This diagnostic modeling study was conducted retrospectively at a single cardiology center in Aoyang Hospital. The study focused on creating and internally validating a multivariable prediction model for pulmonary congestion in patients with HF and permanent AF, using non-invasive hemodynamic, echocardiographic, and clinical parameters.

Patients hospitalized from January 2021 to December 2022 were assessed using predefined eligibility criteria (Table 1). All included patients met the diagnostic criteria for HF and permanent AF based on the European Society of Cardiology (ESC) guidelines [11, 12]. Baseline clinical, echocardiographic, and impedance cardiography data were collected.

Pulmonary congestion, as the study outcome, was defined based on admission chest X-ray findings, interpreted by a board-certified radiologist, and reviewed by two experienced cardiologists from the heart failure center, both of whom were blinded to the clinical data. Radiographic criteria included dilated pulmonary veins, interstitial or alveolar edema patterns (e.g., Kerley B lines, peribronchial cuffing), bilateral hilar blurring, and increased pulmonary vascular markings. Patients were then categorized into a pulmonary congestion group or a non-pulmonary congestion group accordingly (Fig. 1).

Fig. 1.

Study design and procedures.

Ethical approval was secured by Aoyang Hospital ((2024) Ethics Approval No. 003). Consent was waived due to retrospective data.

Candidate predictors were selected from three main domains: demographic and clinical characteristics, laboratory measurements, and non-invasive cardiovascular assessments, including transthoracic echocardiography and ICG. Data were collected within the initial 24 hours of admission from the institutional electronic medical records. Only patients with complete datasets for all candidate variables were included in the analysis to ensure data integrity and prevent bias due to imputation.

Blood pressure and cardiac rhythm metrics were obtained from 24-hour Holter monitoring. Laboratory markers included N-terminal pro-B-type natriuretic peptide (NT-pro-BNP), high-sensitivity cardiac troponin (Hs-cTn), estimated creatinine clearance (using the Cockcroft-Gault formula), serum albumin, hemoglobin, thyroid-stimulating hormone (TSH), total cholesterol, low-density lipoprotein (LDL), and alanine aminotransferase (ALT).

Transthoracic echocardiographic parameters comprised left atrial transverse diameter (LATD), left atrial volume index (LAVI), left ventricular end-diastolic diameter (LVEDD), left ventricular ejection fraction (LVEF), E/e′ ratio, and stroke volume. Given the irregular R-R intervals in patients with AF, echocardiographic measurements were acquired under specific methodological considerations to ensure reliability. For parameters sensitive to beat-to-beat variability, such as LVEF and E/e′ ratio, data were averaged across five consecutive cardiac cycles with visually stable heart rates and image quality following current echocardiographic guidelines for AF [13]. To minimize intra-observer variability, all echocardiographic measurements were conducted by certified senior sonographers and reviewed by two blinded cardiologists from the heart failure center. LVEF was determined via the biplane Simpson method, while the E/e′ ratio was calculated from the mean of the septal and lateral e′ velocities. Transthoracic echocardiography was conducted with the Philips iE33 system and QLAB software (Philips Medical Systems, Andover, MA, USA).

Thirteen hemodynamic variables derived from impedance cardiography (ICG) were considered as candidate predictors: cardiac index (CI), stroke index (SI), chronotropy, stroke volume variation (SVV), thoracic fluid conductivity (TFC), systemic vascular resistance (SVR), stroke systemic vascular resistance index (SSVRI), ejection-phase contraction index (EPCI), left ventricular stroke work index (LSWI), inotropic state index (ISI), contractile inotropy, left ventricular ejection time (LVET), and preejection phase (PEP). These measurements were acquired using the CSM3000 Hemodynamic Monitoring System (Qianfan Medical Co., Ltd, Shenzhen, China). Definitions of each variable are listed in Table 2.

ICG is a non-invasive technique for continuously evaluating thoracic hemodynamics through impedance changes. These variations reflect changes in tissue conductivity caused by fluctuations in intrathoracic blood volume and flow during the cardiac cycle.

