Abstract
Background:
Intraoperative arterial carbon dioxide partial pressure monitoring is essential for pediatric ventilatory management but requires invasive arterial sampling. While end-tidal carbon dioxide offers a noninvasive alternative, its reliability is limited by individual physiologic gradients. This study developed a machine learning model to estimate arterial carbon dioxide partial pressure using end-tidal carbon dioxide and intraoperative clinical features in children.
Methods:
The authors retrospectively analyzed 8,853 paired end-tidal carbon dioxide and arterial carbon dioxide partial pressure measurements from 3,586 pediatric patients in the vital sign registry (VitalDB) database. Clinical and ventilatory features were used to train four machine learning algorithms, with missing data managed via age group–based imputation. Model performance was verified through internal temporal validation using a recent dataset of 2,138 pairs and external validation using an independent dataset of 92 pairs from a distinct hospital. Feature importance was assessed using Shapley additive explanations values.
Results:
The gradient boosting model performed best, yielding a mean absolute error of 2.73 mmHg and root mean squared error of 4.13 mmHg. External validation confirmed generalizability with a mean absolute error of 3.65 mmHg (institutional) and 3.67 mmHg (temporal). End-tidal carbon dioxide, body temperature, fraction of inspired oxygen, and preoperative hemoglobin emerged as the most impactful features.
Conclusions:
The authors’ machine learning model accurately estimates intraoperative arterial carbon dioxide partial pressure using noninvasive parameters. The model demonstrates stable performance across temporal and external cohorts.
Data from 3,586 pediatric patients undergoing nonlaparoscopic, nonthoracoscopic procedures requiring endotracheal intubation were used to develop a machine learning model to estimate intraoperative partial pressure of arterial carbon dioxide from end-tidal carbon dioxide and other clinical features. The arterial carbon dioxide model demonstrated acceptable performance, with a mean absolute error of 2.73 mmHg in the derivation population and 3.65 mmHg in the external validation population. Noninvasive estimation of the partial pressure of arterial carbon dioxide may be feasible in pediatric patients.
Editor’s Perspective
What We Already Know about This Topic
Monitoring partial pressure of arterial carbon dioxide is crucial during pediatric surgery but necessitates invasive arterial sampling. Although end-tidal carbon dioxide provides a noninvasive alternative, the gradient between the partial pressure of arterial carbon dioxide and end-tidal carbon dioxide widely varies in children owing to anatomical and physiologic differences, thereby limiting its utility.
Previous research in adult patients has demonstrated the feasibility of estimating arterial carbon dioxide using noninvasive measures.
What This Article Tells Us That Is New
Data from 3,586 pediatric patients undergoing nonlaparoscopic, nonthoracoscopic procedures requiring endotracheal intubation were used to develop a machine learning model to estimate intraoperative partial pressure of arterial carbon dioxide from end-tidal carbon dioxide and other clinical features.
The arterial carbon dioxide model demonstrated acceptable performance, with a mean absolute error of 2.73 mmHg in the derivation population and 3.65 mmHg in the external validation population.
Noninvasive estimation of the partial pressure of arterial carbon dioxide may be feasible in pediatric patients.
Intraoperative monitoring of partial pressure of arterial carbon dioxide plays a significant role as it reflects the patient’s respiratory status and adequacy of ventilation. The partial pressure of arterial carbon dioxide necessitates arterial blood gas analysis, whereas end-tidal carbon dioxide can be easily measured via exhalation, enabling continuous monitoring with a less invasive approach.1
The disparity between partial pressure of arterial carbon dioxide and end-tidal carbon dioxide persists and is well established2; however, it varies among individual patients. Factors including ventilation–perfusion mismatch, lung pathology, and patient-specific characteristics can influence these discrepancies.3,4 Although extensive research has been conducted on adults, data on partial pressure of arterial carbon dioxide and end-tidal carbon dioxide in pediatric populations remain scarce owing to physiologic differences and smaller anatomical structures. Particularly in neonates, the gradient between partial pressure of arterial carbon dioxide and end-tidal carbon dioxide can significantly vary, ranging from 0 to 20 mmHg, further complicating accurate monitoring and interpretation.5
In pediatric anesthesia, monitoring poses distinct challenges compared to adults due to anatomical and physiologic dissimilarities. For instance, the placement of an arterial catheter is technically more challenging in children owing to their smaller vessels and increased risks of complications, including thrombosis or vascular spasm.6 Furthermore, the dynamic nature of pediatric physiology, including higher metabolic rates and immature respiratory control mechanisms, makes homeostasis maintenance more complex. These factors further complicate the interpretation of surrogate markers, including end-tidal carbon dioxide, which may be less reliable in accurately reflecting partial pressure of arterial carbon dioxide in pediatric patients.
Intraoperative partial pressure of arterial carbon dioxide prediction is difficult owing to the influence of various factors, including age, sex, respiratory rate, ventilation–perfusion mismatch, and individual patient variability. Although various algorithms for estimating partial pressure of arterial carbon dioxide using end-tidal carbon dioxide have been proposed, their clinical application remains lacking.7,8 These strategies frequently lack the accuracy and practicality required for real-time intraoperative decision-making.
Recent advances in machine learning have facilitated the development of precise prediction models for various medical applications. Previous studies have explored methods to identify hidden patterns in large datasets and analyze relationships among variables.9,10 To the best of our knowledge, only one study has employed machine learning for estimating partial pressure of arterial carbon dioxide using end-tidal carbon dioxide in the pediatric population; the targeted population was confined to the intensive care unit.11
This study aimed to explore whether combining end-tidal carbon dioxide with medical records could accurately estimate partial pressure of arterial carbon dioxide, potentially reducing unnecessary invasive procedures and improving patient outcomes. Accordingly, we developed and internally validated, and externally validated in an independent cohort, a multivariable diagnostic model to estimate intraoperative partial pressure of arterial carbon dioxide using end-tidal carbon dioxide and routinely available perioperative variables.
