Avascular Tumor Growth Modelling: Physical Insights to Skin Cancer

  • Martina Ben AmarEmail author
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this chapter I present the state-of-the-art theoretical models for avascular tumor growth which are well established nowadays. I focus on models able to treat morphologic instabilities and phase segregation, two typical features of skin cancer for example melanoma. Contrary to experiments made in vitro on growing colonies, I show that the geometry of melanoma confined in the epidermis in the early stages of tumor growth suppresses the necrotic core and is responsible of inhomogeneities due to aggregation of cancerous cells. A relatively simple model consisting in the adaptation of the two-phase mixture model is enough to explain the morphologies of the tumor not only qualitatively but also quantitatively. Despite the complexity of the nonlinear partial differential equations that results from this model, I also present analytical treatments based on the techniques of nonlinear physics and W.K.B approximation to explain the observed structures in dermatology.


Tumor multiphase modeling Contour instability-Phase segregation Skin cancer morphology Clinical dermatology 



This chapter is a summary of results about tumor modelling obtained in Ecole Normale Supérieure during these last years. I strongly acknowledge three Ph.D students, Julien Dervaux, Clément Chatelain and Thibaut Balois, for their intensive collaboration on this very rich topic between mathematics, nonlinear and soft matter physics and biology. This work is supported in part by AAP INSERM 2012.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Laboratoire de Physique StatistiqueEcole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRSParisFrance
  2. 2.Institut Universitaire de Cancérologie, Faculté de médecineUniversité Pierre et Marie Curie-Paris 6ParisFrance

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