1st Edition

Cellular Potts Models Multiscale Extensions and Biological Applications

By Marco Scianna, Luigi Preziosi Copyright 2013
    300 Pages 19 Color & 118 B/W Illustrations
    by Chapman & Hall

    A flexible, cell-level, and lattice-based technique, the cellular Potts model accurately describes the phenomenological mechanisms involved in many biological processes. Cellular Potts Models: Multiscale Extensions and Biological Applications gives an interdisciplinary, accessible treatment of these models, from the original methodologies to the latest developments.

    The book first explains the biophysical bases, main merits, and limitations of the cellular Potts model. It then proposes several innovative extensions, focusing on ways to integrate and interface the basic cellular Potts model at the mesoscopic scale with approaches that accurately model microscopic dynamics. These extensions are designed to create a nested and hybrid environment, where the evolution of a biological system is realistically driven by the constant interplay and flux of information between the different levels of description. Through several biological examples, the authors demonstrate a qualitative and quantitative agreement with the relative experimental data.

    The cellular Potts model is increasingly being used for the mathematical modeling of a wide range of biological phenomena, including wound healing, tumor growth, and cancer cell migration. This book shows how the cellular Potts model can be used as a framework for model building and how extended models can achieve even better biological practicality, accuracy, and predictive power.

    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

    Biography

    Marco Scianna is a post-doctoral fellow in the Department of Mathematical Sciences at the Politecnico di Torino. He earned a Ph.D. in complex systems in post-genomic biology from the University of Turin. His principal research focuses on mathematical multiscale models applied to biological and biomedical problems, with particular interest in the context of tumor growth, vascular network formation, and cell migration in extracellular matrix.

    Luigi Preziosi is a professor of mathematical physics at the Politecnico di Torino. He earned a Ph.D. in mechanics from the University of Minnesota and in mathematics from the University of Naples. He has authored three books, more than 30 book chapters, and more than 100 articles in international journals. His recent research interests include multiphase models of tumor growth, the mechanics of tissue growth and regenerations, cell migration, and vascular network formation.