Numerical PDE analysis of retinal neovascularization mathematical model computer implementation in R / William E. Schiesser.
| Author/creator | Schiesser, W. E. |
| Format | Electronic |
| Publication Info | London : Elsevier/Academic Press, [2019] |
| Description | viii, 135 pages : illustrations ; 24 cm |
| Supplemental Content | Full text available from eBook - Biomedical Engineering 2019 |
| Subjects |
| Contents | Chapter 1 PDE model formulation; 1.1 Introduction; 1.2 Model Specification; 1.2.1 Capillary tip density; 1.2.2 Blood capillary density; 1.2.3 VEGF concentration; Acknowledgment; References -- Chapter 2 Model implementation; 2.1 Introduction; 2.2 Method of lines routines; 2.2.1 Main program; 2.2.2 ODE/MOL routine; 2.3 Model output; 2.4 Summary and conclusions; References -- Chapter 3 Variation of parameters; 3.1 Introduction; 3.2 MOL analysis; 3.2.1 Main program, source routine; 3.2.2 Model output; 3.3 Summary and conclusions -- Chapter 4 Detailed PDE analysis; 4.1 Introduction; 4.2 Analysis of the t derivatives; 4.2.1 Main program; 4.2.2 ODE/MOL output; 4.3 Analysis of PDE RHS terms; 4.3.1 Main program; 4.4 Summary and conclusions -- Chapter 5 Oxygen effect; 5.1 Introduction; 5.2 Four PDE model; 5.2.1 Main program; 5.2.2 ODE/MOL routine; 5.2.3 Model output, uncoupled PDEs; 5.2.4 Model output, coupled PDEs; 5.3 Summary and conclusions; References -- Chapter 6 Anti-VEGF drug therapy; 6.1 Introduction; 6.2 PDE model; 6.2.1 Main program; 6.2.2 ODE/MOL routine; 6.2.3 Subordinate routine; 6.2.4 Model output -- |
| Contents | 6.3 Summary and Conclusions Appendix A1 Functions dss004, dss044; A1.1 Function dss004; A1.2 Function dss044; Reference; Index; Back Cover |
| Abstract | 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.-- Source other than the Library of Congress. |
| Bibliography note | Includes bibliographical references and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Issued in other form | Ebook version : 9780128184530 |
| Genre/form | Electronic books. |
| LCCN | 2019942173 |
| ISBN | 9780128184523 (pbk.) |
| ISBN | 0128184523 (pbk.) |
| ISBN | (electronic publication) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |