Between June 2022 and June 2024, patients aged 18 years or older who were referred for diagnostic coronary angiography and fractional flow reserve (FFR) assessment at the Department of Cardiology, Xijing Hospital, Fourth Military Medical University, due to stable or unstable angina were screened for enrollment. Written informed consent was obtained in all patients and the study was approved by the research ethics board (Medical Ethics Committee of the First Affiliated Hospital of the Fourth Military Medical University, KY20222192-F-1). Exclusion criteria were as follows: (1) acute myocardial infarction (ST-elevation or non-ST-elevation); (2) allergy to iodine-based contrast agents; (3) significant bleeding risk or coagulation disorders (e.g., malignancy); (4) presence of anemia, infectious diseases, or severe pulmonary diseases; (5) severe ventricular arrhythmias or hemodynamic instability. Angiographic exclusion criteria included suboptimal image quality or severe vascular overlap that precluded accurate assessment.

cWIA was performed using MATLAB R2021a (MathWorks, Natick, MA, USA) to quantitatively assess energy transfer characteristics within coronary arteries. Wave speed was calculated via the single-point method, using the formula c=√(ΔP2/ΔU2) (23). A key methodological choice was to use the wave speed from the resting state for the analysis of both resting and hyperemic conditions. This decision addresses the documented issue of the single-point method underestimating wave speed during hyperemia (24), thereby ensuring a more reliable and consistent comparison between the two states. The net wave intensity (WI) was derived from arterial blood pressure and blood flow velocity signals, applying the formula WI=(dP/dt)⋅(dU/dt) (6). The resulting wave-intensity profile was automatically characterized by compression (dP/dt > 0) vs. decompression (dP/dt < 0), and was subsequently separated into its forward and backward components (6, 25). The variables of interest in this study were the peak wave energy, cumulative wave intensity, and the proportion of cumulative wave intensity of the forward compression wave (FCW), forward decompression wave (FDW), BCW and BDW under resting and hyperemic conditions. The cumulative wave intensity of each wave was calculated by measuring the area under the curve (12). The proportion of cumulative wave intensity was calculated by expressing the cumulative wave intensity of an individual wave as a percentage of the total cumulative wave intensity in the cardiac cycle (12). For reliable computational results, three consecutive cardiac cycles exhibiting stable pressure waveforms (a time period with no significant variation, defined as a variation rate of no more than 5%—in cycle duration, systolic pressure, and diastolic pressure) were chosen from both resting and hyperemic conditions. The average of the cWIA quantitative parameters derived from these three cycles were subsequently employed for statistical analysis.

All statistical analyses were carried out using GraphPad Prism 9.5.0 (GraphPad Software, La Jolla, CA, USA). Continuous variables are presented as their mean ± standard deviation. For paired measurements, differences were assessed using the paired-samples t-test if the differences were normally distributed. If the differences were not normally distributed, the paired-sample Wilcoxon signed-rank test was used. For group comparisons, the independent-samples t-test was applied if the data for each group were normally distributed and variances were equal. Otherwise, the Mann–Whitney U test was performed. Spearman's correlation coefficient was applied to evaluate linear relationships between variables. A p-value of <0.05 was considered to indicate statistical significance.

Traditional cWIA was performed based on blood flow signals measured by Doppler ultrasound technology. Due to the relatively low signal-to-noise ratio of these signals, it was necessary to ensemble the blood flow signals from multiple cycles with reference to the synchronously acquired ECG signals (26). However, as shown in Figure 2, there were certain variations in the blood flow and pressure signals of consecutive cardiac cycles, which would have a certain impact on the cWIA analysis. In this paper, the blood flow velocity signals used for cWIA analysis were calculated based on FFR and blood flow resistance model. Beat-to-beat cWIA analysis was achieved, without the need for multi-cycle signal superposition and ensemble. This method has certain advantages over traditional methods in terms of operational complexity and analysis principles. The pBCW and pBDW values calculated by our method in the resting state were on the order of 10⁵W/m²s², and the magnitudes of cBCW and cBDW were on the order of 10⁴ W/m²s, which aligns with the ranges reported in previous literature (11, 16, 27).

Coronary pulse wave speed serves as an indicator of coronary arterial wall elasticity and provides valuable insights for the diagnosis and prognosis of coronary artery disease (28, 29). In contrast to the two-point measurement technique, the single-point method offers notable advantages in the coronary arteries. The conventional approach relies on quantifying the transit time of the pressure wave between two spatially defined points (24). However, due to the limited length of coronary arteries and the challenge of obtaining adequate time intervals, this method is impractical in this vascular bed (23, 24). The single-point method, which involves simultaneous measurement of pressure and flow velocity, circumvents these limitations. While the single-point method provides reliable estimates of coronary wave speed at rest, it has been documented to underestimate wave speed by approximately 40% during hyperemia (24). Our results aligned with the aforementioned reports in that adenosine-induced hyperemia significantly reduced the pulse wave velocity calculated by the single-point method. However, the average reduction observed in this study was approximately 25%, which is slightly less than that reported in previous literature. Given this observation, the cWIA analysis for the hyperemic state in this paper still utilized the pulse wave velocity calculated under resting conditions. Furthermore, comparisons between FFR-negative and FFR-positive cohorts demonstrated no significant differences in wave speed, either at rest or during hyperemia.

