Cellular Potts Models: Multiscale Extensions and Biological Applications, 1st Edition (Hardback) book cover

Cellular Potts Models

Multiscale Extensions and Biological Applications, 1st Edition

By Marco Scianna, Luigi Preziosi

Chapman and Hall/CRC

301 pages | 19 Color Illus. | 118 B/W Illus.

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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


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


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


Migration Velocities

Migration Modes


A: Computational Implementation

B: Glossary

C: Parameter Values

D: Color Insert



About the Authors

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.

About the Series

Chapman & Hall/CRC Mathematical and Computational Biology

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Subject Categories

BISAC Subject Codes/Headings:
MEDICAL / Biotechnology
SCIENCE / Physics