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" Numerical PDE analysis of retinal neovascularization : "
William E. Schiesser.
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BL
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| Record Number
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872555
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| Main Entry
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Schiesser, W. E.
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| Title & Author
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Numerical PDE analysis of retinal neovascularization : : mathematical model computer implementation in R /\ William E. Schiesser.
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| Edition Statement
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First edition.
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| Publication Statement
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London, United Kingdom :: Academic Press,, [2019]
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| Page. NO
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1 online resource
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| ISBN
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0128184523
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: 0128184531
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: 9780128184523
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: 9780128184530
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Front Cover; Numerical PDE Analysis of Retinal Neovascularization; Copyright; Contents; Preface; 1 PDE Model Formulation; 1.1 Introduction; 1.2 Model Speci cation; 1.2.1 Capillary Tip Density; 1.2.2 Blood Capillary Density; 1.2.3 VEGF Concentration; Acknowledgment; References; 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; 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
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6.3 Summary and ConclusionsA1 Functions dss004, dss044; A1.1 Function dss004; A1.2 Function dss044; Reference; Index; Back Cover
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| Abstract
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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.
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| Subject
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Differential equations, Partial.
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| Subject
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Neovascularization-- Mathematical models.
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Retina-- Blood-vessels.
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Differential equations, Partial.
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MATHEMATICS-- Calculus.
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MATHEMATICS-- Mathematical Analysis.
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| Subject
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Retina-- Blood-vessels.
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| Dewey Classification
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515.353
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| LC Classification
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QA374
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