Spatiotemporal Modeling of Stem Cell Differentiation: Partial Differentiation Equation Analysis in R - Softcover

Über die Autorin bzw. den Autor

Dr. William E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering, and Professor of Mathematics at Lehigh University. He holds a PhD from Princeton University and a ScD (hon) from the University of Mons, Belgium. His research is directed toward numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs), and the development of mathematical models based on ODE/DAE/PDEs. He is the author or coauthor of more than 16 books, and his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and universities, corporations and government agencies.

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Stem cells evolve into specialized cells during tissue formation and diseased tissue regeneration. The process of forming specific cells from stem cells is termed differentiation. As the process of stem cell differentiation occurs in space and time, the mathematical modeling of this spatiotemporal development is expressed in this book as systems of partial differential equations (PDEs).

The mathematical models for stem cell differentiation based on PDEs start with a basic one PDE model for stem cell density as a function of space and time and conclude with detailed six PDE models with dependent variables stem cell density, transit-amplifying cell density, terminally differentiated cell density, and signaling (regulatory) biomolecules 1, 2, and 3.

An important feature of the six PDE model is the movement of the tissue upper apex boundary as a function of time which can represent, for example, the development of tissue in an organ.

The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines, an established general algorithm for PDEs, implemented with cubic splines.

The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the stem differentiation models, such as changes in the PDE parameters (constants) and the form of the model equations.