Potential and limitations of wave intensity analysis in coronary arteries

Clinical use of physiological lesion assessment using pressure guidewires: an expert consensus document of the Japanese association of cardiovascular intervention and therapeutics-update 2022

Fractional flow reserve and instantaneous wave-free ratio are widely accepted and recommended in Western and Japanese guidelines for appropriate percutaneous coronary intervention. There are, however, many differences in clinical situations between Japan and Western countries. Therefore, the Task Force on coronary physiology of the Japanese Association of Cardiovascular Intervention and Therapeutics (CVIT) has proposed an expert consensus document to summarize current evidence and suggest the practical use of physiological lesion assessment in Japan.

Mechanisms of gradual pressure drop in angiographically normal left anterior descending and right coronary artery: Insights from wave intensity analysis

BACKGROUND

This study evaluated the mechanism of decline in coronary pressure from the proximal to the distal part of the coronary arteries in the left anterior descending (LAD) versus the right coronary artery (RCA) from the insight of coronary hemodynamics using wave intensity analysis (WIA).

METHODS

Twelve patients with angiographically normal LAD and RCA were prospectively enrolled. Distal coronary pressure, mean aortic pressure, and average peak velocity were measured at 4 different positions: 9, 6, 3, and 0 cm distal from each coronary ostium.

RESULTS

The distal-to-proximal coronary pressure ratio during maximum hyperemia gradually decreased in proportion to the distance from the ostium (0.92±0.03 and 0.98±0.03 at 9 cm distal to the LAD and RCA ostium). WIA showed the dominant forward-traveling compression wave gradually decreased and the backward-traveling suction wave gradually decreased in proportion to the decrease in coronary pressure through the length of the non-diseased LAD but not the RCA.

CONCLUSIONS

The pushing wave and suction wave intensities on WIA were diminished in proportion to the distance from the ostium of the LAD despite the wave intensity not changing across the length of the RCA, which may lead to gradual intracoronary pressure drop in the angiographically normal LAD.

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

Usefulness of Proximal Coronary Wave Speed for Wave Intensity Analysis in Diseased Coronary Vessels

Background: Wave speed is needed to separate net wave intensity into forward and backward traveling components. However, wave speed in diseased coronary arteries cannot be assessed from hemodynamic measurements obtained distal to a stenosis. Wave speed inherently depends on arterial wall properties which should be similar proximal and distal to a stenosis. Our hypothesis is that proximal wave speed can be used to separate net wave intensity obtained distal to a stenosis.

Methods: We assessed coronary wave speed using the sum-of-squares single-point technique (SPc) based on simultaneous intracoronary pressure and flow velocity measurements in human coronary arteries. SPc at resting flow was determined in diseased coronary vessels of 12 patients both proximal and distal to the stenosis. In seven of these vessels, distal measurements were additionally obtained after revascularization by stent placement. SPc was also assessed at two axial locations in 14 reference vessels without a stenosis.

Results: (1) No difference in SPc was present between proximal and distal locations in the reference vessels. (2) In diseased vessels with a focal stenosis, SPc at the distal location was paradoxically larger than SPc proximal to the stenosis (28.4 ± 3.7 m/s vs. 18.3 ± 1.8 m/s, p < 0.02), despite the lower distending pressure downstream of the stenosis. The corresponding separated wave energy tended to be underestimated when derived from SPc at the distal compared with the proximal location. (3) After successful revascularization, SPc at the distal location no longer differed from SPc at the proximal location prior to revascularization (21.9 ± 2.0 m/s vs. 20.8 ± 1.9 m/s, p = 0.48). Accordingly, no significant difference in separated wave energy was observed for forward or backward waves.

Conclusion: In diseased coronary vessels, SPc assessed from distal hemodynamic signals is erroneously elevated. Our findings suggest that proximal wave speed can be used to separate wave intensity profiles obtained downstream of a stenosis. This approach may extend the application of wave intensity analysis to diseased coronary vessels.

