Reservoir-wave Model Research Articles

Reservoir Pressure Analysis in Group 2 Pulmonary Hypertension

<h3>Purpose</h3> The reservoir-wave model, based on the 3-element Windkessel, proposes that the pressure waveform consists of a reservoir pressure (Pres) related to arterial expansion and recoil and a superimposed pressure wave (excess pressure, Pex) generated by forward (ventricular stroke volume and input impedance) and backward travelling waves (related to local arterial properties). In this study we aim to describe Pres in Group 2 isolated post-capillary (IPC) and combined pre and post-capillary (CPC) pulmonary hypertension (PH). <h3>Methods</h3> Pressure and velocity data were acquired simultaneously using a dual-tipped pressure and doppler flow sensor wire during right heart catheterisation. The data were processed offline using customised Matlab software. CPC PH was defined as pulmonary capillary wedge pressure (PCWP) >15mmHg, mean pulmonary arterial pressure (mPAP)>20mmHg and PVR≥3 WU. <h3>Results</h3> Pres but not Pex was higher in CPC compared to IPC PH (Table). A representative pressures and flow tracing is shown in the figure. Higher PA pressures in CPC PH is due to higher Pres secondary to higher PVR, PAC and PCWP. Pres correlated to pulmonary vascular resistance (PVR)(p=0.002;r=0.58),pulmonary capillary wedge pressure(PCWP)(p<0.001;r=0.84) and heart rate(HR)(p=0.01;r=0.487); and negatively correlated to pulmonary artery capacitance(PAC)(p<0.001; r=0.68), but not stroke volume(SV). <h3>Conclusion</h3> This is the first study to compare Pres in group 2 PH. Higher PA pressures in CPC PH is due to higher Pres and not Pex. This suggests input impedance and wave reflection may not be the dominant mechanism in CPC PH.

Impact of varying diastolic pressure fitting technique for the reservoir-wave model on wave intensity analysis.

The reservoir-wave model assumes that the measured arterial pressure is made of two components: reservoir and excess. The effect of the reservoir volume should be excluded to quantify the effects of forward and backward traveling waves on blood pressure. Whilst the validity of the reservoir-wave concept is still debated, there is no consensus on the best fitting method for the calculation of the reservoir pressure waveform. Therefore, the aim of this parametric study is to examine the effects of varying the fitting technique on the calculation of reservoir and excess components of pressure and velocity waveforms. Common carotid pressure and flow velocity were measured using applanation tonometry and doppler ultrasound, respectively, in 1037 healthy humans collected randomly from the Asklepios population, aged 35 to 55 years old. Different fitting techniques to the diastolic decay of the measured arterial pressure were used to determine the asymptotic pressure decay, which in turn was used to determine the reservoir pressure waveform. The corresponding wave speed was determined using the PU-loop method, and wave intensity parameters were calculated and compared. Different fitting methods resulted in significant changes in the shape of the reservoir pressure waveform; however, its peak and time integral remained constant in this study. Although peak and integral of excess pressure, velocity components and wave intensity changed significantly with changing the diastolic decay fitting method, wave speed was not substantially modified. We conclude that wave speed, peak reservoir pressure and its time integral are independent of the diastolic pressure decay fitting techniques examined in this study. Therefore, these parameters are considered more reliable diagnostic indicators than excess pressure and velocity which are more sensitive to fitting techniques.

Implications of Changing the Asymptotic Diastolic Pressure in the Reservoir-wave Model on Wave Intensity Parameters: A Parametric Study

