Numerical PDE Analysis of Retinal Neovascularization

Mathematical Model Computer Implementation in R
Erscheinungsjahr 2019
ISBN: 978-0-12-818452-3
Verlag: Elsevier Science Publishing Co Inc

Buch, Englisch, 144 Seiten, Format (B × H): 192 mm x 237 mm, Gewicht: 328 g

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.

Autoren/Hrsg.

Schiesser, William E.

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizintechnik, Biomedizintechnik, Medizinische Werkstoffe
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizinische Mathematik & Informatik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Medizintechnik, Biomedizintechnik
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software

Inhaltsverzeichnis

1. PDE Model Formulation

2. Model Implementation

3. Variation of parameters

4. Detailed PDE analysis

5. Oxygen Effect

6. Anti-VEGF Drug Therapy

Über Autor(innen)

Schiesser, William E.
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.