PDE Modeling of Tissue Engineering and Regenerative Medicine

PDE Modeling of Tissue Engineering and Regenerative Medicine

Computer Analysis in R

1st Edition - September 1, 2022

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  • Author: William Schiesser
  • Paperback ISBN: 9780443187407

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PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R presents the formulation and computer implementation of mathematical models for the forefront research areas of tissue engineering and regenerative medicine. The mathematical model discussed in this book consists of a system of eight partial differential equations (PDEs) with dependent variables. The computer-based example models are presented through routines coded 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. Includes detailed examples that the reader can execute on modest computers.

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 as it relates to the mathematical model and algorithms
  • Authored by a leading researcher and educator in PDE models


Researchers in computational modelling and computational biology, mathematicians, Computer Scientists, as well as researchers in Biomedical Engineering

Table of Contents

  • 1. One PDE Stem Cell Model
    1) Introduction
    1.1) O2 transfer, 1D cylindrical coordinates
    1.2) O2 transfer, 2D cylindrical coordinates
    1.3) Summary and conclusions

    2. Implementation of the One PDE Model
    2) Introduction
    2.1) 1D PDE model implementation
    2.1.1) Main program, test cases
    2.1.2) ODE/MOL routine
    2.1.3) Numerical, graphical output
    2.1.4) Main program, application
    2.1.5) ODE/MOL routine
    2.1.6) Numerical, graphical output
    2.2) Summary and conclusions

    3. 2D PDE Model Implementation
    3) Introduction
    3.1) 2D PDE model implementation
    3.1.1) Main program, test cases
    3.1.2) ODE/MOL routine
    3.1.3) Numerical, graphical output
    3.1.4) Main program, application
    3.1.5) ODE/MOL routine
    3.1.6) Numerical, graphical output}
    3.2) Summary and Conclusions

    4. Two PDE Model Formulation
    4) Introduction
    4.1) Coding of six PDE model
    4.1.1) Main program, test cases
    4.1.2) ODE/MOL routine
    4.1.3) Numerical, graphical output
    4.1.4) Main program, application
    4.1.5) ODE/MOL routine
    4.1.6) Numerical, graphical output
    4.2) Summary and conclusions

    5. Stem Cell Metabolism and Differentiation
    5) Introduction
    5.1) Metabolism
    5.2) Differentiation
    5.3) Implementation of metabolism and differentiation model
    5.3.1) Main program
    5.3.2) ODE/MOL routine
    5.3.3) Numerical, graphical output
    5.4) Summary and conclusions

Product details

  • No. of pages: 200
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: September 1, 2022
  • Imprint: Academic Press
  • Paperback ISBN: 9780443187407

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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