Abstract
Objectives
This study aims to investigate the relationship between calculated serum osmolarity levels and 90-day mortality in patients with acute pancreatitis (AP), an association that remains understudied in the intensive care unit (ICU).
Methods
This study utilized clinical data from patients diagnosed with AP in the Medical Information Mart for Intensive Care database. Localized Weighted Scatterplot Smoothing (LOWESS) regression, Restricted Cubic Spline (RCS) analysis, and the U test were employed to examine the nonlinear relationship between calculated serum osmolarity and patient outcomes. Additionally, multivariate logistic regression analysis was applied to assess the impact of calculated serum osmolarity on prognosis after adjusting for potential confounding factors such as Demographic data, disease severity scores, and comorbidities.
Results
The study included 2046 patients with AP. Calculated serum osmolarity levels differed significantly between survivors and non-survivors (302.4 ± 14.9 vs. 308.9 ± 19.6 mOsm/L, P < 0.001). Both univariate and multivariate logistic regression analyses demonstrated that calculated serum osmolarity was an independent prognostic factor for 90-day mortality (P < 0.05 in both analyses). LOWESS regression, RCS analysis, and U-test results revealed a U-shaped relationship between calculated serum osmolarity and 90-day mortality, with an inflection point (lowest mortality risk) at 293.3 mOsm/L. The excessively high calculated serum osmolarity levels were associated with increased mortality risk (P < 0.05). Subgroup analysis revealed that high calculated serum osmolarity was significantly associated with higher 90-day mortality (P < 0.05). Survival analysis revealed a significant increase in mortality risk when calculated serum osmolarity reached the fourth quartile or higher (all P < 0.05), whereas no significant differences were observed among lower quartile groups.
Conclusions
The results of this study indicate that calculated serum osmolarity levels exhibit a U-shaped correlation with 90-day all-cause mortality among patients with AP admitted to the ICU, with high calculated serum osmolarity serving as an independent risk factor for 90-day mortality.
Supplementary Information
The online version contains supplementary material available at 10.1186/s12876-026-04798-2.
Keywords: Serum osmolarity, Acute Pancreatitis, Risk factors, Cohort study, Critical care
Introduction
Acute pancreatitis (AP) is one of the primary conditions among patients hospitalized for gastrointestinal diseases [1]. It imposes a significant medical burden and cost—for instance, hospitalization expenses in the United States exceed $30,000 per patient—making it crucial to reduce both the burden and costs associated with AP [2]. Studies indicate that AP exhibits high incidence and mortality rates, with the overall incidence increasing by 3.07% annually and the overall mortality rate reaching approximately 1%. Patients experiencing organ failure or pancreatic necrosis face significantly higher mortality rates [2]. Regarding prognosis, AP can cause localized or systemic damage. Organ failure occurs in approximately 20% of AP cases, including acute respiratory failure, acute kidney injury (AKI), and cardiovascular failure, indicating that AP may lead to severe outcomes [3, 4]. A study of AP patients found that the relative risk of death doubled when organ failure or infected pancreatic necrosis coexisted [5]. However, conventional prognostic tools such as APACHE Ⅱ score and BISAP score are limited by complexity in calculation and delayed availability, while biomarkers like C-reactive protein lack early predictive value. Thus, exploring simple, accessible, and reliable prognostic biochemical markers for critically ill AP patients remains an unmet clinical need.
Serum osmolarity plays a crucial role in regulating intracellular and extracellular water distribution, maintained by homeostasis mechanisms primarily governed by the collective concentration of solutes in blood plasma (e.g., sodium and associated anions, potassium, glucose, and urea) [6]. Serum osmolarity is crucial for regulating water and electrolyte balance, maintaining fluid equilibrium, and modulating renal function. In critically ill AP patients, serum osmolarity homeostasis is frequently disrupted by multiple factors: excessive capillary leakage induced by SIRS leads to hypovolemia and subsequent hyperosmolality, while aggressive fluid resuscitation (a cornerstone of SAP management) may cause hemodilution and hypo-osmolality [7]. Abnormal serum osmolarity, in turn, exacerbates cellular dysfunction—hyperosmolality induces cell dehydration and organ hypoperfusion, while hypo-osmolality contributes to cerebral edema and pulmonary edema—forming a vicious cycle that may worsen disease severity. This suggests that serum osmolarity could serve as a direct, real-time surrogate for fluid balance and organ function in critically ill AP patients.
Emerging evidence indicates that abnormal serum osmolarity correlates with increased mortality in critically ill populations, such as those with sepsis and diabetic ketoacidosis (DKA). For instance, studies reveal a U-shaped relationship between serum osmolarity and 28-day mortality in sepsis patients: elevated serum osmolarity (> 303.21 mOsm/L) increased 28-day mortality by 99%, while elevated serum osmolarity (≥ 305.80 mOsm/L) increased 28-day mortality by 59% [8]. Additionally, studies on DKA revealed that elevated amylase levels correlate with both pH and serum osmolarity, whereas elevated lipase levels correlate solely with serum osmolarity [9]. However, current research on the relationship between serum osmolarity and prognosis in critically ill AP patients remains scarce: existing studies have failed to elucidate the distribution characteristics of serum osmolarity or identify optimal cutoff values for predicting mortality. Furthermore, it remains unclear whether bidirectional deviations (both high and low) in serum osmolarity are independently associated with adverse outcomes in this cohort.
To address these gaps, this retrospective cohort study extracted clinical, biochemical, and prognostic data from critically ill AP patients in the MIMIC-III Clinical Database CareVue subset and MIMIC-IV databases (two large-scale, publicly available intensive care unit(ICU) databases with comprehensive records of critically ill patients). We aimed to: (1) characterize the distribution of serum osmolarity in critically ill AP patients; (2) investigate the correlation between serum osmolarity levels (including bidirectional deviations) and 90-day mortality; and (3) explore the potential of serum osmolarity as a prognostic marker for this population. We hypothesized that serum osmolarity outside the normal reference range (275–295 mOsm/L) would be independently associated with an increased risk of 90-day mortality in critically ill AP patients.
