from impedance analysis: Implications of the time-domain windkessel, FASEB J, 2007, 21, A826 - A827, ISSN: 0892-6638
Davies JE, Hadjiloizou N, Whinnett ZI, Francis DP, Manisty CH, Hughes AD, Parker KH, Mayet J. Evidence to support the augmentation of coronary blood flow in systole, by wave reflection from the aorta, Eur Heart J, 2006, 27, 512 - 512, ISSN: 0195-668X
Davies JE, Whinnett ZI, Francis DP, Manisty CH, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. Coronary blood flow is not augmented by aortic wave reflection: An invasive assessment using wave intensity analysis, Heart, 2006, 92, A35 - A35, ISSN: 1355-6037
Davies JE, Whinnett, ZI Francis DP, Manisty CH, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. Evidence of a dominant backward-propagating "suction" wave, responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy, Heart, 2006, 92, A2 - A3, ISSN: 1355-6037
Khir AW, Hughes AD, Parker KH, The inflection point is not a reliable method for the determination of the augmentation index, J Am Coll Cardiol, 2006, 47, 315A - 315A, ISSN: 0735-1097
Davies JE, Whinnett ZI, Francis DP, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. Effect of left ventricular hypertrophy on human coronary artery haemodynamics., J Am Coll Cardiol, 2005, 45, 431A - 431A, ISSN: 0735-1097
Cunningham SL, Parker KH, Mayet J, Foale RA, Thom SAM, Hughes AD. Peripheral haemodynamics are altered in diastolic heart failure, HEART, 2004, 90, 32 - 32, ISSN: 1355-6037
Khir AW, Price S, Hale C, Young DA, Henein MY, Parker KH, Pepper JR. The effects of hydrostatic pressure gradient in the aorta on the results of intra aortic balloon pumping, Heart, 2003, 89, A26 - A26, ISSN: 1355-6037
Cunningham SL, Mayet J, Parker KH, Foale RA, Thom SAM, Hughes AD. Wave intensity analysis: Insights in haemodynamic abnormalities in heart failure, Heart, 2003, 89, 37 - 37
Khir AW, Price S, Henein MY, Parker KH, Pepper J. The effect of intra aortic balloon pumping on coronary and transmitral flow, J Am Coll Cardiol, 2002, 39, 200A - 200A, ISSN: 0735-1097
Khir AW, Price S, Hale C, Young DA, Henein MY, Parker KH, Pepper JR. The effects of hydrostatic pressure gradient in the aorta on the results of intra aortic balloon pumping, Heart, 2003, 89, 82, ISSN: 1355-6037
Zambanini A, Thom SAM, Hughes AD, Parker KH. Central aortic pressure influences pulse wave velocity, Hypertension, 2002, 40, E10 - E10, ISSN: 0194-911X
Khir AW, Parker KH. Measurements of wave speed and reflected waves in elastic tubes and bifurcations (vol 35, pg 775, 2002), J Biomech, 2002, 35, 1149 - 1150, ISSN: 0021-9290
Zambanini A, Byrd SM, Parker KH, Thom SAM, Hughes AD. Aortic reflections contribute minimally to the radial artery pressure waveform., Hypertension, 2001, 38, 976 - 976, ISSN: 0194-911X
Zambanini A, Byrd SM, Parker KH, Thom SAM, Hughes AD. Expansion waves in muscular arteries: A sign of healthy endothelium?, Hypertension, 2001, 38, 970 - 970, ISSN: 0194-911X
Cunningham SL, Zambanini A, Parker KH, Mayet J, Foale RA, Thorn SAMCG, Hughes AD. Heart failure patients with hypertension have different patterns of wave reflection, Eur Heart J, 2001, 22, 532 - 532, ISSN: 0195-668X
Zambanini A, Byrd SM, Parker KH, Thom SAM, Hughes AD. Expansion waves in muscular arteries: a sign of healthy endothelium?, Hypertension, 2001, 38, A08, ISSN: 1524-4563
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1. In general I disapprove of the practice of 'verbing' nouns. For example, 'The injured player was stretchered off the field'. 'Authored' seemed to me to be a particularly bad example of this practice, which I first encountered in an advertisement for a technical book from O****d University Press ('... each chapter is authored by an internationally recognised expert...'). It seems to me that 'write' is a perfectly good word that conveys exactly the same meaning and there is no need for this neologism. However, a computer expert colleague has pointed out to me that the preparation of a web page requires design as well as writing and so there may be a need for new word to describe this activity. This, however, does not excuse the above usage by O****d University Press.
The Resisters. Anyone curious about the relative lack of my scientific output in the late 1970s and early 1980s might find some clues here.