Materials and Methods
Data Source and Ethics
The institutional review board of Seoul National University Hospital (Seoul, South Korea) approved this retrospective study (Nos. H-2405-134-1539, H-2512-001-1695) and waived the requirement for written informed consent owing to its retrospective nature. Also, the data analysis and statistical plan were written and filed with the institutional review board before the data were accessed for analysis. This study was conducted and reported in accordance with the Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD) guidelines for the development and validation of prediction models.
Data Collection
A retrospective analysis was conducted using prospective data from the intraoperative vital sign registry (VitalDB).12 The intraoperative vital signs data used in this study were collected using the Vital Recorder Program,12 which collected data from various medical devices during general anesthesia.
Pediatric patients who underwent surgery during general anesthesia from January 2020 to December 2023 at a tertiary referral center, Seoul National University Children’s Hospital (Seoul, South Korea), were included. The following were the inclusion criteria: (1) age younger than 19 yr, including newborns and immature infants; (2) patients’ American Society of Anesthesiologists (ASA; Schaumburg, Illinois) Physical Status classification system score of less than VI; and (3) surgery performed during general anesthesia with anesthesia workstations—Dräger Primus (Drägerwerk AG & Co. KGaA, Germany), GE Carestation 650 (GE Healthcare, USA), and Flow-i (Getinge AB, Sweden)—using an endotracheal tube with arterial blood gas monitoring. Pediatric patients undergoing surgery with one lung ventilation and requiring cardiopulmonary bypass were excluded, as these conditions markedly alter respiratory physiology, potentially compromising the reliability of the model developed for general pediatric surgical settings. Laparoscopic and thoracoscopic surgeries were also excluded due to the absence of objective data on intraoperative carbon dioxide insufflation parameters, including the onset, pressure, and flow rate of insufflation, which may affect the gradient. A total of 8,853 data from 3,586 pediatric patients were collected and included in the analysis. The patients were randomly categorized at the patient level into the training (70%), validation (15%), and testing (15%) subsets (fig. 1).
Fig. 1.
A flow chart of the study cohort was used for model development and validation. Initially identified based on predefined inclusion and exclusion criteria. ABG, arterial blood gas; intraop_pco2, intraoperative partial pressure of arterial carbon dioxide.
Data collected from patients’ electronic medical records included the following: (1) demographic data, including age, sex, height, weight, and body mass index (BMI); (2) preoperative data, including ASA Physical Status, and laboratory data, including hemoglobin, albumin, and creatinine; and (3) intraoperative data, including surgical position, blood pressure or arterial pressure, and ventilator machine parameters (fraction of inspired oxygen, minute volume, tidal volume, compliance, peak inspiratory pressure, minimal alveolar compliance, and positive end-expiratory pressure). All signal data were continuously collected with a 500-Hz sampling rate, and the data are presented in table 1.
Table 1.
Summary of Collected Data Characteristics
| Data | Type | Descriptions |
|---|---|---|
| Demographic data | ||
| Age | Numeric | Patient’s age |
| Sex | Categorical | Patient’s sex (male or female) |
| Height | Numeric | Patient’s height |
| Weight | Numeric | Patient’s weight |
| Preoperative data | ||
| ASA Physical Status | Categorical | American Society of Anesthesiologists (Physical Status, I–VI) |
| Hemoglobin | Numeric | Preoperative hemoglobin laboratory test |
| Albumin | Numeric | Preoperative albumin laboratory test |
| Creatinine | Numeric | Preoperative creatinine laboratory test |
| Intraoperative data | ||
| Surgical position | Categorical | Anesthetic patient positioning information (supine, lithotomy, reverse Trendelenburg, Trendelenburg, prone, left lateral decubitus, right lateral decubitus, and sitting) |
| Arterial blood pressure | Signal | Sampled at 500 Hz |
| Fraction of inspired oxygen | Signal | Sampled at 500 Hz |
| Minute volume | Signal | Sampled at 500 Hz |
| Tidal volume | Signal | Sampled at 500 Hz |
| Compliance | Signal | Sampled at 500 Hz |
| Peak inspiratory pressure | Signal | Sampled at 500 Hz |
| Minimum alveolar concentration | Signal | Sampled at 500 Hz |
| Positive end-expiratory pressure | Signal | Sampled at 500 Hz |
| Arterial blood gas analysis | Numeric | Intraoperative arterial blood gas analysis |
| Comorbidities | ||
| Cardiac diseases | Categorical (binary) | Presence of congenital or acquired cardiac disease |
| Pulmonary diseases | Categorical (binary) | Presence of pulmonary disease |
ASA, American Society of Anesthesiologists.
In addition, detailed cardiac and pulmonary comorbidities were extracted from anesthesia records and preoperative medical histories. Cardiac comorbidities included 21 specific diagnoses, such as atrial septal defect, ventricular septal defect, patent ductus arteriosus, tetralogy of Fallot, transposition of the great arteries, single-ventricle physiology, and Fontan circulation, which may influence baseline hemodynamics, autonomic tone, and tolerance to anesthetic and surgical stress. Pulmonary comorbidities included seven conditions, such as pneumonia, bronchopulmonary dysplasia, atelectasis, consolidation, and asthma, which are relevant to gas exchange, ventilatory mechanics, and the propensity for perioperative respiratory instability (Supplemental Digital Content table S4, Supplemental Digital Content fig. S1, https://links.lww.com/ALN/E643). Each comorbidity was encoded as a binary variable (present/absent) and incorporated as an interpretable covariate, allowing the model inputs and outputs to be understood in the context of established cardiopulmonary physiology.
Data Extraction
The partial pressure of arterial carbon dioxide measurement in the arterial blood gas analysis was conducted through an arterial catheter. During blood sampling, blood pressure artifacts can cause a sudden surge in the mean arterial pressure. To address this, we extracted the mean arterial pressure data for peak detection to accurately estimate the precise timing of arterial blood gas analysis (fig. 2).