Materials and methods
Study design
The researchers conducted this study following the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) framework guidelines for reporting studies in epidemiology [10].
Data sources
The researchers obtained data for this study from the MIMIC-IV v2.0 and MIMIC-III Clinical Database CareVue subset v1.4 databases, specifically the records of ICU patients at the Beth Israel Deaconess Medical Center [11, 12]. Ruan completed the Collaborative Institutional Training Initiative (CITI) online training course, securing authorization to access and utilize data from the MIMIC databases. Ethical approval was secured from the Ethics Committee of Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology (Approval Number: TJ-IRB202507049). Given the retrospective nature of this study, the requirement for informed consent was deemed waived. Figure 1 depicts the research methodology.
Fig. 1.
Flow chart of the study design
Study population
The study cohort comprised adult patients (aged ≥ 18 years) diagnosed with AP who were admitted to the ICU for the first time in the Beth Israel Deaconess Medical Center. Inclusion criteria were established based on the International Classification of Diseases (ICD), with reference to ICD-9 and ICD-10 to define the AP group (Supplementing Table 1). The following exclusion criteria were applied: (1) presence of duplicate admission records; (2) pediatric patients (aged < 18 years); (3) patients with missing information of sodium, potassium, glucose, and urea.
Study variables
The primary objective of this study was to investigate the impact of calculated serum osmolarity on 90-day mortality in AP patients, calculated using the formula (Na + K) × 2 + (glucose/18) + (urea/2.8) [13]. The calculations utilized plasma sodium, potassium, glucose, and urea values measured from a single blood sample collected at the same time point within the first 24 h after admission. Patients lacking sufficient data for calculated serum osmolarity calculation were excluded. Plasma protein levels were omitted as they contribute only ~ 0.4% to calculated serum osmolarity [14]. Sensitivity analysis showed highly consistent results using osmolarity formulas with and without potassium, with similar effect sizes, 95% CIs, and statistical significance in logistic regression for 90-day mortality. Confounding variables: Demographic data (age, sex, race), clinical characteristics (ICU admission diagnosis, vital signs at admission), disease severity scores (Sequential Organ Failure Assessment(SOFA), Organ Failure Assessment and Information System(OASIS), Glasgow Coma Scale (GCS), Charlson Comorbidity Index(CCI)) measured within 24 h of ICU admission, and comorbidities (hypertension, congestive heart failure, renal disease, chronic pulmonary disease) were collected as potential confounding factors [15–20]. Intensive care treatment (vasopressin, dopamine, norepinephrine, mechanical ventilation, continuous renal replacement therapy (CRRT)) is considered a mediating variable(Supplementing Fig. 2, Supplementing Table 2, Supplementing Table 3). Age was stratified into elderly (≥ 60 years) and non-elderly (< 60 years) groups, consistent with previous AP prognostic studies [21]. Race was categorized as white and non-white due to limited sample size in minority groups. Multicollinearity among confounding variables was assessed using Variance Inflation Factor (VIF), with all VIF values < 10 indicating no significant multicollinearity (Supplementing Table 4).
Categorical variables were defined as follows: Sex was categorized as male or female based on biological sex. Race was divided into white and non-white groups. Age was stratified into elderly (≥ 60 years) and non-elderly groups using 60 years as the cutoff. The CCI was used to assess the impact of comorbidities on patient prognosis. The CCI is a tool that evaluates clinical status and prognostic outlook based on patient comorbidities and health status [16]. Given the lack of direct pathophysiological associations between certain components of the CCI and the exposures and outcomes in this study, and to avoid potential overcorrection or residual confounding from including unrelated comorbidities, we selected hypertension, congestive heart failure, chronic pulmonary disease and renal disease—conditions highly correlated with the mechanisms of acute pancreatitis based on other studies—as core comorbidities to include as covariates in the multivariate model. GCS was used to assess patients’ level of consciousness [17]. Additionally, the SOFA and OASIS scores were employed to measure disease severity [15, 18–20].
Clinical outcome
The primary clinical outcome of this study was defined as the 90-day all-cause mortality rate in patients with AP. Secondary clinical outcomes included assessments of the 28-day all-cause mortality rate, 60-day all-cause mortality rate, and in-hospital mortality rate. Mortality status and follow-up time were confirmed using the MIMIC database’s discharge records, social security death index, and hospital follow-up registry.
Statistical analysis
All statistical analyses were performed using Stata 18.0 (StataCorp LLC, College Station, TX, USA). A two-sided P value < 0.05 was considered statistically significant.
Descriptive statistics
Continuous variables were tested for normality using the Shapiro-Wilk test. Normally distributed variables were expressed as mean ± standard deviation (SD) and compared using independent samples t-test; non-normally distributed variables were presented as median (interquartile range, IQR [Q1, Q3]) and compared using the Mann-Whitney U test (two groups) or Kruskal-Wallis H test (three groups). Categorical variables were expressed as counts (percentages) and compared using the χ² test or Fisher’s exact test (when expected frequency < 5).
Non-linear and U-shaped association tests
Localized Weighted Scatterplot Smoothing (LOWESS) with a smoothing coefficient of 0.8 was used for preliminary visualization of non-linear relationships between calculated serum osmolarity and 90-day mortality. Restricted Cubic Spline (RCS) regression (incorporated into Logistic models) was further applied to quantify non-linear associations, with 4 knots (at the 5th, 35th, 65th, and 95th percentiles of calculated serum osmolarity) to balance flexibility and stability. The actual values corresponding to the 5th, 35th, 65th, and 95th percentiles of calculated serum osmolarity distribution are 282.98, 296.99, 306.27, and 335.49 mOsm/L, respectively. Trend analysis is conducted by integrating the RCS of calculated serum osmolarity into logistic regression. U-shaped associations were tested using the “utest” command in Stata, with the minimum mortality risk point as the inflection point.
