• Corpus ID: 18073785

Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model

@article{Kolbe2014NumericalSO,
  title={Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model},
  author={Niklas Kolbe and Jana Kaťuchov{\'a} and Nikolaos Sfakianakis and Nadja Hellmann and M{\'a}ria Luk{\'a}cov{\'a}-Medvidov{\'a}},
  journal={arXiv: Numerical Analysis},
  year={2014}
}
In the present work we investigate the chemotactically and proteolytically driven tissue invasion by cancer cells. The model employed is a system of advection-reaction-diffusion equations that features the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of this system constitutes a challenge due to the merging, emerging, and travelling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate… 
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3 Citations

Galerkin finite element method for cancer invasion mathematical model
A biophysical model of tumor invasion
A Multiscale Mathematical Model of Tumour Invasive Growth
TLDR
A new two-scale moving boundary model of cancer invasion is presented that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system and demonstrates a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer.

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