The procedure was performed in a resting supine position, under stable hemodynamic conditions, and required minimal patient cooperation. Four pairs of surface electrodes were applied: two pairs positioned on the neck and two on the chest. At each site, one pair delivered an alternating current characterized by high frequency and low amplitude, while the other pair detected impedance changes. After signal rectification, real-time thoracic impedance waveforms were generated, from which hemodynamic indices were calculated by the internal algorithms [14]. The illustrative depiction of the electrode configuration is shown in Fig. 2. In patients with AF, irregular RR intervals may affect aortic blood volume fluctuations and subsequently influence ICG measurements. To minimize this impact, we implemented strict patient screening, included only ICG data recorded during relatively stable heart rate periods, and excluded recordings with poor signal quality or significant heart rate variability. Additionally, all ICG-derived parameters were calculated as the average of 5 to 10 cardiac cycles with visually stable RR intervals to ensure measurement reliability and reproducibility in the setting of AF. These measures enhance the reliability and validity of the ICG-derived parameters in this study.

Fig. 2.

Schematic illustration of the impedance cardiography (ICG) principle and measurement workflow. Impedance is measured based on Ohm’s law. The process includes: delivery of a high-frequency low-amplitude current, selection of the aortic segment as the measurement pathway, monitoring of cardiac systole and diastole, detection of aortic blood volume fluctuations, calculation of thoracic impedance values, generation of impedance waveforms (impedance cardiogram), and derivation of hemodynamic parameters.

To construct the prediction model, candidate variables were first screened using univariate comparisons to identify differences between patients with and without pulmonary congestion.

Due to the limited sample size, the dataset was not split for cross-validation. Instead, all available cases were used for model development, and internal validation was performed using bootstrap resampling with 500 iterations to estimate the optimism of the model and assess the robustness of its predictive performance. Variables with a p-value less than 0.05 were incorporated into a multivariable logistic regression model. Backward stepwise variable selection, guided by the Akaike Information Criterion (AIC), was conducted to identify the simplest adequate model with optimal fit.

Model performance was assessed based on discrimination, calibration, and clinical utility. Discrimination was evaluated through receiver operating characteristic (ROC) curve analysis, with the area under the curve (AUC) used for quantification. Calibration was examined by the Hosmer-Lemeshow test and calibration plots that compared predicted and observed risks.

Clinical applicability was assessed with decision curve analysis (DCA), which plotted net benefit across various threshold probabilities. Additionally, a nomogram was constructed based on the final logistic regression model to facilitate individualized risk estimation in clinical practice.

To enhance interpretability and assess clinical value, we compared the model AUC with that of individual predictors. Besides, patients were divided into three equal risk categories (low, intermediate, and high) according to increasing total nomogram scores. Differences in the distribution of pulmonary congestion across these groups were then examined to assess the capacity of the model to distinguish risk levels.

Analyses were performed in IBM SPSS Statistics, version 25.0 (IBM Corp., Armonk, NY, USA), GraphPad Prism, version 9.3 (GraphPad Software, San Diego, CA, USA), R, version 4.4.2 (R Foundation for Statistical Computing, Vienna, Austria). p 0.05 (two-sided) was considered significant.

The Shapiro-Wilk test was employed to evaluate the normality of the continuous variables. Data following a normal distribution were presented as mean $\pm$ standard deviation and analyzed using the independent samples t-test. Non-normally distributed data were presented as medians with interquartile ranges (IQR) and compared using the Mann-Whitney U test. Categorical variables were described using counts and percentages and analyzed with the Chi-square test or Fisher’s exact test.

Univariate analysis was initially used to identify candidate predictors of pulmonary congestion. Variables with p 0.05 were included in the multivariable logistic regression model. The final model was derived using backward stepwise selection based on the AIC. The discrimination was assessed through the AUC. Calibration was evaluated using the Hosmer-Lemeshow goodness-of-fit test and depicted with calibration plots. The clinical utility was assessed using DCA. Internal validation was performed with bootstrap resampling (500 iterations) to estimate model optimism and assess performance robustness. A nomogram was constructed to provide individualized risk estimates based on the final model.

The analysis included 66 patients, comprising 31 patients with pulmonary congestion and 35 without. Groups were similar in demographics, comorbidities, and laboratory parameters, with no significant differences detected (Table 3). The echocardiographic evaluation showed that the pulmonary congestion group exhibited markedly decreased LVEF (p 0.001) and an elevated E/e′ ratio (p = 0.003) relative to the non-congestion group. No substantial between-group alterations were observed in other transthoracic echocardiographic parameters.

As shown in Table 4, among the thirteen non-invasive hemodynamic parameters derived from ICG, only TFC showed a significant between-group difference. Patients with pulmonary congestion exhibited substantially higher TFC values compared to those without congestion (p = 0.008). No meaningful group differences were detected for the remaining parameters.

Three variables, including LVEF (OR = 0.934, 95% CI = 0.879–0.992), TFC (OR = 1.237, 95% CI = 1.070–1.431), and E/e′ ratio (OR = 1.229, 95% CI = 1.029–1.467), were retained in the final multivariable logistic regression model after backward stepwise selection based on the AIC.

The established model achieved an AIC of 71.61 and explained a substantial proportion of variability in pulmonary congestion (residual deviance: 63.61 vs. null deviance: 91.25). The regression equation was as detailed below: logit(p) = –5.413 – 0.069 $\times$ LVEF + 0.213 $\times$ TFC + 0.206 $\times$ E/e′. Where p represents the predicted probability of pulmonary congestion. In this model, higher TFC and E/e′ values were linked to increased pulmonary congestion risk, whereas elevated LVEF was protective.

Table 5 presents the statistical characteristics of the predictors included in the final model equation. No significant multicollinearity was observed among these predictors, with all variance inflation factors (VIFs) being less than 1.20, indicating good model stability (Table 5).

A nomogram was derived from the established model to facilitate individualized prediction of pulmonary congestion risk. The specific values of LVEF, E/e′, and TFC can be used to locate the corresponding points on the nomogram. By totaling the values for each factor, the final score maps to an estimated probability of pulmonary congestion, as illustrated in Fig. 3.

Fig. 3.

Nomogram of the prediction model for pulmonary congestion in patients with HF and permanent AF. The nomogram integrates TFC, E/e′ ratio, and LVEF. Points for each variable are summed to estimate the probability of pulmonary congestion. HF, heart failure; AF, atrial fibrillation; TFC, thoracic fluid conductivity; LVEF, left ventricular ejection fraction.

The prediction performance of the final model was appraised via multiple complementary metrics. The ROC curve analysis showed strong discriminative performance, achieving an AUC of 0.865 (95% CI = 0.773–0.956) (Fig. 4A). Bootstrap resampling (500 iterations) for internal validation produced a corrected AUC of 0.853 (95% CI = 0.763–0.942), supporting the robustness and generalizability of the model (Fig. 4B).

Fig. 4.

Discriminative performance and calibration of the nomogram for predicting pulmonary congestion in patients with HF and permanent AF. (A) ROC curve for the development cohort. (B) ROC curve for the internal validation cohort based on 500 bootstrap resamples. (C) Calibration plot for the development cohort. (D) Calibration plot for the internal validation cohort based on 500 bootstrap iterations. ROC, receiver operating characteristic; HF, heart failure; AF, atrial fibrillation.

Calibration was estimated via the Hosmer-Lemeshow goodness-of-fit test, which indicated acceptable agreement between predicted and observed probabilities (p $>$ 0.05). Visual inspection of the calibration curve revealed that the predicted probabilities generally matched the diagonal reference line in both the derivation and assessment cohorts, demonstrating acceptable calibration (Fig. 4C,D). In addition, the Brier score was 0.153, further supporting adequate calibration.

Clinical utility was assessed via DCA. The model demonstrated a net clinical benefit across a wide range of threshold probabilities, with maximum benefits observed between 0.04 and 0.80 in the development cohort (Fig. 5A) and between 0.06 and 0.78 in the bootstrap cohort (Fig. 5B). Notably, five-fold cross-validation was also performed during model construction, demonstrating high consistency between the original and cross-validated decision curves, further supporting the robustness of its clinical applicability (Fig. 5A). These findings collectively support the strong discriminative ability, reliable calibration, and potential clinical utility of the model in identifying pulmonary congestion risk among patients with HF and permanent AF.

Fig. 5.

Clinical utility of the nomogram-based prediction model for pulmonary congestion. (A) Decision curve analysis (DCA) for the development cohort. The red dashed curve represents the original model; the blue solid curve corresponds to the five-fold cross-validation. (B) DCA for the internal validation cohort based on 500 bootstrap iterations.

To quantify the diagnostic enhancement offered by the tool, its discriminative performance was compared with that of each predictor. The final model, integrating LVEF, E/e′ ratio, and TFC, achieved an AUC of 0.865 (95% CI = 0.773–0.956). This value was notably greater than the AUCs of the individual components: LVEF (AUC = 0.759, 95% CI = 0.638–0.880, p = 0.035), E/e′ ratio (AUC = 0.716, 95% CI = 0.592–0.840, p = 0.012), and TFC (AUC = 0.690, 95% CI = 0.561–0.819, p = 0.007). Fig. 6A shows no statistically significant differences among the three predictive variables (p $>$ 0.05).