Association analysis
A logistic regression model was used to assess the association between calculated serum osmolarity and 90-day mortality. To avoid mediating variable adjustment, stratified analyses were conducted according to admission SOFA score (≤ 4, 4–8, > 8). RCS models showed a significant nonlinear association between calculated serum osmolarity and 90-day mortality in the overall cohort (P < 0.001), which persisted in patients with low (P = 0.007) and moderate SOFA scores (P = 0.042) but not in those with high SOFA scores (P = 0.565). Calculated serum osmolarity(Q2, Q4) and moderate SOFA scores were significant (P < 0.05). Calculated serum osmolarity was categorized into quintiles (Q1-Q5). Five models were constructed: Model 1 (unadjusted crude model); Model 2 (adjusted for demographic variables: age and sex); Model 3 (fully adjusted model, including Model 2 variables plus ethnicity) ; Model 4 (fully adjusted model including variables from Model 3 plus GCS, SOFA, and OASIS); Model 5 (fully adjusted model including variables from Model 4 plus hypertension, congestive heart failure, renal disease). Odds ratios (OR) and 95% confidence intervals (CI) were reported. The events‑per‑variable (EPV) ratio was calculated for each multivariable model to assess the risk of overfitting(Supplementing Table 5).
Prognosis analysis
Kaplan-Meier survival analysis and Cox proportional hazards models were employed to evaluate the relationship between different calculated serum osmolarity levels and prognosis. Calculated serum osmolarity was grouped into quintiles (Q1-Q5). Pairwise log-rank tests and Cox regression were used to calculate hazard ratios (HR) and 95% confidence intervals. Using LASSO regression, 13 variables were evaluated: calculated serum osmolarity, age, sex, GCS, SOFA, CCI, OASIS, Hypertension, Congestive Heart Failure, Chronic Pulmonary Disease, Renal Disease, Vasopressors, and Mechanical Ventilation. Machine learning models were constructed to predict 90-day all-cause mortality. Thirteen clinical features were selected via LASSO regression with 5-fold cross-validation, including age, sex, GCS, SOFA, OASIS, comorbidities, vasopressors, mechanical ventilation, calculated serum osmolarity, and CCI. Missing continuous values were imputed by mean; categorical variables were one-hot encoded, and all features were standardized. The dataset was split into 70% training and 30% test sets (fixed random state). Random Forest, SVM, Gradient Boosting, and XGBoost models were developed, with hyperparameter optimization to reduce overfitting. Model performance was evaluated by AUC (95% CIs via 1000 bootstrap resamplings), calibration curves, and decision curve analysis. Predictive performance was compared with the traditional SOFA score, with AUC differences tested via bootstrap. Feature importance was derived from the optimal Random Forest model.
Missing data handling
Using retrospectively collected clinical data involving 2,046 patients, statistical tests revealed that the pattern of missing values for the clinical variable GCS was not completely random. For GCS, missing values were imputed using a combined K-nearest neighbor (KNN) and Random Forest algorithm: the dataset was split into training (70%) and testing (30%) sets; KNN interpolation (K = 3, optimal based on minimum root mean square error [RMSE]) was applied to the training set, followed by a Random Forest model (with age, sex, and SOFA score as features) to optimize imputation. The final RMSE on the testing set was 3.041, indicating reliable imputation (Supplementing Fig. 3). A sensitivity analysis using complete-case analysis (excluding observations with missing GCS) yielded results virtually identical to those from our primary analysis that employed KNN and Random Forest algorithm.
Sensitivity analysis
Sensitivity analyses were conducted to address potential dynamic fluctuations in blood glucose and the effects of CRRT, which may limit the interpretation of a single baseline osmolality measurement. The primary exposure was calculated serum osmolality using sodium, potassium, glucose, and urea measured simultaneously within 24 h of admission. Logistic regression with restricted cubic splines was used to evaluate the nonlinear association with 90-day mortality. We further performed sensitivity analyses including repeated testing, CRRT stratification, and glucose subgroup analyses to validate the robustness of the single-point measurement and partially compensate for the lack of serial data(Supplementing Tables 6, 7 and 8).
Proportional Hazards (PH) assumption
We tested the PH assumption for the main exposure (calculated serum osmolarity). In the linear Cox model, the PH test yielded χ² = 0.14 (P = 0.708). In the restricted cubic spline model, all spline terms of calculated serum osmolarity satisfied the PH assumption (all P > 0.05, minimum P = 0.496). These results confirm that the main exposure met the PH assumption in both linear and nonlinear models.
Results
Baseline characteristics of the study population
A total of 2,046 critically ill AP patients were included in the final analysis. Among them, 1,014 (49.6%) were elderly (≥ 60 years), 1,179 (57.6%) were male, and 1,325 (64.8%) were White. Based on 90-day survival status after ICU admission, patients were divided into the survivor group (n = 1,704) and non-survivor group (n = 342), with an overall 90-day mortality rate of 16.7%. Baseline characteristics stratified by 90-day mortality are summarized in Table 1.
Table 1.
