Numerical PDE Analysis of Retinal Neovascularization

Numerical PDE Analysis of Retinal Neovascularization

Mathematical Model Computer Implementation in R

1st Edition - June 14, 2019

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  • Author: W. E. Schiesser
  • eBook ISBN: 9780128184530
  • Paperback ISBN: 9780128184523

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Description

Numerical PDE Analysis of Retinal Neovascularization Mathematical Model Computer Implementation in R provides a methodology for the analysis of neovascularization (formation of blood capillaries) in the retina. It describes the starting point—a system of three partial differential equations (PDEs)—that define the evolution of (1) capillary tip density, (2) blood capillary density and (3) concentration of vascular endothelial growth factor (VEGF) in the retina as a function of space (distance along the retina), x, and time, t, the three PDE dependent variables for (1), (2) and (3), and designated as u1(x, t), u2(x, t), u3(x, t), amongst other topics.

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

Readership

Biomedical engineers, researchers, and clinicians in biology, neuroscience, biophysics, biochemistry, and applied mathematics

Table of Contents

  • 1. PDE Model Formulation

    2. Model Implementation

    3. Variation of parameters

    4. Detailed PDE analysis

    5. Oxygen Effect

    6. Anti-VEGF Drug Therapy

Product details

  • No. of pages: 144
  • Language: English
  • Copyright: © Academic Press 2019
  • Published: June 14, 2019
  • Imprint: Academic Press
  • eBook ISBN: 9780128184530
  • Paperback ISBN: 9780128184523

About the Author

W. E. 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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