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Submit a ProposalBiofluids Modeling
 | Methods, Perspectives and Solutions By Wilson C. Chin and Jamie A. Chin Copyright: 2024 | Status: Published ISBN: 9781119910428 | Hardcover | 499 pages Price: $225 USD  |
One Line Description
The first book offering analytical and modern computational solutions to important biofluids problems, such as non-Newtonian flows in blood vessels, clogged arteries and veins, bifurcated arteries and veins, arbitrary stent geometries, tissue properties prediction, and porous media Darcy flow simulation in large-scale organ analysis, this is a must-have for any library.
Audience
Medical practitioners, researchers, biomedical engineers and students interested in quantitative fluid flow modeling
Medical practitioners, researchers, biomedical engineers and students interested in quantitative fluid flow modeling
Description
This book introduces new methods for biofluids modeling and biological engineering. The foregoing subjects are treated rigorously, with all modeling assumptions stated and solutions clearly derived. But that’s not all. Key supporting physics-based ideas, algorithmic details, and software design interfaces are equally emphasized, in order to support our overriding objective in getting the anatomical and clinical information that physicians need.
Importantly, this volume provides a self-contained exposition that includes all required biological concepts, plus the background preparation needed in fluid mechanics, basic differential equations and modern numerical analysis. The presentation style will appeal to medical practitioners, researchers, biomedical engineers and students interested in quantitative fluid flow modeling, as well as engineering students eager to learn about advances in a rapidly growing and changing biological science. As such, the book represents “must reading” suitable at the advanced undergraduate level, and motivated readers should be able to embark on related research following guided study.
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This book introduces new methods for biofluids modeling and biological engineering. The foregoing subjects are treated rigorously, with all modeling assumptions stated and solutions clearly derived. But that’s not all. Key supporting physics-based ideas, algorithmic details, and software design interfaces are equally emphasized, in order to support our overriding objective in getting the anatomical and clinical information that physicians need.
Importantly, this volume provides a self-contained exposition that includes all required biological concepts, plus the background preparation needed in fluid mechanics, basic differential equations and modern numerical analysis. The presentation style will appeal to medical practitioners, researchers, biomedical engineers and students interested in quantitative fluid flow modeling, as well as engineering students eager to learn about advances in a rapidly growing and changing biological science. As such, the book represents “must reading” suitable at the advanced undergraduate level, and motivated readers should be able to embark on related research following guided study.
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Author / Editor Details
Wilson Chin, PhD, has published over twenty books with Wiley-Scrivener and other leading book publishers, more than one hundred papers for scientific and scholarly journals, and holds four dozen patents. He is recipient to five awards with the United States Department of Energy in fluid and computational physics, and he has developed engineering flow simulation models for numerous Fortune 500 companies.
Wilson Chin, PhD, has published over twenty books with Wiley-Scrivener and other leading book publishers, more than one hundred papers for scientific and scholarly journals, and holds four dozen patents. He is recipient to five awards with the United States Department of Energy in fluid and computational physics, and he has developed engineering flow simulation models for numerous Fortune 500 companies.
Jamie A. Chin, a biologist affiliated with the Beijing International School, is expanding her research interests, recently publishing innovative biofluids approaches that model complicated clotting effects in non-circular distorted blood vessels and complex multi-branched arterial systems.