Baseline characteristics of patients with AP stratified by 90-Day mortality
| Characteristics | Overall (n = 2046) | Survivor (n = 1704) | Non-survivor (n = 342) | P |
|---|---|---|---|---|
| Calculated serum osmolarity(mOsm/L) | 303.5 ± 16.0 | 302.4 ± 14.9 | 308.9 ± 19.6 | < 0.001 |
| Age, n (%) | < 0.001 | |||
| < 60 | 1032 (50.4) | 925 (54.3) | 107 (31.3) | |
| ≥ 60 | 1014 (49.6) | 779 (45.7) | 235 (68.7) | |
| Sex, n (%) | 0.396 | |||
| Male | 1179 (57.6) | 989 (58.0) | 190 (55.6) | |
| Female | 867 (42.4) | 715 (42.0) | 152 (44.4) | |
| Race, n (%) | 0.497 | |||
| White | 1325 (64.8) | 1109 (65.1) | 216 (63.2) | |
| Non-white | 721 (35.2) | 595 (34.9) | 126 (36.8) | |
| Comorbidity, n (%) | ||||
| Diabetes | 619 (30.3) | 515 (30.2) | 104 (30.4) | 0.945 |
| Hypertension | 896 (43.8) | 764 (44.8) | 132 (38.6) | 0.034 |
| Congestive heart failure | 442 (21.6) | 335 (19.7) | 107 (31.3) | < 0.001 |
| Pulmonary disease | 391 (19.1) | 318 (18.7) | 73 (21.3) | 0.249 |
| Renal disease | 336 (16.4) | 252 (14.8) | 84 (24.6) | < 0.001 |
| Treatment, n (%) | ||||
| Vasopressors | 575 (28.1) | 364 (21.4) | 211 (61.7) | < 0.001 |
| Mechanical ventilation | 900 (44.0) | 685 (40.2) | 215 (62.9) | < 0.001 |
| CRRT | 75 (3.7) | 47 (2.8) | 28 (8.2) | < 0.001 |
| Critical Care Score | ||||
| GCS | 14 (13,15) | 15 (13,15) | 14 (9,15) | < 0.001 |
| CCI | 4 (2,6) | 4 (2,6) | 6 (5,8) | < 0.001 |
| SOFA | 5 (3,8) | 4 (2,7) | 9 (5,13) | < 0.001 |
| OASIS | 32 (26,40) | 31 (25,37) | 40 (33,49) | < 0.001 |
Calculated serum osmolarity (mOsm/L): (Na + K) × 2 + (glucose/18) + (urea/2.8); CRRT Continuous Renal Replacement Therapy, GCS Glasgow Coma Scale, CCI Charlson Comorbidity Index, SOFA Sequential Organ Failure Assessment, OASIS Oxford Acute Severity of Illness Score. Continuous variables are expressed as mean ± standard deviation (e.g. Calculated serum osmolarity) or median (interquartile range) (e.g. Critical Care Score). Categorical variables are presented as n (%)
Calculated serum osmolarity differed significantly between the two groups: the survivor group had a lower mean calculated serum osmolarity than the non-survivor group (302.4 ± 14.9 vs. 308.9 ± 19.6 mOsm/L, P < 0.001). Regarding clinical treatments, the non-survivor group had a significantly higher rate of vasopressor use (61.7% vs. 21.4%, P < 0.001), mechanical ventilation (62.9% vs. 40.2%, P < 0.001), and CRRT (8.2% vs. 2.8%, P < 0.001) compared with the survivor group. The most common comorbidities were hypertension (43.8%), diabetes mellitus (30.3%), and congestive heart failure (21.6%). Notably, the non-survivor group had a higher prevalence of congestive heart failure (31.3% vs. 19.7%, P < 0.001) and renal disease (24.6% vs. 14.8%, P < 0.001) than the survivor group. Disease severity scores (SOFA, CCI, OASIS) were significantly higher in non-survivors, while the GCS score was lower (all P < 0.001), indicating more severe organ failure and acute illness in non-survivors.
Nonlinear association between calculated serum osmolarity and 90-day mortality
LOWESS regression revealed a non-linear relationship between calculated serum osmolarity and 90-day mortality, with mortality risk first decreasing and then increasing with increasing calculated serum osmolarity (Fig. 2a). RCS regression further confirmed this significant non-linear association (P for non-linearity < 0.001, Fig. 2b). The U-test validated a U-shaped relationship between calculated serum osmolarity and 90-day mortality (P < 0.001), with the inflection point (minimum mortality risk) identified at 293.3 mOsm/L, but the quadratic term was not statistically significant (z = 1.16, P = 0.245). Likelihood ratio testing comparing linear and RCS models (χ² = 10.67, P = 0.005) and joint Wald testing of RCS terms (χ² = 12.78, P = 0.005) both confirmed significant nonlinearity. To validate the robustness of this U‑shaped relationship, we performed a sensitivity analysis: excluding patients with serum sodium < 130 mOsm/L and excluding those with congestive heart failure or renal disease. The U‑shaped association remained statistically significant in both sensitivity analyses (all P for nonlinearity < 0.001, Supplementing Fig. 5).
Fig. 2.
Nonlinear relationship between calculated serum osmolarity and 90-day mortality. Panel a: Local LOWESS (smoothing factor = 0.8) was used to analyze the nonlinear association between calculated serum osmolarity and 90-day mortality, showing a trend of decreasing mortality followed by an increase with rising calculated serum osmolarity. Panel b: RCS regression model was applied to quantify this nonlinear relationship (P for nonlinearity < 0.001), with the inflection point corresponding to the calculated serum osmolarity of 293.3 mOsm/L at the lowest mortality risk. The spline was constructed with four knots at the 5th (282.98 mOsm/L), 35th (296.99 mOsm/L), 65th (306.27 mOsm/L), and 95th (335.49 mOsm/L) percentiles of calculated serum osmolarity. Panel c: Q1 (calculated serum osmolarity ≤ 291.82 mOsm/L, n = 410), Q2 (291.82–298.55 mOsm/L, n = 409), Q3 (298.55–304.62 mOsm/L, n = 409), Q4 (304.62–313.92 mOsm/L, n = 409), Q5 (≥ 313.92 mOsm/L, n = 409). The distribution of each group and their respective 90-day mortality rates (12.4%, 11.3%, 11.7%, 19.6%, and 28.6%) is presented
Additionally, calculated serum osmolarity was categorized into five quantiles for trend analysis: Q1 (calculated serum osmolarity ≤ 291.82 mOsm/L, n = 410), Q2 (291.82–298.56 mOsm/L, n = 409), Q3 (298.56–304.62 mOsm/L, n = 409), Q4 (304.62–313.92 mOsm/L, n = 409), Q5 (≥ 313.92 mOsm/L, n = 409) (Fig. 2c). The 90-day mortality rate gradually decreased from Q1 (12.4%) to Q2 (11.3%), then progressively increased in Q3 (11.7%), Q4 (19.6%), and Q5 (28.6%), confirming a U-shaped trend.
