Our study adhered to the Declaration of Helsinki and postoperative ethical standards. The ethics committee of the Nanjing First Hospital approved this study (Grant No. KY20220518-KS-01) and waived the need for informed consent.

We retrospectively collected data from 419 adult patients who had undergone non-isolated CABG surgery in the intensive care unit (ICU) of Nanjing First Hospital from April 2019 to February 2022, from electronic medical records (EMR) and physiological monitors. All patients included in this study underwent CABG for documented coronary artery disease. Concurrently, some patients underwent additional cardiac procedures due to coexisting cardiac pathologies (such as valvular disease, aortic pathology, or congenital anomalies) as shown in Table 1. Patients were excluded under the following conditions: (i) if they underwent isolated CABG (CABG only) without any concomitant procedure; (ii) if they had LCOS within 1 hour; and (iii) if they died or were discharged during or within 48 hours after surgery. Patients who had LCOS within 1 hour were excluded to avoid confounding by transient hemodynamic instability associated with anesthesia emergence, rewarming, or immediate post-bypass circulatory adjustment, which often resolves spontaneously without therapeutic intervention [3]. The study included 378 patients, which was in accordance with the sample size requirements of the binary outcome prediction model [15].

The outcome was the occurrence of LCOS between 1 h and 48 h postoperatively. With reference to Hong et al. [3], we set three LCOS-defining criteria as follows: (i) a cardiac index (CI) reduced to < 2.2 L/min/m²; (ii) systolic blood pressure > 90 mmHg with signs of tissue hypoperfusion, including oliguria (urine output < 1 mL/kg·h), and/or elevated lactate (Lac) level (> 3.0 mmol/L) persisting for > 10 minutes; (iii) the requirement of mechanical circulatory support or the simultaneous administration of two or more inotropic agents (such as dopamine, dobutamine, milrinone, or levosimendan) for ≥ 12 hours to maintain hemodynamics after optimizing preload. This composite approach reflects the heterogeneous clinical presentation of LCOS and enhances sensitivity in capturing cases that may not satisfy all criteria simultaneously. Isolated reliance on any single criterion, such as CI only, may lead to missing patients with clinically significant hypoperfusion despite preserved CI, or those requiring prolonged inotropic support without documented low CI [1]. LCOS was not diagnosed in patients who received vasoconstrictive drugs to increase peripheral vascular resistance while maintaining normal cardiac output. LCOS was diagnosed if the patient met ≥ 1 of the criteria. CI and Lac measurements were routinely obtained for all patients as part of standardized postoperative monitoring. CI was measured using invasive hemodynamic monitoring, which is routinely applied in non‑isolated CABG cases. Lac was measured for all patients immediately upon ICU admission.

Based on previous studies [3, 11], we selected and extracted potential predictors of LCOS from the EMR database. Demographic data were collected for age, sex, weight (kg), height (m), and body mass index (BMI, kg/m²). Echocardiographic parameters [16] collected using color Doppler ultrasound at the patientʼs bedside before surgery included measurements of the aortic diameter (AoD), left atrial diameter (LAD), left ventricular end-systolic diameter (LVDs), left ventricular posterior wall thickness (LVPW), ejection fraction (EF), and fractional shortening (FS). Preoperative laboratory indicators included white blood cell (WBC), Alpha-1 Antitrypsin (AAT), thyroid-stimulating hormone (TSH), low-density lipoprotein (LDL), thyroxine (T4), Lac, indirect bilirubin, direct bilirubin, total bilirubin, lymphocyte, aminomethyltransferase (AMT), urea, globulin, Triiodothyronine (T3), hemoglobin, platelet (PLT), neutrophil, total protein, and maximum preoperative creatinine (preop_max_cr). Patientʼs operation time (optime), the utilization of cardiopulmonary bypass (CPB) time (cpbtime), and aortic cross-clamping time (actime) were additionally recorded.

To better characterize the hemodynamic status, we calculated the time, area under the curve (AUC), and time-weighted AUC (TWA) below the thresholds for mean arterial pressure (MAP) (< 65, < 60, < 55, and < 50 mmHg) and above the thresholds for central venous pressure (CVP) (> 12, > 16, and > 20 mmHg) using the time-series data automatically recorded by the intraoperative monitor.

The first value of Lac was recorded within 30 minutes postoperatively, between discharge from non-isolated CABG surgery in the operating theatre and admission to the ICU.

The outcome was the development of LCOS > 1 hour after surgery. There were no uniform clinical criteria to define LCOS. Thus, we referred to and applied the definition set in the study by Hong et al. [3].

In this dataset, variables with missing values > 15 % were excluded. The missing values were imputed using the K-Nearest Neighbors (KNN) method. The dataset was divided into training and test sets in a 7:3 ratio to prevent overfitting. To eliminate the dimensional influence of different features and improve the model accuracy and training speed, the segmented data were normalized. The training set was used for feature selection, fitting the model, and adjusting the hyperparameters, while the test set was used for internal validation to assess the modelʼs ability to generalize unknown data.

