Book chapter
Modeling and simulation of age- and space-structured biological systems
Current developments in mathematical biology : proceedings of the Conference on Mathematical Biology and Dynamical Systems, the University of Texas at Tyler, 7-9 October 2005, pp.107-130
K & E series on knots and everything, v. 38, World Scientific
2007
DOI: 10.1142/9789812706799_0006
Abstract
This expository paper provides an introduction to computational methods for solving continuous models of certain biological systems. These systems have important behavior in space and within the age distribution of individuals. Very often, the spatial behavior depends critically on the age structure of the population. The different spatial scales induce different time scales in the problem, whereas age and time advance together.
Age- and space-structured multiscale systems arise in a wide variety of biological problems ranging from multicellular and tissue-level phenomena to problems in ecology and evolutionary biology. We describe a general modeling framework used to represent such biological systems. We then discuss computational methods used to solve the model equations, beginning with a treatment of the moving-grid Galerkin method used to decouple age and time while they advance together, introduce how this discretization in age works with discretizations in time and space, and then review how more complicated nonlinear problems would be treated. We close by presenting two example systems, swarm-colony development of the bacteria Proteus mirabilis and tumor invasion, which differ in some important respects from the general model, but which are effectively treated by the computational methods presented in this paper.
Details
- Title: Subtitle
- Modeling and simulation of age- and space-structured biological systems
- Creators
- Bruce P Ayati - University of Iowa, Mathematics
- Resource Type
- Book chapter
- Publication Details
- Current developments in mathematical biology : proceedings of the Conference on Mathematical Biology and Dynamical Systems, the University of Texas at Tyler, 7-9 October 2005, pp.107-130
- Series
- K & E series on knots and everything; v. 38
- DOI
- 10.1142/9789812706799_0006
- Publisher
- World Scientific; Singapore
- Language
- English
- Date published
- 2007
- Academic Unit
- Orthopedics and Rehabilitation; Mathematics
- Record Identifier
- 9983985820002771
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