Calculated serum osmolarity as an independent prognostic factor for 90-day mortality
In univariate logistic regression analysis, incorporating the nonlinear relationship between RCS-fitted calculated serum osmolarity revealed a significant association with outcome variables (P < 0.001, Table 2), indicating its importance as a prognostic indicator. In the multivariate logistic regression model, after adjusting for covariates including age, comorbidities, and disease severity scores, calculated serum osmolarity remained significantly associated with 90-day mortality (P < 0.05, Table 2). Sensitivity analysis demonstrated that the RCS-fitted calculated serum osmolarity model outperformed the linear calculated serum osmolarity model (P < 0.05). This further confirms the existence of a genuine and robust nonlinear association between calculated serum osmolarity and 90-day mortality, ruling out any potential bias in the results due to the model specification. It suggests that a nonlinear fit for calculated serum osmolarity better reflects its true prognostic characteristics, further supporting its reliability and stability as an independent prognostic indicator(Supplementing Fig. 6).
Table 2.
Univariate and multivariate logistic regression analysis of risk factors for 90-Day mortality in patients with AP
| Characteristics | Univariate analysis | Multivariate analysis | ||
|---|---|---|---|---|
| Odds Ratio (95% CI) | P-value | Odds Ratio (95% CI) | P-value | |
| Calculated serum osmolarity | < 0.001 | 0.006 | ||
| Age (< 60 vs.≥60) | 0.383(0.299–0.491) | < 0.001 | 0.380(0.281–0.512) | < 0.001 |
| Sex (Man vs. Female) | 0.904(0.715–1.142) | 0.396 | ||
| Race (non-white vs. White) | 1.087(0.854–1.384) | 0.497 | ||
| Comorbidity | ||||
| Diabetes | 1.009(0.784–1.299) | 0.945 | ||
| Hypertension | 0.773(0.610–0.981) | 0.034 | 0.787(0.584–1.060) | 0.115 |
| Congestive heart failure | 1.861(1.438–2.408) | < 0.001 | 1.333(0.987–1.802) | 0.061 |
| Pulmonary disease | 1.183(0.889–1.574) | 0.250 | ||
| Renal disease | 1.876(1.418–2.483) | < 0.001 | 0.847(0.588–1.220) | 0.372 |
| Critical Care Score | ||||
| GCS | 0.872(0.846-0.900) | < 0.001 | 1.012(0.971–1.054) | 0.572 |
| SOFA | 1.232(1.198–1.267) | < 0.001 | 1.171(1.124–1.220) | < 0.001 |
| OASIS | 1.092(1.079–1.106) | < 0.001 | 1.037(1.018–1.056) | < 0.001 |
Calculated serum osmolarity(mOsm/L): (Na + K) × 2 + (glucose/18) + (urea/2.8); CRRT Continuous Renal Replacement Therapy, GCS Glasgow Coma Scale, SOFA Sequential Organ Failure Assessment, OASIS Oxford Acute Severity of Illness Score
Calculated serum osmolarity correlates with disease severity
Spearman’s rank correlation analysis showed that calculated serum osmolarity was significantly correlated with all disease severity scores (all P < 0.001) (Fig. 3). Weak positive correlations were observed between calculated serum osmolarity and SOFA score (rho = 0.258, P < 0.001), CCI (rho = 0.271, P < 0.001), and OASIS (rho = 0.240, P < 0.001), indicating that calculated serum osmolarity increased moderately with the severity of organ failure, chronic comorbidity burden, and acute illness. This trend is consistent with the pathophysiology of critical illness, as hyperosmolality may result from acute kidney injury, microcirculatory dysfunction, or hyperglycemia in critically ill AP patients [22]. A weak negative correlation was found between calculated serum osmolarity and GCS score (rho=-0.126, P < 0.001). Since a lower GCS score indicates more severe impaired consciousness, this correlation suggests that patients with deeper consciousness disturbance may have higher calculated serum osmolarity. Although the correlation strength is weak (indicating calculated serum osmolarity is not the primary driver of consciousness impairment), it has clinical warning value: for critically ill AP patients with deteriorating consciousness, timely detection and correction of reversible factors causing hyperosmolality (e.g., severe dehydration, hypernatremia) are recommended [23].
Fig. 3.
