Numerical PDE Analysis of Retinal Neovascularization : Mathematical Model Computer Implementation in R

William E. Schiesser

ISBN 10: 0128184523 / ISBN 13: 9780128184523

Published by Elsevier Inc Jun 2019, 2019

About this Item

Neuware - 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.

Seller Inventory # 9780128184523

Bibliographic Details

• Title: Numerical PDE Analysis of Retinal Neovascularization : Mathematical Model Computer Implementation in R
• Publisher: Elsevier Inc Jun 2019
• Publication Date: 2019
• Language: English
• ISBN 10: 0128184523
• ISBN 13: 9780128184523
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 191H x 8D millimeters 235 millimeters width by 191 millimeters height by 8 millimeters depth
• Weight: 262 grams

About this title

Synopsis

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.

• 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 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.