I Basic Cellular Potts Model and Applications
Basic CPM
The CPM Domain
The CPM Algorithm
The Hamiltonian
Evaluation of Some Kinematic Parameters
Some Illustrative Simulations
HGF-Induced Cell Scatter
Biological Introduction
Mathematical Model for ARO Aggregates
Scattering of ARO Aggregates
Mathematical Model for MLP-29 Aggregates
Scattering of MLP-29 Aggregates
Mesothelial Invasion of Ovarian Cancer
Biological Introduction
Mathematical Model
Single Cell Transmigration
Multicellular Spheroid Invasion
II Extended Cellular Potts Model and Applications
Extended Cellular Potts Model
Advantages and Limitations of the Basic CPM
Compartmentalization Approach
Nested Approach
Motility of Individuals
Wound Healing Assay
Biological Introduction
Mathematical Model
Simulations
Effect of Calcium-Related Pathways on Single Cell Motility
Biological Introduction
Mathematical Model
Simulation Details and Parameter Estimates
Simulations in Standard Conditions
Interfering with Calcium Machinery
Altering Cell Morphology
Varying the Chemical Source
Tumor-Derived Vasculogenesis
Biological Introduction
Mathematical Model
Simulations in Standard Conditions
Varying Cell Density
Testing Anti-Angiogenic Therapies
Different Morphologies of Tumor Invasion Fronts
Biological Introduction
Mathematical Model
Simulations in Standard Conditions
Varying Cell Adhesive Properties
Varying Cell Elasticity
Altering Cell-Substrate Interactions
Effect of Cell Proliferation
Early Stages of Tumor Spheroid Growth
Mathematical Model
Simulations
Cell Migration in Extracellular Matrices
Biological Introduction
Mathematical Model
Isotropic Matrices
Anisotropic 2D and 3D Matrices
Varying Fiber Density
Varying Cell-Fiber Adhesiveness
Varying Fiber Elasticity of 3D Matrix Scaffold
Effect of Varying Nucleus Compressibility in 3D
Effect of Matrix Degradation in 3D
Cancer Cell Migration in Matrix Microchannels
Biological Introduction
Mathematical Model
Simulations
Migration Velocities
Migration Modes
Appendices
A: Computational Implementation
B: Glossary
C: Parameter Values
D: Color Insert
Bibliography
Index