Fig. 2.
Peak detection estimating the precise arterial blood gas analysis timing. Mean arterial pressure data are analyzed using a peak detection algorithm to identify the precise time point corresponding to the arterial blood gas analysis measurement. The red peak represents the estimated arterial blood gas analysis timing based on the waveform analysis.
To determine the arterial blood collecting time, peak detection was performed using mean arterial pressure using the SciPy package (SciPy developers, open-source; https://scipy.org). The detection process aimed to identify the arterial blood gas analysis checking time. To enhance the accuracy and remove the noise of peak detection, data collected within 20 min before and after the start and end of the surgery were excluded. Only the first peak was considered in cases wherein multiple peaks were detected within a 5-min window.
The intraoperative partial pressure of arterial carbon dioxide measurement times were used as the reference for validation. As a time gap frequently exists between the actual blood draw and the arterial blood gas analysis measurement, a peak was considered to be correctly detected when it was within 20 min of the arterial blood gas analysis checking time. Peaks detected outside this range were considered false positives. The ±20-min window was selected based on typical intraoperative workflows, accounting for the time required to draw, process, and upload arterial blood gas analysis results, thereby ensuring the physiologic relevance of the extracted features. This threshold was validated by comparing known sampling timestamps and record entry times, with an average delay of approximately 1.89 min, well within the chosen window. To ensure statistical independence and minimize the potential distortion caused by extreme outliers or overrepresented patients, the number of data points per patient was limited to a maximum of five. When more than five arterial blood gas analyses were available for a single patient, the first five temporally distinct measurements were selected. The time point identified through peak detection was designated as the reference time point T. Regarding VitalDB data, measurements from 30 to 60 s before T were extracted and utilized for analysis. The average value within this period was used for the mean arterial pressure, whereas the maximum values were used for all other vital parameters. For feature extraction, summary statistics were selected based on the physiologic relevance of each variable to the prediction of arterial carbon dioxide partial pressure. Maximum values were used for ventilatory and anesthetic parameters, including end-tidal carbon dioxide, fraction of inspired oxygen, tidal volume, minute volume, peak inspiratory pressure, lung compliance, minimum alveolar concentration, and positive end-expiratory pressure, as peak exposures are more likely to influence gas exchange and arterial carbon dioxide levels. In contrast, mean values were used for hemodynamic and systemic variables such as mean blood pressure to minimize the impact of transient artifacts and better reflect overall physiologic status.
Patients were categorized into one of two age groups: 0 to 5 and 6 to 18 yr. This classification was based on developmental milestones, with age 6 yr typically marking the transition from preschool to school age, characterized by significant physiologic shifts in the respiratory and cardiovascular systems. These thresholds also align with established clinical trial guidelines.13–16 Furthermore, demographic data from patients matched with vital signals data were utilized. Demographic data, including age, sex, BMI, ASA Physical Status, and surgical position, were analyzed in each group (table 2).
Table 2.
Input Features Used for Partial Pressure of Arterial Carbon Dioxide Estimation Modeling
| Category | Features | Feature Details |
|---|---|---|
| Clinical information | Sex | Female or male |
| Age | Year | |
| BMI (weight, height) | kg/m2 | |
| ASA | I–V (VI excluded) | |
| Position | “Supine,” “lithotomy,” “reverse Trendelenburg,” “Trendelenburg,” “prone,” “left lateral decubitus,” “right lateral decubitus,” and “sitting.” | |
| Preoperative laboratory test | Hemoglobin | g/dl |
| Albumin | g/dl | |
| Creatinine | mg/dl | |
| Hemodynamic parameters | Mean arterial pressure | mmHg |
| Body temperature | °C | |
| End-tidal carbon dioxide | mmHg | |
| Lung compliance | ml/cm H2O | |
| Peak inspiratory pressure | cm H2O | |
| Fraction of inspired oxygen | ||
| Tidal volume | ml | |
| Minute volume | l/min | |
| Minimum alveolar concentration | % | |
| Peak expiratory-end pressure | cm H2O |
ASA, American Society of Anesthesiologists Physical Status classification; BMI, body mass index.
Demographic information was available for all patients; however, in the VitalDB data, several intraoperative variables were missing, including body temperature, ventilatory parameters, and selected laboratory measurements. In machine learning, data quality is essential, making the appropriate handling of missing values crucial. To address these missing values, we initially used multiple imputation by chained equations, a widely accepted, statistically robust method. However, given the distinct physiologic patterns across pediatric age groups, a subgroup-based imputation strategy was also evaluated. Patients were stratified into two age groups (younger than 6 yr and 6 yr or older), and age-specific mean values (table 3) were used to impute missing data. Furthermore, a comparative analysis demonstrated that the age-based imputation method achieved superior predictive performance compared to multiple imputation by chained equations, particularly in both internal and external validation. Therefore, this method was adopted for the final model training. Given the unique age-related trends in pediatric vital sign data, this approach improved the model’s predictive performance, providing a method to address missing values in future partial pressure arterial carbon dioxide estimation data. The missing rates for each variable are summarized in Supplemental Digital Content table S1 (https://links.lww.com/ALN/E643), and the model performance comparisons by imputation strategy are provided in Supplemental Digital Content table S2 (https://links.lww.com/ALN/E643).
Table 3.
