A latent burden–HVPG mathematical framework for threshold mapping and delay-differential scenario analysis in portal hypertension

Portal hypertension is clinically defined by invasive hepatic venous pressure gradient (HVPG) thresholds, whereas routine assessment relies on non-invasive markers that are biologically heterogeneous and only indirectly related to portal pressure. We have developed a computational framework designed as a threshold-translation and scenario-exploration tool rather than a predictive or mechanistic model with three explicitly separated components: a data-driven empirical core, a literature-informed delayed dynamic layer, and a synthetic scenario module. Using HVPG-linked datasets, the empirical core has constructed a constrained latent burden score from liver stiffness, inverse platelet count, spleen diameter, inverse albumin, and bilirubin and has compared it with an equal-weight score. The constrained score has improved threshold discrimination more than continuous prediction at clinically relevant HVPG levels. A monotone burden-to-HVPG mapping has translated the latent burden axis into the clinically interpretable HVPG scale and has yielded cohort-specific burden thresholds. Leave-one-source-out (LOSO) technique shows that pooled burden learning is informative but not source-invariant, indicating limited transportability across cohorts. To examine delayed separation between latent burden evolution and visible pressure manifestation, we have introduced a delay differential equation model with literature-informed parameters. The resulting temporal gaps are illustrative scenario outputs and not patient-specific predictions. Overall, the framework provides a transparent, threshold-oriented computational approach for translating heterogeneous biomarkers into interpretable HVPG thresholds while linking data-based burden learning with scenario-based dynamic simulation.