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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.--

Differential equations, Partial. --- Neovascularization --- Retina --- R (Computer program language) --- Retinal Neovascularization. --- Models, Theoretical. --- Computer Simulation. --- Mathematical Computing. --- Mathematical models. --- Blood-vessels. --- Computing, Statistical --- Mathematic Computing --- Statistical Programs, Computer Based --- Statistical Computing --- Computing, Mathematic --- Computing, Mathematical --- Computings, Mathematic --- Computings, Mathematical --- Computings, Statistical --- Mathematic Computings --- Mathematical Computings --- Statistical Computings --- Computerized Models --- In Silico --- Computer Models --- Models, Computer --- Computer Model --- Computer Simulations --- Computerized Model --- In Silicos --- Model, Computer --- Model, Computerized --- Models, Computerized --- Silico, In --- Silicos, In --- Simulation, Computer --- Simulations, Computer --- Experimental Model --- Experimental Models --- Mathematical Model --- Model, Experimental --- Models (Theoretical) --- Models, Experimental --- Models, Theoretic --- Theoretical Study --- Mathematical Models --- Model (Theoretical) --- Model, Mathematical --- Model, Theoretical --- Models, Mathematical --- Studies, Theoretical --- Study, Theoretical --- Theoretical Model --- Theoretical Models --- Theoretical Studies --- Computer Simulation --- Systems Theory --- Neovascularization, Optic Disc --- Neovascularization, Retinal --- Optic Disc Neovascularization --- Optic Disk Neovascularization --- Sea Fan Neovascularization --- Disk Neovascularization, Optic --- Neovascularization, Optic Disk --- Neovascularization, Sea Fan --- Optic Disc Neovascularizations --- Optic Disk Neovascularizations --- Sea Fan Neovascularizations --- GNU-S (Computer program language) --- Domain-specific programming languages --- Blood-vessels --- Partial differential equations --- Growth

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Drug resistance in microorganisms --- R (Computer program language) --- Antibiotics --- Mathematical models. --- Anti-infective agents --- Microbial metabolites --- Allelopathic agents --- Antibiosis --- Pharmaceutical microbiology --- Phytoncides --- GNU-S (Computer program language) --- Domain-specific programming languages --- Antibiotic resistance in microorganisms --- Antibiotics resistance in microorganisms --- Bacterial resistance to antibiotics --- Drug resistance in micro-organisms --- Microbial drug resistance --- Resistance to drugs in microorganisms --- Microorganisms --- Effect of drugs on

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PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R presents the formulation and computer implementation of mathematical models for the forefront research areas of tissue engineering and regenerative medicine. The mathematical model discussed in this book consists of a system of eight partial differential equations (PDEs) with dependent variables. The computer-based example models are presented through routines coded in R—a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Includes detailed examples that the reader can execute on modest computers.

Differential equations, Partial. --- R (Computer program language) --- Regenerative medicine. --- Medicine --- Regeneration (Biology) --- GNU-S (Computer program language) --- Domain-specific programming languages --- Partial differential equations --- Tissue engineering --- Tissue Engineering --- Regenerative Medicine --- Models, Theoretical --- Mathematical models. --- Tissue Engineering. --- Regenerative Medicine. --- Models, Theoretical.

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ODE/PDE Alpha-Synuclein Models for Parkinson's Disease discusses a mechanism for the evolution of Parkinson's Disease (PD) based on the dynamics of the protein?-synuclein, a monomer that has been implicated in this disease. Specifically,?-synuclein morphs and aggregates into a polymer that can interfere with functioning neurons and lead to neurodegenerative pathology. This book first demonstrates computer-based implementation of a prototype ODE/PDE model for the dynamics of the?-synuclein monomer and polymer, and then details the methodology for the numerical integration of ODE/PDE systems which can be applied to computer-based analyses of alternative models based on the reader's interest. This book facilitates immediate computer use for research without the necessity to first learn the basic concepts of numerical analysis for ODE/PDEs and programming algorithms.

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