Average Feature Values by Pediatric Age Group under 6 and 6 to 18 yr
| Features/Age | < 6 | ≤ 18 |
|---|---|---|
| Mean arterial pressure, mmHg | 66.41 | 75.21 |
| Body temperature, °C | 35.97 | 36.12 |
| End-tidal carbon dioxide, mmHg | 36.15 | 36.50 |
| Positive end-expiratory pressure, cm H2O | 5.07 | 5.09 |
| Lung compliance, ml/cm H2O | 6.97 | 28.61 |
| Peak inspiratory pressure, cm H2O | 19.19 | 17.58 |
| Fraction of inspired oxygen, % | 33.27 | 21.62 |
| Tidal volume, ml/kg | 80.43 | 295.89 |
| Minute volume, l/min | 1.92 | 4.16 |
| Minimum alveolar concentration, % | 1.21 | 0.40 |
| Hemoglobin, g/dl | 12.40 | 12.76 |
| Albumin, g/dl | 4.02 | 4.23 |
| Creatinine, mg/dl | 0.49 | 0.63 |
Values are presented as mean values for each age group. Hemodynamic parameters are intraoperatively measured, whereas preoperative laboratory values are obtained before surgery.
Feature Engineering and Data Preprocessing
Several studies have been conducted to identify the correlation between partial pressure of arterial carbon dioxide and end-tidal carbon dioxide, and several features, including age,17sex,18 BMI, ASA Physical Status,19 and surgical position,20 are being considered in actual clinical practice for partial pressure of arterial carbon dioxide monitoring. The relevant study reported that increasing the number of effective features in partial pressure of arterial carbon dioxide estimation promotes the model’s accuracy. Therefore, we identified key features associated with partial pressure of arterial carbon dioxide by extracting time series and demographic data. The overall study flow is depicted in figure 3.
Fig. 3.
Data sampling flow. (A) Estimation of the ABG collection time, (B) extraction of demographic and hemodynamic features within a defined time window around the ABG collection point, and (C) labeling of target variables, including partial pressure of arterial carbon dioxide and end-tidal carbon dioxide. ABG, arterial blood gas; ABGA, arterial blood gas analysis; EtCO2, end-tidal carbon dioxide; OP, operation; PaCO2, partial pressure of arterial carbon dioxide.
Statistical Analysis
Model Training
A partial pressure of arterial carbon dioxide model was developed for continuous, noninvasive estimation. A positive outcome was defined as the intraoperative partial pressure of arterial carbon dioxide laboratory results, and the machine learning algorithm was trained using these outcomes at each time point.
All continuous features among the extracted variables were initially normalized to adjust the scale in different domains. The minimum–maximum normalization method was used according to the following formula21:
To develop a clinically meaningful and generalized model, the final model was constructed by dividing the data into two subgroups (younger than 6 yr and 6 yr or older) based on the preschool age of 6 yr.
The dataset configuration and hyperparameters used for these models are as follows. The patients were divided into training (70%), validation (15%), and test (15%) subsets. This patient-level randomization ensured statistical independence between datasets and prevented data leakage, as measurements from the same patient were not included across multiple sets. To ensure generalizability and prevent cohort bias, we assessed the demographic and procedural characteristics (age, sex, ASA Physical Status, BMI, and surgical position) across the training, validation, and testing sets after patient-level randomization. For model training, patient demographics (age, sex, and BMI), surgery-related clinical data (ASA Physical Status and surgical position), preoperative laboratory results (hemoglobin, albumin, and creatinine), and 2-s interval data from the VitalDB (mean arterial pressure, body temperature, end-tidal carbon dioxide, lung compliance, peak inspiratory pressure, fraction of inspired oxygen, tidal volume, minute volume, minimum alveolar concentration, and positive end-expiratory pressure) were used as the input features, and the intraoperative partial pressure of arterial carbon dioxide laboratory finding was employed as the output feature.
To benchmark the clinical utility of the proposed machine learning models, a baseline model using only end-tidal carbon dioxide was additionally constructed. This end-tidal carbon dioxide–only model was implemented as a linear regression, reflecting the conventional clinical approach in which partial pressure of arterial carbon dioxide is inferred directly from end-tidal carbon dioxide values. The performance of this baseline model was evaluated using the same training, validation, and test splits and identical evaluation metrics, allowing a direct comparison between standard monitoring and the proposed various machine learning models.
We considered the following four machine learning algorithms for partial pressure of arterial carbon dioxide estimation: gradient boosting,22 multilayer perceptron,23 decision tree,24 and random forest.25
Each algorithm was tuned with its own hyperparameters and was developed on the basis of two age subgroups (younger than 6 yr and 6 yr or older). The following were the hyperparameters for the four machine learning algorithms: gradient boosting was evaluated with learning rate of 0.1, a maximum tree depth (max_depth) of 5, and number of trees at 300 for both the younger than 6 yr and 6 yr or older models. Random forest was evaluated using the hyperparameters of the number of trees at 400, the number of features to consider at each split at square root of the total number of features (sqrt), and the minimum leaf size at 3 for both the younger than 6 yr and 6 yr or older models. A multilayer perceptron was trained using the following hyperparameters: alpha, 0.001; hidden layer size, (100,100); and maximum iteration, 200, for the younger than 6 yr model; and alpha, 0.001; hidden layer size, (300,300); and maximum iteration, 200, for the 6 yr or older model. We evaluated the decision tree using the hyperparameter alpha of 0.0001 for both the younger than 6 yr and 6 yr or older models.
To determine the optimal hyperparameters, a fivefold cross-validation was performed. The training set was partitioned into five subsets, where the model was sequentially trained on four subsets and validated on the remaining one. To ensure robustness, this process was repeated five times, and model performance was evaluated using the following four distinct evaluation matrices: mean absolute error, mean absolute percentage error, mean squared error, and root mean squared error.