A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

One-dimensional (1D) hemodynamic models of arteries have increasingly been applied to coronary circulation. In this study, we have adopted flow and pressure profiles in Olufsen's 1D structured tree as coronary boundary conditions, with terminals coupled to the dynamic pressure feedback resulting from the intra-myocardial stress because of ventricular contraction. We model a trifurcation structure of the example coronary tree as two adjacent bifurcations. The estimated results of blood pressure and flow rate from our simulation agree well with the clinical measurements and published data. Furthermore, the 1D model enables us to use wave intensity analysis to simulate blood flow in the developed coronary model. Six characteristic waves are observed in both left and right coronary flows, though the waves' magnitudes differ from each other. We study the effects of arterial wall stiffness on coronary blood flow in the left circumflex artery (LCX). Different diseased cases indicate that distinct pathological reactions of the cardiovascular system can be better distinguished through Wave Intensity analysis, which shows agreement with clinical observations. Finally, the feedback pressure in terminal vessels and measurement deviation are also investigated by changing parameters in the LCX. We find that larger feedback pressure increases the backward wave and decreases the forward one. Although simplified, this 1D model provides new insight into coronary hemodynamics in healthy and diseased conditions. We believe that this approach offers reference resources for studies on coronary circulation disease diagnosis, treatment and simulation.

Clinical use of physiological lesion assessment using pressure guidewires: an expert consensus document of the Japanese Association of Cardiovascular Intervention and Therapeutics

In this document, the background, concept, and current evidence are briefly summarized. The focus is on the clinical application of physiological lesion assessment from a practical standpoint for facilities that do not have ample experience. Finally, the characteristics of new resting indexes are summarized.

Functional Approach for Coronary Artery Disease: Filling the Gap Between Evidence and Practice

The presence of myocardial ischemia is the most important prognostic factor in patients with coronary artery disease, and ischemia-directed revascularization has been a standard of care. Fractional flow reserve (FFR) is an invasive method used to detect the functionally significant epicardial coronary stenosis, and FFR-guided revascularization strategy has been proven to be superior to angiography-guided strategy. Recently, a hyperemia-free index, instantaneous wave free ratio (iFR), was developed and showed its non-inferiority for clinical outcomes compared with FFR-guided strategy. While evidence supporting the benefit of pressure wire assessment exists, there remain several unresolved issues, such as the mechanism of discordance between resting and hyperemic physiologic indices, clinical outcomes of patient/lesions with discordant results among the physiologic indices, role of physiologic indices beyond per-vessel decision tool, and the role of microvascular dysfunction in patient prognosis. The current article will review the recent studies performed to address these questions.

Major influence of a 'smoke and mirrors' effect caused by wave reflection on early diastolic coronary arterial wave intensity

KEY POINTS

Coronary wave intensity analysis (WIA) is an emerging technique for assessing upstream and downstream influences on myocardial perfusion. It is thought that a dominant backward decompression wave (BDW_dia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDW_dia ) and compression (FCW_dia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDW_dia , FCW_dia and BDW_dia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDW_dia , whereas distal suction dominated in a computer model representing a hypertensive human. Non-linear addition/subtraction of mechanistically distinct waves (e.g. wave reflection and distal suction) obfuscates the true contribution of upstream and downstream forces on measured waves (the 'smoke and mirrors' effect). The mechanisms underlying coronary WIA are more complex than previously thought and the impact of wave reflection should be considered when interpreting clinical and experimental data.

ABSTRACT

Coronary arterial wave intensity analysis (WIA) is thought to provide clear insight into upstream and downstream forces on coronary flow, with a large early-diastolic surge in coronary flow accompanied by a prominent backward decompression wave (BDW_dia ), as well as a forward decompression wave (FDW_dia ) and forward compression wave (FCW_dia ). The BDW_dia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDW_dia and FCW_dia are thought to be transmitted from the aorta into the coronary arteries. Based on an established multi-scale computational model and high-fidelity measurements from the proximal circumflex artery (Cx) of 18 anaesthetized sheep, we present evidence that wave reflection has a major impact on each of these three waves, with a non-linear addition/subtraction of reflected waves obscuring the true influence of upstream and downstream forces through concealment and exaggeration, i.e. a 'smoke and mirrors' effect. We also describe methods, requiring additional measurement of aortic WIA, for unravelling the separate influences of wave reflection versus active upstream/downstream forces on coronary waves. Distal wave reflection accounted for ∼70% of the BDW_dia in sheep, but had a lesser influence (∼25%) in the computer model representing a hypertensive human. Negative reflection of the BDW_dia at the coronary-aortic junction attenuated the Cx FDW_dia (by ∼40% in sheep) and augmented Cx FCW_dia (∼5-fold), relative to the corresponding aortic waves. We conclude that wave reflection has a major influence on early-diastolic WIA, and thus needs to be considered when interpreting coronary WIA profiles.

