Comprehensive conventional TTE at rest was performed using a commercially available ultrasound machine (Vivid E95, GE HealthCare, Horten, Norway), based on the latest guideline (17). Left ventricular ejection fraction (LVEF) was calculated by the biplane Simpson's method. The left atrial volume index (LAVI) was calculated as left atrial volume divided by body surface area. In the apical four-chamber view, Doppler ultrasound was applied to measure mitral valve inflow. Accordingly, mitral valve septal annulus movement was recorded by tissue Doppler imaging.

Baseline two-dimensional grayscale images were initially recorded from the apical four-chamber, three-chamber, and two-chamber views at frame rates ranging from 50 to 80 fps to facilitate speckle-tracking and myocardial work analysis. We then used Doppler mapping with a 0.25 m/s velocity scale to find the baseline LAD. The scale was actively modified to provide optimal images. The mid-distal LAD was searched in modified apical two- and three-chamber views or modified parasternal short- and long-axis views. A sample volume (1.5–2 mm) was placed on the color signal in the mid-distal LAD to obtain pulse-wave Doppler flowmetry. Finally, the patients underwent regadenoson SE under a dose of 0.4 mg bolus injection according to the latest guideline (18). Pulse-wave Doppler flowmetry of mid-distal LAD and cine loop of apical four-chamber, three-chamber, and two-chamber views at hyperemic peak were recorded for CFVR analysis or stress myocardial work analysis. The interruption criteria were severe, intolerable chest pain, intolerable dyspnea, marked electrocardiography positivity, significant arrhythmia, excessive hypotension [systolic blood pressure (SBP) ≤ 90 mmHg, diastolic blood pressure (DBP) ≤ 60 mmHg], or hypertension (SBP ≥ 220 mmHg, DBP ≥ 120 mmHg). Blood pressure was recorded at baseline and 1 min intervals after regadenoson injection. CFVR was defined as the ratio between hyperemic peak and baseline diastolic coronary flow velocities. CFVR < 2.5 was defined as ischemia. The examination was performed under continuous electrocardiography and blood pressure monitoring. The aminophylline was prepared to reverse regadenoson in necessity.

Left ventricular global longitudinal strain (GLS) was analyzed on a vendor-specific workstation (Echopac version 204; GE Vingmed Ultrasound AS, GE Medical Systems). Following the initiation of the Q-analysis module and manual adjustment of the LV endocardium, the workstation tracked the LV endocardium automatically. The GLS was calculated from the average longitudinal strain of all the LV segments.

MW was calculated on the same workstation. In the dynamic video of the apical three-chamber view, the first frame of the opening and closure of the aortic and mitral valves was selected as the time point of valve switching. After calculating the strain, inputting the stored branchial blood pressure, and identifying the opening and closure of the mitral valve and aortic valve, we could obtain the non-invasive LV pressure–strain loop (LV PSL). Global work index (GWI) is the total work done by the ventricle during mechanical systole (area within the LV PSL curve). Global contractive work (GCW) is positive work performed by a segment in systole and negative work (segment lengthening) during isovolumic relaxation. Global waste work (GWW) is negative work (segment lengthening) during systole and positive work (segment shortening) during isovolumic relaxation. Global work efficiency (GWE) is equal to GCW/(GCW + GWW).

GLS and MW were measured both at baseline and at hyperemic peak. The reserve of LVEF, GLS, or MW is defined as the difference between the peak state and baseline state divided by the baseline state, recorded as Δ.

All the patients underwent either coronary angiography or coronary CT angiography. The interval between coronary angiography/coronary CT and SE should be no more than 3 months. Obstructive coronary artery disease (CAD) was defined as ≥50% stenosis in one or more major epicardial vessels.

The statistical analysis was performed by SPSS version 25.0 (IBM Corp., Armonk, NY, USA), Medcalc 18.2.1 (MedCalc Software, Ltd., Ostend, Belgium), GraphPad Prism 8.0 (GraphPad Software, Boston, MA, USA), and R version 4.2.3 (R Foundation for Statistical Computing, Vienna, Austria). According to a normal distribution, continuous variables were presented as mean ± SD or median (Q1, Q3). Categorical variables were expressed as number (%). Accordingly, continuous variables were compared either by Student's t-test or Mann–Whitney U test. Parameters of pre- and post-stress were compared by paired rank sum tests or t-tests. The categorical data were analyzed by chi-squared tests or Fisher's exact tests. To avoid problems of overfitting and collinearity, multicollinearity was assessed using collinearity diagnostics (i.e., variance inflation factor >10). The correlation between continuous variables was tested using Spearman's or Pearson's correlation. The independent correlation with CFVR was tested with multivariate stepwise logistic regression. The diagnostic performance of the model and variables was reflected by the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The calibration of the model was reflected by the calibration curve. The model was validated in the validation cohort. All tests were two-sided, and P < 0.05 was statistically significant.

