Cellular Potts Models

Cellular Potts Models: Multiscale Extensions and Biological Applications

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Features

  • Represents the first book entirely devoted to cellular Potts models and applications
  • Starts with basic models that are progressively extended to introduce the latest developments
  • Covers both biological and informatics aspects
  • Illustrates the models through real examples in biology and biomedicine
  • Describes popular model packages and how to build your own code in the appendices

Summary

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.

Table of Contents

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

Author Bio(s)

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.

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