A review of wave mechanics in the pulmonary artery with an emphasis on wave intensity analysis

Mean pulmonary arterial pressure and pulmonary vascular resistance (PVR) remain the most common haemodynamic measures to evaluate the severity and prognosis of pulmonary hypertension. However, PVR only captures the non-oscillatory component of the right ventricular hydraulic load and neglects the dynamic compliance of the pulmonary arteries and the contribution of wave transmission. Wave intensity analysis offers an alternative way to assess the pulmonary vasculature in health and disease. Wave speed is a measure of arterial stiffness, and the magnitude and timing of wave reflection provide information on the degree of impedance mismatch between the proximal and distal circulation. Studies in the pulmonary artery have demonstrated distinct differences in arterial wave propagation between individuals with and without pulmonary vascular disease. Notably, greater wave speed and greater wave reflection are observed in patients with pulmonary hypertension and in animal models exposed to hypoxia. Studying wave propagation makes a valuable contribution to the assessment of the arterial system in pulmonary hypertension, and here, we briefly review the current state of knowledge of the methods used to evaluate arterial waves in the pulmonary artery.

Diastolic Backward-Traveling Decompression (Suction) Wave Correlates With Simultaneously Acquired Indices of Diastolic Function and Is Reduced in Left Ventricular Stunning

Background—

Wave intensity analysis can distinguish proximal (propulsion) and distal (suction) influences on coronary blood flow and is purported to reflect myocardial performance and microvascular function. Quantifying the amplitude of the peak, backwards expansion wave (BEW) may have clinical utility. However, simultaneously acquired wave intensity analysis and left ventricular (LV) pressure–volume loop data, confirming the origin and effect of myocardial function on the BEW in humans, have not been previously reported.

Methods and Results—

Patients with single-vessel left anterior descending coronary disease and normal ventricular function (n=13) were recruited prospectively. We simultaneously measured LV function with a conductance catheter and derived wave intensity analysis using a pressure–low velocity guidewire at baseline and again 30 minutes after a 1-minute coronary balloon occlusion. The peak BEW correlated with the indices of diastolic LV function: LV dP/dt min ( r s =−0.59; P =0.002) and τ ( r s =−0.59; P =0.002), but not with systolic function. In 12 patients with paired measurements 30 minutes post balloon occlusion, LV dP/dt max decreased from 1437.1±163.9 to 1299.4±152.9 mm Hg/s (median difference, −110.4 [−183.3 to −70.4]; P =0.015) and τ increased from 48.3±7.4 to 52.4±7.9 ms (difference, 4.1 [1.3–6.9]; P =0.01), but basal average peak coronary flow velocity was unchanged, indicating LV stunning post balloon occlusion. However, the peak BEW amplitude decreased from −9.95±5.45 W·m –2 /s 2 ×10 5 to −7.52±5.00 W·m –2 /s 2 ×10 5 (difference 2.43×10 5 [0.20×10 5 to 4.67×10 5 ; P =0.04]).

Conclusions—

Peak BEW assessed by coronary wave intensity analysis correlates with invasive indices of LV diastolic function and mirrors changes in LV diastolic function confirming the origin of the suction wave. This may have implications for physiological lesion assessment after percutaneous coronary intervention.

Clinical Trial Registration—

URL: http://www.isrctn.org . Unique identifier: ISRCTN42864201.

Accurate and Standardized Coronary Wave Intensity Analysis

OBJECTIVE

Coronary wave intensity analysis (cWIA) has increasingly been applied in the clinical research setting to distinguish between the proximal and distal mechanical influences on coronary blood flow. Recently, a cWIA-derived clinical index demonstrated prognostic value in predicting functional recovery postmyocardial infarction. Nevertheless, the known operator dependence of the cWIA metrics currently hampers its routine application in clinical practice. Specifically, it was recently demonstrated that the cWIA metrics are highly dependent on the chosen Savitzky-Golay filter parameters used to smooth the acquired traces. Therefore, a novel method to make cWIA standardized and automatic was proposed and evaluated in vivo.

METHODS

The novel approach combines an adaptive Savitzky-Golay filter with high-order central finite differencing after ensemble-averaging the acquired waveforms. Its accuracy was assessed using in vivo human data. The proposed approach was then modified to automatically perform beat wise cWIA. Finally, the feasibility (accuracy and robustness) of the method was evaluated.

RESULTS

The automatic cWIA algorithm provided satisfactory accuracy under a wide range of noise scenarios (≤10% and ≤20% error in the estimation of wave areas and peaks, respectively). These results were confirmed when beat-by-beat cWIA was performed.

CONCLUSION

An accurate, standardized, and automated cWIA was developed. Moreover, the feasibility of beat wise cWIA was demonstrated for the first time.

SIGNIFICANCE

The proposed algorithm provides practitioners with a standardized technique that could broaden the application of cWIA in the clinical practice as enabling multicenter trials. Furthermore, the demonstrated potential of beatwise cWIA opens the possibility investigating the coronary physiology in real time.

Automatic selection of optimal Savitzky-Golay filter parameters for Coronary Wave Intensity Analysis

Coronary Wave Intensity Analysis (cWIA) is a technique capable of separating the effects of proximal arterial haemodynamics from cardiac mechanics. The cWIA ability to establish a mechanistic link between coronary haemodynamics measurements and the underlying pathophysiology has been widely demonstrated. Moreover, the prognostic value of a cWIA-derived metric has been recently proved. However, the clinical application of cWIA has been hindered due to the strong dependence on the practitioners, mainly ascribable to the cWIA-derived indices sensitivity to the pre-processing parameters. Specifically, as recently demonstrated, the cWIA-derived metrics are strongly sensitive to the Savitzky-Golay (S-G) filter, typically used to smooth the acquired traces. This is mainly due to the inability of the S-G filter to deal with the different timescale features present in the measured waveforms. Therefore, we propose to apply an adaptive S-G algorithm that automatically selects pointwise the optimal filter parameters. The newly proposed algorithm accuracy is assessed against a cWIA gold standard, provided by a newly developed in-silico cWIA modelling framework, when physiological noise is added to the simulated traces. The adaptive S-G algorithm, when used to automatically select the polynomial degree of the S-G filter, provides satisfactory results with ≤ 10% error for all the metrics through all the levels of noise tested. Therefore, the newly proposed method makes cWIA fully automatic and independent from the practitioners, opening the possibility to multi-centre trials.

Physiologic Assessment of Coronary Artery Disease: Focus on Fractional Flow Reserve

The presence of myocardial ischemia is the most important prognostic factor in patients with ischemic heart disease. Fractional flow reserve (FFR) is a gold standard invasive method used to detect the stenosis-specific myocardial ischemia. FFR-guided revascularization strategy is superior to angiography-guided strategy. The recently developed hyperemia-free index, instantaneous wave free ratio is being actively investigated. A non-invasive FFR derived from coronary CT angiography is now used in clinical practice. Due to rapid expansion of invasive and non-invasive physiologic assessment, comprehensive understanding of the role and potential pitfalls of each modality are required for its application. In this review, we focus on the basic and clinical aspects of physiologic assessment in ischemic heart disease.

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

Percutaneous Coronary Intervention Enhances Accelerative Wave Intensity in Coronary Arteries

Background

The systolic forward travelling compression wave (sFCW) and diastolic backward travelling decompression waves (dBEW) predominantly accelerate coronary blood flow. The effect of a coronary stenosis on the intensity of these waves in the distal vessel is unknown. We investigated the relationship between established physiological indices of hyperemic coronary flow and the intensity of the two major accelerative coronary waves identified by Coronary Wave Intensity analysis (CWIA).

Methodology / Principal Findings

Simultaneous intracoronary pressure and velocity measurement was performed during adenosine induced hyperemia in 17 patients with pressure / Doppler flow wires positioned distal to the target lesion. CWI profiles were generated from this data. Fractional Flow Reserve (FFR) and Coronary Flow Velocity Reserve (CFVR) were calculated concurrently. The intensity of the dBEW was significantly correlated with FFR (R = -0.70, P = 0.003) and CFVR (R = -0.73, P = 0.001). The intensity of the sFCW was also significantly correlated with baseline FFR (R = 0.71, p = 0.002) and CFVR (R = 0.59, P = 0.01). Stenting of the target lesion resulted in a median 178% (interquartile range 55–280%) (P<0.0001) increase in sFCW intensity and a median 117% (interquartile range 27–509%) (P = 0.001) increase in dBEW intensity. The increase in accelerative wave intensity following PCI was proportionate to the baseline FFR and CFVR, such that stenting of lesions associated with the greatest flow limitation (lowest FFR and CFVR) resulted in the largest increases in wave intensity.

