Spatiotemporal Modeling of Stem Cell Differentiation

Spatiotemporal Modeling of Stem Cell Differentiation

Partial Differentiation Equation Analysis in R

1st Edition - September 1, 2021

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  • Author: William Schiesser
  • Paperback ISBN: 9780323907972
  • eBook ISBN: 9780323914130

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Spatiotemporal Modeling of Stem Cell Differentiation: Partial Differentiation Equation Analysis in R  covers topics surrounding how stem cells evolve into specialized cells during tissue formation and in diseased tissue regeneration. As the process of stem cell differentiation occurs in space and time, the mathematical modeling of spatiotemporal development is expressed in this book as systems of partial differential equations (PDEs). In addition, the book explores important feature of six PDE model which can represent, for example, the development of tissue in organs. In addition, the book covers the computer-based implementation of example models through routines coded (programmed) in R. The routines described in the book are available from a download link so that 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.

Key Features

  • Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models
  • Offers transportable computer source codes for readers in R, with line-by-line code descriptions for mathematical models and algorithms
  • Authored by a leading researcher and educator in PDE models


Biomedical engineers, researchers, and clinicians in biology, neuroscience, biophysics, biochemistry, and applied mathematics. Research scientists and engineers in the fields of medical and biological sciences

Table of Contents

  • 1. One PDE Stem Cell Model
    2. Implementation of the One PDE Model
    3. Six PDE Model for Stem Cell Differentiation
    4. Implementation of the Six PDE Model
    5. Detailed ODE/PDE Model Analysis

Product details

  • No. of pages: 134
  • Language: English
  • Copyright: © Academic Press 2021
  • Published: September 1, 2021
  • Imprint: Academic Press
  • Paperback ISBN: 9780323907972
  • eBook ISBN: 9780323914130

About the Author

William Schiesser

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.

Affiliations and Expertise

Professor of Chemical and Biomolecular Engineering and Professor of Mathematics, Lehigh University, USA

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