Abstract
This chapter originated from the idea that carcinogenesis can be considered as a multiscale morphogenetic process. A mathematical framework for modeling cell dynamics in multicellular systems is proposed. This framework is developed on the basis of the formal structures that are offered by the Kinetic Theory for Active Particles. A specific model for cancer evolution in epithelial cells is derived by the proposed mathematical framework. This model describes the morphogenesis of multiple sub-populations of cancer cells at different malignancy stages. Simulations are developed with an exploratory aim. The obtained results offer insights into the role played by mutation, proliferation and differentiation phenomena on the morphogenesis of sub-populations of cancer cells.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100:57–70
Gatenby RA (2006) Commentary: carcinogenesis as Darwinian evolution? Do the math! Int J Epidemiol 35:1165–1167
Nowak MA, Komarova NL, Sengupta A, Jallepalli PV, Shih I, Vogelstein B, Lengauer C (2002) The role of chromosomal instability in tumor initiation. Proc Natl Acad Sci U S A 99:16226–16231
Nowell PC (2002) Tumor progression: a brief historical perspective. Semin Cancer Biol 12:261–266
Martins ML, Ferreira SC Jr, Vilela MJ (2007) Multiscale models for the growth of avascular tumors. Phys Life Rev 4:128–156
Weinberg RA (2007) The biology of cancer. Garland Science, New York
Kim Y, Stolarska MA, Othmer HG (2007) A hybrid model for tumour spheroid growth in vitro. I: theoretical development and early results. Math Model Method Appl Sci 17:1773–1798
Kinzler KW, Vogelstein B (1996) Lessons from hereditary colorectal cancer. Cell 87:159–170
Bellomo N, Li NK, Maini PK (2008) On the foundations of cancer modeling. Math Model Method Appl Sci 18:593–646
Bellomo N, Bianca C, Delitala M (2009) Complexity analysis and mathematical tools towards the modeling of living systems. Phys Life Rev 6:144–175
Hartwell HL, Hopfield JJ, Leibner S, Murray AW (1999) From molecular to modular cell biology. Nature 402:c47–c52
Bellouquid A, Delitala M (2006) Mathematical modeling of complex biological systems. A kinetic theory approach. Birkhäuser, Boston
Bellomo N, Delitala M (2008) From the mathematical kinetic, and stochastic game theory to modeling mutations, onset, progression and immune competition of cancer cells. Phys Life Rev 5:183–206
Tomlinson IPM, Novelli MR, Bodmer WF (1996) The mutation rate and cancer. Proc Natl Acad Sci U S A 93:14800–14803
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Delitala, M., Lorenzi, T. (2013). Formation of Evolutionary Patterns in Cancer Dynamics. In: Capasso, V., Gromov, M., Harel-Bellan, A., Morozova, N., Pritchard, L. (eds) Pattern Formation in Morphogenesis. Springer Proceedings in Mathematics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20164-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-20164-6_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20163-9
Online ISBN: 978-3-642-20164-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)