Conclusions

Increasing ischemia severity is associated with proportionate reductions in cumulative intensity of both major accelerative coronary waves. Impaired diastolic microvascular decompression may represent a novel, important pathophysiologic mechanism driving the reduction in coronary blood flow in the setting of an epicardial stenosis.

Measurement and modeling of coronary blood flow

Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.

Wave speed in human coronary arteries is not influenced by microvascular vasodilation: implications for wave intensity analysis

Wave intensity analysis and wave separation are powerful tools for interrogating coronary, myocardial and microvascular physiology. Wave speed is integral to these calculations and is usually estimated by the single-point technique (SPc), a feasible but as yet unvalidated approach in coronary vessels. We aimed to directly measure wave speed in human coronary arteries and assess the impact of adenosine and nitrate administration. In 14 patients, the transit time Δt between two pressure signals was measured in angiographically normal coronary arteries using a microcatheter equipped with two high-fidelity pressure sensors located Δs = 5 cm apart. Simultaneously, intracoronary pressure and flow velocity were measured with a dual-sensor wire to derive SPc. Actual wave speed was calculated as DNc = Δs/Δt. Hemodynamic signals were recorded at baseline and during adenosine-induced hyperemia, before and after nitroglycerin administration. The energy of separated wave intensity components was assessed using SPc and DNc. At baseline, DNc equaled SPc (15.9 ± 1.8 vs. 16.6 ± 1.5 m/s). Adenosine-induced hyperemia lowered SPc by 40 % (p < 0.005), while DNc remained unchanged, leading to marked differences in respective separated wave energies. Nitroglycerin did not affect DNc, whereas SPc transiently fell to 12.0 ± 1.2 m/s (p < 0.02). Human coronary wave speed is reliably estimated by SPc under resting conditions but not during adenosine-induced vasodilation. Since coronary wave speed is unaffected by microvascular dilation, the SPc estimate at rest can serve as surrogate for separating wave intensity signals obtained during hyperemia, thus greatly extending the scope of WIA to study coronary physiology in humans.

Novel wave intensity analysis of arterial pulse wave propagation accounting for peripheral reflections

We present a novel analysis of arterial pulse wave propagation that combines traditional wave intensity analysis with identification of Windkessel pressures to account for the effect on the pressure waveform of peripheral wave reflections. Using haemodynamic data measured in vivo in the rabbit or generated numerically in models of human compliant vessels, we show that traditional wave intensity analysis identifies the timing, direction and magnitude of the predominant waves that shape aortic pressure and flow waveforms in systole, but fails to identify the effect of peripheral reflections. These reflections persist for several cardiac cycles and make up most of the pressure waveform, especially in diastole and early systole. Ignoring peripheral reflections leads to an erroneous indication of a reflection-free period in early systole and additional error in the estimates of (i) pulse wave velocity at the ascending aorta given by the PU-loop method (9.5% error) and (ii) transit time to a dominant reflection site calculated from the wave intensity profile (27% error). These errors decreased to 1.3% and 10%, respectively, when accounting for peripheral reflections. Using our new analysis, we investigate the effect of vessel compliance and peripheral resistance on wave intensity, peripheral reflections and reflections originating in previous cardiac cycles.

Enhancing coronary Wave Intensity Analysis robustness by high order central finite differences

Background

Coronary Wave Intensity Analysis (cWIA) is a technique capable of separating the effects of proximal arterial haemodynamics from cardiac mechanics. Studies have identified WIA-derived indices that are closely correlated with several disease processes and predictive of functional recovery following myocardial infarction. The cWIA clinical application has, however, been limited by technical challenges including a lack of standardization across different studies and the derived indices' sensitivity to the processing parameters. Specifically, a critical step in WIA is the noise removal for evaluation of derivatives of the acquired signals, typically performed by applying a Savitzky–Golay filter, to reduce the high frequency acquisition noise.

