Cellular potts models : multiscale extensions and biological applications

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.

Author Notes

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.

Preface	p. xi
I Basic Cellular Potts Model and Applications	p. 1
1 Basic CPM	p. 3
1.1 The CPM Domain	p. 3
1.2 The CPM Algorithm	p. 6
1.3 The Hamiltonian	p. 7
1.4 Evaluation of Some Kinematic Parameters	p. 11
1.5 Some Illustrative Simulations	p. 11
2 HGF-Induced Cell Scatter	p. 17
2.1 Biological Introduction	p. 17
2.2 Mathematical Model for ARO Aggregates	p. 19
2.3 Scattering of ARO Aggregates	p. 21
2.4 Mathematical Model for MLP-29 Aggregates	p. 25
2.5 Scattering of MLP-29 Aggregates	p. 27
3 Mesothelial Invasion of Ovarian Cancer	p. 33
3.1 Biological Introduction	p. 33
3.1.1 Single Cell Transmigration	p. 34
3.1.2 Multicellular Spheroid Invasion	p. 36
3.2 Mathematical Model	p. 38
3.3 Single Cell Transmigration	p. 40
3.4 Multicellular Spheroid Invasion	p. 43
II Extended Cellular Potts Model and Applications	p. 47
4 Extended Cellular Potts Model	p. 49
4.1 Advantages and Limitations of the Basic CPM	p. 49
4.2 Compartmentalization Approach	p. 50
4.3 Nested Approach	p. 56
4.4 Motility of Individuals	p. 61
5 Wound Healing Assay	p. 67
5.1 Biological Introduction	p. 67
5.2 Mathematical Model	p. 70
5.2.1 Cell-Level Model	p. 70
5.2.2 Molecular-Level Model	p. 72
5.3 Simulations	p. 75
6 Effect of Calcium-Related Pathways on Single Cell Motility	p. 81
6.1 Biological Introduction	p. 81
6.2 Mathematical Model	p. 83
6.2.1 Cell-Level Model	p. 84
6.2.2 Molecular-Level Model	p. 88
6.3 Simulation Details and Parameter Estimates	p. 93
6.4 Simulations in Standard Conditions	p. 94
6.5 Interfering with Calcium Machinery	p. 99
6.6 Altering Cell Morphology	p. 109
6.7 Varying the Chemical Source	p. 111
7 Tumor-Derived Vasculogenesis	p. 115
7.1 Biological Introduction	p. 115
7.2 Mathematical Model	p. 119
7.2.1 Cell-Level Model	p. 119
7.2.2 Molecular-Level Model	p. 121
7.3 Simulations in Standard Conditions	p. 121
7.4 Varying Cell Density	p. 126
7.5 Testing Anti-Angiogenic Therapies	p. 128
8 Different Morphologies of Tumor Invasion Fronts	p. 137
8.1 Biological Introduction	p. 137
8.2 Mathematical Model	p. 139
8.2.1 Cell-Level Model	p. 139
8.2.2 Molecular-Level Model	p. 142
8.3 Simulations in Standard Conditions	p. 143
8.4 Varying Cell Adhesive Properties	p. 146
8.5 Varying Cell Elasticity	p. 149
8.6 Altering Cell-Substrate Interactions	p. 149
8.7 Effect of Cell Proliferation	p. 152
8.8 Early Stages of Tumor Spheroid Growth	p. 156
8.9 Mathematical Model	p. 157
8.10 Simulations	p. 158
9 Cell Migration in Extracellular Matrices	p. 165
9.1 Biological Introduction	p. 165
9.2 Mathematical Model	p. 167
9.2.1 Simulation Details	p. 169
9.3 Isotropic Matrices	p. 171
9.4 Anisotropic 2D and 3D Matrices	p. 172
9.5 Varying Fiber Density	p. 175
9.6 Varying Cell-Fiber Adhesiveness	p. 180
9.7 Varying Fiber Elasticity of 3D Matrix Scaffold	p. 182
9.8 Effect of Varying Nucleus Compressibility in 3D	p. 184
9.9 Effect of Matrix Degradation in 3D	p. 186
10 Cancer Cell Migration in Matrix Microchannels	p. 189
10.1 Biological Introduction	p. 189
10.2 Mathematical Model	p. 190
10.3 Simulations	p. 192
10.4 Migration Velocities	p. 198
10.5 Migration Modes	p. 200
III Appendix	p. 203
A Computational Implementation	p. 205
B Glossary	p. 209
C Parameter Values	p. 221
D Color Insert	p. 231
Bibliography	p. 241
Index	p. 277

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