Gradient Boosting–based Feature Selection
A substantial increase in the number of features enhances the model performance; however, overfitting frequently occurs, reducing the accuracy and speed of partial pressure of arterial carbon dioxide estimation. Therefore, to identify the most sensitive partial pressure of arterial carbon dioxide–related characteristics and reduce the dimension, an effective feature selection process is necessary. In this study, the process was conducted on the basis of a gradient boosting; to reduce the dimension, we attempted to increase the partial pressure of arterial carbon dioxide predictive accuracy by eliminating the features that exhibited a significant prediction error among all extracted features to determine the optimal number and combination of features.26
Feature importance was derived from Shapley additive explanations values calculated by the gradient boosting model. The selection process was repeated five times to minimize random errors, and features were ranked by average importance. The feature subset that minimized both the mean absolute error and mean squared error was selected for the final model. This process enabled the identification of the optimal feature combination that balances model simplicity and predictive accuracy. Ultimately, the final gradient boosting model was trained using the top-ranked features identified through this selection procedure.
Model Internal and External Validation
To assess the model’s generalizability and reliability, external validations were conducted using two independent datasets. First, a dataset from Chungnam National University Hospital (CNUH; Daejeon, South Korea) was used, comprising 50 pediatric patients with 92 partial pressure of carbon dioxide measurements collected between January 2022 and December 2022. In addition, a temporal external validation was performed using a more recent cohort of 499 pediatric patients with 2,138 partial pressure of carbon dioxide measurements collected from Seoul National University Hospital between January 2024 and June 2025.
To maintain consistency with the developed model, the same patient cohort selection criteria and missing value imputation methods were applied. However, the presence of several outliers in the tidal volume represented one major difference. After the clinical review, data identified as device errors and outliers were replaced with tidal volume values adjusted on the basis of the standard body weight for age, following the pediatric guidelines. The detailed demographic and clinical characteristics of the external validation cohorts are presented in Supplemental Digital Content table S3 (https://links.lww.com/ALN/E643).
All model development and validation processes were performed using Python (version 3.10.3; Python Software Foundation, https://www.python.org/) and open libraries, including Pandas, NumPy, and Scikit-learn.
Results
Baseline Characteristics
Overall, 4,412 pediatric patients undergoing surgery during general anesthesia were identified as having arterial blood gas analysis checked. Of these patients, 56 were excluded owing to lacking VitalDB data. A total of 4,356 patients were included for feature engineering and data processing, resulting in 3,586 pediatric patients with 8,853 data for the model development (fig. 1). Because some patients underwent multiple arterial blood gas analyses during surgery, the number of observations per patient ranged from 1 to 14, with a mean of 2.47 measurements per patient. To minimize the risk of model overfitting due to disproportionately large data contributions from certain patients, we limited the maximum number of records per patient to five during model development.
The baseline patient characteristics are presented in table 4. Patient demographics, including age, sex, BMI, ASA Physical Status, and surgical position, were comparable between the training and test sets. The distribution of these characteristics across the datasets was well balanced, indicating appropriate allocation into the training, test, and holdout validation sets among the patients.
Table 4.
Comparison of Patient Demographics and Characteristics between the Training and Test Sets
| Features | Total (%) | Training Set (n = 6,197) |
Test Set (n = 1,328) |
P Value | Standardized Mean Difference | |
|---|---|---|---|---|---|---|
| Age, yr | 6.05 ± 5.40 | 5.65 ± 5.28 | 5.43 ± 5.33 | 0.28 | 0.04 | |
| Male | 4,818 (54.42) | 2,078 (56.56) | 492 (54.06) | 0.98 | 0.00 | |
| BMI, kg/m2 | 17.72 ± 4.42 | 17.54 ± 3.95 | 17.64 ± 4.22 | 0.52 | −0.02 | |
| ASA | I | 710 (8.02) | 193 (7.06) | 69 (7.57) | 0.76 | −0.01 |
| II | 4,476 (50.56) | 1,317 (48.15) | 462 (50.66) | |||
| III | 3,095 (34.96) | 1,046 (38.24) | 335 (36.73) | |||
| IV | 538 (6.08) | 172 (6.29) | 45 (4.93) | |||
| V | 34 (0.38) | 7 (0.26) | 1 (0.11) | |||
| Lateral position | 977 (11.03) | 316 (11.55) | 126 (13.82) | 0.65 | −0.02 | |
Values are presented as mean ± SD for continuous variables and as numbers (percentages) for categorical variables.
ASA, American Society of Anesthesiologists Physical Status classification; BMI, body mass index.
Model Performance in Estimating Partial Pressure of Arterial Carbon Dioxide
Table 5 summarizes the model performances. Among the four models, the gradient boosting demonstrated the best overall performance, achieving the lowest mean absolute error (2.73), mean absolute percentage error (6.75), mean squared error (17.08), and root mean squared error (4.13). Furthermore, the multilayer perceptron exhibited a strong performance, particularly in mean absolute error (3.20) and mean absolute percentage error (8.04), indicating relatively low prediction errors. In contrast, across all metrics, the decision tree showed the highest error values, with a root mean squared error of 5.29, suggesting that it can be more susceptible to overfitting or variability in predictions. The scatter plot in figure 4 visualizes the model performance results. As shown in the scatter plot, the gradient boosting model exhibits the most tightly clustered points, indicating better accuracy. Moreover, the multilayer perceptron, gradient boosting, and random forest models demonstrate relatively well-clustered distributions, whereas the decision tree model has a more scattered distribution, suggesting more significant variability in its estimations.
Table 5.
Performance Comparison of the Machine Learning Algorithms
| Machine Learning Algorithm | Mean Absolute Error | Mean Absolute Percentage Error | Mean Squared Error | Root Mean Squared Error |
|---|---|---|---|---|
| Gradient boosting | 2.73 | 6.75 | 17.08 | 4.13 |
| Random forest | 2.84 | 7.54 | 20.78 | 4.55 |
| Decision tree | 3.45 | 8.58 | 28.05 | 5.29 |
| Multilayer perceptron | 3.20 | 8.04 | 24.20 | 4.91 |
Fig. 4.
