Computational modelling of liver fibrosis stages: the role of 3D Voronoi structural connectivity in elastography...

Objective. This study proposes a novel 3D modelling framework based on Voronoi tessellation to simulate the progression of liver fibrosis across all METAVIR stages (F0-F4), addressing the limitations of traditional simplified 2D geometries in representing hepatic tissue heterogeneity.Approach. A 3D structural model was developed where microstructural connectivity was translated into macroscopic elastic properties. Numerical simulations of shear wave propagation were performed using thek-Wave toolbox, using GPU acceleration to process high-resolution 3D volumes. The framework's performance was validated by comparing simulated Young's modulus values with clinical gold standards from existing literature.Main results. A collagen fibre velocity of 7.55 m s^-1was obtained using a calibration method to match clinical data results. The simulations demonstrated a good correlation (R²= 0.976) with clinical data. A critical structural percolation threshold was identified during the transition from F2 to F3, where isolated collagen clusters merge into interconnected bridges, causing a marked increase stiffness increment. Furthermore, a significant discrepancy was observed between dimensions, with 2D models underestimating cirrhosis stiffness (F4) by approximately 35% compared to 3D estimations (15.23 kPa vs 23.57 kPa).Significance. The findings underscore the necessity of accounting for 3D structural connectivity to achieve accurate elastography modelling. This validated framework provides a robust virtual environment for developing advanced diagnostic sequences and improves the understanding of wave propagation in heterogeneous fibrotic tissues, potentially refining non-invasive fibrosis staging.