In the training set, univariate regression analysis was initially performed on 53 candidate predictors, and all variables with p < 0.1 were further included in the least absolute shrinkage and selection operator (LASSO) regression. LASSO introduces the L1 paradigm penalty as a regularization term based on the traditional linear regression model, which can compress the coefficients of unimportant variables to 0, thereby enabling automatic feature selection [17]. We assessed multicollinearity among the selected variables using the variance inflation factor (VIF) < 5. Features showing high collinearity (VIF > 5) were excluded to ensure model stability [18].

To build the best prediction model, we selected five algorithms—including L2 regularized LR (LR with L2), RF classifier (RFC), XGB, light gradient boosting machine (LGBM), and SVM—to develop predictive models based on the training set. In the training set, a grid search method with ten-fold cross-validation was used to find the best hyperparameters for each model (Table S1).

In the test set, the AUC quantified the discriminative ability of the model. Sensitivity, specificity, precision, and accuracy of the model were calculated by determining the optimal threshold based on the maximum Youden index. Moreover, the area under the precision-recall curve (AUPRC) was calculated to evaluate model performance amidst unbalanced data. Sensitivity analysis was conducted to assess the potential risk of data leakage between the LCOS definition and the predictor sets, particularly regarding the model’s predictive performance’s potential over-reliance on early Lac indicators involved in the diagnosis of LCOS. Using the same hyperparameters as the prediction model, a model was constructed without incorporating postoperative Lac characteristics. Furthermore, we calculated the area under the receiver operating characteristic curve (AUROC) and other evaluation indicators for both models on independent test sets and compared the differences in AUROC between the two models using the DeLong test, 95% CI was also reported. We also considered precision and recall. Positive predictive value (PPV) was used to assess the accuracy of the model in predicting the occurrence of low cardiac output in patients. Recall was used to assess the performance of the model in identifying the actual occurrence of low cardiac output. A lower Brier score indicates a more accurate probabilistic prediction by the model. Calibration curves were used to evaluate the concordance between the predicted probability of the model and the actual observed occurrence. The decision curve analysis (DCA) was carried out to evaluate the clinical utility of the predictive models [19]. We are convinced that the optimal model results from rigorous evaluation. In addition, an interactive web calculator was built with Streamlit (https://lcos-cabg-xgb-model.streamlit.app/).

We used Shapley Additive exPlanations (SHAP) [20] to compute the SHAP value for each feature in the prediction model. The SHAP summary bar chart illustrates the significant impact of each feature on predicting LCOS, providing insight into the modelʼs predictions.

Upon assessment by the Shapiro-Wilk test, continuous variables that were normally distributed were analyzed using Studentʼs t-test, with results presented as the median [interquartile range (IQR)]. Non-normally distributed continuous variables were tested using the Mann-Whitney U-test and expressed as the median (IQR). Categorical variables were tested using the chi-square test or Fisherʼs exact test and expressed as a percentage. To analyse the differences in the data distributions and their significance, we compared the data balance between the LCOS and non-LCOS groups as well as between the training and test sets. The R programming language (version 4.3.2) was used for data visualization and statistical analysis, while Python (version 3.8.10) was used for ML operations. p-values were considered statistically significant when they were less than 0.05. All p-values were two-tailed.

378 patients were included in this study (Figure 1). 121 (32.0%) of the included patients developed LCOS, out of which 11 had CABG only, 23 developed LCOS within 1 hour after surgery, and 7 died or were discharged within 48 hours after surgery. The study population comprised 69.3% males, with the overall population’s median age being 68.00 (IQR, 62.00–73.25).

Table 1 and Table S2 show the baseline data for LCOS and non-LCOS cohorts. It was observed that sex, age, AAT, AoD, optime, cpbtime, actime, and time-weighted AUC (TWA-MAP, with thresholds set at 65, 60, 55, and 50; as well as TWA-CVP, with thresholds set at 16 mmHg and 20 mmHg) did not significantly differ between patients with and without LCOS (p > 0.05).

The study’s feature selection employed the LASSO regression incorporated with all variables. The model’s resultant output highlighted 9 key variables: preop_max_cr (1 mg/dL = 88.4 μmol/L), direct bilirubin (1 mg/dL = 17.1 µmol/L), lymphocyte, T3, EF, LVDs, MAP_55_time, BMI, and Lac (1 mmol/L = 9.0 mg/dL). All correlations between the output features and predictive output of the study’s model were further evaluated using SHAP, with the outcome shown in Figure 2A. The interactive web-based calculator can be accessed via https://lcos-cabg-xgb-model.streamlit.app/.