Fig. 6.

Model interpretability and risk-stratification performance of the nomogram. (A) ROC curves comparing the complete model (TFC+ LVEF + E/e′) with its predictors. (B) Distribution of total nomogram scores in patients with and without pulmonary congestion. (C) Risk stratification based on the nomogram score. ROC, Receiver operating characteristic; LVEF, left ventricular ejection fraction; TFC, thoracic fluid conductivity. **** indicates p 0.0001 (Mann-Whitney U test).

To facilitate clinical interpretation, patients were stratified into three equal-sized risk groups (low, intermediate, and high) according to the total scores from the nomogram. The pulmonary congestion rates showed a consistent gradient: 9.1%, 50.0%, and 81.8% in the low-, intermediate-, and high-risk groups, respectively. This stepwise increase suggested that our model can differentiate risk levels meaningfully (Fig. 6C).

Furthermore, the total nomogram scores differed significantly between patients classified as congested or non-congested (Fig. 6B). The median score within the congested cohort was 50.78 (17.88), compared to 30.78 (15.55) within the non-congested cohort (p 0.001), supporting the discriminative capacity of the model-derived scoring system.

Catheter-based measurement of wedge pressure remains the gold standard for assessing pulmonary congestion [15, 16]. However, its invasive nature, procedural complexity, and associated risks limit its routine clinical use.

Non-invasive alternatives, including clinical symptom evaluation and natriuretic peptide levels, offer limited diagnostic accuracy. While NT-pro-BNP or BNP serve as conventional markers of cardiac dysfunction, their reliability in predicting pulmonary congestion has been questioned, particularly due to their variable correlation with pulmonary capillary wedge pressure obtained through invasive monitoring, especially in individuals with renal dysfunction or a preserved ejection fraction [17, 18, 19, 20].

Lung ultrasound (LUS) has emerged as an attractive alternative for bedside assessment of pulmonary congestion, as it visualizes B-lines that correlate with extravascular lung water. Compared to chest radiography, LUS offers bedside feasibility. Nonetheless, its diagnostic reliability can be affected by conditions like obesity, chest wall anatomy, and coexisting pulmonary disease. Moreover, LUS remains heavily operator-dependent, and the lack of standardized cut-off values, as well as inconsistencies in image acquisition, limits its widespread adoption in routine practice [21, 22]. Collectively, current diagnostic methods for pulmonary congestion each have inherent limitations. Therefore, there is a clear need to explore complementary tools that are less dependent on operator expertise, easy to perform, and suitable for repeated bedside application.

In this study, pulmonary congestion was classified based on admission chest radiography, a widely used tool for detecting pulmonary fluid overload in routine clinical practice. Radiographic features, such as vascular redistribution, interstitial edema, and hilar blurring, have been shown to correlate closely with invasive measurements of pulmonary capillary wedge pressure in decompensated heart failure [23].

Despite its widespread clinical use, chest radiography has inherent limitations in detecting pulmonary congestion, including variability in image acquisition, interobserver interpretation, limited sensitivity to dynamic changes in fluid status, and the requirement for patient cooperation to achieve optimal positioning. To minimize potential misclassification, we standardized image timing and interpretation procedures. All radiographs were obtained within 24 hours of admission, before the initiation of decongestive therapy, and were initially assessed by an experienced radiologist, with blinded adjudication by two independent cardiologists. Although chest radiography is not considered a definitive gold standard, it remains a practical and commonly used reference in real-world clinical settings. Given these considerations, we selected it as the reference standard for pulmonary congestion in this study, acknowledging its limitations but reinforcing its relevance in routine clinical decision-making.

Pulmonary congestion in heart failure primarily results from elevated left-sided filling pressures, which increase pulmonary capillary hydrostatic pressure and promote fluid transudation into the pulmonary interstitium and alveoli. In patients with AF, this cascade is further exacerbated by the loss of effective atrial contraction, resulting in impaired left ventricular filling, increased fluctuations in left atrial pressure, and a greater susceptibility to fluid overload.

The predictive model developed in this study integrates three non-invasive variables, LVEF, E/e′ ratio, and TFC, each of which corresponds to a distinct phase of the pulmonary congestion pathway. The E/e′ ratio serves as an indirect measure of left-sided preload and has been reported to correlate with pulmonary capillary wedge pressure [24, 25, 26]. It reflects the early hemodynamic burden associated with reduced ventricular compliance and increased preload, features particularly relevant in AF, where diastolic dysfunction is frequently observed. LVEF, as a marker of global systolic performance, contributes mechanistically to backward failure and elevated left atrial pressures when reduced. Its prognostic value in predicting pulmonary congestion has been demonstrated in large clinical cohorts [27].

TFC, measured via ICG, is a direct, non-invasive index of total thoracic fluid volume. ICG operates by transmitting a high-frequency, low-amplitude alternating current through the thorax using surface electrodes. As fluid conducts electricity more readily than air or tissue, changes in thoracic impedance are inversely proportional to the amount of intrathoracic fluid. A lower impedance reflects greater fluid accumulation, which is quantified as higher TFC values.

TFC specifically reflects the cumulative fluid content within the thoracic cavity, including both intravascular and extravascular compartments. It acts as a downstream marker of volume overload, detecting subclinical pulmonary congestion without obvious respiratory symptoms or radiographic alterations. Previous research has shown its association with pulmonary capillary wedge pressure and its capacity to dynamically monitor fluid status changes in HF patients [28, 29, 30].

In patients with AF, where beat-to-beat variability can complicate the interpretation of pressure- or flow-based indices, TFC offers an advantage due to its relative insensitivity to rhythm irregularity. Rather than relying on single-cycle measurements, ICG-derived TFC averages impedance changes over multiple cardiac cycles, thereby providing a more stable and reproducible signal even in the presence of RR interval variability. This makes TFC particularly suitable for evaluating pulmonary congestion in AF populations. Overall, TFC complements upstream pressure markers, such as E/e′, and structural indices, like LVEF, by providing a real-time estimate of thoracic fluid accumulation, thereby completing the pathophysiological profile from hemodynamic stress to end-organ congestion.

Cumulatively, these three parameters provide a physiologically coherent framework for assessing pulmonary congestion. By combining upstream (E/e′), central (LVEF), and downstream (TFC) markers, the model captures the continuum from hemodynamic stress to overt pulmonary fluid overload, thereby enhancing diagnostic precision in this complex patient population.

The predictive model developed in this study provides a practical and non-invasive approach for assessing pulmonary congestion in patients with HF and permanent AF. By combining LVEF, E/e′ ratio, and TFC, it integrates structural, functional, and hemodynamic insights into a single tool, facilitating more accurate and individualized evaluation of congestion.

All three variables are easily accessible using bedside technologies. With the increasing availability of portable echocardiography, both LVEF and E/e′ can be rapidly obtained at the point of care. Importantly, these two parameters require relatively simple acquisition protocols and are less dependent on operator expertise compared to comprehensive echocardiographic assessments. Similarly, ICG offers real-time thoracic fluid monitoring, eliminating operator variability and the need for invasive procedures. These features render the model particularly suitable for routine use in general wards, emergency settings, or outpatient clinics.

In terms of diagnostic performance, the model demonstrated excellent discrimination and calibration, with internal validation via bootstrap resampling confirming its robustness. Decision curve analysis further indicated a favorable net clinical benefit across a broad range of decision thresholds. Moreover, the derived nomogram provides a visually intuitive tool to support individualized bedside decision-making. Additionally, model interpretability analysis supported its added value and practical utility in risk stratification, showing a stepwise increase in congestion rates across risk groups.

This model complements existing methods by providing a rapid, repeatable, and less operator-dependent approach to assessing pulmonary congestion, particularly in HF patients with permanent AF. Its simplicity, non-invasiveness, and real-time feedback make it a promising adjunct for ongoing congestion surveillance, especially where continuous fluid status monitoring is essential.

This study is subject to several limitations. First, pulmonary congestion was defined based on chest radiography rather than invasive measurement of pulmonary capillary wedge pressure, which may introduce classification bias despite standardized imaging and blinded interpretation protocols. Second, this single-center study with a modest sample size and no external validation may restrict the generalizability of the results. Third, the study did not include a direct head-to-head comparison with techniques such as LUS, which may restrict conclusions regarding relative diagnostic performance. Additionally, due to the inherent limitations of observational design, causal inference cannot be established. Finally, the strict exclusion criteria improved internal reliability but limited generalizability; broader studies are needed to confirm applicability in various clinical settings and diverse HF subgroups.