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Governing Equations of Tissue Modelling and Remodelling: A Unified Generalised Description of Surface and Bulk Balance
- Source :
- PLoS ONE, PLoS ONE, Vol 11, Iss 4, p e0152582 (2016)
- Publication Year :
- 2015
-
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 time signatures of BMD or TMD during remodelling events may provide a way to detect these events occurring at lower, unseen spatial resolutions from microCT scans.<br />Comment: 14 pages, 8 figures. V2: minor stylistic changes, more detailed derivation of Eqs (30)-(31), additional comments on implication of BMD and TMD signatures for microCT scans
- Subjects :
- 0301 basic medicine
Physiology
lcsh:Medicine
Bone Matrix
02 engineering and technology
Biochemistry
Bone remodeling
Bone Density
Animal Cells
Cell Behavior (q-bio.CB)
Medicine and Health Sciences
Tissues and Organs (q-bio.TO)
lcsh:Science
Connective Tissue Cells
Physics
Bone mineral
Multidisciplinary
Mechanics
medicine.anatomical_structure
Biological Physics (physics.bio-ph)
Connective Tissue
Osteocyte
Physical Sciences
Tissue material
Bone Remodeling
Anatomy
Cellular Types
Material properties
Research Article
Bone and Mineral Metabolism
0206 medical engineering
Materials Science
Material Properties
FOS: Physical sciences
Mineralogy
Models, Biological
Osteocytes
03 medical and health sciences
medicine
Animals
Humans
Physics - Biological Physics
Bone Resorption
Quantitative Biology - Populations and Evolution
Bone
Osteoblasts
lcsh:R
Populations and Evolution (q-bio.PE)
Time evolution
Biology and Life Sciences
Quantitative Biology - Tissues and Organs
Cell Biology
020601 biomedical engineering
Formalism (philosophy of mathematics)
030104 developmental biology
Mineral density
Biological Tissue
Metabolism
FOS: Biological sciences
Quantitative Biology - Cell Behavior
lcsh:Q
Physiological Processes
Subjects
Details
- ISSN :
- 19326203
- Volume :
- 11
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- PloS one
- Accession number :
- edsair.doi.dedup.....dd136d758e6d064637bf6e0073c8fed2