Although the AUC of the model without Lac (0.842) showed a marginal difference from the AUC of the Lac-incorporated model (0.868), which was observed to be very close, with significant overlap in CI noted, the observed difference was not statistically significant. This therefore suggests that the model’s predictive ability does not significantly decrease with the exclusion of variables such as Lac from the postoperative data, thus highlighting the robustness of the model. Inferentially, the risk of data leakage is relatively low (Table S3 and Table S4).

The predictive outcome of the chosen model, XGB, was subjected to the SHAP algorithm for further visualized interpretation. Figure 2A summarily presents a visualized ranking of the features in order of their impact on the model’s predictive output. The three most influential features on the model’s predictive output were EF, LVDs, and Lac (Figure 2A). SHAP value distributions of the various features included in the model are represented by beeswarm plots (Figure 2B). This visualized chart combines feature importance and feature impact to provide an overview of the distribution of SHAP values for each feature. A higher SHAP value was depicted by the redder sample swarm and consequently implied an increased likelihood of developing LCOS. The red colour correlates with the increased likelihood of developing LCOS. This implies an inverse association between EF and low cardiac output, while suggesting a direct relationship between low cardiac output and both Lac and LVDs (Figure 2B).

To enhance the usefulness of the model in real-world clinical settings, a user-friendly, interactive web-based tool (https://lcos-cabg-xgb-model.streamlit.app/) was developed for early postoperative risk stratification, specifically during the immediate postoperative period upon ICU admission after non-isolated CABG. The web-based calculator requires clinicians to input the nine key predictors, including preop_max_cr, direct bilirubin, lymphocyte, T3, EF, LVDs, MAP_55_time, BMI, and Lac, to generate a personalized predicted risk of LCOS, which is presented both numerically and graphically. The developed model incorporates readily available clinical and laboratory variables for early LCOS risk stratification and hence enhances its application in routine care. Furthermore, the transparency offered by the visual interpretability of feature contributions enhances clinicians’ understanding and clinical acceptance, facilitating informed decision-making.

Our current study was characterized by several strengths. Firstly, we developed an ML-based model specifically for predicting LCOS after non-isolated CABG surgery. Secondly, the user-friendly design of the web-based calculator renders the model readily accessible for clinicians, using variables easily accessible from hospital EMR. Thirdly, unlike conventional statistical scoring models, our model employed advanced ML algorithms to significantly reduce the risk of bias in the substantial dataset, thereby improving prediction accuracy. Finally, the dataset was characterized by a large and broader spectrum of variables, including multi-period variables such as laboratory testing, hemodynamic monitoring, and demographic information, which provided improved risk classification [36].

Despite the strengths noted, the study was also marked by limitations. As a single-center retrospective study with a relatively modest sample size, the generalizability of the findings may be limited by the custom demographic characteristics of the study population and variability in institutional practices. For instance, myocardial protection interventions such as cardioplegia type and temperature management, inotrope and vasopressor protocols including timing, agent selection, and thresholds for initiation, and hemodynamic monitoring practices such as routine use of pulmonary artery catheters, cardiac output measurement frequency, can be significantly variable across cardiac surgical centers, thus highlighting the need for external validation. In effect, the incidence of LCOS and the predictor data obtained from patients may be influenced by these noted differences across centers, likely altering the discrimination and calibration of the model when externally applied. Notably, this study was marked by limitations in providing a fully comprehensive presentation of all patient characteristics due to the inherent complexity of cardiac surgical practice, thereby resulting in a certain degree of clinical heterogeneity of our study population. In addition, the potential introduction of heterogeneity within the LCOS cohort may result from the multiple diagnostic criteria employed by the study. Another limitation observed was that the modelʼs calibration in extremely high-risk patients required cautious interpretation, and as such, further evaluation through multicenter studies with external validation in larger cohorts is recommended. Another inherent limitation associated with our study is the possible overestimation of the modelʼs discriminatory performance due to the dual role of Lac as both a predictor and a component of the outcome definition. Moreover, overfitting generally remains a concern in any predictive modeling study, particularly in studies where sample size is relatively modest and associated with numerous candidate predictive variables [15]. Although we employed regularization strategies as demonstrated in Figure S2 and Table S5, it is important to note that the model may still be associated with some degree of noise custom to our dataset, emphasizing the need for external validation in a larger, independent cohort to assure robustness and generalizability during application in a real-world clinical setting. Finally, prospective studies may be further explored to further assess the modelʼs predictive performance and practical effect on the prevention and management of LCOS after non-isolated CABG.

The study developed ML-based models for early prediction of LCOS following non-isolated CABG surgery, with the XGB model showing the best performance. The model’s output was based on nine specific predictors, with EF, LVDs, and Lac levels emerging as the most clinically significant, demonstrating good explainability. It thus enhances clinical acceptance, aids risk stratification, and ultimately enhances early detection of LCOS risk. Nonetheless, prospective external validation via a multicenter study in a larger cohort is recommended to enhance its reassurance in clinical application.