Contour instabilities in early tumor growth models.
M Ben Amar1, C Chatelain, P Ciarletta
1Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France.
Physical Review Letters
|May 13, 2011
Summary
Tumor growth models can exhibit contour instabilities, leading to loss of symmetry. This study identifies tumor cell concentration as a key factor, with implications for melanoma diagnosis and tissue remodeling.
Area of Science:
- Mathematical Biology
- Biophysics
- Computational Biology
Background:
- Multiphase mixture models are frequently used for simulating tumor growth.
- These models can potentially exhibit contour instabilities, affecting tumor morphology.
Purpose of the Study:
- To investigate contour instabilities in simplified tumor growth models.
- To identify control parameters that induce symmetry breaking in tumor shapes.
- To explore the relevance of these instabilities for melanoma diagnosis.
Main Methods:
- Application of bifurcation theory techniques to a simplified multiphase mixture model.
- Analysis of a model incorporating elastic cell-to-cell interaction and nutrient-dependent growth.
- Mathematical proof of symmetry breaking driven by border cell concentration.
Main Results:
- Demonstrated that tumor cell concentration at the border acts as a control parameter.
- Identified a bifurcation leading to the loss of circular symmetry in tumor models.
- Determined that the threshold wavelength corresponds to the size of the proliferating peritumoral zone.
Conclusions:
- Contour instabilities are a predictable outcome of certain tumor growth models.
- Tumor cell concentration is a critical factor influencing tumor shape dynamics.
- Findings have direct applications in melanoma diagnosis and broader tissue growth/remodeling research.
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