Intro
Preface
Editor biographies
Trine Krogh-Madsen
David J Christini
Contributors
Chapter 1 Quantitative description of cardiac action potentials
1.1 Cardiac action potentials
1.1.1 Ionic gradients and action potential generation
1.1.2 Ventricular action potential
1.1.3 Sinoatrial node action potential
1.2 Modeling cardiac action potentials
1.2.1 Voltage clamp recordings
1.2.2 Gates and channels
1.2.3 Quantitative description of voltage clamp data
1.2.4 Example current models
1.2.5 Beyond the Hodgkin-Huxley formalism
1.2.6 Cardiac model development
References
Chapter 2 Modeling the molecular details of ion channels
2.1 Introduction
2.2 Lessons from Hodgkin and Huxley
2.3 Movement to Markov models
2.4 Inclusion of molecular level detail in Markov models
2.5 The power of molecular dynamics
2.6 MD simulations of ion channels
2.7 Intermediate modeling techniques
2.8 Concluding remarks
References
Chapter 3 Modeling cardiac calcium signaling, regulation, and control
3.1 Calcium in cardiac physiology
3.1.1 Fundamentals of cardiac ECC and Ca2+ homeostasis
3.1.2 The role of models in the study of cardiac Ca2+ signaling
3.2 Models of Ca2+ transport and Ca2+ binding
3.2.1 Models of cardiac Ca2+ channels
3.2.2 Models of cardiac Ca2+ pumps and exchangers
3.2.3 Cardiac Ca2+ buffers and cytosolic bulk transport
3.3 Multiscale cardiac ECC and Ca2+ homeostasis
3.3.1 Structural details and protein localization
3.3.2 Models of Ca2+ sparks, couplons, and local control
3.3.3 Spatial models of subcellular Ca2+ signaling
3.3.4 Zero-dimensional models of myocyte Ca2+ handling
3.3.5 Emergent instabilities in multiscale cardiac Ca2+ signaling
3.4 The future of models in cardiac Ca2+ signaling
Acknowledgements
References.

Chapter 4 Cardiac cell modeling
4.1 Introduction
4.2 Types of cardiac models
4.2.1 Hodgkin-Huxley type versus Markov type
4.2.2 Phenomenological models versus physiologically detailed models
4.2.3 Action potentials for different regions of the heart
4.2.4 Action potential across different species
4.3 Examples of cardiac models
4.3.1 The modified FitzHugh-Nagumo model
4.3.2 The Noble model
4.3.3 The Karma model
4.3.4 The Beeler-Rueter model
4.3.5 The Luo-Rudy model
4.3.6 The Fenton-Karma model
4.3.7 The ten Tusscher et al model
4.3.8 The O'Hara et al model
4.3.9 Some dynamics of cardiac models in 2D
4.4 Discussion
List of video files
Acknowledgements
References
Chapter 5 Modeling cardiomyocyte signaling pathways
5.1 Introduction to modeling of protein kinase signaling pathways
5.1.1 Biophysical representation of chemical reactions
5.1.2 Physical derivation of rate constants for biochemical reactions
5.2 Mathematical modeling of electrical signaling
5.3 Mathematical modeling of protein kinase signaling pathways
5.3.1 Dynamic models of CaMKII signaling
5.3.2 Dynamic models of the β1-adrenergic signaling pathway
5.3.3 Mathematical modeling of cross talk between PKA and CaMKII signaling pathways
5.4 Systems biology: the next frontier for mathematical modeling of cell signaling
5.5 Conclusions and future directions
References
Chapter 6 Modelling cardiomyocyte energetics
6.1 Introduction to cardiomyocyte energetics
6.2 Mathematical modelling of biochemical energetics
6.2.1 Modelling biochemical systems
6.2.2 Energy-based modelling of biochemical processes
6.2.3 Thermodynamics of ion movement
6.2.4 Bond graph formalism for biochemical energetics
6.3 Coupled reactions: thermodynamics of ATPases.

6.3.1 Thermodynamic modelling of coupled enzyme cycles
6.3.2 ATP hydrolysis reaction: driving energetically unfavourable reactions
6.4 Modelling cardiomyocyte bioenergetics
6.4.1 SERCA
6.4.2 Na+/K+ ATPase
6.4.3 Force generation
6.4.4 Mitochondrial ATP generation
6.4.5 Coupling ATP supply and demand in the cardiomyocyte
6.4.6 Measuring and modelling mechano-energetics
6.5 Current research, controversies, and future directions
6.5.1 How is mitochondrial energy generation regulated?
6.5.2 Creatine kinase shuttle
6.5.3 Role of cellular architecture: spatial models of cardiomyocyte energetics
6.5.4 Multiscale modelling of cardiac mechano-energetics: from cell to organ
References
Chapter 7 Tissue and organ scale modeling: coupled cells, wave propagation, simulated arrhythmia
7.1 Overview
7.2 Tissue conductivity
7.3 Continuum representation
7.3.1 Homogenization
7.4 Governing equations
7.4.1 Bidomain equations
7.5 Action potential propagation
7.5.1 Safety factor
7.5.2 Liminal length
7.5.3 Propagation speed
7.6 Regional differences
7.6.1 Ventricles
7.6.2 Atria
7.6.3 Sinoatrial node
7.6.4 Atrioventricular node
7.6.5 His-Purkinje system
7.6.6 Coupling tissues
7.7 Arrhythmia
7.7.1 Initiating reentry
7.7.2 Macroreentry
7.7.3 Rotors
7.7.4 Fibrillation
7.8 Conclusion
References
Chapter 8 Clinical translation of patient-specific organ level cardiac models
8.1 Introduction
8.2 Current anatomy modelling workflows
8.2.1 Geometry
8.2.2 Scar and fibrosis
8.2.3 Mesh generation
8.2.4 Fibres
8.3 Current parameterization techniques for electrophysiology models
8.3.1 Electrophysiology models and data
8.3.2 Personalized ventricular models
8.3.3 Personalized atrial models
8.4 Universal coordinate systems.

8.4.1 Universal ventricular coordinates
8.4.2 Universal atrial coordinates
8.5 Simulation costs
8.6 Scaling-up modelling pipelines
8.7 Future perspective
8.8 Conclusion
References.