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E-raamat: Numerical Pde Analysis Of The Blood Brain Barrier: Method Of Lines In R

(Lehigh Univ, Usa)
  • Formaat: 264 pages
  • Ilmumisaeg: 21-Dec-2018
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813275812
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Numerical Pde Analysis Of The Blood Brain Barrier: Method Of Lines In RSuurem pilt
  • Formaat: 264 pages
  • Ilmumisaeg: 21-Dec-2018
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813275812
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The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O) 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.
Preface ix
Chapter 1 PDE Model Formulation
1(8)
1.1 Introduction
1(7)
1.2 Two PDE Model 2 Reference
8(1)
Chapter 2 PDE Model Computer Implementation
9(34)
2.1 Introduction
9(1)
2.2 Two PDE Model
9(33)
2.2.1 Main program
9(10)
2.2.2 ODE/MOL routine
19(6)
2.2.3 Model output
25(17)
2.3 Summary and Conclusions 41 References
42(1)
Chapter 3 Three PDE Models of Blood Brain Transfer
43(60)
3.1 Introduction
43(1)
3.2 Three PDE Model
43(40)
3.2.1 Main program
45(11)
3.2.2 ODE/MOL routine
56(8)
3.2.3 Model output
64(19)
3.3 3D Visualization of the PDE Solutions
83(18)
3.3.1 Main program
84(10)
3.3.2 ODE/MOL routine
94(1)
3.3.3 Model output
94(7)
3.4 Summary and Conclusions 101 Reference
101(2)
Chapter 4 Nonlinear PDE Models
103(48)
4.1 Introduction
103(1)
4.2 First Nonlinear PDE Model
103(27)
4.2.1 Main program
104(11)
4.2.2 ODE/MOL routine
115(4)
4.2.3 Model output
119(11)
4.3 Second Nonlinear PDE Model
130(19)
4.3.1 Main program
131(6)
4.3.2 ODE/MOL routine
137(5)
4.3.3 Model output
142(7)
4.4 Summary and Conclusions
149(2)
Chapter 5 Multicomponent Blood Brain Barrier Models
151(44)
5.1 Introduction
151(1)
5.2 Two Component BBB Model
151(42)
5.2.1 Main program
154(20)
5.2.2 ODE/MOL routine
174(10)
5.2.3 Model output
184(9)
5.3 Summary and Conclusions 193 Reference
193(2)
Chapter 6 Application of Calibrated PDE Models to the BBB
195(36)
6.1 Introduction
195(1)
6.2 One Component Model
195(2)
6.2.1 Main program
197(23)
6.2.2 ODE/MOL routine
206(1)
6.2.3 Model output
207(13)
6.3 Variants of the Model
220(9)
6.4 Summary and Conclusions 229 References
229(2)
Appendix A1 Function dss004 231(4)
Appendix A2 Function dss044 235(4)
Appendix A3 Function vanl 239(4)
Appendix A4 Functions super, smart 243(6)
Index 249
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