The interplay between the myocardium and the coronary arteries gives the coronary arteries special pulsating nature. The BCW and BDW, which start in the microvasculature, hold most of the energy of the pulse wave, both at rest and during hyperemia. Earlier research had suggested that the BCW was related to ventricular systolic function, while the BDW more reflected ventricular diastolic function (10–12, 15). However, there hasn't been much research looking at how these two waves relate to each other. Our results indicated that BCW and BDW exhibit a very strong correlation in the resting state, for both peak and cumulative wave intensity. This strong correlation suggests that, despite appearing at different times during the cardiac cycle, the two waves may be more intrinsically linked than previously thought. Therefore, the common practice of independently considering them as distinct indicators of systolic or diastolic function, as done in the past, is debatable. Our findings point to the need for a more integrated understanding of their relationship in the assessment of coronary physiology.

Only a limited number of studies had investigated the impact of adenosine on quantitative cWIA parameters. Claridge et al. reported significant increases in both cBCW and cBDW from measurements in 36 vessels across 8 subjects following adenosine administration (11). Similarly, DeMarchi et al. observed a significant rise in cBDW induced by adenosine (26). However, our results presented a contrasting picture: adenosine-induced hyperemia led to a significant increase in pBCW and cBCW, but a significant decrease in pBDW, with no significant effect on cBDW. This discrepancy might stem from methodological differences: DeMarchi et al. required alignment and reconstruction of 30-s continuously acquired raw pressure and blood flow velocity data based on ECG (26). Given adenosine's very short half-life [typically around 20 s (30)], this extended data segment may have inadvertently included phases where adenosine's effect was diminishing. In contrast, our study analyzed data from independent cardiac cycles, ensuring greater temporal accuracy of the data. Furthermore, our results were consistent with the observed cWIA waveform changes: the BDW waveform exhibited a lower peak and a longer duration during hyperemia. The hemodynamic changes induced by adenosine are relatively complex: in addition to the significant increase in diastolic blood flow velocity caused by microvascular dilation, a notable decrease in perfusion pressure can also be clearly observed, which may have an impact on the myocardial-coronary interaction. Our results suggest that the interaction between myocardial relaxation and coronary blood flow become less intense but more prolonged under hyperemic conditions. In addition, it can be seen from the experimental results that the quantitative parameters of cWIA are greatly affected by adenosine, which suggests that changes in the baseline hemodynamic state have a significant impact on the quantitative analysis of cWIA. When attempting to investigate the relationship between the absolute values of these parameters and various physiological or pathological changes, special attention must be paid to the corresponding baseline hemodynamic state.

Conflicting reports existed regarding the influence of functional stenosis on quantitative cWIA parameters. Narayan et al. compared cWIA parameters in 17 patients before and after percutaneous coronary intervention (PCI) and found significant increases in cBDW post-PCI (31). In contrast, DeMarchi et al. reported no significant correlation between BDW quantitative parameters and the presence of stenotic lesions (26). Our results indicated that while there were some differences in cWIA wave quantitative parameters between the FFR-positive and FFR-negative groups, these differences did not reach statistical significance. We therefore hypothesized that despite functional stenosis leading to a reduction in distal perfusion pressure and associated blood flow, its impact on the interaction between the myocardium and coronary blood flow was limited.

It is generally believed that the interaction between the myocardium and coronary blood flow is significantly weaker in the RCA compared to the LAD, primarily due to the substantially lower pressures in the right ventricle (25). However, our results showed no significant differences in the quantitative parameters of the microvascular-originated waves between these two vessel types, regardless of whether in a resting or hyperemic state, or during systole or diastole. We further analyzed the pressure and flow velocity waveforms collected from RCA cases. Among 23 RCA vessels, 21 exhibited instances where P_d was greater than P_a during systole, leading to clearly observable retrograde blood flow. Our findings point to the possibility that the myocardial-coronary interaction also significantly influences the pulsatile flow pattern in the RCA, a hypothesis that warrants further investigation.

Several limitations of this study warrant consideration. First, the blood flow calculation method employed in this study was applicable only to patients with epicardial obstructive lesions who underwent FFR examination. This inherent selection criterion might introduce a degree of bias into the patient cohort. Second, individual variability in blood viscosity and rheology—a well-recognized challenge across CFD-based methodologies—may introduce deviations in our calculation results, which might be a potential source of systematic error. Third, the number of FFR-positive cases and RCA cases included in this study was relatively small. Despite our current statistical findings of no significant impact on the cWIA quantification results, future research is warranted to expand the sample size for further validation. Finally, due to existing constraints, this study was unable to investigate the clinical diagnostic value of cWIA quantitative parameters in coronary artery disease, a crucial area for future research.