Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. 2006

Greg Lemon, and John R King, and Helen M Byrne, and Oliver E Jensen, and Kevin M Shakesheff
Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, UK. greg.lemon@maths.nottingham.ac.uk

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.

UI MeSH Term Description Entries
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011108 Polymers Compounds formed by the joining of smaller, usually repeating, units linked by covalent bonds. These compounds often form large macromolecules (e.g., BIOPOLYMERS; PLASTICS). Polymer
D011312 Pressure A type of stress exerted uniformly in all directions. Its measure is the force exerted per unit area. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Pressures
D002449 Cell Aggregation The phenomenon by which dissociated cells intermixed in vitro tend to group themselves with cells of their own type. Aggregation, Cell,Aggregations, Cell,Cell Aggregations
D002452 Cell Count The number of CELLS of a specific kind, usually measured per unit volume or area of sample. Cell Density,Cell Number,Cell Counts,Cell Densities,Cell Numbers,Count, Cell,Counts, Cell,Densities, Cell,Density, Cell,Number, Cell,Numbers, Cell
D002465 Cell Movement The movement of cells from one location to another. Distinguish from CYTOKINESIS which is the process of dividing the CYTOPLASM of a cell. Cell Migration,Locomotion, Cell,Migration, Cell,Motility, Cell,Movement, Cell,Cell Locomotion,Cell Motility,Cell Movements,Movements, Cell
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D014867 Water A clear, odorless, tasteless liquid that is essential for most animal and plant life and is an excellent solvent for many substances. The chemical formula is hydrogen oxide (H2O). (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed) Hydrogen Oxide

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