Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics

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Springer Science & Business Media, Apr 15, 2004 - Computers - 322 pages
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Biomedical research is at a critical point at present. The research has led to an enormous amount of data and models describing these data, but - proachesforapplication,formalizationand integrationof this knowledgefrom the molecular to the system level are still topics of ongoing research and c- tainly far from fully developed. Also in cardiology the di'erent anatomical and physiological constituents as well as the coupling between them are being researchedin increasing detail and areoften described using computer-based models. But for this domain an integrative framework is still missing. The application of computer-based modeling as a research, development and clinical tool often necessitates the coupling of various models from di?- ent levels. Describing the interactions between these models, which are both physically sound and computationally e'cient, determines the applicability of such promising computer-based attempts. Myhopeisthatthisbookwillcontributetothecomprehension,spreadand impact of computer-based modeling in cardiology,both from a teaching point of view and by summarizing knowledge from several, commonly delimited topics relating to the cardiac manifoldness. The book evolved from revision and extension of my professorial disser- tion(Habilitationsschrift)"MathematicalModelingoftheMammalianHeart" written in 2002. This dissertation was based on notes for the lectures "C- putational Biology: Bioelectromagnetism and Biomechanics," "Simulation of Physical Fields in the Human Body," and "Anatomical, Physical and Fu- tional Models of the Human Body," which I gaveat the Universita ̈t Karlsruhe (TH) from 1998 to 2003. Salt Lake City, 1 February 2004 Frank B. Sachse VI Preface Acknowledgement Manypeople meritmy gratitudefor their assistanceandsupportin this work.
 

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Contents

Introduction
1
12 Organization
3
Mathematical and Numerical Foundation
5
22 Einstein Summation Convention
6
24 Numerics of Systems of Linear Equations
9
242 Direct Methods
10
243 Iterative Methods
12
244 Singular Value Decomposition
20
62 Microscopic Structures and Molecular Organization
121
622 Gap Junctions
131
623 Connective Tissue Structures
133
63 Macroscopic Structures
134
632 Atria
137
633 Blood Vessels
139
635 System of Excitation Conduction and Initiation
140
636 Nervous System
141

25 Numerical Integration of Functions
21
252 Trapezoidal Rule
22
254 Gauss Quadrature
23
262 Euler Method
24
263 RungeKutta Method
25
27 Numerics of Partial Differential Equations
27
272 Initial Values and Boundary Conditions
29
273 Finite Element Method
30
274 Finite Differences Method
43
Theory of Electric Fields
49
32 Physical Laws
50
322 Poissons Equation for Stationary Current Fields
51
323 Electromagnetic Properties of Biological Tissues
52
33 Numerical Solution of Poissons Equation
57
332 Finite Differences Method
63
Theory of Continuum Mechanics
69
42 Definitions and Physical Laws
70
422 Strain Tensors
73
423 Stress Tensors
74
424 Stress Equilibrium
75
425 Constitutive Relationships
78
43 Numerical Solution
83
432 Interpolation via ShapeFunctions
84
433 Determination of Element Equations
87
Digital Image Processing
91
52 Digital Representation of Images
92
53 Preprocessing
93
533 Filtering Methods
98
54 Segmentation Techniques
102
542 Thresholding
103
543 Region Growing
104
544 Watershed
105
545 Deformable Models
106
546 Manual Methods
112
56 Texture Orientation
115
563 Interpolation
117
Cardiac Anatomy
119
64 Modeling of Anatomy
142
643 Imaging Systems and Data Sources
144
644 Modeling of Orientation and Lamination of Myocytes
145
645 Models from the Visible Human Project
146
646 Models from Magnetic Resonance Imaging
152
Cardiac Electrophysiology
156
72 Cellular Electrophysiology
158
722 Modeling of Cellular Components
164
723 Models of Cardiac Myocytes
171
73 Excitation Propagation
189
732 Modeling Approaches
194
733 Cellular Automata
195
734 Reaction Diffusion Systems
203
735 Comparison of Macroscopic Models of Excitation Propagation
214
Cardiac Mechanics
221
82 Mechanical Properties of Myocardium
222
822 Modeling Approaches
224
83 Tension Development
236
832 Experimental Studies
240
833 Mathematical Modeling Approaches
245
84 Mechanics in Anatomical Models
260
Modeling of Cardiac ElectroMechanics
267
92 Electrophysiology and Force Development of Single Cells
268
93 Cellular Automaton of Cardiac Force Development
273
94 ElectroMechanics of the Myocardium
275
942 Simulations
278
943 Limitations and Perspectives
287
A Physical Units and Constants
290
B Differential Operators
292
C1 Model Assumptions
293
C2 General Formulation
294
C3 Restricted Formulation in Material Coordinate System
296
C4 Coordinate System Transformation
298
References
299
Index
323
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