Hybrid reservoir-wave models assume that the measured arterial pressure can be separated into two additive components, reservoir/windkessel and excess/wave pressure waveforms. Therefore, the effect of the reservoir volume should be excluded to properly quantify the effects of forward/backward-travelling waves on blood pressure. However, there is no consensus on the value of the asymptotic diastolic pressure decay (P∞) which is required for the calculation of the reservoir pressure. The aim of this study was to examine the effects of varying the value of P∞ on the calculation of reservoir and excess components of the measured pressure and velocity waveforms.Common carotid pressure and flow velocity were measured using appalanation tonometery and Doppler ultrasound, respectively, in 1037 healthy humans aged 35–55 years; a subset of the Asklepios population. Wave speed was determined using the PU-loop (Pressure-Velocity Loop) method, and used to separate the reservoir and wave pressures. Wave intensity analysis was performed and its parameters have been analysed with varying P∞ between −75% to +75% of its initial calculated value.The underestimation (up to −75%) of P∞ (with respect to a reference value of 48.6 ± 21 mmHg) did not result in any substantial change in either hemodynamic or wave intensity parameters, whereas its overestimation (from +25% to +100%) brought unrealistic increases of the studied parameters and large standard deviations. Nevertheless, reservoir pressure features and wave speed seemed insensitive to changes in P∞.We conclude that underestimation and overestimation of P∞ produce different hemodynamic effects; no change and substantially unrealistic change, respectively on wave intensity parameters. The reservoir pressure features and wave speed are independent of changes in P∞, and could be considered more reliable diagnostic indicators than other hemodynamic parameters, which are affected by changes in P∞.

The reservoir-wave model

This paper is based on a talk given at the Arterial Hemodynamics: Past, Present and Future symposium in June 2016. Like the talk it is divided into three different but related parts. Part 1 describes the calculation of reservoir and excess pressure from clinical pressure waveforms measured at 5 different aortic sites in 40 patients. The main results are that the reservoir pressure waveform propagates down the aorta and is effectively constant from the aortic root to the aortic bifurcation. Part 2 describes a low-frequency asymptotic analysis of the input impedance of an arterial tree. Neglecting terms of second order, the results show that the low-frequency component of the pressure waveform is uniform throughout the arterial tree and is delayed by an effective wave travel time that depends on the properties of the network. The low-frequency pressure waveform shares all of the properties of the reservoir pressure waveform, but it is premature to say that they are identical. Part 3 describes the analysis of arterial hemodynamicsusing wave fronts. It shows that every wave front introduced at the root of the aorta generates an exponentially increasing number of reflected and transmitted waves with exponentially decreasing amplitudes. The long-time response of the arterial tree can be described by a number of exponentially decaying eigen-modes, each with a different time constant. The analysis is applied to a 55-artery model of the human circulation and the modes and their time constants are shown. This theory provides an alternative method for studying arterial hemodynamics and helps in the interpretation of reservoir and excess pressure.

PS 11-47 ARTERIAL RESERVOIR FUNCTIONS ARE ASSOCIATED WITH CLINICAL OUTCOMES IN PATIENTS WITH ACUTE HEART FAILURE SYNDROME

Objective: Excessive arterial wave reflections play an important role in the pathogenesis of acute heart failure (AHF). Alternatively, the pulsatile hemodynamics can be analyzed by a reservoir wave model incorporating elements from both reservoir functions and wave analysis. The present study investigated the prognostic values of the arterial reservoir functions in AHF. Design and Method: A total of 220 AHF patients (70 ± 15 years, 76.8% men, 66.8% HFrEF) were enrolled and followed for one year after discharge. Measures of the pulsatile hemodynamics, including carotid-femoral pulse wave velocity (cf-PWV), carotid pulse pressure (PPc), carotid augmentation index (cAI), carotid augmentation pressure (cAP), the amplitude of reflected wave (Pb), and those based on the reservoir wave model: excess pressure integral (XSPI), reservoir pressure integral (PRI), amplitude of reservoir pressure (Pres), and systolic and diastolic rate constant, were obtained before discharge. Results: During a mean follow-up of 305 ± 108 days, a total of 91 subjects incurred either AHF re-admission or mortality. Patients with post-discharge events were older, had lower eGFR, higher cf-PWV, PPc, cAI, cAP and Pb, and higher XSPI, Pres, and diastolic rate constant. PPc, Pb, XSPI and diastolic rate constant remained significantly independently associated with the post-discharge events (HR and 95%CI per-1SD: 1.36, 1.10–1.68; 1.14, 1.04–1.24; 1.29,1.04–1.59; 1.37,1.03–1.82, respectively) in a multi-variable Cox model accounting for age, sex, eGFR and NTproBNP. Using a backward stepwise model, both XSPI and diastolic rate constant but not PPc or Pb, persistently stayed in the prediction model (1.37, 1.11–1.70 and 1.56, 1.16–2.09, respectively). Combining PPc and diastolic rate constant further stratified the risks of the patients. (Figure) In addition, the add-on of XSPI and diastolic rate constant to the prediction model of baseline characteristics and PPc improved the net reclassification by 7.2% (P = 0.044). Conclusions: Arterial reservoir functions measured by the reservoir wave model are independent prognostic indicators in patients with AHF. Combining parameters of wave reflections arterial reservoir functions may further improve the prediction of post-discharge adverse events.

