Graph-Driven Reconstruction of the Hepatic PV–CV Axis: A Topology-Aware Framework for Continuous Zonation and Gradient Gene Discovery

Abstract

The spatial heterogeneity of liver metabolic function, known as liver zonation, is fundamental to its execution of complex detoxification and synthesis tasks. Although single cell sequencing has revealed cellular diversity, traditional methods often struggle to precisely quantify the continuous metabolic gradient from the portal vein (PV) to the central vein (CV) while preserving intact tissue topology. Existing spatial trajectory inference algorithms also face challenges when handling irregular tissue morphologies and noisy data. This study proposes a robust graph theoretic computational framework to reconstruct the PV–CV axis from spatial transcriptomics data. The method first identifies high confidence PV and CV “seed points” using classic marker genes; subsequently, it constructs a spatial k nearest neighbor graph of spots and employs Dijkstra’s algorithm to compute geodesic distance fields from each point to the seed sets. A continuous zonation axis coordinate is then defined by normalizing the ratio of bidirectional distances. Furthermore, we introduce local vector flow field analysis and gradient strength metrics to visualize the directionality and sharpness of metabolic gradients, thereby identifying novel zonation genes that vary monotonically along the axis. Application to mouse liver spatial transcriptomics datasets demonstrates that this method successfully reconstructs a smooth PV–CV axis consistent with physiological structures, effectively overcoming geometric biases caused by tissue section deformation. Local flow field analysis clearly visualizes a virtual metabolic flow directed from the portal tract toward the central vein. PV specific and CV specific genes identified based on this axis show high concordance with established literature, and several potential zonation regulators not previously well documented were discovered. This pipeline provides an interpretable, robust, and training free tool for liver zonation analysis. It not only quantifies spatial metabolic gradients but also offers new quantitative metrics for analyzing zonation disruption in liver disease states.