Numerical Pde Analysis of the Blood Brain Barrier
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Book Overview The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O₂) and nutrients in the brai...
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.
Book Details Format: Hardcover | Pages: 264 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9813275790
FormatHardcover
Pages264
LanguageEnglish
ISBN9813275790
EAN9789813275799
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date2018-12-13
Edition1
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.16 Pounds
Length9.0 Inches
Width6.0 Inches
Height0.63 Inches
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