{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T14:11:10Z","timestamp":1790345470551,"version":"4.1.0"},"reference-count":81,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T00:00:00Z","timestamp":1757030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100019945","name":"Direcci\u00f3 General de Recerca, Generalitat de Catalunya","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100019945","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Bioeng. Biotechnol."],"abstract":"<jats:sec><jats:title>Introduction<\/jats:title><jats:p>Intervertebral disc (IVD) degeneration is a primary contributor to low back pain, with nutritional stress due to the IVD\u2019s avascularity recognized as a key factor. Solute transport within the disc relies predominantly on diffusion, which is governed by tissue morphology and mechanical deformation. However, the interplay between disc geometry, poro-mechanical strain, diffusion, and degeneration remains incompletely characterized. Previous specimen-specific models have captured inter-subject variability in metabolite transport, but the isolated effects of disc height and degeneration-dependent material composition have not been systematically assessed. Moreover, although strain-dependent diffusion coefficients are commonly modeled as porosity functions, the role of intra-element diffusivity gradients <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m1\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>\u2207<\/mml:mi><mml:mi>D<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:inline-formula>, arising under large deformation, has been largely overlooked.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>The present study focuses on poro-mechanical finite element (FE) models of three patient-personalized L4-L5 lumbar IVD geometries, representing varying heights categorized as <jats:italic>thin<\/jats:italic>, <jats:italic>medium<\/jats:italic>, and <jats:italic>tall<\/jats:italic> IVDs. Three days of physiological mechanical load cycles, comprising 8 hours of rest and 16 hours of activity, were simulated, under both \u2019healthy\u2019 (Pfirrmann grade 1) and degenerated (Pfirrmann grade 3) tissue conditions.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Simulation outcomes demonstrated that a one-third reduction in disc height (relative to medium height) led to <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m2\"><mml:mrow><mml:mo>&gt;<\/mml:mo><mml:mn>30<\/mml:mn><mml:mi>%<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> increases in oxygen and glucose concentrations and <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m3\"><mml:mrow><mml:mo>\u2265<\/mml:mo><mml:mn>20<\/mml:mn><mml:mi>%<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> decreases in lactate levels, particularly in the nucleus and anterior regions. Conversely, a one-third height increase resulted in <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m4\"><mml:mrow><mml:mo>&gt;<\/mml:mo><mml:mn>30<\/mml:mn><mml:mi>%<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> reductions in oxygen and glucose and a corresponding rise in lactate levels. These deviations were more pronounced in degenerated tissues, highlighting the synergistic role of morphology and matrix integrity in determining metabolic homeostasis. Importantly, the inclusion of <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m5\"><mml:mrow><mml:mi>\u2207<\/mml:mi><mml:mi>D<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> in the diffusion-reaction model produced negligible changes in solute concentration profiles.<\/jats:p><\/jats:sec><jats:sec><jats:title>Discussion<\/jats:title><jats:p>These findings underscore the predominant influence of disc geometry and matrix composition on IVD metabolic homeostasis, suggesting limited relevance of the <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m6\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>\u2207<\/mml:mi><mml:mi>D<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:inline-formula> term in practical simulations. Simplified diffusion models, without <jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"m297\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>\u2207<\/mml:mi><mml:mi>D<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:inline-formula>, may be sufficient for future IVD mechano-transport FE modeling.<\/jats:p><\/jats:sec>","DOI":"10.3389\/fbioe.2025.1651786","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T09:34:22Z","timestamp":1757064862000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Influence of disc height and strain-dependent solute diffusivity on metabolic transport in patient-personalized intervertebral disc models"],"prefix":"10.3389","volume":"13","author":[{"given":"Zerihun G.","family":"Workineh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Estefano","family":"Mu\u00f1oz-Moya","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlos","family":"Ruiz Wills","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dimitrios","family":"Lialios","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Noailly","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1002\/jor.21010","article-title":"Nanostructure of collagen fibrils in human nucleus pulposus and its correlation with macroscale tissue mechanics","volume":"28","author":"Aladin","year":"2010","journal-title":"J. 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