PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R - Softcover

Schiesser, William E.

Softcover

ISBN 10: 0443187401 ISBN 13: 9780443187407

Publisher: Academic Press, 2022

Synopsis

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.

• 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

About this title

About the Author

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.

From the Back Cover

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 u1m; u2m; u1; u2; u3; u4; u5; u6.These variables are explained as follows: normalized variable u1m =O2 level in seeded stem cells; normalized variable u2m = nutrient level in seeded stem cells; normalized variable u1 = stem cell density; normalized variable u2 = transit-amplifying (TA) cell density; normalized variable u3 = terminally differentiated (TD) cell density; normalized variable u4 = signaling (regulatory) biomolecule 1 concentration produced by u1, u2, u3, u6; normalized variable u5 = signaling (regulatory) biomolecule 2 concentration produced by u1, u2, u3, u6; normalized variable u6= signaling (regulatory) biomolecule 3 concentration produced by u4, u5.u3 (r; z; t) is of particular interest since it expresses the level of the terminally differentiated (TD) cell density, the final goal/product of tissue engineering. If successful, tissue engineering and regenerative medicine will end the dependency on organ donors. The computer-based implementation of the example models in the book 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 can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.The eight PDE models presented in the book can be used for computer-based experimentation via the R routines. For example, parameter variation and changes in the model equations or alternate models can be studied to enhance a quantitative understanding of a postulated tissue engineering and regenerative medicine procedure. 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. As additional background, a library of PDE routines is available to readers to support the research in the book. These library routines pertaining to PDE analysis have received over 1,100,000 visits.

Edition details

• Publisher: Academic Press
• Publication date: 2022
• ISBN 10: 0443187401
• ISBN 13: 9780443187407
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 188