Scatter plot visualizing model performance. Each subplot displays the relationship between the estimated and measured partial pressure of arterial carbon dioxide using (A) gradient boosting, (B) random forest, (C) decision tree, and (D) multilayer perceptron. The dashed line represents the line of identity; the more accurate the predictions, the more closely the points are clustered around the diagonal. MLP, multilayer perceptron; PaCO2, partial pressure of arterial carbon dioxide.
Model Performance Compared with End-tidal Carbon Dioxide–only Baseline
To evaluate the clinical utility of our proposed model, we compared its performance with that of a baseline model that used only end-tidal carbon dioxide as a feature. The gradient boosting model significantly outperformed the end-tidal carbon dioxide-only model, achieving a lower mean absolute error (2.73 mmHg vs. 3.56 mmHg) and demonstrating superior accuracy across all evaluation metrics. Notably, the end-tidal carbon dioxide–only model consistently underestimated the partial pressure of carbon dioxide, particularly at higher levels, whereas the proposed model maintained greater fidelity across the full physiologic spectrum.
The superiority of the machine learning model was further visualized using a Bland–Altman plot (fig. 5), which highlighted narrower limits of agreement and reduced systematic bias compared to the conventional end-tidal carbon dioxide-based estimation.
Fig. 5.
Bland–Altman plot comparing the full-feature gradient boosting model (blue) and the end-tidal carbon dioxide (EtCO2)–only model (red).
Feature Importance
In this model development study, the feature importance of the gradient boosting model, the model with the best performance among the four models, was determined using Shapley additive explanations values (fig. 6). Subsequently, to identify the most significant features, the iterative feature selection method was applied. This method was adopted to optimize model performance by reducing noise and complexity, validate Shapley additive explanations–based feature importance through stepwise evaluation, and improve interpretability by identifying the most impactful features in high-dimensional medical data. Consequently, 10 features were identified; among the 10 features, end-tidal carbon dioxide, body temperature, and fraction of inspired oxygen were the top 3 most significant features in the model. Because Shapley additive explanations allow directional interpretation of feature effects, high feature values (e.g., high end-tidal carbon dioxide or body temperature) were found to shift model outputs toward higher estimated partial pressure of carbon dioxide, whereas lower values tended to lower estimations, indicating bidirectional and physiologically consistent influence patterns.
Fig. 6.
Contribution of each input variable to the partial pressure of carbon dioxide estimation using the Shapley additive explanations values. Features are ranked by their overall impact on the model output, with the color indicating the magnitude of the feature value (red, high; blue, low). Higher feature values (such as end-tidal carbon dioxide or other physiologic inputs) tended to shift predictions toward higher partial pressure of carbon dioxide, whereas lower values showed the opposite trend. Alb, albumin; ASA, American Society of Anesthesiologists; BMI, body mass index; Cr, creatinine; EtCO2, end-tidal carbon dioxide; FiO2, fraction of inspired oxygen; Hb, hemoglobin, MAC, minimum alveolar concentration; PEEP, positive end-expiratory pressure; PIP, peak inspiratory pressure; preop, preoperative; SHAP, Shapley additive explanations.
Model Performance Considering Feature Importance
Figure 7 shows the association between mean absolute error and mean squared error according to the number of features in the partial pressure of arterial carbon dioxide estimation. When the number of features reached 10, mean absolute error and mean squared error were the lowest in the range of the stabilized stage when estimating partial pressure of arterial carbon dioxide. Finally, the following were the 10 selected features: end-tidal carbon dioxide, body temperature, minute volume, age, fraction of inspired oxygen, presence of cardiac disease, compliance, preoperative laboratory results of hemoglobin, BMI, and mean arterial pressure.
Fig. 7.
Association between mean absolute error and mean squared error according to the number of features in the partial pressure of arterial carbon dioxide estimation. Mean absolute error (red) and mean squared error (blue) plotted according to the number of selected features. The lowest value is achieved when utilizing 10 features. MAE, mean absolute error; MSE, mean squared error.
Table 6 presents the model performances. Integrating the top 10 features of the gradient boosting model from the primary analysis, this analysis demonstrated a similar performance trend. The gradient boosting delivered the best results again, with the lowest mean absolute error (2.80). The random forest followed closely, performing better than the decision tree and multilayer perceptron.
Table 6.
Performance Comparison of Machine Learning Algorithms with Selected Features
| Features | Mean Absolute Error | Mean Absolute Percentage Error | Mean Squared Error | Root Mean Squared Error |
|---|---|---|---|---|
| Gradient boosting | 2.80 | 6.90 | 19.44 | 4.40 |
| Random forest | 2.91 | 7.67 | 22.09 | 4.70 |
| Decision tree | 3.49 | 9.08 | 29.07 | 5.39 |
| Multilayer perceptron | 3.22 | 8.28 | 25.63 | 5.06 |
External Validation
The final model, trained using the top 10 selected features, was evaluated on an independent external validation dataset from CNUH and a temporally separated cohort from Seoul National University Hospital (table 7).
Table 7.
Performance Comparison of the Machine Learning Algorithms with Selected Features for External Validation
| Validation Set | Machine Learning Algorithm | Mean Absolute Error | Mean Absolute Percentage Error | Mean Squared Error | Root Mean Squared Error |
|---|---|---|---|---|---|
| CNUH external validation |
Gradient boosting | 3.65 | 9.79 | 31.98 | 5.65 |
| Random forest | 3.36 | 8.97 | 20.99 | 4.58 | |
| Decision tree | 3.09 | 8.45 | 19.03 | 4.36 | |
| Multilayer perceptron | 3.56 | 9.61 | 23.34 | 4.83 | |
| SNUH temporal validation |
Gradient boosting | 3.67 | 10.57 | 21.44 | 4.63 |
| Random forest | 3.94 | 11.29 | 24.56 | 4.95 | |
| Decision tree | 4.05 | 11.49 | 27.41 | 5.23 | |
| Multilayer perceptron | 4.62 | 12.73 | 45.47 | 6.74 |
CNUH, Chungnam National University Hospital; SNUH, Seoul National University Hospital.