Spearman’s rank correlation analysis of calculated serum osmolarity and disease severity score in patients with AP. Calculated serum osmolarity was correlated with SOFA, CCI, OASIS, and GCS scores. Fitted lines and correlation coefficients (rho) demonstrated: Calculated serum osmolarity showed weak positive correlations with SOFA scores (rho = 0.258, P < 0.001), CCI (rho = 0.271, P < 0.001), and OASIS (rho = 0.240, P < 0.001); and a weak negative correlation with GCS scores (ρ = −0.126, P < 0.001). Results indicate that calculated serum osmolarity mildly increases with organ failure, chronic comorbid burden, and acute disease severity, and mildly increases with decreased level of consciousness
High calculated serum osmolarity is a risk factor for 90-day mortality
Given the observed U-shaped relationship between calculated serum osmolarity and 90-day mortality, this study evaluated the impact of calculated serum osmolarity on 90-day mortality in AP patients by constructing and adjusting a logistic regression model (Table 3). In the crude model (Model 1), both the Q4 group (OR = 1.919, 95% CI: 1.296–2.840) and the Q5 group (OR = 3.162, 95% CI: 2.175–4.597) were significantly associated with 90-day mortality. After adjusting for demographic variables (age, sex) in Model 2, the Q4 group (OR = 1.730, 95% CI: 1.163–2.574) and the Q5 group (OR = 2.772, 95% CI: 1.896–4.051) remained significantly associated with increased mortality risk. After adjusting for demographic variables (age, sex, race) in Model 3, the Q4 group (OR = 1.731, 95% CI: 1.164–2.576) and Q5 group (OR = 2.741, 95% CI: 1.873–4.011) remained significantly associated with mortality. After adjusting for demographic variables and disease severity scores (age, sex, race, GCS score, SOFA score, and OASIS score) in Model 4, only Q5 remained significantly associated with increased mortality risk (OR = 1.621, 95% CI: 1.073–2.448). In the fully adjusted model (Model 5), which included comorbidities (hypertension, congestive heart failure, renal disease), and disease severity scores (GCS, SOFA, OASIS), Q5 remained significantly associated with increased mortality risk (OR = 1.610, 95% CI: 1.061–2.444). After stepwise adjustment for demographic variables (models 2 and 3), disease severity scores (model 4), and comorbidities (model 5), this association remained stable and statistically significant (P < 0.05). These findings indicate that high calculated serum osmolarity is an independent predictor of 90-day mortality, with this association remaining robust across multiple potential confounders. To further verify the robustness of the above findings and explore the potential impact of the lowest calculated serum osmolarity group (Q1) on the results, supplementary analyses were performed. A total of 410 patients (20.04%) were included in Q1, with a 90-day mortality rate of 51/410. Baseline characteristics showed that patients in Q1 had lower disease severity and fewer comorbidities, exhibiting significant heterogeneity compared with the three intermediate quintiles. Consistent non-significant results were obtained using clinical threshold grouping (calculated serum osmolarity < 275 mOsm/L, calculated serum osmolarity > 295 mOsm/L, with 275–295 mOsm/L as the reference group; Supplementing Table 9). Both grouping strategies confirmed the same findings: there was no independent, significant risk of mortality associated with low-penetration status, whereas risks associated with high penetration were significant in the more sensitive five-digit analysis and showed a consistent trend in the threshold analysis.
Table 3.
Effect size of calculated serum osmolarity on 90-day mortality in patients with AP
| Q1 | Q2 | Q3 | Q4 | Q5 | P for trend | |
|---|---|---|---|---|---|---|
| Crude model(model 1) | 1.121(0.733–1.714) | Ref. | 1.049(0.683–1.613) | 1.919(1.296–2.840) | 3.162(2.175–4.597) | < 0.001 |
| P-value | 0.598 | 0.826 | 0.001 | < 0.001 | ||
| Model 2 | 1.318(0.856–2.030) | Ref. | 1.019(0.660–1.572) | 1.730(1.163–2.574) | 2.772(1.896–4.051) | < 0.001 |
| P-value | 0.210 | 0.934 | 0.007 | < 0.001 | ||
| Model 3 | 1.317(0.855–2.027) | Ref. | 1.018(0.660–1.571) | 1.731(1.164–2.576) | 2.741(1.873–4.011) | < 0.001 |
| P-value | 0.212 | 0.936 | 0.007 | < 0.001 | ||
| Model 4 | 1.432(0.901–2.276) | Ref. | 0.958(0.603–1.521) | 1.314(0.858–2.013) | 1.621(1.073–2.448) | < 0.001 |
| P-value | 0.128 | 0.855 | 0.209 | 0.022 | ||
| Model 5 | 1.433(0.900-2.281) | Ref. | 0.984(0.618–1.565) | 1.330(0.867–2.042) | 1.610(1.061–2.444) | < 0.001 |
| P-value | 0.129 | 0.945 | 0.191 | 0.025 |
Model 2: adjusted for age and sex; Model 3: adjusted for race, age, and sex; Model 4: adjusted for race, age, sex, GCS, SOFA, and OASIS. Model 5: adjusted for race, age, sex, GCS, SOFA, OASIS, Hypertension, Congestive Heart Failure, and Renal disease. Q1 (calculated serum osmolarity ≤ 291.82 mOsm/L, n = 410), Q2 (291.82–298.55 mOsm/L, n = 409), Q3 (298.55–304.62 mOsm/L, n = 409), Q4 (304.62–313.92 mOsm/L, n = 409), Q5 (≥ 313.92 mOsm/L, n = 409)
Additionally, Kaplan-Meier survival analysis and paired comparisons revealed a significant increase in mortality risk when calculated serum osmolarity is at its highest (P < 0.05), whereas no significant differences were observed among lower quartile groups(Fig. 4a, Supplementing Table 10). Based on LASSO analysis using 10-fold cross-validation, this study successfully identified 13 key variables predicting the risk of 90-day mortality. 13 variables were evaluated: calculated serum osmolarity, age, sex, GCS, SOFA, CCI, OASIS, Hypertension, Congestive Heart Failure, Chronic Pulmonary Disease, Renal Disease, Vasopressors, and Mechanical Ventilation. The variable importance ranking revealed that the Charlson Comorbidity Index (standardized coefficient = 0.848), OASIS score (0.539), and SOFA score (0.380) were the three most significant predictors, reflecting the central role of patients’ underlying disease burden and organ function status. Calculated serum osmolarity (standardized coefficient = 0.088) ranked eighth in importance among all selected variables. Although its predictive power was lower than that of comprehensive clinical scoring systems, it was retained in the final model by the LASSO algorithm, indicating its independent predictive value for mortality risk. This finding suggests that calculated serum osmolarity, as a biomarker reflecting fluid balance and cellular function, can provide valuable supplementary information to traditional clinical scoring systems when assessing the prognosis of critically ill patients. A LASSO coefficient path map was generated(Fig. 4b). These were incorporated into machine learning models. Among these models, the Random Forest model demonstrated the most effective predictive performance, achieving an AUC of 0.847. Its 95% confidence interval was [0.782, 0.857]; this model fits the characteristics of clinical data and can effectively capture the complex nonlinear relationships among 13 clinical indicators, and it adapts well to imbalanced data. At the same time, the model performed excellently on the test set, with an overall accuracy of 80.0%, a recall rate of 75.0% for the positive class (90-day mortality), significantly reducing the risk of missed fatal cases, while the precision for the negative class was 94.0% and the negative predictive value was 96.0%, which helps minimize excessive interventions in low-risk populations, achieving a dual balance for clinical needs (Fig. 4c-d). Moreover, the model showed slight overfitting but had good generalization ability, meeting the practical requirements for clinical models. Compared with traditional prognostic scores (such as the SOFA score), the random forest model demonstrated significantly better predictive performance than the SOFA score (P < 0.05). Feature importance ranking and SHAP analysis further clarified the correlation between calculated serum osmolarity levels in AP patients and mortality risk (Fig. 4e-f).
