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Med. Biol."],"published-print":{"date-parts":[[2026,8,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective<\/jats:italic>\n                    . This study proposes a novel 3D modelling framework based on Voronoi tessellation to simulate the progression of liver fibrosis across all METAVIR stages (F0\u2013F4), addressing the limitations of traditional simplified 2D geometries in representing hepatic tissue heterogeneity.\n                    <jats:italic>Approach<\/jats:italic>\n                    . A 3D structural model was developed where microstructural connectivity was translated into macroscopic elastic properties. Numerical simulations of shear wave propagation were performed using the\n                    <jats:italic>k<\/jats:italic>\n                    -Wave toolbox, using GPU acceleration to process high-resolution 3D volumes. The framework\u2019s performance was validated by comparing simulated Young\u2019s modulus values with clinical gold standards from existing literature.\n                    <jats:italic>Main results<\/jats:italic>\n                    . A collagen fibre velocity of 7.55 m s\n                    <jats:sup>\u22121<\/jats:sup>\n                    was obtained using a calibration method to match clinical data results. The simulations demonstrated a good correlation (\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>2<\/jats:sup>\n                    = 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).\n                    <jats:italic>Significance<\/jats:italic>\n                    . 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.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/ae8ca2","type":"journal-article","created":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T22:55:34Z","timestamp":1784328934000},"page":"155006","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational modelling of liver fibrosis stages: the role of 3D Voronoi structural connectivity in elastography simulations"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0188-7761","authenticated-orcid":true,"given":"M\u00e1rio","family":"Santos","sequence":"first","affiliation":[{"name":"University of Coimbra, ARISE, CEMMPRE"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8980-1992","authenticated-orcid":true,"given":"Fernando","family":"Perdig\u00e3o","sequence":"additional","affiliation":[{"name":"University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4936-9434","authenticated-orcid":false,"given":"Jaime","family":"Santos","sequence":"additional","affiliation":[{"name":"University of Coimbra, ARISE, CEMMPRE"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5547-9424","authenticated-orcid":true,"given":"Jo\u00e3o","family":"Madaleno","sequence":"additional","affiliation":[{"name":"University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"key":"pmbae8ca2bib1","author":"A","year":"1990","type":"book"},{"key":"pmbae8ca2bib2","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1136\/jcp.31.5.395","type":"journal-article","article-title":"The morphology of cirrhosis. 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