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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 (BDWdia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDWdia ) and compression (FCWdia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDWdia , FCWdia and BDWdia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDWdia , 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 (BDWdia ), as well as a forward decompression wave (FDWdia ) and forward compression wave (FCWdia ). The BDWdia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDWdia and FCWdia 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

Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.

Although adenosine markedly increases fetal pulmonary blood flow, the specific changes in pulmonary trunk (PT), ductus arteriosus (DA), and conduit pulmonary artery (PA) flow interactions that support this increased flow are unknown. To address this issue, seven anesthetized late-gestation fetal sheep were instrumented with PT, DA, and left PA micromanometer catheters and transit-time flow probes. Blood flow profile and wave intensity analyses were performed at baseline and after adenosine infusion to increase PA flow approximately fivefold. With adenosine infusion, DA mean and phasic flows were unchanged, but increases in mean PT (500 ± 256 ml/min, P = 0.002) and the combined left and right PA flow (479 ± 181 ml/min, P < 0.001) were similar (P > 0.7) and related to a larger flow-increasing forward-running compression wave arising from right ventricular (RV) impulsive contraction. Moreover, while the increased PT flow was confined to systole, the rise in PA flow spanned systole (316 ml/min) and diastole (163 ml/min). This elevated PA diastolic flow was accompanied by a 170% greater discharge from a PT and main PA reservoir filled in systole (P < 0.001), but loss of retrograde blood discharge from a conduit PA reservoir that was evident at baseline. These data suggest that 1) an increase in fetal pulmonary blood flow produced by adenosine infusion is primarily supported by a higher PT blood flow (i.e., RV output); 2) about two-thirds of this increased RV output passes into the pulmonary circulation during systole; and 3) the remainder is transiently stored in a central PT and main PA systolic reservoir, from where it discharges into the lungs in diastole.

Constriction of the fetal ductus arteriosus (DA) has disparate effects on mean and phasic hemodynamics, as mean DA blood flow is preserved until constriction is severe, but DA systolic and diastolic blood velocities change with only mild constriction. To determine the basis of this disparity and its physiological significance, seven anesthetized late-gestation fetal sheep were instrumented with pulmonary trunk (PT), DA, and left pulmonary artery (PA) micromanometer catheters and transit-time flow probes. Blood flow profile and wave intensity analyses were performed at baseline and during mild, moderate, and severe DA constriction (defined as pulmonary-aortic mean pressure differences of 4, 8, and 14 mmHg, respectively), produced with an adjustable snare. With DA constriction, mean DA flow was initially maintained but decreased with severe constriction (P < 0.05) in conjunction with a reduction (P < 0.05) in PT flow (i.e., right ventricular output). By contrast, DA systolic flow fell progressively during DA constriction (P < 0.001), due to decreased transmission of both early and midsystolic proximal flow-enhancing forward-running compression waves into the DA. However, DA constriction was also accompanied by greater systolic storage of blood in the PT and main PA (P < 0.025), and increased retrograde diastolic flow from compliant major branch PA (P < 0.001). Transductal discharge of these central and conduit PA blood reservoirs in diastole offset systolic DA flow reductions. These data suggest that, during DA constriction in the fetus, enhanced central and conduit PA reservoir function constitutes an important compensatory mechanism that contributes to preservation of mean DA flow via a systolic-to-diastolic redistribution of phasic DA flow.

OBJECTIVES: Arterial wave reflection has traditionally been quantified from pressure and flow measurements using wave separation and wave intensity (WI) analysis. In the recently proposed reservoir-wave paradigm, these analyses are performed after dividing pressure into 'reservoir' and 'excess' components, yielding a modified wave intensity (WI(RW)). This new approach has led to controversial conclusions about the nature and significance of arterial wave reflection. Our aim was to assess whether WI or WI(RW) more accurately represent wave phenomena. METHODS: We studied two computer models (a simple network and a full model of the systemic arterial tree) in which all systolic forward waves and reflection properties were known a priori. Results of these models were compared with haemodynamic measurements in the ascending aorta of five adult sheep at baseline and after incremental arterial constriction. RESULTS: The key findings of model studies were that the reservoir-wave approach markedly underestimated or eliminated reflected compression waves, overestimated or artefactually introduced forward and backward expansion waves, and displayed nonphysical interactions between distal reflection sites and early systolic waves. These errors arose because, contrary to a key assumption of the reservoir-wave approach, reservoir pressure was not spatially uniform during systole. In-vivo results were qualitatively similar to model results, with baseline WI and WI(RW) suggesting that the arterial network was dominated by positive and negative wave reflection, respectively, while under all conditions, reflected WI(RW) compression waves were substantially smaller than corresponding WI waves. CONCLUSION: We conclude that the reservoir-wave paradigm introduces error into arterial wave analyses.

Separating pressure, flow/velocity and wave intensity signals into forward and backward components provide insights about arterial wave propagation and reflection. A linear wave separation is normally used, but ignores the pressure-dependence of wave speed. While a non-linear separation could incorporate this pressure-dependence, no such method exists for wave intensity decomposition. Moreover, although linear separation errors for pressure (5-10 %) have been quantified previously, errors for velocity and wave intensity have not. Accordingly, we describe a non-linear wave separation technique based on the method of characteristics. Data from a computer model suggest that the percentage linear separation errors for velocity and wave intensity are approximately one-half and twice that for pressure, respectively. Although comparable to measurement uncertainty in many instances, linear separation errors may become more significant: (1) if wave speed varies substantially over the cardiac cycle, e.g. if pulse pressure or vessel compliance is high, (2) if the degree of wave reflection in the arterial system is large, or (3) if the constant wave speed used for the linear separation is closer to the minimum or maximum pressure-dependent value rather than the mean. Consideration of linear separation errors may therefore be important in some physiological settings.