Fig. 4.
Calculated serum osmolarity-based risk scores effectively predict 90-day mortality in patients with acute pancreatitis. Panel a: Kaplan-Meier Survival Analysis of 90-Day Mortality in Patients with AP Stratified by Calculated serum osmolarity. Panel b: This figure illustrates the process of selecting predictive variables through LASSO regression with 10-fold cross-validation. The vertical axis displays standardized regression coefficients, while the horizontal axis shows the increasing regularization parameter λ (log-scale). Each colored path represents the trajectory of a predictive variable’s coefficient value as λ varies. Panel c: ROC curves for predicting 90-day mortality using various machine learning models: Random Forest model AUC = 0.847(95% CI: 0.782–0.857); SVM model AUC = 0.825(95% CI: 0.759–0.835); Gradient Boosting model AUC = 0.832(95% CI: 0.768–0.848); XGBoost model AUC = 0.839(95% CI: 0.766–0.842); SOFA Score AUC = 0.763(95% CI: 0.704–0.797). Panel d: Decision curves representing performance metrics for various machine learning models. Panel e: Feature importance ranking in the Random Forest model. Panel f: Shapley value additive interpretation visualization, demonstrating the impact of individual features on the Random Forest prediction model results. Color indicates the degree of influence, with warm tones representing higher standardized eigenvalues and cool tones indicating lower standardized eigenvalues
Association between calculated serum osmolarity and secondary clinical outcomes
The high calculated serum osmolarity was significantly associated with all secondary outcomes (28-day mortality, 60-day mortality, and in-hospital mortality) (Table 4). The fifth quartile of calculated serum osmolarity was associated with an increased 28-day mortality (Q5: OR = 1.759, 95% CI: 1.094–2.826, P = 0.020), 60-day mortality (Q5: OR = 1.668, 95% CI: 1.084–2.568, P = 0.020), and in-hospital mortality (Q5: OR = 1.889, 95% CI: 1.186–3.009, P = 0.007), whereas no significant differences were observed in Q1, Q3, or Q4.
Table 4.
Effect size of calculated serum osmolarity on secondary clinical outcome in patients with AP
| Q1 | Q2 | Q3 | Q4 | Q5 | P for trend | |
|---|---|---|---|---|---|---|
| 28-day mortality | 1.497(0.874–2.564) | Ref. | 0.964(0.560–1.660) | 1.236(0.750–2.036) | 1.759(1.094–2.826) | < 0.001 |
| P-value | 0.141 | 0.895 | 0.406 | 0.020 | ||
| 60-day mortality | 1.356(0.833–2.207) | Ref. | 0.984(0.607–1.595) | 1.134(0.721–1.782) | 1.668(1.084–2.568) | < 0.001 |
| P-value | 0.220 | 0.947 | 0.586 | 0.020 | ||
| in-hospital mortality | 1.483(0.875–2.514) | Ref. | 1.111(0.659–1.873) | 1.391(0.857–2.259) | 1.889(1.186–3.009) | < 0.001 |
| P-value | 0.143 | 0.692 | 0.182 | 0.007 |
Q1 (calculated serum osmolarity ≤ 291.82 mOsm/L, n = 410), Q2 (291.82–298.55 mOsm/L, n = 409), Q3 (298.55–304.62 mOsm/L, n = 409), Q4 (304.62–313.92 mOsm/L, n = 409), Q5 (≥ 313.92 mOsm/L, n = 409)
Discussion
This study aimed to investigate the association between calculated serum osmolarity and 90-day mortality in patients with AP. Both univariate and multivariate logistic regression analyses showed that calculated serum osmolarity was an independent predictor of mortality in AP patients. Nonlinear correlation analysis demonstrated a U-shaped association, with higher mortality risk observed at extremely low or high calculated serum osmolarity levels. Notably, after adjustment for potential confounders, only high calculated serum osmolarity was significantly associated with 90-day mortality (P < 0.05), further supporting the prognostic value of extremely high calculated serum osmolarity in AP patients. In addition, Kaplan‑Meier survival analysis confirmed the prognostic significance of calculated serum osmolarity: patients with high calculated serum osmolarity (> 304.62 mOsm/L) had a significantly higher 90-day all‑cause mortality rate compared with those with moderate or low calculated serum osmolarity (log‑rank P < 0.05). In summary, our results confirm a U‑shaped relationship between calculated serum osmolarity and 90‑day mortality in AP patients, with high calculated serum osmolarity identified as an independent risk factor and showing a more pronounced adverse prognostic impact. The body has buffering capacity against mild osmolarity deviations, but poor tolerance to markedly elevated osmolarity (hypertonicity, Q5). These findings indicate a substantially elevated mortality risk associated with severe hyperosmolarity, representing a clinical condition that warrants close monitoring and timely intervention.
