Computational Models in Biomedical Engineering: Finite Element Models Based on Smeared Physical Fields: Theory, Solutions, and Software

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Computational Models in Biomedical Engineering
Computational Models in Biomedical Engineering: Finite Element Models Based on Smeared Physical Fields: Theory, Solutions, and Software
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Contents
1 - Basic processes in living organisms
	1.1 Introduction: mass transport as a vital process in living organisms
	1.2 Circulatory system
	1.3 Tissue
	1.4 Cells
	1.5 Specificities of the body organs with respect to transport
	1.6 Tissue microenvironment within organs and physiological barriers to transport
	References
2 - Fundamental laws for physical fields and mechanics
	2.1 Diffusion
		2.1.1 Diffusion within a continuum
		2.1.2 One-dimensional diffusion
		2.1.3 Diffusion with convection
	2.2 Heat conduction
	2.3 Flow through porous media
	2.4 Electrostatics
		2.4.1 Ohm's law and continuity equation for current flux density
		2.4.2 One-dimensional electrical conduction—the cable equation
	2.5 Fluid flow
		2.5.1 Three-dimensional fluid flow
		2.5.2 Pipe flow
	2.6 Mechanics of solids
		2.6.1 Kinematics of deformation
		2.6.2 Stresses
		2.6.3 Principle of virtual work
		2.6.4 Constitutive relations
	References
3 - Kojic transport model (KTM) for physical fields
	3.1 Introduction: finite element method as the most powerful computational method
	3.2 Finite element formulation for field problems
		3.2.1 General 3D problems
		3.2.2 One-dimensional problems
	3.3 Kojic transport model as a multiscale multidomain FE model of mutually dependent smeared physical fields
		3.3.1 Formulation of the connectivity finite elements
		3.3.2 Transport tensor
		3.3.3 Composite smeared finite element (CSFE)
	References
4 - Smeared finite element formulation for mechanics
	4.1 FE modeling of 3D solid deformation
	4.2 Shell deformation
	4.3 Large strain FE formulation
		4.3.1 Use of Green–Lagrange strains
		4.3.2 Application of logarithmic strains in the FE models
		4.3.3 Generalization of logarithmic strains
	4.4 Fluid mechanics
	4.5 Solid–fluid and solid–solid interaction
		4.5.1 Solid–fluid interaction
		4.5.2 Solid–solid interaction
	4.6 Composite smeared finite element for mechanics (CSFEM)
		4.6.1 A general expressions for the virtual power for composite media
		4.6.2 Contact elements for interaction between domains
		4.6.3 Formulation of composite smeared finite element for mechanics (CSFEM)
	4.7 Numerical examples
		4.7.1 Verification examples
		4.7.2 Application of the smeared model to tumor growth
	References
5 - Multiscale hierarchical models for diffusion in composite media and tissue
	5.1 Introduction
	5.2 Multiscale diffusion and numerical homogenization
		5.2.1 Diffusion within nanochannels with surface interaction effects
		5.2.2 MD-FE hierarchical model for diffusion
		5.2.3 Numerical homogenization
		5.2.4 Mass release curves as constitutive relations for diffusion
		5.2.5 Partitioning
	5.3 Coupled convective and diffusive transport within vessels and tissue
	5.4 Examples
	References
6 - Application of Kojic transport model (KTM) to convective-diffusive transport and electrophysiology in tissue and capill ...
	6.1 Introduction—mass transport in living organisms
	6.2 KTM for convective and diffusive transport
		6.2.1 Biological tissue as a composite medium
		6.2.2 Composite smeared finite element (CSFE) for mass transport
		6.2.3 Connectivity elements and partitioning
		6.2.4 Accuracy of CSFE models and correction function
	6.3 Application of KTM in electrophysiology
		6.3.1 Introduction to computational modeling in electrophysiology
		6.3.2 KTM computational model for electric potential
		6.3.3 Coupling electric potential field and ionic transport
	6.4 KTM for drug release from nanofibers
		6.4.1 Introduction—technical solutions for controlled drug release from nanofibers
		6.4.2 Radial finite element for modeling drug release
		6.4.3 Application of KTM to drug release from nanofibers
	6.5 Examples
		6.5.1 Convective-diffusive transport
		6.5.2 Electric potential field in tissue
		6.5.3 Coupling electric potential field and ionic transport—example
		6.5.4 Accuracy of CSFE models and correction function—example
		6.5.5 Models of mass release from nanofibers
	References
7 - Heart electrophysiology and mechanics
	7.1 Heart physiology
	7.2 Electrophysiology
		7.2.1 Conduction within the heart tissue
		7.2.2 Traditional computational models in the heart electrophysiology
		7.2.3 Application of the KTM to electrophysiology—a summary of equations
		7.2.4 Relation of the KTM (smeared) methodology to other computational models in electrophysiology
		7.2.5 Examples of the FE models for heart electrophysiology
	7.3 Heart mechanics
		7.3.1 Composition of heart tissue
		7.3.2 Finite element models for heart
	7.4 Computational models for the heart tissue passive mechanical response
		7.4.1 Introduction—a review of constitutive relations for the cardiac tissue
		7.4.2 Computational procedure using directly the constitutive curves
		7.4.3 Verification of the computational procedure
	7.5 Finite element models of the left ventricle—wall deformation and blood flow
		7.5.1 Simplified parametric model
		7.5.2 FE model based on echocardiogram for the motion of the ventricle internal surface
	References
8 - Description of the software accompanying the book
	8.1 Introduction
	8.2 General structure of graphical user interface (GUI) software accompanying the book
		8.2.1 Title bar
		8.2.2 Main menu
			8.2.2.1 Examples—description of software modules
			8.2.2.2 File
			8.2.2.3 View
				8.2.2.3.1 Zoom
				8.2.2.3.2 Pan A
				8.2.2.3.3 Viewpoint
				8.2.2.3.4 Shading
				8.2.2.3.5 Clip plane
				8.2.2.3.6 Layers
				8.2.2.3.7 Options
			8.2.2.4 Calculation
			8.2.2.5 Results
				8.2.2.5.1 Result options
				8.2.2.5.2 Contour plot
				8.2.2.5.3 Misc
					8.2.2.5.3.1 Help
		8.2.3 Workspace
		8.2.4 Common menu bar
	8.3 Procedures for running examples and visualization of results
	References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	Y
	Z
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