Reservoir and reservoir-less pressure effects on arterial waves in the canine aorta.

A time-domain approach to couple the Windkessel effect and wave propagation has been recently introduced. The technique assumes that the measured pressure in the aorta (P) is the sum of a reservoir pressure (Pr), due to the storage of blood, and an excess pressure (Pe), due to the waves. Since the subtraction of Pr from P results in a smaller component of Pe, we hypothesized that using the reservoir-wave approach would produce smaller values of wave speed and intensities. Therefore, the aim of this study is to quantify the differences in wave speed and intensity using P, wave-only, and Pe, reservoir-wave techniques. Pressure and flow were measured in the canine aorta in the control condition and during total occlusion at four sites. Wave speed was determined using the PU-loop (c) and PeU-loop (ce) methods, and wave intensity analysis was performed using P and separately using Pe; the magnitude and time of the main waves and the reflection index were calculated. Both analyses produced similar wave intensity analysis curves, and no significant differences in the timing of the waves, except onset of the forward expansion wave, indicated that distal occlusions have little effect on haemodynamics in the ascending aorta. We consistently found lower values of wave speed and intensities when the reservoir-wave model was applied. In particular, the magnitude of the backward waves was markedly smaller, even during proximal occlusions. In the absence of other independent techniques or evidence, it is not currently possible to decide which of the two models is more correct.

Genesis of the characteristic pulmonary venous pressure waveform as described by the reservoir-wave model.

Conventional haemodynamic analysis of pulmonary venous and left atrial (LA) pressure waveforms yields substantial forward and backward waves throughout the cardiac cycle; the reservoir wave model provides an alternative analysis with minimal waves during diastole. Pressure and flow in a single pulmonary vein (PV) and the main pulmonary artery (PA) were measured in anaesthetized dogs and the effects of hypoxia and nitric oxide, volume loading, and positive-end expiratory pressure (PEEP) were observed. The reservoir wave model was used to determine the reservoir contribution to PV pressure and flow. Subtracting reservoir pressure and flow resulted in 'excess' quantities which were treated as wave-related.Wave intensity analysis of excess pressure and flow quantified the contributions of waves originating upstream (from the PA) and downstream (from the LA and/or left ventricle (LV)).Major features of the characteristic PV waveform are caused by sequential LA and LV contraction and relaxation creating backward compression (i.e.pressure-increasing) waves followed by decompression (i.e. pressure-decreasing) waves. Mitral valve opening is linked to a backwards decompression wave (i.e. diastolic suction). During late systole and early diastole, forward waves originating in the PA are significant. These waves were attenuated less with volume loading and delayed with PEEP. The reservoir wave model shows that the forward and backward waves are negligible during LV diastasis and that the changes in pressure and flow can be accounted for by the discharge of upstream reservoirs. In sharp contrast, conventional analysis posits forward and backward waves such that much of the energy of the forward wave is opposed by the backward wave.

