On interfaces between cell populations with different mobilities

Tommaso Lorenzi, Alexander Lorz, Benoit Perthame

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Partial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.
Original languageEnglish
Pages (from-to)299-311
JournalKinetic and Related Models
Issue number1
Early online date1 Nov 2016
Publication statusPublished - Mar 2017


  • Cell populations
  • Tissue growth
  • Cancer invasion
  • Interfaces
  • Travelling waves
  • Pattern formation


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