Numerical Pde Analysis of the Blood Brain Barrier: Method of Lines in R, William E. Schiesser
Автор: Schiesser, W. E. Название: Schiesser-Numerical PDE Analysis of Retinal ISBN: 0128184523 ISBN-13(EAN): 9780128184523 Издательство: Elsevier Science Рейтинг: Цена: 19370.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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 models
Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms
Authored by a leading researcher and educator in PDE models
Автор: Schiesser William E Название: Computational Chemotaxis Models For Neurodegenerative Disease ISBN: 9813207450 ISBN-13(EAN): 9789813207455 Издательство: World Scientific Publishing Рейтинг: Цена: 12830.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The mathematical model presented in this book, based on partial differential equations (PDEs) describing attractant-repellent chemotaxis, is offered for a quantitative analysis of neurodegenerative disease (ND), e.g., Alzheimer's disease (AD). The model is a representation of basic phenomena (mechanisms) for diffusive transport and biochemical kinetics that provides the spatiotemporal distribution of components which could explain the evolution of ND, and is offered with the intended purpose of providing a small step toward the understanding, and possible treatment of ND.
The format and emphasis of the presentation is based on the following elements:
A statement of the PDE system, including initial conditions (ICs), boundary conditions (BCs) and the model parameters.
Algorithms for the calculation of numerical solutions of the PDE system with a minimum of mathematical formality.
A set of R routines for the calculation of numerical solutions, including a detailed explanation of all of the sections of the code. The R routines can be executed after a straightforward download of R, an open-source scientific computing system available from the Internet.
Presentation of the numerical solutions, particularly in graphical (plotted) format to enhance the visualization of the solution.
Summary and conclusions concerning the principal results from the model that might serve as the basis for a next step in the modeling of ND.
In other words, a methodology for numerical PDE modeling is presented that is flexible, open ended and readily implemented on modest computers. If the reader is interested in an alternate model, it might possibly be implemented by: (1) modifying and/or extending the current model (for example, by adding terms to the PDEs or adding additional PDEs), or (2) using the reported routines as a prototype for the model of interest.
These suggestions illustrate an important feature of computer-based modeling, that is, the readily available procedure of numerically experimenting with a model. The current model is offered as only a first step toward the resolution of this urgent medical problem.
Автор: Schiesser William E Название: Computational Chemotaxis Models For Neurodegenerative Disease ISBN: 9813208910 ISBN-13(EAN): 9789813208919 Издательство: World Scientific Publishing Рейтинг: Цена: 7603.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The mathematical model presented in this book, based on partial differential equations (PDEs) describing attractant-repellent chemotaxis, is offered for a quantitative analysis of neurodegenerative disease (ND), e.g., Alzheimer's disease (AD). The model is a representation of basic phenomena (mechanisms) for diffusive transport and biochemical kinetics that provides the spatiotemporal distribution of components which could explain the evolution of ND, and is offered with the intended purpose of providing a small step toward the understanding, and possible treatment of ND.
The format and emphasis of the presentation is based on the following elements:
A statement of the PDE system, including initial conditions (ICs), boundary conditions (BCs) and the model parameters.
Algorithms for the calculation of numerical solutions of the PDE system with a minimum of mathematical formality.
A set of R routines for the calculation of numerical solutions, including a detailed explanation of all of the sections of the code. The R routines can be executed after a straightforward download of R, an open-source scientific computing system available from the Internet.
Presentation of the numerical solutions, particularly in graphical (plotted) format to enhance the visualization of the solution.
Summary and conclusions concerning the principal results from the model that might serve as the basis for a next step in the modeling of ND.
In other words, a methodology for numerical PDE modeling is presented that is flexible, open ended and readily implemented on modest computers. If the reader is interested in an alternate model, it might possibly be implemented by: (1) modifying and/or extending the current model (for example, by adding terms to the PDEs or adding additional PDEs), or (2) using the reported routines as a prototype for the model of interest.
These suggestions illustrate an important feature of computer-based modeling, that is, the readily available procedure of numerically experimenting with a model. The current model is offered as only a first step toward the resolution of this urgent medical problem.
Автор: Schiesser, William Название: ODE/PDE Analysis of Multiple Myeloma ISBN: 0367471353 ISBN-13(EAN): 9780367471354 Издательство: Taylor&Francis Рейтинг: Цена: 17609.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models for multiple myeloma, a form of bone cancer. The models are stated as systems of ordinary and partial differential equations (ODE/PDEs).
Автор: Schiesser, W.e. (lehigh University, Bethlehem, Pennsylvania, Usa) Название: Time delay ode/pde models ISBN: 0367427974 ISBN-13(EAN): 9780367427979 Издательство: Taylor&Francis Рейтинг: Цена: 17609.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs) in biomedical science and engineering (BMSE).
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru