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Table of Contents
Preface
Acknowledgements
Dedication
1. Fluid Physics in Circulatory Systems – Problems, Analogies and Methods
Presentation philosophy
1.1 Basic Biological Notions and Fluid-Dynamical Ideas
Conduit flow examples
Basic continuous flow concepts
Eulerian versus Lagrangian descriptions
Steady versus transient models
Newtonian versus non-Newtonian flows
Porous media continuum flow models
Darcy flows in human and animal tissue
Objectives in conduit and Darcy flow modeling
1.2 Quantitative Modeling Perspectives
1.2.1 Rheology considerations in conduit flows
Better arterial flow models needed
1.2.2 Darcy flow model in continuous media
Temperature diffusion
Darcy flow pressure diffusion
Important porous media approach
Relevance of Darcy flows to biofluids
1.3 Preview of Complicated but Simple Boundary Value Problem Solutions
Closing remarks
1.4 References
2. Math Models, Differential Equations and Numerical Methods
2.1 Presentation Approach
What we won’t do
Pursuing studies that uncover the physics
Examples on presentation approach
2.2 Diffusion Processes, Partial Differential Equations and Formulation Development
2.2.1 Heat transfer applications
2.2.2 Heat equation derivation
2.2.3 Pressure diffusion in porous media
2.2.4 Dynamically coupled heat and pressure diffusion
2.3 Boundary-Conforming Curvilinear Grid Generation
2.3.1 Comments on classical coordinate transforms and conformal mapping
2.3.2 Curvilinear gridding method for irregular domains
2.3.2.1 Grid generation for eccentric annular flow
Mapping formalism and key ideas
Thompson’s mapping
Some reciprocity relations
Relation to conformal mapping, finally
Solutions to mesh generation equations
Boundary conditions
Fast iterative solutions
On Laplacian transformations
2.3.2.2 Grid generation for singly-connected conduit flow
2.4 Finite Difference Solutions Made Easy – Iterative Methods, Programming and Source Code Details
2.4.1 Basic ideas in finite differences
A simple differential equation
Variable coefficients and grids
2.4.2 Formulating steady flow problems
Direct versus iterative solutions
Iterative methods
Convergence acceleration
Wells and internal boundaries
Peaceman well corrections
Derivative discontinuities
Point relaxation methods
Observations on relaxation methods
Minimal computing resources
Good numerical stability
Fast convergence
Why relaxation methods converge
Over-relaxation
Line and point relaxation
Curvilinear grid generation and relaxation solutions
Coupled equations on curvilinear meshes
2.5 References
3. Hagen-Poiseuille Extensions – Real Flow Effects and General Bifurcations
3.1 Blood Rheology and Overview
3.1.1 Hagen-Poiseuille – Misunderstandings and limitations
3.1.2 Ideal versus non-Newtonian rheology
3.1.3 Some conventional rheological models
3.1.4 Perfect concentric flow velocity, pressure and flow rate relations
Newtonian flow solution
Bingham Plastic pipe flow
Power Law fluid pipe flow
Herschel-Bulkley pipe flow
Ellis fluid pipe flow
3.1.5 Example solutions for imperfect arteries with stenosis and book presentation outline
Book presentation outline
3.2 Newtonian Flow in Simple Bifurcations
3.2.1 Theory – Two uneven bifurcated blood vessels with Q1 specified
Case 1. Flow rate Q1 prescribed
Case 2. Inlet pressure Pi prescribed
Case 3. Identical outlet pressures Po,2 and Po,3 given
3.2.2 Software – Two uneven bifurcated arteries with Q1 specified (Reference, CODE-1)
An example computation
An additional validation
3.2.3 Theory – Two uneven bifurcated arteries with Pi specified
3.2.4 Software – Two uneven bifurcated arteries with Pi specified (Reference, CODE-2)
A practical example
3.3 Theory – Complicated Arteries with Chained Bifurcations
3.4 Network with Arbitrary Number of Bifurcations
3.5 Bifurcated Newtonian Flow in Noncircular Clogged Blood Vessels
3.6 References
4. Non-Newtonian Flow in Circular Conduits and Networks
Bifurcation model and analytical approach
Different rheological applications
Validation procedures
4.1 Power Law Fluids with Inlet Flow Rate Prescribed
Iterative “half-step” solution for Pa and Pi
Shear stress
Typical parameters
Example calculations
4.2 Herschel-Bulkley Fluids and Yield Stress
4.2.1 Analytical and numerical approach
Yield stress modeling
4.2.2 BIFURC-6 runs assuming τy = 0 psi (Power Law limit)
4.2.3 BIFURC-6 runs assuming τy = 0.00001 psi
4.3 Newtonian and Herschel-Bulkley Examples
Power Law limitations
4.4 References
5. Flows in Clogged Arteries and Veins
5.1 Hagen-Poiseuille Revisited – Rectangular Coordinates
Newtonian pipe flow recapitulation
A physical description
Detailed assessments
Recapitulation
5.2 Non-Newtonian Power Law Circular Pipe Flow in Rectangular Coordinates
5.3 Clinical Implications for Pressure Gradient and Viscous Shear Stress
5.4 Evolutionary Approaches for Complicated Geometries
Static versus evolutionary approaches
5.5 A Detailed Clog Flow Computation
Simulation 1 – Newtonian flow in perfect circle
Simulation 2 – Power Law flow in perfect circle
Simulation 3 – Power Law flow in a clogged blood vessel
5.6 References
6. Square Stents, Centrifugal Effects, Pulsatile Flow, Clogged Bifurcations and Axial Variations
6.1 Stent Geometry Effects on Volume Flow Rate
6.1.1 Conventional stents, analytical flow model
Stent detailed function
Analytical modeling
Exact analytical Hagen-Poiseuille solution
6.1.2 Finite difference method
6.1.3 Square stent designs, analytical and numerical models
Exact analytical solution for rectangular stents
Finite difference solution
Example calculation
6.2 General Formulations and Solutions for Complicated Geometries and Arbitrary Fluids
Recapitulation
6.3 Centrifugal Force Influence on Volume Flow Rate
Straight, closed ducts
Hagen-Poiseuille flow between planes
Flow between concentric plates
Typical calculations
Flows in closed curved ducts
6.4 Unsteady Pulsatile Flow Model for Complicated Duct Cross-Sections
6.5 Bifurcated Conduits with Newtonian Flow in Clogged Geometric Cross-sections
6.6 Modeling Axial Variations with Pseudo-Three-Dimensional Method
6.7 Modeling Transient Wall Effects
6.8 Steady Bifurcated Newtonian Flows With Arbitrary Clogs, A Numerical Example
6.8.1 Motivating questions and examples
6.8.2 Detailed single-element pipe flow solutions
6.8.3 Method for bifurcated systems with clogged piping elements
6.8.4. Effective radius flow properties
6.8.5 Discussion and conclusions
6.9 References
7. Tissue Properties from Steady and Transient Syringe Pressure Analysis
7.1 Importance of Compressibility, Permeability, Anisotropy, Pressure and Porosity in Medical Applications
Compressibility
Permeability
Anisotropy
Local pressures
Porosity
Additional highlights
7.2 Geoscience Perspectives and Background
7.3 Formation Testing in Petroleum Well Logging
7.4 Operational Guidelines to Biofluids Pressure Testing
Intelligent syringe concepts
Multiprobe syringe assemblies for anisotropy and heterogeneity mapping
7.5 Intelligent Syringe Fundamentals
7.5.1 Background and Motivation
7.5.2 Clinical and Diagnostic Objectives
7.5.3 Syringe Flow Basics and Porous Media Pressure Conventions
7.5.4 Single Intelligent Syringe Basic Layout
Figure 3A description
Figure 3B description
Figure 3C description
Figure 3D description
Figure 3E description
General comments
7.5.5 Syringe Arrays for Heterogeneity Mapping and Biopsy Sampler
Array syringe and biopsy sampler
Array syringe general concept
7.6 Mathematical Models for Porous Media Flow
7.6.1 Transient Isotropic Darcy Flow – Forward Solutions
7.6.2 Transient Transversely Isotropic Darcy Flow – Forward Solutions
7.6.3 Transient Isotropic and Transversely Isotropic Darcy Flow – Inverse Solutions
7.6.4 Steady Transversely Isotropic Flow – Inverse Solutions
7.6.5 Modeling Notes and Physical Consequences
Geometric factor
Flowline compressibility
Flowline pressure drops
Pressure effects on tissue
7.6.6 Anisotropic Permeabilities from Oscillatory Pressure Fields
7.6.7 Formulation for Supercharged Damage Zones
7.6.8 General Properties, Calculated Results and Validations
Example 1. Forward and Inverse Simulations in Isotropic Media Using Drawdown Method
Example 2. Forward and Inverse Simulations in Transversely Isotropic Media Using Pure Drawdown (or Pure Buildup) Methods
Example 3. Forward and Inverse Simulations in Transversely Isotropic Media Using Drawdown-Buildup Method
Example 4. Forward and Inverse Simulations in Transversely Isotropic Media Using Drawdown and Phase Delay Method
Example 5. Forward and Inverse Simulations in Transversely Isotropic Media for Flows with Nonzero Dip Angle
7.6.9 Application to Subcutaneous Injection Yorkshire Swine Laboratory Data
Experimental details
Laboratory setup and raw data analysis
Example 1. Needle Gauge Effect on Mobility Predictions
Example 2. Transversely Isotropic (kh = 20 md, kv = 30 md) Prediction of kh and kv from Steady Pressure Drops
Example 3. Transversely Isotropic (kh = 30 md, kv = 20 md) Prediction of kh and kv from Steady Pressure Drops
Example 4. Anisotropic Transient Method for Effective Permeability
Example 5. Effects of Compressibility
7.6.10 Application to Subcutaneous Injection Adult Human Laboratory Data
Example 1. Pressure Analysis for Figure 7-1D
Example 2. Pressure Analysis for Figures 7-1A,B,C
7.6.11 Laboratory Notes for Flowline Geometry and Frictional Effects
7.6.12 Closing Remarks
7.7 References
8. Artery, Capillary and Vein Interactions in Anisotropic Heterogeneous Porous Tissue Flows
Intuitive physical ideas
Concrete simulation examples
8.1 Qualitative Review of the Circulatory System
8.2 Porous Media Flows in the Geosciences and in Biofluids Applications
Biofluids applications
8.3 Electrical and Biological Analogies
Series and parallel electrical circuits
Cardiovascular system model
Validating examples
Simulation 1. Baseline run with three active capillary bed groups (see Figure 8-18a)
Simulation 2. Baseline run with two active capillary groups (middle group, with smaller permeability, is altered)
Simulation 3. Calculating flow rate versus pressure drop
Tissue masses connected in series
8.4 References
9. Geoscience Ideas in Biofluids Modeling
Solution strategies and perspectives
Blood vessel assumptions revisited
9.1 Multisim Background and Biofluids Applications
Interesting possibilities
Multisim limitations in our applications
What Multisim does and how it works
9.2 Running Multisim
9.2.1 Simulation 1. Set-up and “Flatman” visual display
Rendering “Flatman” in Multisim
9.2.2 Simulation 2 – Simple aneurysm model
9.2.3 Simulation 3 – Mimicking pressure drops in blood vessels
9.2.4 Simulation 4 – Pressure versus flow rate specifications
Run 1. Pressure-pressure specification
Run 2. Flow rate – flow rate specification
Run 3. Pressure – flow rate specification
9.3 Closing Remarks
9.4 References
Cumulative References
Index
About the Authors
Back to Top
Preface
Acknowledgements
Dedication
1. Fluid Physics in Circulatory Systems – Problems, Analogies and Methods
Presentation philosophy
1.1 Basic Biological Notions and Fluid-Dynamical Ideas
Conduit flow examples
Basic continuous flow concepts
Eulerian versus Lagrangian descriptions
Steady versus transient models
Newtonian versus non-Newtonian flows
Porous media continuum flow models
Darcy flows in human and animal tissue
Objectives in conduit and Darcy flow modeling
1.2 Quantitative Modeling Perspectives
1.2.1 Rheology considerations in conduit flows
Better arterial flow models needed
1.2.2 Darcy flow model in continuous media
Temperature diffusion
Darcy flow pressure diffusion
Important porous media approach
Relevance of Darcy flows to biofluids
1.3 Preview of Complicated but Simple Boundary Value Problem Solutions
Closing remarks
1.4 References
2. Math Models, Differential Equations and Numerical Methods
2.1 Presentation Approach
What we won’t do
Pursuing studies that uncover the physics
Examples on presentation approach
2.2 Diffusion Processes, Partial Differential Equations and Formulation Development
2.2.1 Heat transfer applications
2.2.2 Heat equation derivation
2.2.3 Pressure diffusion in porous media
2.2.4 Dynamically coupled heat and pressure diffusion
2.3 Boundary-Conforming Curvilinear Grid Generation
2.3.1 Comments on classical coordinate transforms and conformal mapping
2.3.2 Curvilinear gridding method for irregular domains
2.3.2.1 Grid generation for eccentric annular flow
Mapping formalism and key ideas
Thompson’s mapping
Some reciprocity relations
Relation to conformal mapping, finally
Solutions to mesh generation equations
Boundary conditions
Fast iterative solutions
On Laplacian transformations
2.3.2.2 Grid generation for singly-connected conduit flow
2.4 Finite Difference Solutions Made Easy – Iterative Methods, Programming and Source Code Details
2.4.1 Basic ideas in finite differences
A simple differential equation
Variable coefficients and grids
2.4.2 Formulating steady flow problems
Direct versus iterative solutions
Iterative methods
Convergence acceleration
Wells and internal boundaries
