An Introduction to Modeling of Transport Processes Applications to Biomedical Systems 1st Edition by Ashim Datta, Vineet Rakesh ISBN 0521119243 9780521119245

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ISBN 10: 0521119243 
ISBN 13: 9780521119245
Author: Ashim Datta, Vineet Rakesh

An Introduction to Modeling of Transport Processes Applications to Biomedical Systems 1st Table of contents:

I Essential steps
1 Problem formulation: From reality to realistic computer representation
1.1 Context: biomedical transport processes
1.1.1 Heat transfer and thermal therapy
1.1.2 Mass transfer and drug delivery
1.1.3 Quantification of goals in a biomedical process
1.2 What is problem formulation?
1.3 Steps in problem formulation
1.4 Defining goals for problem formulation
1.5 Simplify, simplify, simplify
1.6 Geometry: setting the computational domain
1.6.1 What regions need to be included?
Connectivity between the regions
1.6.2 How much of a very large region should be included?
1.6.3 How many dimensions are needed?
1.6.4 How can we consider symmetry to reduce the domain?
How to implement a 1D problem in 2D
1.7 Governing equations
1.7.1 Which governing equations?
Conservation equation for total mass (continuity equation)
Momentum conservation equations (fluid flow equations)
Energy conservation equation (heat transfer equation)
Mass species conservation equation (mass transfer equation)
1.7.2 What terms remain in the governing equation?
Transient
Convection
Diffusion
Generation (or source)
Deciding on 2D/3D/axisymmetric
1.8 Boundary and initial conditions
1.8.1 How many boundary conditions are needed?
1.8.2 What kind of boundary condition?
1.8.3 Boundary conditions changing with time
1.8.4 Boundary condition at an infinite region
1.8.5 Boundary condition at an interface between two materials
1.8.6 Flux boundary condition versus volumetric heat generation
1.8.7 Initial condition
1.9 Material properties
1.9.1 Questions to ask
1.9.2 Simplification is generally needed
1.9.3 When accurate data are not available
1.10 Other input parameters
1.11 Summary
References
1.12 Problems
1.12.1 Short questions
1.12.2 Choice of domain size: heating tumors with ferromagnetic materials
1.12.3 Choice of domain size: drug delivery in the brain
Questions on problem formulation: instructions
1.12.4 Drug delivery in the brain
1.12.5 Heat generation from tooth drilling
1.12.6 Drug delivery from a stent
1.12.7 Laser-interstitial thermal therapy (LITT)
1.12.8 Nitrogen elimination in alveoli
1.12.9 Drug release from a nicotine patch
1.12.10 Therapeutic heating
1.12.11 Radiofrequency ablation
1.12.12 Radiofrequency heating to destroy a tumor
1.12.13 Cryosurgery
1.12.14 Drug release from a therapeutic contact lens
1.12.15 Oxygen transport in alveoli
1.12.16 Refractive laser vision surgery
1.12.17 Conditioning of air in the nose

2 Software implementation 1: What to solve (preprocessing)
2.1 Choosing a software
2.2 Software is not to be used as a blackbox
2.3 Organization of a typical CAE software: preprocessing, processing and postprocessing
2.4 Some general guidelines to preprocessing
2.5 Introduction to preprocessing in a computational software (COMSOL)
2.6 Geometry and analysis type
2.6.1 Geometry
2.6.2 Analysis
2.7 Geometry creation
2.7.1 Drawing geometry in COMSOL
Geometry in 1D
Geometry in 2D
Geometry in 3D
2.7.2 Obtaining exact geometry from a CAD program
2.8 Governing equations
2.8.1 Convection, transient and source terms
2.8.2 Example of heat source: implementing blood flow term in the bioheat equation
2.8.3 Example of mass source: implementing reactions
2.9 Boundary conditions
2.9.1 General implementation
2.9.2 Special cases: time-varying boundary conditions
2.9.3 Example: specifying a parabolic inlet velocity profile
2.10 Initial conditions
2.11 Material properties
2.11.1 Variable properties
2.11.2 Zero diffusivity
2.12 Miscellaneous implementation aspects
2.12.1 Solving ordinary differential equations
2.12.2 Using logical expressions
2.12.3 Modeling in COMSOL Script
References
2.13 Problems
2.13.1 Short questions
2.13.2 Questions on software implementation

3 Software implementation 2: How to solve (processing)
3.1 Which numerical method to use
3.2 Items needed in specifying the solution methodology
3.3 How to discretize the domain: mesh
3.3.1 Elements and mesh
3.3.2 Structured (mapped) versus unstructured (free) mesh
3.3.3 Meshing in COMSOL: 1D geometry
3.3.4 Meshing in COMSOL: 2D geometry
Structured (mapped) mesh
Unstructured (free) mesh
3.3.5 Meshing in COMSOL: 3D geometry
Structured mesh
Unstructured mesh
Combination of structured and unstructured mesh
3.3.6 Deciding on a mesh
3.4 How to choose a time step
3.4.1 Implementation of time step in COMSOL
3.4.2 Specifying end times and saving data in COMSOL
3.5 How to choose a solver to solve the system of linear equations
3.5.1 Solver selection in COMSOL
3.5.2 Setting tolerances for a time-dependent problem
3.6 Problems
3.6.1 Guidelines for mesh and time step
3.6.2 Need for non-uniform mesh
3.6.3 Choice of mesh
3.6.4 Choice of mesh: Case studies VI, VIII, IX and X
3.6.5 Choice of time steps: Case studies I, II, III and IV

4 Software implementation 3: Visualizing and manipulating solution (postprocessing)
4.1 Useful information in a biomedical context
4.2 Obtaining data at a particular location
4.3 Plotting transient data at one or more points, line or surface as a function of time
4.4 Obtaining surface/contour plots (in 2D problems) for observing variation within a region
4.4.1 Contour plot
4.4.2 Surface plot
4.4.3 Additional options for surface and contour plots
4.5 Obtaining a surface plot in a 3D problem
4.5.1 For the entire geometry
4.5.2 For different sections of the geometry
4.6 Obtaining average values at a particular time or as a function of time
4.6.1 Average values at any particular time
4.6.2 Average values as a function of time
4.7 Obtaining arbitrary functions of computed variables
4.8 Creating animations
4.9 Dedicated plotting and postprocessing software
4.10 Relating to the goals of the simulation: guidelines for postprocessing
4.11 Analysis of data obtained from postprocessing
4.12 Presenting the simulation results to others
4.13 Problems
4.13.1 Postprocessing: Case study I
4.13.2 Postprocessing: Case study II
4.13.3 Postprocessing: Case study III
4.13.4 Postprocessing: Case study IV
4.13.5 Postprocessing: Case study VII
4.13.6 Postprocessing: Case study X
4.14 Appendix

5 Validation, sensitivity analysis, optimization and debugging
5.1 Types of errors and error reduction
5.1.1 Defining uncertainty and error
Uncertainty
Error
Acknowledged errors
Unacknowledged errors
5.1.2 Classification of errors
Physical approximation error
Computer round-off error
Iterative convergence error
Discretization errors
Computer programming errors
Usage errors
5.2 Estimating error: validation of the model
5.2.1 What level of agreement is desirable?
5.2.2 Use your eyes and common sense (qualitative checks)
5.2.3 Compare with alternative solutions
5.2.4 Compare with experimental data
5.2.5 Error estimation through sensitivity analysis
5.3 Sensitivity analysis
5.3.1 Parameters to analyze
5.3.2 Methods of sensitivity analysis
5.3.3 Sample sensitivity analysis in COMSOL
5.4 Optimization
5.5 Debugging
5.5.1 Guidelines
5.5.2 Common errors and debugging
References
5.6 Problems
5.6.1 Short questions
5.6.2 Validation and debugging
5.6.3 Sensitivity analysis and optimization

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Tags: Ashim Datta, Vineet Rakesh, Transport Processes, Biomedical Systems