This study reveals a significant U-shaped relationship between calculated serum osmolarity and mortality, suggesting potential clinical value of calculated serum osmolarity in guiding fluid and metabolic management of critically ill AP patients. Previous studies have confirmed that both hypoosmolar and hyperosmolar states are associated with increased mortality in critically ill populations [24, 25]. Calculated serum osmolarity serves as an important integrated marker reflecting body water‑electrolyte balance and metabolic homeostasis, and abnormal values have been linked to compromised cellular function related to disturbed intracellular‑extracellular fluid distribution [26]. Current guidelines for AP emphasize fluid balance maintenance but lack dynamic strategies targeting calculated serum osmolarity [27]. Mechanistically, hyperosmolality in AP patients may result from dehydration, hypernatremia, or hyperglycemia—conditions that have been associated with cellular dehydration, cerebral dysfunction, and hemodynamic instability, which align with our finding of a weak negative correlation between calculated serum osmolarity and GCS score (rho=-0.126). Conversely, hypo-osmolality may reflect excessive fluid resuscitation, hyponatremia, or severe hepatic/renal dysfunction, which have been associated with cellular edema and impaired organ perfusion. Theoretically, both extremes of osmolarity have been associated with disrupted metabolic stability and organ function, which may in turn be related to an increased risk of death. However, this study found that compared with Q2, there was no significant increase in risk for Q1/Q3/Q4, whereas high osmolality was associated with a significantly increased risk. Therefore, dynamic monitoring of calculated serum osmolarity (especially in cases of high osmolality) and targeted adjustments may improve fluid management and prognostic assessment in critical care. Future studies should explore personalized fluid resuscitation strategies based on this calculated serum osmolarity threshold to validate their efficacy in preserving multi-organ function and reducing mortality.
We further established a 90-day mortality prediction model for AP patients. LASSO regression was used to screen 13 potential prognostic factors, and receiver operating characteristic (ROC) curve analysis in the validation set (training: testing = 7:3) demonstrated that the Random Forestmodel outperformed SVM, Gradient Boosting, XGBoost models and SOFA, achieving an AUC of 0.847—supporting its utility in early identification of poor prognosis. Simultaneously, SHAP analysis confirmed that CCI, SOFA, and vasopressors are the main predictive factors, highlighting the key role of critical illness scores in the prognosis of AP. Calculated serum osmolarity also ranked fifth among these factors, confirming its potential as a biomarker for metabolic disturbances in severe AP.
This study leverages a large sample size from the MIMIC database to comprehensively explore the correlation between calculated serum osmolarity and prognosis in P-admitted AP patients, enriching the literature on this specific subgroup. However, several limitations exist. First, the retrospective nature of MIMIC data precludes differentiation between AP subtypes (e.g. necrotizing vs. edematous pancreatitis) and specific causes of death, limiting in-depth analysis of subtype-specific associations. Second, patient selection bias cannot be fully eliminated despite strict inclusion/exclusion criteria to reduce duplicates; missing data were imputed using KNN to minimize information bias, and multivariate models adjusted for known confounders. Third, although MIMIC is multicenter, the findings may still reflect institution-specific treatment patterns (e.g., fluid resuscitation protocols), emphasizing the need for external validation across diverse populations to confirm generalizability. And then due to the limitations of the retrospective data in the MIMIC database, we were unable to accurately determine the specific timing and dosages of interventions such as fluid resuscitation and hypertonic saline administered to patients prior to calculated serum osmolarity measurements. Finally, no significant increase in risk was observed in the low calculated serum osmolarity. Several factors may underlie this observation. First, baseline differences in disease severity and comorbidity burden existed between patients with low and moderate calculated serum osmolarity levels, and such heterogeneity may introduce residual confounding despite multivariable adjustment. Second, variations in clinical management, including fluid resuscitation, supportive care, and hemodynamic interventions, may have modified the observed association between low calculated serum osmolarity and clinical outcomes. In addition, calculated serum osmolarity was measured at a single time point rather than as a dynamic longitudinal trajectory, which could introduce measurement variability and dilute the underlying physiological relationship. Taken together, these factors may explain the attenuated statistical significance at the lower end of the osmolarity spectrum. So it should be confirmed in a larger cohort.
Future prospective studies should further explore the clinical utility of calculated serum osmolarity monitoring and targeted management in AP patients. As a reflection of fluid balance and intracellular-extracellular water distribution, calculated serum osmolarity can guide the adequacy of fluid resuscitation and identify early prognostic risk. For ICU-admitted AP patients, dynamic calculated serum osmolarity monitoring may facilitate timely detection of dehydration, fluid overload, or electrolyte disturbances, thereby optimizing fluid therapy regimens. Prospective intervention studies could design personalized protocols—for example, adjusting crystalloid/colloid infusion according to calculated serum osmolarity thresholds to maintain cellular homeostasis. Comparing calculated serum osmolarity-guided fluid management with conventional strategies in terms of organ dysfunction, ICU length of stay, and 28/90-day mortality will clarify its clinical value, providing evidence-based support for precision fluid therapy in critically ill AP patients.
Conclusion
In summary, calculated serum osmolarity is a valuable prognostic indicator for critically ill AP patients, and maintaining its homeostasis may serve as a potential target for precision fluid management to improve clinical outcomes.
Supplementary Information
Acknowledgements
The figures were drawn using the Figdraw2.0 tool. The author has obtained authorization to use the image (AAAWT4ffb2) (URWPI9ee00) (TRUTOd08d7).
Authors’ contributions
S-Y. L. was responsible for the initial draft of the manuscript. H.R. conducted data cleaning and contributed to the study design, data analysis, and interpretation. S‒S.L. contributed to revising the manuscript critically for intellectual content and approved the final version for publication. All authors reviewed the manuscript critically for intellectual content and have read and approved the final manuscript.
Funding
This work was supported by the China Postdoctoral Science Foundation under Grant Number 2025M772200.
Data availability
The datasets and codes employed in this study can be accessed from the corresponding author upon reasonable request.
Declarations
Ethics approval and consent to participate
Ethical approval was secured from the Ethics Committee of Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology (approval number: TJ-IRB202507049). Given the retrospective nature of this study, the requirement for informed consent was deemed waived. Clinical trial number.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Shi-Yan Liu and Hang Ruan contributed equally to this work.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The datasets and codes employed in this study can be accessed from the corresponding author upon reasonable request.