Integration of Hematoma Volume and Density Heterogeneity via the Harmonic Mean Is Associated With Improved Early Prediction of Hematoma Progression in Frontal Lobe Contusion: A Multicenter Retrospective Cohort Study

Technical Summary: Integration of Hematoma Volume and Density Heterogeneity via the Harmonic Mean for Early Prediction of Hematoma Progression in Frontal Lobe Contusion

1. Problem Statement

Frontal lobe contusion (FCL) is a common and highly heterogeneous lesion following traumatic brain injury (TBI). A critical clinical challenge is the early identification of patients at risk for hematoma progression (HPC), defined as a ≥25% increase in hematoma volume within 72 hours of injury. HPC is strongly associated with secondary neurological deterioration, elevated intracranial pressure, and poor outcomes.

Current clinical assessment relies heavily on qualitative CT signs and surgeon experience, which suffer from low inter-observer agreement due to the "pepper-salt" appearance of FCLs. While quantitative metrics exist, they have limitations when used in isolation:

• Baseline Hematoma Volume (V): Reflects spatial load but fails to indicate whether the lesion interior is in an active bleeding or unstable coagulation state.
• Density Coefficient of Variation (DCV): Quantifies internal density heterogeneity (a marker of mixed old/new bleeding) but is a relative indicator that ignores the absolute physical size of the lesion.

The study posits that neither dimension alone is sufficient to characterize the risk of early progression and that an integrated, mathematically principled index is needed to capture the joint configuration of lesion size and density instability.

2. Methodology

Study Design and Cohorts
This was a multicenter retrospective cohort study adhering to the TRIPOD+AI guidelines.

• Development Cohort: 341 patients with FCL from the General Hospital of Ningxia Medical University (August 2020–October 2025).
• External Validation Cohort: 273 patients from The Second Affiliated Hospital, Hengyang Medical School, University of South China (January 2020–December 2025).
• Inclusion Criteria: Emergency non-contrast CT (NCCT) confirming FCL, first NCCT within 6 hours of injury, follow-up NCCT within 72 hours, GCS ≥9, and complete data.
• Exclusion Criteria: Immediate emergency surgery, GCS <9, or missing data.

Data Processing and Feature Engineering

• Segmentation: Baseline hematoma volume ($V$) and density statistics (Mean, Standard Deviation $SD$) were extracted using 3D Slicer (v5.8.1) by two neurosurgeons with >5 years of experience.
• Density Coefficient of Variation (DCV): Calculated as $DCV = SD / Mean$.
• Volume-Density Integration Index (VDII): A new composite marker constructed using the harmonic mean of baseline volume ($V$) and DCV:
  $$VDII = \frac{2}{(1/V) + (1/DCV)}$$
  The harmonic mean was chosen because it is sensitive to smaller values; thus, a low value in either volume or heterogeneity significantly suppresses the overall index. This aligns with the pathophysiology that high-risk lesions require both a certain spatial scale and significant internal heterogeneity.
• Covariates: Clinical variables included GCS, age, and laboratory markers (SIRI, LMR, eosinophil count, blood glucose, albumin).

Model Development
Four logistic regression models were constructed and compared:

1. VDII-only: Standardized VDII alone.
2. Model 1 (Raw Component): Included raw $V$, $DCV$, and clinical/laboratory variables.
3. Model 2 (VDII Integrated): Replaced raw $V$ and $DCV$ with standardized VDII, retaining other clinical variables.
4. Model 3 (Extended): Model 2 + blood glucose + albumin.

Statistical Analysis

• Variable Selection: LASSO regression with 10-fold cross-validation and the Boruta algorithm.
• Performance Metrics: Area Under the Curve (AUC) with DeLong test for comparison (Bonferroni-corrected threshold $P < 0.0083$), calibration (Brier score, calibration curves), Decision Curve Analysis (DCA), and Integrated Discrimination Improvement (IDI).
• Validation: Internal bootstrap validation and external validation on the independent cohort.
• Non-linearity: Restricted Cubic Spline (RCS) analysis was used to assess the relationship between VDII and HPC risk.

3. Key Results

Demographics and Baseline
The development cohort had an HPC rate of 29.0% (training) and 28.3% (testing), while the external validation cohort had a rate of 21.0%. The external cohort was significantly older, had lower GCS scores, and higher raw VDII values, indicating population heterogeneity suitable for testing generalizability.

Discriminative Performance

• Single Indicators: In the testing set, VDII-only (AUC 0.745) significantly outperformed Volume-only (AUC 0.514) and DCV-only (AUC 0.659).
• Model Comparison (External Validation):
  • Model 2 (VDII Integrated) achieved an AUC of 0.763 (95% CI: 0.698–0.824).
  • Model 1 (Raw Components) achieved an AUC of 0.699 (95% CI: 0.627–0.769).
  • The improvement of Model 2 over Model 1 was statistically significant ($P < 0.001$).
  • Model 3 (adding glucose and albumin) did not significantly improve discrimination over Model 2 (AUC 0.758 vs. 0.763, $P = 0.649$).
• Robustness: Bootstrap internal validation confirmed that Model 2 maintained superior performance over Model 1 after optimism correction.

Multivariable Analysis and Associations

• Independent Predictor: Lower standardized VDII was independently associated with a higher risk of HPC (OR 0.425, 95% CI: 0.269–0.671, $P < 0.001$).
• Non-linearity: RCS analysis revealed a significant nonlinear association ($P$ for nonlinearity = 0.0007). The risk of HPC decreased as VDII increased, with a steeper risk reduction in the lower VDII range.
• Subgroup Analysis: The predictive value of VDII was stronger in patients with small-volume lesions (OR 0.26) compared to large-volume lesions (OR 0.58), with a significant interaction ($P = 0.005$).

Calibration and Clinical Utility

• Model 2 demonstrated better calibration (lower Brier score) and higher net benefit in Decision Curve Analysis compared to Model 1 in the external validation set.
• A nomogram was developed based on Model 2 to facilitate personalized risk prediction.

4. Key Contributions

1. Novel Imaging Marker: Introduction of the Volume-Density Integration Index (VDII), a harmonic mean-based composite marker that mathematically integrates lesion volume and density heterogeneity.
2. Superior Predictive Power: Demonstration that VDII provides better discrimination for early hematoma progression than volume or heterogeneity alone, and that replacing raw components with VDII improves model generalizability in external validation.
3. Clinical Stratification: Identification that VDII is particularly effective in stratifying risk for small-volume lesions, a group often underestimated in traditional clinical practice.
4. Model Parsimony: Evidence that adding systemic inflammatory/metabolic markers (glucose, albumin) did not provide significant incremental value over the imaging-based VDII model, suggesting the lesion's intrinsic imaging characteristics are the primary drivers of early progression risk in this context.

5. Significance and Limitations (Author's Perspective)

The authors claim that VDII offers a new, quantitative tool for early risk stratification in FCL, potentially guiding CT follow-up strategies and surveillance intensity. By capturing the "short board" effect where both size and heterogeneity are required for high risk, VDII addresses the limitations of single-dimension metrics.

However, the authors maintain a modest tone regarding clinical implementation:

• Retrospective Nature: The study is observational; results show association, not causation, and do not prove that using VDII improves patient outcomes.
• Generalizability: The study was limited to two centers in China with specific scanner protocols. The model's performance in other regions, trauma systems, or with different imaging parameters remains unverified.
• Workflow Constraints: Current measurement requires semi-automatic segmentation and manual correction, which limits real-time clinical application.
• Definition Bias: The definition of HPC (relative volume increase) may inherently favor the detection of progression in smaller lesions, influencing the observed strength of VDII in that subgroup.
• Future Needs: The authors emphasize that prospective validation, automated measurement workflows, and impact analysis are required before VDII can be recommended for routine clinical decision-making.