The case against the reservoir-wave approach

We read with interest Tyberg et al.'s case for the reservoir-wave approach (RWA), appropriately described as a “controversial approach to [the analysis of] arterial hemodynamics” [ [1] Tyberg J.V. Bouwmeester J.C. Parker K.H. Shrive N.G. Wang Jr., J. The case for the reservoir-wave approach. Int J Cardiol. 2014; 172: 299-306 Abstract Full Text Full Text PDF PubMed Scopus (44) Google Scholar ]. Lest readers of IJC be exposed to a one-sided debate, we feel it is important to also present the case against this approach, some aspects of which have been aired previously [ 2 Mynard J.P. Penny D.J. Davidson M.R. Smolich J.J. The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study. J Hypertens. 2012; 30: 734-743 Crossref PubMed Scopus (45) Google Scholar , 3 Mynard J.P. Penny D.J. Davidson M.R. Smolich J.J. The reservoir-wave paradigm. J Hypertens. 2012; 30: 1881-1883 Crossref Scopus (4) Google Scholar , 4 Mynard J.P. Smolich J.J. The reservoir-wave paradigm may be plausible, but is it valid?. J Physiol. 2013; 591 ([Suppl.]): 1171-1173 Crossref PubMed Scopus (22) Google Scholar , 5 Segers P. Mynard J. Taelman L. Vermeersch S. Swillens A. Wave reflection: myth or reality?. Artery Res. 2012; 6: 7-11 Abstract Full Text Full Text PDF Scopus (21) Google Scholar , 6 Mynard J.P. Assessment of conceptual inconsistencies in the hybrid reservoir-wave model. in: Proc. Ann. Int. Conf. IEEE Eng. Med. Biol. Soc. Osaka, Japan. 2013: 213-216 Crossref Scopus (14) Google Scholar ].

Wave reflections in the pulmonary arteries analysed with the reservoir-wave model.

Conventional haemodynamic analysis of pressure and flow in the pulmonary circulation yields incident and reflected waves throughout the cardiac cycle, even during diastole. The reservoir-wave model provides an alternative haemodynamic analysis consistent with minimal wave activity during diastole. Pressure and flow in the main pulmonary artery were measured in anaesthetized dogs and the effects of hypoxia and nitric oxide, volume loading and positive end-expiratory pressure were observed. The reservoir-wave model was used to determine the reservoir contribution to pressure and flow and once subtracted, resulted in 'excess' quantities, which were treated as wave-related. Wave intensity analysis quantified the contributions of waves originating upstream (forward-going waves) and downstream (backward-going waves). In the pulmonary artery, negative reflections of incident waves created by the right ventricle were observed. Overall, the distance from the pulmonary artery valve to this reflection site was calculated to be 5.7 ± 0.2 cm. During 100% O2 ventilation, the strength of these reflections increased 10% with volume loading and decreased 4% with 10 cmH2O positive end-expiratory pressure. In the pulmonary arterial circulation, negative reflections arise from the junction of lobar arteries from the left and right pulmonary arteries. This mechanism serves to reduce peak systolic pressure, while increasing blood flow.

Partitioning pulmonary vascular resistance using the reservoir-wave model

The conventional determination of pulmonary vascular resistance does not indicate which vascular segments contribute to the total resistance of the pulmonary circulation. Using measurements of pressure and flow, the reservoir-wave model can be used to partition total pulmonary vascular resistance into arterial, microcirculation, and venous components. Changes to these resistance components are investigated during hypoxia and inhaled nitric oxide, volume loading, and positive end-expiratory pressure. The reservoir-wave model defines the pressure of a volume-related reservoir and the asymptotic pressure. The mean values of arterial and venous reservoir pressures and arterial and venous asymptotic pressures define a series of resistances between the main pulmonary artery and the pulmonary veins: the resistance of large and small arteries, the microcirculation, and veins. In 11 anaesthetized, open-chest dogs, pressure and flow were measured in the main pulmonary artery and a single pulmonary vein. Volume loading reduced each vascular resistance component, whereas positive end-expiratory pressure only increased microcirculation resistance. Hypoxia increased the resistance of small arteries and veins, whereas nitric oxide only decreased small-artery resistance significantly. The reservoir-wave model provides a novel method to deconstruct total pulmonary vascular resistance. The results are consistent with the expected physiological responses of the pulmonary circulation and provide additional information regarding which segments of the pulmonary circulation react to hypoxia and nitric oxide.

