ArticlePloS one2016
Governing Equations of Tissue Modelling and Remodelling: A Unified Generalised Description of Surface and Bulk Balance.
Article in PloS one, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- A mathematical model of osteocyte network control of bone mechanical adaptation.Biomechanics and modeling in mechanobiology · 2026Article
- Women's bone health trajectories from pregnancy to postpartum: Associations with bone-seeking metal exposure mixtures during pregnancy.Ecotoxicology and environmental safety · 2025Article
- Mineral density differences between femoral cortical bone and trabecular bone are not explained by turnover rate alone.Bone reports · 2020Article
- Integrated Design Approaches for 3D Printed Tissue Scaffolds: Review and Outlook.Materials (Basel, Switzerland) · 2019Review
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1 author.
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Abstract
Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different "patches", i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific signatures of the time evolution of BMD or TMD during remodelling events are exhibited. These signatures may provide a way to detect remodelling events at lower, unseen spatial resolutions from microCT scans.
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