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

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 modelsOffers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithmsAuthored by a leading researcher and educator in PDE models

1. PDE Model Formulation

2. Model Implementation

3. Variation of parameters

4. Detailed PDE analysis

5. Oxygen Effect

6. Anti-VEGF Drug Therapy