The study prospectively included 126 patients with known or suspected coronary artery disease. Eleven patients were excluded (four with inadequate acoustic window, three with insufficient raw data for analysis, two with significant valvular disease, one with atrial fibrillation, one with extensive hypotension), and 115 patients were included in the study. There were 48 patients with CFVR < 2.5, accounting for 41.74% of the study (Figure 1). All the demographic data, clinical characteristics, coronary status, laboratory results, and current medication treatment were compared between the two groups in Table 1. The average age of the enrolled population was 61.00 (56–66.5) years; 61.40% of the subjects were male. As shown in Table 1, there are 64 (55.65%) patients with obstructive CAD. Of these patients, 25% had coronary stenosis between 50% and 70%, and 35.4% had coronary stenosis of 70% or more. Approximately 55.65% of patients' culprit vessel was LAD. There were no significant differences between the two groups in the culprit vessels, stenosis rate, and the number of coronary arteries involved. Patients with CFVR < 2.5 tended to be older (P = 0.016) and have lower hemoglobin (P = 0.005) than those in patients with CFVR > 2.5. In addition, the baseline characteristics of the two groups were not statistically different.

The cardiac chamber quantification, left ventricular systolic function, and diastolic function were compared between the two groups, shown in Table 2. There was no statistical difference in any of the conventional echocardiographic parameters between the two groups.

We assessed multicollinearity by collinearity diagnosis (tolerance < 0.1, variance inflation factor >10). Firstly, univariate logistic regression was performed. The parameters with P < 0.1 were selected for multivariate logistic regression. The diagnostic value of the parameters was evaluated by receiver operating characteristic (ROC) curves, and the area under the curve (AUC) was calculated (Supplementary Table S1). ΔGCW was the single index with the highest diagnostic value (Supplementary Table S1). Age, Hb, △SBP, △LVEF, △GWI, Peak GCW, and △GCW were all included in the multivariate logistic regression. Hb (OR = 0.971, P = 0.008) and △GCW (OR = 0.894, P = 0.002) were independent predictors of CFVR abnormality after adjusting for confounders (Table 4).

We then developed a full model integrating Hb and ΔGCW. The ROC curve of the model had an AUC of 0.844, and ΔGCW contributed most to the discrimination of myocardial ischemia (Table 5, Figure 3A, Supplementary Table S1). ΔGCW was moderately related to CFVR (rho = 0.467, P < 0.001) (Supplementary Figure S1). The calibration ability of the model was evaluated by the Hosmer–Lemeshow goodness of fit (χ² = 4.7337, P = 0.785) and calibration curve (Figure 3B). The decision curve analysis reflects the benefits of the full model compared with a single indicator for the identification of high-risk populations and further clinical management (Figure 3C). The CFVR < 2.5 probability developed by the logistic regression was expressed as follows: probability of CFVR < 2.5 = 1{1+exp[−Logit(P)]}, Logit(P) = 3.972 − 0.03 × Hb − 0.134 × ΔGCW. A personal myocardial ischemia could be conveniently calculated using nomography (Figure 3D). The different sensitivity and specificity of the model at different cutoff points were displayed in Supplementary Table S2. We defined the probability of 20% and 70% as the cutoff value of low, medium, and high risk. Among 22 patients classified into the high-risk group, 19 patients (86.36%) were proven to have myocardial ischemia. However, in 30 patients with a probability of <20%, only 2 patients (6.67%) had myocardial ischemia (Figure 3E).

Finally, the predictive ability of the model was validated in a group of 62 patients. In this cohort, 31 patients (50%) had CFVR < 2.5. Of these 62 patients, 20 patients were defined as low risk, 16 (80%) of whom had true-negative diagnoses. In contrast, 10 patients were classified as high risk and were then totally confirmed as CFVR < 2.5 (Supplementary Figures S2A,B). The model showed good discrimination between patients with high risk and low risk of ischemia (AUC = 0.82) in the validation cohort (Supplementary Figure 2C).

The reproducibility of MW was tested in 20 patients. Excellent intra-observer and inter-observer variabilities were observed in the measurement of MW parameters, which were demonstrated by intra-class correlation (ICC) (Supplementary Table S3) and Bland–Altman plots (Supplementary Figure S3).