Methods

The impact of the filter parameter selection on cWIA output, and on the derived clinical metrics (integral areas and peaks of the major waves), is first analysed. The sensitivity analysis is performed either by using the filter as a differentiator to calculate the signals' time derivative or by applying the filter to smooth the ensemble-averaged waveforms.

Furthermore, the power-spectrum of the ensemble-averaged waveforms contains little high-frequency components, which motivated us to propose an alternative approach to compute the time derivatives of the acquired waveforms using a central finite difference scheme.

Results and Conclusion

The cWIA output and consequently the derived clinical metrics are significantly affected by the filter parameters, irrespective of its use as a smoothing filter or a differentiator. The proposed approach is parameter-free and, when applied to the 10 in-vivo human datasets and the 50 in-vivo animal datasets, enhances the cWIA robustness by significantly reducing the outcome variability (by 60%).

Coronary wave intensity during the Valsalva manoeuvre in humans reflects altered intramural vessel compression responsible for extravascular resistance

Our aim was to investigate the effect of altered cardiac-coronary interaction during the Valsalva manoeuvre (VM) on coronary wave intensity and the response of coronary microvascular resistance. In 13 patients, left ventricular (P(LV)) and aortic pressure were measured during catheterization, together with intracoronary pressure and blood flow velocity (U) via a dual-sensor guide wire advanced into an angiographically normal coronary artery. Signals were analysed for the following phases of VM: baseline (B1), onset of strain (S1), sustained strain (S2), onset of release (R1), maximal response during recovery (R2), and baseline after VM. The immediate effects of VM were most evident from diastolic P(LV) (LVDP), which increased from 11.0 ± 2.3 to 36.4 ± 2.7 mmHg between B1 and S1 and fell from 28.3 ± 3.4 to 8.3 ± 1.9 mmHg between S2 and R1. Wave intensities and rate pressure product (RPP) were only minimally affected at these transient phases, but coronary wave energies decreased by about 50% and RPP by 38% from S1 to S2, together with a 30% depression of LVdP/dt. All signals were restored to baseline values during the recovery. U did not vary significantly throughout the VM. Despite the depressed cardiac performance during VM strain, microvascular resistance, calculated with LVDP as backpressure, decreased by 31% from B1 to S2, whereas an increase via metabolically induced vasoconstriction was expected. Since coronary U remained essentially constant despite the marked reduction in oxygen consumption, microvascular vasoconstriction must have been compensated by a decrease in the contraction-mediated impediment on coronary blood flow, as confirmed by the reduced coronary wave energies.

The multi-scale modelling of coronary blood flow

Coronary flow is governed by a number of determinants including network anatomy, systemic afterload and the mechanical interaction with the myocardium throughout the cardiac cycle. The range of spatial scales and multi-physics nature of coronary perfusion highlights a need for a multiscale framework that captures the relevant details at each level of the network. The goal of this review is to provide a compact and accessible introduction to the methodology and current state of the art application of the modelling frameworks that have been used to study the coronary circulation. We begin with a brief description of the seminal experimental observations that have motivated the development of mechanistic frameworks for understanding how myocardial mechanics influences coronary flow. These concepts are then linked to an overview of the lumped parameter models employed to test these hypotheses. We then outline the full and reduced-order (3D and 1D) continuum mechanics models based on the Navier–Stokes equations and highlight, with examples, their application regimes. At the smaller spatial scales the case for the importance of addressing the microcirculation is presented, with an emphasis on the poroelastic approach that is well-suited to bridge an existing gap in the development of an integrated whole heart model. Finally, the recent accomplishments of the wave intensity analysis and related approaches are presented and the clinical outlook for coronary flow modelling discussed.

Initiation of ventricular contraction as reflected in the aortic pressure waveform

Prior to aortic valve opening, aortic pressure is perturbed by ventricular contraction. The onset of this pressure perturbation coincides with the onset of the left ventricular (LV) isovolumic contraction, and hence will be referred to as the start of the arterially detected isovolumic contraction (AIC(start)). In the present study we test the hypothesis that the pressure perturbation indeed has a cardiac origin. In ten Yorkshire-Landrace swine, waveform intensity analysis demonstrated that AIC(start) was followed by a positive intensity wave (0.3 × 10(5) ± 0.3 × 10(5) W (m(2) s(2))(-1)). Timing analysis of LV and aortic pressure waveform showed that AIC(start) was preceded by a LV pressure perturbation (3.8 ± 1.8 ms, p < 0.001). These novel cardiac timing and aortic wave intensity findings reveal the cardiac origin of the pressure perturbation. In 15 Yorkshire-Landrace swine, myocardial motion analysis showed a significantly higher rate of segment shortening during the first part of the LV pressure perturbation. Therefore, both the LV and aortic pressure perturbation are most likely caused by the early phase of myocardial contraction, which also causes mitral valve closure. Consequently, AIC(start) is useful in the determination of the isovolumic contraction period, a well-known marker to quantify cardiac dysfunction.