On the CNUH external validation dataset, the decision tree achieved the best overall performance among all models, with a mean absolute error of 3.09; mean absolute percentage error, 8.45; mean squared error, 19.03; and root mean squared error, 4.36. This indicates that the model maintained strong predictive performance even on a completely independent institutional dataset.
For temporal validation using the Seoul National University Hospital cohort, the gradient boosting model showed relatively consistent performance with a mean absolute error of 3.67; mean absolute percentage error, 10.57; mean squared error, 21.44; and root mean squared error, 4.63. These findings confirm that the model demonstrates robustness and generalizability across both external institutions and temporally distinct datasets, supporting its potential for broader clinical application. Despite the decision tree’s marginally lower error on the small CNUH set (n = 50), gradient boosting was selected for its best internal performance and consistent generalization.
Discussion
This study revealed that by using machine learning, continuous end-tidal carbon dioxide values were feasible for intraoperatively estimating partial arterial pressure of carbon dioxide in children using end-tidal carbon dioxide, body temperature, fraction of inspired oxygen, preoperative laboratory results of hemoglobin, BMI, age, mean arterial pressure, presence of cardiac disease, compliance, and minute volume. Typically, end-tidal carbon dioxide is 2 to 5 mmHg lower than partial pressure of arterial carbon dioxide owing to the dead space in the airway, alveolar–arterial gradient, and ventilation-perfusion mismatch.2 These differences cannot be fundamentally eliminated; however, several studies have been conducted for estimating partial pressure of arterial carbon dioxide using the noninvasive monitoring method of end-tidal carbon dioxide–utilizing nomograms, test results, or clinical information, including mechanical ventilation parameters and laboratory test results.11,27–29 This study is significant in that it represents the first attempt to estimate the partial pressure of arterial carbon dioxide in pediatric patients using intraoperative data.
Arterial catheters, while essential for blood gas analysis, pose risks of iatrogenic anemia—a critical concern in neonates already facing surgical blood loss.30 Beyond anemia, certain clinical scenarios require strict control of arterial carbon dioxide partial pressure, yet may justify avoiding arterial cannulation.31,32 In short pediatric neurosurgical procedures like shunt revisions, where precise regulation of cerebral blood flow and intracranial pressure is paramount, the risk of vascular injury in small infants often outweighs the benefits of invasive monitoring. Our model provides value in this gray zone by offering more accurate estimates of arterial carbon dioxide partial pressure than end-tidal carbon dioxide alone, thereby supporting neuroprotective strategies without arterial access. Ultimately, this tool is intended to complement existing monitoring by providing continuous insights between intermittent blood gas measurements rather than replacing accepted standard invasive techniques.
In various clinical situations, the end-tidal carbon dioxide and partial pressure of arterial carbon dioxide gradient would be valuable surrogate markers. This gradient may be associated with in-hospital mortality in patients after cardiac arrest, those with acute respiratory distress syndrome, or those with blunt brain injury.33–35 However, these high-risk patient groups were not included in this study, which may explain why the observed difference was comparable to that of previous studies. To assess the impact of this gradient in a broader patient population, including those with critical illness, further studies are warranted.
End-tidal carbon dioxide is frequently utilized in the operating room when performing endotracheal intubation or using a laryngeal mask airway. Under these conditions, end-tidal carbon dioxide measurements are highly reliable, enabling a predictable estimation of the end-tidal carbon dioxide and partial pressure of arterial carbon dioxide difference. Usually a rough estimate of partial pressure of arterial carbon dioxide from end-tidal carbon dioxide is acceptable in routine clinical practice. However, even a small absolute estimation error can be clinically meaningful in patients with increased intracranial pressure or impaired cerebral blood flow. It is well known that the cerebral blood flow changes by approximately 2 to 4% per 1-mmHg change in partial arterial pressure of carbon dioxide; therefore, an estimation error of approximately 3 mmHg may translate into a 6 to 12% change in cerebral perfusion, which could be clinically significant in these vulnerable populations.36 Ventilator adjustments are commonly made in increments intended to change partial pressure of arterial carbon dioxide by only a few millimeters of mercury, meaning that a 3-mmHg error is on the same scale as a typical clinical intervention. Consequently, even small systematic errors can prompt changes in ventilator management, such as adjustments in respiratory rate or minute ventilation, or trigger confirmatory arterial blood gas analysis when sampling is intermittent and partial pressure of arterial carbon dioxide targets are narrowly defined.
Beyond airway management, intraoperative factors, including laparoscopic procedures, which have increasingly become the standard of care in pediatric surgery, can also influence end-tidal carbon dioxide levels. The use of carbon dioxide pneumoperitoneum, which is essential for maintaining surgical field visibility, may alter carbon dioxide exchange and impact the end-tidal carbon dioxide and partial pressure of arterial carbon dioxide gradient. In our analysis, intraoperative factors, including surgical position, were considered to improve the interpretation of partial pressure of arterial carbon dioxide estimation based on end-tidal carbon dioxide, highlighting the need for further investigation into how laparoscopic conditions affect the accuracy of end-tidal carbon dioxide in reflecting partial pressure of arterial carbon dioxide during surgery.
The random forest model identified 10 key features for estimating arterial carbon dioxide partial pressure, including end-tidal carbon dioxide, body temperature, and fraction of inspired oxygen. As the most significant factor, end-tidal carbon dioxide reflects the carbon dioxide diffusing from the bloodstream. Pediatric patients are especially vulnerable to intraoperative hypothermia, which causes abrupt changes in metabolic rate and carbon dioxide production, directly influencing the arterial–to–end-tidal carbon dioxide gradient.37 Similarly, due to smaller lung volumes and higher metabolic rates, changes in fraction of inspired oxygen significantly alter alveolar ventilation and end-tidal carbon dioxide levels. Furthermore, integrating cardiac comorbidities significantly improved model performance by accounting for underlying physiologic shunts and dead space ventilation, which are critical determinants of the carbon dioxide gradient.