Estimation of left ventricular stroke volume by impedance cardiography: its relation to the aortic reservoir

Impedance cardiography is a non-invasive technique used to estimate left ventricular (LV) stroke volume (SV) using the change in thoracic impedance (ΔZ). It remains controversial, partly because impedance cardiographic parameters have not been successfully related to haemodynamic events. We hypothesized that the change in ΔZ may be proportional to the variation in thoracic (primarily aortic) blood volumes. Nine anaesthetized and ventilated dogs were divided into the following two groups: the 'aortic volume group' (n = 5), in which aortic and IVC (inferior vena caval) dimensions were measured ultrasonically; and the 'reservoir volume group', in which aortic and IVC reservoir volumes were calculated using the reservoir-wave model. Measurements were made in control conditions, in the presence of nitroprusside and methoxamine and after volume loading. In both the aortic volume group and the reservoir volume group, the maximal rate of increase in ΔZ [(dZ/dt)max] strongly correlated with the maximal rate of change in aortic/reservoir blood volume (R(2) = 0.85 and 0.95, respectively), which in turn was proportional to the LV SV. The LV and IVC contributions to ΔZ were small in control conditions (∼5 and 1%, respectively), but the LV contribution increased slightly (to 7%) with administration of methoxamine and after volume loading (to 10%). It is concluded that the change in thoracic impedance (ΔZ) during the cardiac cycle is proportional to the change in aortic reservoir (i.e. Windkessel) volume, which provides a mechanistic explanation for previously demonstrated good correlations with standard measures of cardiac output.

Rebuttal from Nico Westerhof and Berend E. Westerhof

Tyberg et al. (2013) present new information of which few people are aware, namely that the time differences between the forward and backward wave are comparable at different aortic locations and therefore the backward wave appears to be travelling forward, i.e. to the periphery. This apparent inconsistency with generally accepted thinking needs attention. Tyberg et al. (2013) and we (Westerhof & Westerhof, 2013) appear to agree that forward and backward waves exist. However, we disagree with the suggestion that forward and backward wave waves do not represent reality. Waves do represent reality, but the interpretation of waves requires reconsideration. Interpretation (including Tyberg et al. 2013) is most often based on a uniform tube, an incorrect representation of the real arterial system. In this model, forward and backward waves maintain their shape and differ only in timing while traveling to the end of the tube and back. In the arterial system, with its many reflection sites, the waves are reflected and re-reflected; thus, forward and backward waves are compound waves. Compare an echo in a single hallway with the compound echo arising from a system of corridors. Echos from many sites and directions, including reverberation, result in a compound wave, in which the return time does not provide a measure of the length of the corridor. Thus, the backward wave is a compound wave arising from many reflections and not a single wave travelling backwards as in the tube model. At any location, the reflection depends on characteristic impedance and distal input impedance. The input impedance phase angle determines the time difference between forward and backward waves, and these phases are similar at different aortic locations. The reservoir-wave model (Wang et al. 2003) predicts the (reservoir) pressure of Frank's Windkessel plus an ‘excess pressure’ coined by Lighthill (1978), who was not aware of the three-element Windkessel with characteristic impedance (Westerhof et al. 1971). Indeed, Wang et al. (2003) and others (Vermeersch et al. 2009) have shown that the ‘excess pressure’ almost exactly equals characteristic impedance multiplied by flow. The reservoir pressure is twice the backward pressure; both run simultaneously to arrive later in the periphery (Wang et al. 2011). The ‘self-cancelling forward and backward flow waves’ model is correct if reflection is complete, i.e. when measured flow is negligible, such as at the distal end of a closed-ended tube (not in the arterial tree) and at closed aortic valves (in diastole). Implications The data of Tyberg et al. (2013) imply that backward wave return time, the inflection point of measured pressure, and augmentation index should be reconsidered (Baksi et al. 2009; Westerhof & Westerhof, 2012).

Describing waves in the pulmonary veins: Application of a reservoir-wave model

Describing waves in the pulmonary veins: Application of a reservoir-wave model