Schiesser-Numerical PDE Analysis of Retinal, Schiesser, W. E.
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 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.
The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O₂) and nutrients in the brain. These metabolism components are supplied to the brain by an intricate blood circulatory system (vasculature). The blood brain barrier (BBB), which is the central topic of this book, determines the rate of transfer from the blood to the brain tissue.
In particular, mathematical models are developed for mass transfer across the BBB based on partial differential equations (PDEs) applied to the blood capillaries, the endothelial membrane, and the brain tissue. The PDEs derived from mass balances and computer routines in R are presented for the numerical (computer-based) solution of the PDEs. The computed concentration profiles of the transferred components are functions of time and space within the BBB system, i.e., spatiotemporal solutions.
The R routines and the associated numerical algorithms for computing the numerical solutions are discussed in detail. The discussion is introductory, without formal mathematics, e.g., theorems and proofs. The general methodology (algorithm) for numerical PDE solutions is the method of lines (MOL).
The models are used to study the transfer of oxygen and nutrients, harmful substances that should not enter the brain such as chemicals and pathogens (viruses, bacteria), and therapeutic drugs. The intent of the book is to provide a quantitative approach to the study of BBB dynamics using a computer-based methodology programmed in R, a quality open-source scientific programming system that is easily downloaded from the Internet for execution on modest computers.
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).
An introduction to the computer-based modeling of influenza, a continuing major worldwide communicable disease.
The use of (1) as an illustration of a methodology for the computer-based modeling of communicable diseases.
For the purposes of (1) and (2), a basic influenza model is formulated as a system of partial differential equations (PDEs) that define the spatiotemporal evolution of four populations: susceptibles, untreated and treated infecteds, and recovereds. The requirements of a well-posed PDE model are considered, including the initial and boundary conditions. The terms of the PDEs are explained.
The computer implementation of the model is illustrated with a detailed line-by-line explanation of a system of routines in R (a quality, open-source scientific computing system that is readily available from the Internet). The R routines demonstrate the straightforward numerical solution of a system of nonlinear PDEs by the method of lines (MOL), an established general algorithm for PDEs.
The presentation of the PDE modeling methodology is introductory with a minumum of formal mathematics (no theorems and proofs), and with emphasis on example applications. The intent of the book is to assist in the initial understanding and use of PDE mathematical modeling of communicable diseases, and the explanation and interpretation of the computed model solutions, as illustrated with the influenza model.
An introduction to the computer-based modeling of influenza, a continuing major worldwide communicable disease.
The use of (1) as an illustration of a methodology for the computer-based modeling of communicable diseases.
For the purposes of (1) and (2), a basic influenza model is formulated as a system of partial differential equations (PDEs) that define the spatiotemporal evolution of four populations: susceptibles, untreated and treated infecteds, and recovereds. The requirements of a well-posed PDE model are considered, including the initial and boundary conditions. The terms of the PDEs are explained.
The computer implementation of the model is illustrated with a detailed line-by-line explanation of a system of routines in R (a quality, open-source scientific computing system that is readily available from the Internet). The R routines demonstrate the straightforward numerical solution of a system of nonlinear PDEs by the method of lines (MOL), an established general algorithm for PDEs.
The presentation of the PDE modeling methodology is introductory with a minumum of formal mathematics (no theorems and proofs), and with emphasis on example applications. The intent of the book is to assist in the initial understanding and use of PDE mathematical modeling of communicable diseases, and the explanation and interpretation of the computed model solutions, as illustrated with the influenza model.
Автор: William E. Schiesser Название: Spatiotemporal Modeling of Cancer Immunotherapy ISBN: 3030176355 ISBN-13(EAN): 9783030176358 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The focus of this book is a detailed discussion of a dual cancer vaccine (CV)-immune checkpoint inhibitor (ICI) mathematical model formulated as a system of partial differential equations (PDEs) defining the spatiotemporal distribution of cells and biochemicals during tumor growth.A computer implementation of the model is discussed in detail for the quantitative evaluation of CV-ICI therapy. The coding (programming) consists of a series of routines in R, a quality, open-source scientific computing system that is readily available from the internet. The routines are based on the method of lines (MOL), a general PDE algorithm that can be executed on modest computers within the basic R system. The reader can download and use the routines to confirm the model solutions reported in the book, then experiment with the model by varying the parameters and modifying/extending the equations, and even studying alternative models with the PDE methodology demonstrated by the CV-ICI model.Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in R facilitates the use of the model, and more generally, computer- based analysis of cancer immunotherapy mathematical models, as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer.To download the R routines, please visit: http://www.lehigh.edu/~wes1/ci_download
Автор: Joe G. Hollyfield; Robert E. Anderson; Matthew M. Название: Retinal Degenerative Diseases and Experimental Therapy ISBN: 1475772246 ISBN-13(EAN): 9781475772241 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: To create a forum for scientists and clinicians interested in degenerative retinal diseases, we began in 1984 to organize a biennial symposium on Retinal Degeneration as a satellite meeting of the International Congress of Eye Research.
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