Vitreous Humor Biochemical Markers and Non-Linear Regression for Post-Mortem Interval Estimation in Indonesian Tropical Autopsy Cases

Abstract

Introduction: Accurate post-mortem interval (PMI) estimation remains a critical challenge in tropical forensic pathology, where accelerated biochemical decomposition makes temperate-derived formulae unreliable. This prospective validation study investigated non-linear regression modeling of vitreous humor potassium (K+), hypoxanthine (Hx), and urea nitrogen (BUN) for PMI estimation in Indonesian tropical autopsy cases (January–December 2025).  

Methods: A total of 85 consecutive forensic autopsy cases were enrolled at the Department of Forensic Medicine, Hospital X, Palembang, Indonesia. PMI was verified by at least two independent sources (mean verification uncertainty ±1.4 hours). Vitreous K+ was measured by ion-selective electrode; Hx by enzymatic colorimetry; BUN by the urease-GLDH method. Logarithmic, quadratic, and square-root non-linear regression models were fitted for each biomarker; model selection was guided by R², adjusted R², and Akaike Information Criterion (AIC). Cross-validation was performed by leave-one-out cross-validation (LOOCV).

Results: Vitreous K+ demonstrated the strongest quadratic association with PMI (R² = 0.957, LOOCV-R² = 0.942, RMSE = 0.38 mmol/L). BUN showed a quadratic pattern (R² = 0.837, LOOCV-R² = 0.819, RMSE = 1.75 mg/dL) and Hx a square-root pattern (R² = 0.438, RMSE = 3.83 µmol/L). The combined multivariate non-linear model [PMI = 56.19·ln(K++1) + 1.85·√Hx + 1.86·BUN − 136.08] achieved R² = 0.951, LOOCV-R² = 0.934, and RMSE = 4.75 hours. Variance inflation factors for all predictors were ≤2.8, confirming acceptable multicollinearity. K+ and BUN were independent significant predictors (both p < 0.001); Hx did not reach independent significance (p = 0.095). The combined model is valid for K+ ≥ 4.2 mmol/L.

Conclusion: Non-linear regression of vitreous biochemical markers provides accurate, locally validated PMI estimation for Indonesian tropical forensic practice, with a combined model RMSE of 4.75 hours over 1–72 hours post-mortem.