Coronary-aortic interaction during ventricular isovolumic contraction

In earlier work, we suggested that the start of the isovolumic contraction period could be detected in arterial pressure waveforms as the start of a temporary pre-systolic pressure perturbation (AIC(start), start of the Arterially detected Isovolumic Contraction), and proposed the retrograde coronary blood volume flow in combination with a backwards traveling pressure wave as its most likely origin. In this study, we tested this hypothesis by means of a coronary artery occlusion protocol. In six Yorkshire × Landrace swine, we simultaneously occluded the left anterior descending (LAD) and left circumflex (LCx) artery for 5 s followed by a 20-s reperfusion period and repeated this sequence at least two more times. A similar procedure was used to occlude only the right coronary artery (RCA) and finally all three main coronary arteries simultaneously. None of the occlusion protocols caused a decrease in the arterial pressure perturbation in the aorta during occlusion (P > 0.20) nor an increase during reactive hyperemia (P > 0.22), despite a higher deceleration of coronary blood volume flow (P = 0.03) or increased coronary conductance (P = 0.04) during hyperemia. These results show that the pre-systolic aortic pressure perturbation does not originate from the coronary arteries.

Wave energy patterns of counterpulsation: a novel approach with wave intensity analysis

BACKGROUND

In counterpulsation, diastolic augmentation increases coronary blood flow and systolic unloading reduces left ventricular afterload. We present a new approach with wave intensity analysis to revisit and explain counterpulsation principles.

METHODS

In an acute porcine model, a standard intra-aortic balloon pump was placed in descending aorta in 4 pigs. We measured pressure and velocity with probes in left anterior descending artery and aorta during and without intra-aortic balloon pump assistance. Wave intensities of aortic and left coronary waves were derived from pressure and flow measurements with synchronization correction.

RESULTS

We identified predominating waves in counterpulsation. In the aorta, during diastolic augmentation, intra-aortic balloon inflation generated a backward compression wave, with a "pushing" effect toward the aortic root that translated to a forward compression wave into coronary circulation. During systolic unloading, intra-aortic balloon pump deflation generated a backward expansion wave that "sucked" blood from left coronary bed into the aorta. While this backward expansion wave translated to reduced left ventricular afterload, the "sucking" effect resulted in left coronary blood steal, as demonstrated by a forward expansion wave in left anterior descending coronary flow. The waves were sensitive to inflation and deflation timing, with just 25 ms delay from standard deflation timing leading to weaker forward expansion wave and less coronary regurgitation.

CONCLUSIONS

Intra-aortic balloon pumps generate backward-traveling waves that predominantly drive aortic and coronary blood flow during counterpulsation. Wave intensity analysis of arterial circulations may provide a mechanism to explain diastolic augmentation and systolic unloading of intra-aortic balloon pump counterpulsation.

euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling

The loss of cardiac pump function accounts for a significant increase in both mortality and morbidity in Western society, where there is currently a one in four lifetime risk, and costs associated with acute and long-term hospital treatments are accelerating. The significance of cardiac disease has motivated the application of state-of-the-art clinical imaging techniques and functional signal analysis to aid diagnosis and clinical planning. Measurements of cardiac function currently provide high-resolution datasets for characterizing cardiac patients. However, the clinical practice of using population-based metrics derived from separate image or signal-based datasets often indicates contradictory treatments plans owing to inter-individual variability in pathophysiology. To address this issue, the goal of our work, demonstrated in this study through four specific clinical applications, is to integrate multiple types of functional data into a consistent framework using multi-scale computational modelling.

Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed

A local estimation of pulse wave speed c, an important predictor of cardiovascular events, can be obtained at arterial locations where simultaneous measurements of blood pressure (P) and velocity (U), arterial diameter (D) and U, flow rate (Q) and cross-sectional area (A), or P and D are available, using the PU-loop, sum-of-squares (∑(2)), lnDU-loop, QA-loop or new D(2)P-loop methods. Here, these methods were applied to estimate c from numerically generated P, U, D, Q and A waveforms using a visco-elastic one-dimensional model of the 55 larger human systemic arteries in normal conditions. Theoretical c were calculated from the parameters of the model. Estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the ∑(2). The smaller differences between estimates and theoretical values were obtained using the D(2)P-loop method, with root-mean-square errors (RMSE) smaller than 0.18 ms(-1), followed by averaging the two c given by the PU- and lnDU-loops (RMSE <2.99 ms(-1)). In general, the errors of the PU-, lnDU- and QA-loops decreased at locations where visco-elastic effects were small and nearby junctions were well-matched for forward-travelling waves. The ∑(2) performed better at proximal locations.

Effect of the Valsalva maneuver on cardiac-coronary interaction assessed by wave intensity analysis

The Valsalva maneuver (VM) provokes strong changes in the cardiovascular system and is therefore well suited to study the cardiac-coronary interaction in humans. In 12 patients undergoing catheterization we simultaneously recorded aortic pressure, left ventricular pressure, and intracoronary pressure (Pd) and flow velocity (U) while the patients were performing a VM. Coronary wave intensity was calculated (dI = dP*dU) at characteristic phases of the VM and related to hemodynamic parameters of left ventricular (LV) performance. During the strain, blood pressure increased transiently followed by a significant decrease (p < 0.001) at maximum strain. Changes in mean LV pressure followed the same pattern, while LV end-diastolic pressure increased to almost 40 mmHg (p < 0.001), with a 30% reduction in LV dP/dt (p < 0.005). Coronary flow velocity remained fairly constant throughout the VM. All hemodynamic values returned to the baseline at conclusion of the maneuver. Coronary wave intensity was strongly reduced during the strain and was related to the depression in LV performance. Wave intensity analysis clearly revealed the inherent features of cardiac-coronary interaction.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Mechanisms of myocardium-coronary vessel interaction

The mechanisms by which the contracting myocardium exerts extravascular forces (intramyocardial pressure, IMP) on coronary blood vessels and by which it affects the coronary flow remain incompletely understood. Several myocardium-vessel interaction (MVI) mechanisms have been proposed, but none can account for all the major flow features. In the present study, we hypothesized that only a specific combination of MVI mechanisms can account for all observed coronary flow features. Three basic interaction mechanisms (time-varying elasticity, myocardial shortening-induced intracellular pressure, and ventricular cavity-induced extracellular pressure) and their combinations were analyzed based on physical principles (conservation of mass and force equilibrium) in a realistic data-based vascular network. Mechanical properties of both vessel wall and myocardium were coupled through stress analysis to simulate the response of vessels to internal blood pressure and external (myocardial) mechanical loading. Predictions of transmural dynamic vascular pressure, diameter, and flow velocity were determined under each MVI mechanism and compared with reported data. The results show that none of the three basic mechanisms alone can account for the measured data. Only the combined effect of the cavity-induced extracellular pressure and the shortening-induced intramyocyte pressure provides good agreement with the majority of measurements. These findings have important implications for elucidating the physical basis of IMP and for understanding coronary phasic flow and coronary artery and microcirculatory disease.

An introduction to wave intensity analysis

Wave intensity analysis applies methods first used to study gas dynamics to cardiovascular haemodynamics. It is based on the method of characteristics solution of the 1-D equations derived from the conservation of mass and momentum in elastic vessels. The measured waveforms of pressure P and velocity U are described as the summation of successive wavefronts that propagate forward and backward through the vessels with magnitudes dP (+/-) and dU (+/-). The net wave intensity dPdU is the flux of energy per unit area carried by the wavefronts. It is positive for forward waves and negative for backward waves, providing a convenient tool for quantifying the timing, direction and magnitude of waves. Two methods, the PU-loop and the sum of squares, are given for calculating the wave speed c from simultaneous measurements of P and U at a single location. Given c, it is possible to separate the waveforms into their forward and backward components. Finally, the reservoir-wave hypothesis that the arterial and venous pressure can be conveniently thought of as the sum of a reservoir pressure arising from the total compliance of the vessels (the Windkessel effect) and the pressure associated with the waves is discussed.