Preoperative hemoglobin levels are weakly inversely correlated with mean end-tidal carbon dioxide and arterial carbon dioxide partial pressure,38 likely due to hemoglobin’s role in oxygen transport and metabolic regulation. Mean arterial pressure, a key indicator of cardiac output and organ perfusion, was also included because decreased pressure reduces pulmonary blood flow and impairs carbon dioxide clearance.39–41 These factors highlight the physiologic link between cardiovascular function and respiratory gas exchange. Additionally, lung compliance and minute volume were incorporated as they directly correlate with carbon dioxide elimination; reductions in these parameters lead to carbon dioxide retention, while hyperventilation causes excessive elimination.42 Integrating these multifactorial dynamics ensures a more robust estimation of arterial carbon dioxide partial pressure.
While the correlation between age and arterial carbon dioxide partial pressure is often weak in adults, age emerged as a key feature in our pediatric model. This importance likely reflects the high prevalence of diverse comorbidities in pediatric surgical cases compared to the general healthy population. Furthermore, stratifying the cohort into two age groups—infants versus older children—yielded superior model performance and clinical applicability compared to standard statistical methods like multiple imputation by chained equations.
The model was externally validated using a 50-patient cohort, yielding a mean absolute error of 3.65 mmHg. To enhance generalizability, a larger temporal validation was conducted at Seoul National University Hospital between January 2024 and June 2025. This confirmed stable predictive accuracy across different timeframes and clinical environments, affirming the robustness of the machine learning–based estimation of arterial carbon dioxide partial pressure. Building on these findings, the model could theoretically be integrated into real-time monitoring displays to present trends in the estimated partial pressure of arterial carbon dioxide, enabling continuous ventilatory assessment without invasive sampling. It also serves as an early detection tool, prompting clinicians to consider arterial blood gas analysis or ventilator adjustments when discrepancies between estimated and measured values exceed predefined thresholds. This “digital safety net” is particularly valuable in settings requiring tight carbon dioxide control, such as neurosurgical anesthesia, to support timely and precise clinical decision-making.
This study has several limitations. First, the model excluded nonintubated patients. Given that pediatric sedation for diagnostic procedures (e.g., magnetic resonance imaging) often occurs without intubation, extending partial pressure of arterial carbon dioxide estimation to these scenarios remains clinically relevant. Second, laparoscopic and thoracoscopic cases were excluded because essential parameters, such as carbon dioxide insufflation pressure and timing, were unavailable. Including these cases without such data could have introduced significant confounding, potentially compromising model reliability. Future research should validate the model in surgical settings involving exogenous carbon dioxide insufflation. Next, the observed mean absolute error of 2.73 mmHg may call into question the clinical value of the model in some patients. Finally, while this study establishes a robust algorithmic foundation, the model has not yet been deployed as a functional clinical decision support system. Successful implementation requires integration into electronic medical record and physiologic monitoring architectures to ensure real-time data synchronization. The need to integrate electronic medical record (e.g., hemoglobin, ASA Physical Status, BMI) with real-time physiologic data presents a challenge that was not addressed in the current work. Prospective clinical trials are necessary to refine the user interface and verify that the system effectively supports, rather than distracts, the clinical workflow.
Conclusions
In conclusion, we developed a model to estimate arterial carbon dioxide partial pressure using end-tidal carbon dioxide and routinely available clinical variables, demonstrating good performance. While the model is not intended to replace arterial blood gas analysis or invasive monitoring when clearly indicated, it may serve as a supportive tool to assist clinicians in situations where arterial sampling is intermittent or arterial catheter placement is undesirable. Further prospective studies are warranted to evaluate the feasibility of model implementation and the model’s impact on clinical decision-making and patient outcomes in real-world settings.
Research Support
This study was supported and funded by the Seoul National University Hospital Lee Kun-hee Child Cancer and Rare Disease Project, Seoul National University Hospital, Seoul, Republic of Korea (grant No.: 22C-003-0100). This work was supported by a National Research Foundation of Korea grant funded by the Ministry of Science and ICT, Sejong, Republic of Korea (RS-2025-00553891). This research was supported by a grant of the Korea Health Technology Research and Development Project through the Korea Health Industry Development Institute (KHIDI), Cheongju, Republic of Korea (RS-2025-02313278, RS-2025-02223731).
Competing Interests
The authors declare no competing interests.
Supplemental Digital Content
Supplemental tables and figures, https://links.lww.com/ALN/E643
Supplementary Material
Abbreviations:
- ASA
- American Society of Anesthesiologists
- BMI
- body mass index
- CNUH
- Chungnam National University Hospital
Supplemental Digital Content is available for this article. Direct URL citations appear in the printed text and are available in both the HTML and PDF versions of this article. Links to the digital files are provided in the HTML text of this article on the Journal’s Web site (www.anesthesiology.org).
Sachin Kheterpal, M.D., M.B.A., served as Handling Editor for this article.
Part of the work presented in this article has been presented at the Aotearoa New Zealand Anaesthesia Annual Scientific Meeting in Auckland, New Zealand, November 7 to 9, 2024.
J.H.P. and C.C. contributed equally to this article.
The article processing charge was funded by a National Research Foundation of Korea grant funded by the Korean government (Ministry of Science and ICT) (No. RS-2025-00553891).
Contributor Information
Ju Hyoun Park, Email: 08juuj80@gmail.com.
Hee-Soo Kim, Email: kksoo716@gmail.com.
Boohwi Hong, Email: koho0127@gmail.com.
Chang-Hoon Koo, Email: vollock9@snubh.org.
Kwangsoo Kim, Email: kksoo716@gmail.com.
Hyun Ho Kim, Email: hyunhokim@jbnu.ac.kr.
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