In the present study, general myocardial mechanical indices such as RWMA and GLS at rest and stress were not statistically significant between the two groups (19–22). Peak GLS only achieved an AUC of 0.581 (0.473–0.690) to predict CFVR abnormality, while ΔGCW achieved 0.777 (0.694–0.861) (Supplementary Table S1). MW is superior in the following aspects: Firstly, LV PSL is measured during the whole cardiac cycle, reflecting the energy utilization throughout the cardiac cycle (15). The use of multiple MW indices allows for quantitative evaluation of positive and negative output (23). Secondly, MW could overcome the afterload-dependent limitation of strain (24–26). Our study further demonstrates that the reserve of MW (ΔGCW) is a more accurate predictor of myocardial ischemia in CCS the absolute values of MW. In the ischemia group, the vasodilator would induce horizontal and vertical steel in the blood supply, resulting in uncoordinated local myocardial motion, impaired cardiac output. The GCW has precisely quantified the energy consumed by the myocardium that effectively contributes to cardiac output. Our study is consistent with the studies of Guo et al. (19) and Leitman et al. (27); GCW was sensitive to functional myocardial ischemia. But it is not consistent with Liu et al.'s (22) study that peak GLS differs in the coronary microvascular disease (CMD) group and the non-CMD group. It is possible that Liu et al.'s study was established in angina with non-obstructive coronary arteries rather than in heterogenous CCS. Consequently, the utilization of MW reserve in the diagnosis of myocardial ischemia may circumvent the intricacies and heterogeneities of CCS, offering a comparatively objective indicator of how diverse subtypes of CCS respond to stressors.

Moreover, we conduct a novel diagnostic model to predict myocardial ischemia in CCS, which is currently lacking. In the multivariate diagnostic model, we include ΔGCW and Hb to increase the diagnostic value from 0.777 to 0.844. Our study demonstrated that Hb is an independent risk factor for myocardial ischemia (OR = 0.971, 95% CI: 0.949–0.992), which is consistent with the ARIC cohort study. The ARIC study may be the first to suggest that anemia is an independent risk factor for ischemia-related cardiovascular outcomes in the general population (HR = 1.41, 95% CI: 1.01–1.95) (28). Numerous studies have also shown that anemia is associated with poor outcomes in patients with cardiovascular disease due to chronic inflammation, inhibition of the renin–angiotensin–aldosterone system, and renal dysfunction (29–31). The degree of anemia is therefore associated with myocardial ischemia.

A combination of clinical data and stress MW indices in a multivariate model might rectify the overlap of a single factor between the two groups. A further invasive investigation into coronary physiology could be more costly and technically challenging. With a probability calculator in this study, the probability of myocardial ischemia is very low if the probability is below 20%. Of the 30 participants in this study with a probability below 20%, only 2 had myocardial ischemia. These patients could be free from further invasive coronary physiology investigation. Those with a probability of >70% were classified into the high-risk category. The probability of myocardial ischemia is relatively high among 22 patients at high risk. Only three did not have myocardial ischemia. Tight control of lipid levels, the use of anti-angina therapy, and outpatient follow-up are essential if additional testing is not preferred. Additional testing is needed for those with moderate-risk (probability 20%–70%). The model was also applied in the validation cohort, which also showed good discrimination. The algorithm provides a framework that can be used to determine identified probability in the diagnosis of myocardial ischemia, based on a clinical and an echocardiographic parameter, rather than a binary category (present or absent).

Reserve of MW could help us infer the probability of CFVR abnormality in vasodilator SE. Although this study was based on vasodilator stress, it also suggests that myocardial work reserve might be used to predict CFVR in situations with low CFVR success rates. The probability of myocardial ischemia in CCS could be calculated through the nomogram. The calculated likelihoods can assist clinicians in making clinical decisions.

There are several potential limitations of the study. Firstly, this study was conducted at a single center with a small sample size, which may lead to statistical error. Further large-scale and multicenter studies need to verify the preliminary results. Secondly, the definition of myocardial ischemia was a CFVR abnormality. However, we merely measured CFVR in LAD. Myocardial ischemia in other coronary territories may be misdiagnosed. However, a study has shown that the LAD supplies approximately half of the myocardium, and ischemia in the region of LAD is strongly associated with prognosis (8). In the following study, we will validate the relation between MW and myocardial ischemia by SPECT or PET. Thirdly, only the response of MW to regadenoson was studied, and it remains unclear how MW in CCS changes under other stress modalities.