Many different single-cell-based models have been developed and applied to biological and medical problems. Computational approaches used are Monte-Carlo simulations, energy minimisation techniques, volume conservation laws, solutions of the equations of motion for each individual cell or for each point on the cell membrane. They differ in the level of detail that defines the cell structure and subsequently in the number of individual cells that the model can incorporate.
This volume presents a collection of mathematical and computational single-cell-based models and their application. The main sections cover four general model groupings: hybrid cellular automata, cellular potts, lattice-free cells, and viscoelastic cells. Each section is introduced by a discussion of the applicability of the particular modelling approach and its advantages and disadvantages, which will make the book suitable for students starting research in mathematical biology as well as scientists modelling multicellular processes.
Зміст
Hybrid Multiscale Models.- A Hybrid Multiscale Model of Solid Tumour Growth and Invasion: Evolution and the Microenvironment.- Lattice-gas Cellular Automaton Modeling of Developing Cell Systems.- Two-dimensional Multiscale Model of Cell Motion in a Chemotactic Field.- The Cellular Potts Model and Its Variants.- Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model.- The Cellular Potts Model and Biophysical Properties of Cells, Tissues and Morphogenesis.- The Cellular Potts Model in Biomedicine.- The Glazier-Graner-Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study.- Off-lattice Cell Models.- Center-based Single-cell Models: An Approach to Multi-cellular Organization Based on a Conceptual Analogy to Colloidal Particles.- Models with Lattice-free Center-based Cells Interacting with Continuum Environment Variables.- Modeling Multicellular Structures Using the Subcellular Element Model.- Viscoelastic Cell Models.- Cell-based Models of Blood Clotting.- A 3-D Deformable Ellipsoidal Cell Model with Cell Adhesion and Signaling.- Modelling the Development of Complex Tissues Using Individual Viscoelastic Cells.
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