Peaceman well corrections
Derivative discontinuities
Point relaxation methods
Observations on relaxation methods
Minimal computing resources
Good numerical stability
Fast convergence
Why relaxation methods converge
Over-relaxation
Line and point relaxation
Curvilinear grid generation and relaxation solutions
Coupled equations on curvilinear meshes
2.5 References
3. Hagen-Poiseuille Extensions – Real Flow Effects and General Bifurcations
3.1 Blood Rheology and Overview
3.1.1 Hagen-Poiseuille – Misunderstandings and limitations
3.1.2 Ideal versus non-Newtonian rheology
3.1.3 Some conventional rheological models
3.1.4 Perfect concentric flow velocity, pressure and flow rate relations
Newtonian flow solution
Bingham Plastic pipe flow
Power Law fluid pipe flow
Herschel-Bulkley pipe flow
Ellis fluid pipe flow
3.1.5 Example solutions for imperfect arteries with stenosis and book presentation outline
Book presentation outline
3.2 Newtonian Flow in Simple Bifurcations
3.2.1 Theory – Two uneven bifurcated blood vessels with Q1 specified
Case 1. Flow rate Q1 prescribed
Case 2. Inlet pressure Pi prescribed
Case 3. Identical outlet pressures Po,2 and Po,3 given
3.2.2 Software – Two uneven bifurcated arteries with Q1 specified (Reference, CODE-1)
An example computation
An additional validation
3.2.3 Theory – Two uneven bifurcated arteries with Pi specified
3.2.4 Software – Two uneven bifurcated arteries with Pi specified (Reference, CODE-2)
A practical example
3.3 Theory – Complicated Arteries with Chained Bifurcations
3.4 Network with Arbitrary Number of Bifurcations
3.5 Bifurcated Newtonian Flow in Noncircular Clogged Blood Vessels
3.6 References
4. Non-Newtonian Flow in Circular Conduits and Networks
Bifurcation model and analytical approach
Different rheological applications
Validation procedures
4.1 Power Law Fluids with Inlet Flow Rate Prescribed
Iterative “half-step” solution for Pa and Pi
Shear stress
Typical parameters
Example calculations
4.2 Herschel-Bulkley Fluids and Yield Stress
4.2.1 Analytical and numerical approach
Yield stress modeling
4.2.2 BIFURC-6 runs assuming τy = 0 psi (Power Law limit)
4.2.3 BIFURC-6 runs assuming τy = 0.00001 psi
4.3 Newtonian and Herschel-Bulkley Examples
Power Law limitations
4.4 References
5. Flows in Clogged Arteries and Veins
5.1 Hagen-Poiseuille Revisited – Rectangular Coordinates
Newtonian pipe flow recapitulation
A physical description
Detailed assessments
Recapitulation
5.2 Non-Newtonian Power Law Circular Pipe Flow in Rectangular Coordinates
5.3 Clinical Implications for Pressure Gradient and Viscous Shear Stress
5.4 Evolutionary Approaches for Complicated Geometries
Static versus evolutionary approaches
5.5 A Detailed Clog Flow Computation
Simulation 1 – Newtonian flow in perfect circle
Simulation 2 – Power Law flow in perfect circle
Simulation 3 – Power Law flow in a clogged blood vessel
5.6 References
6. Square Stents, Centrifugal Effects, Pulsatile Flow, Clogged Bifurcations and Axial Variations
6.1 Stent Geometry Effects on Volume Flow Rate
6.1.1 Conventional stents, analytical flow model
Stent detailed function
Analytical modeling
Exact analytical Hagen-Poiseuille solution
6.1.2 Finite difference method
6.1.3 Square stent designs, analytical and numerical models
Exact analytical solution for rectangular stents
Finite difference solution
Example calculation
6.2 General Formulations and Solutions for Complicated Geometries and Arbitrary Fluids
Recapitulation
6.3 Centrifugal Force Influence on Volume Flow Rate
Straight, closed ducts
Hagen-Poiseuille flow between planes
Flow between concentric plates
Typical calculations
Flows in closed curved ducts
6.4 Unsteady Pulsatile Flow Model for Complicated Duct Cross-Sections
6.5 Bifurcated Conduits with Newtonian Flow in Clogged Geometric Cross-sections
6.6 Modeling Axial Variations with Pseudo-Three-Dimensional Method
6.7 Modeling Transient Wall Effects
6.8 Steady Bifurcated Newtonian Flows With Arbitrary Clogs, A Numerical Example
6.8.1 Motivating questions and examples
6.8.2 Detailed single-element pipe flow solutions
6.8.3 Method for bifurcated systems with clogged piping elements
6.8.4. Effective radius flow properties
6.8.5 Discussion and conclusions
6.9 References
7. Tissue Properties from Steady and Transient Syringe Pressure Analysis
7.1 Importance of Compressibility, Permeability, Anisotropy, Pressure and Porosity in Medical Applications
Compressibility
Permeability
Anisotropy
Local pressures
Porosity
Additional highlights
7.2 Geoscience Perspectives and Background
7.3 Formation Testing in Petroleum Well Logging
7.4 Operational Guidelines to Biofluids Pressure Testing
Intelligent syringe concepts
Multiprobe syringe assemblies for anisotropy and heterogeneity mapping
7.5 Intelligent Syringe Fundamentals
7.5.1 Background and Motivation
7.5.2 Clinical and Diagnostic Objectives
7.5.3 Syringe Flow Basics and Porous Media Pressure Conventions
7.5.4 Single Intelligent Syringe Basic Layout
Figure 3A description
Figure 3B description
Figure 3C description
Figure 3D description
Figure 3E description
General comments
7.5.5 Syringe Arrays for Heterogeneity Mapping and Biopsy Sampler
Array syringe and biopsy sampler
Array syringe general concept
7.6 Mathematical Models for Porous Media Flow
7.6.1 Transient Isotropic Darcy Flow – Forward Solutions
7.6.2 Transient Transversely Isotropic Darcy Flow – Forward Solutions
7.6.3 Transient Isotropic and Transversely Isotropic Darcy Flow – Inverse Solutions
7.6.4 Steady Transversely Isotropic Flow – Inverse Solutions
7.6.5 Modeling Notes and Physical Consequences
Geometric factor
Flowline compressibility
Flowline pressure drops
Pressure effects on tissue
7.6.6 Anisotropic Permeabilities from Oscillatory Pressure Fields
7.6.7 Formulation for Supercharged Damage Zones
7.6.8 General Properties, Calculated Results and Validations
Example 1. Forward and Inverse Simulations in Isotropic Media Using Drawdown Method
Example 2. Forward and Inverse Simulations in Transversely Isotropic Media Using Pure Drawdown (or Pure Buildup) Methods
Example 3. Forward and Inverse Simulations in Transversely Isotropic Media Using Drawdown-Buildup Method
Example 4. Forward and Inverse Simulations in Transversely Isotropic Media Using Drawdown and Phase Delay Method
Example 5. Forward and Inverse Simulations in Transversely Isotropic Media for Flows with Nonzero Dip Angle
7.6.9 Application to Subcutaneous Injection Yorkshire Swine Laboratory Data
Experimental details
Laboratory setup and raw data analysis
Example 1. Needle Gauge Effect on Mobility Predictions
Example 2. Transversely Isotropic (kh = 20 md, kv = 30 md) Prediction of kh and kv from Steady Pressure Drops
Example 3. Transversely Isotropic (kh = 30 md, kv = 20 md) Prediction of kh and kv from Steady Pressure Drops
Example 4. Anisotropic Transient Method for Effective Permeability
Example 5. Effects of Compressibility
7.6.10 Application to Subcutaneous Injection Adult Human Laboratory Data
Example 1. Pressure Analysis for Figure 7-1D
Example 2. Pressure Analysis for Figures 7-1A,B,C
7.6.11 Laboratory Notes for Flowline Geometry and Frictional Effects
7.6.12 Closing Remarks
7.7 References
8. Artery, Capillary and Vein Interactions in Anisotropic Heterogeneous Porous Tissue Flows
Intuitive physical ideas
Concrete simulation examples
8.1 Qualitative Review of the Circulatory System
8.2 Porous Media Flows in the Geosciences and in Biofluids Applications
Biofluids applications
8.3 Electrical and Biological Analogies
Series and parallel electrical circuits
Cardiovascular system model
Validating examples
Simulation 1. Baseline run with three active capillary bed groups (see Figure 8-18a)
Simulation 2. Baseline run with two active capillary groups (middle group, with smaller permeability, is altered)
Simulation 3. Calculating flow rate versus pressure drop
Tissue masses connected in series
8.4 References
9. Geoscience Ideas in Biofluids Modeling
Solution strategies and perspectives
Blood vessel assumptions revisited
9.1 Multisim Background and Biofluids Applications
Interesting possibilities
Multisim limitations in our applications
What Multisim does and how it works
9.2 Running Multisim
9.2.1 Simulation 1. Set-up and “Flatman” visual display
Rendering “Flatman” in Multisim
9.2.2 Simulation 2 – Simple aneurysm model
9.2.3 Simulation 3 – Mimicking pressure drops in blood vessels
9.2.4 Simulation 4 – Pressure versus flow rate specifications
Run 1. Pressure-pressure specification
Run 2. Flow rate – flow rate specification
Run 3. Pressure – flow rate specification
9.3 Closing Remarks
9.4 References
Cumulative References
Index
About the Authors
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