Theoretical models for growth of melanoma

Wednesday, May 18, 2011 - 9:00am - 10:00am
Lind 305
Martine Ben Amar (École Normale Supérieure)
Like many biological systems, tumours undergo morphological changes during their evolution. For melanoma, these changes are the main diagnosis of the clinicians. In response to external (e.g. nutrient availability) or internal (e.g. genetic mutations) perturbations, a neoplasm may switch from an initially benign and highly localized symmetric state to an aggressive behaviour [1]. This rapid invasion of the surrounding tissues usually involves a morphological instability due to the heterogeneous nature of the growth process. This symmetry breaking is crucial in the clinical evaluation of the malignant character of a tumour. In order to describe this instability and highlight a fundamental process at work in morphogenesis, we first model the tumour as a ring of proliferative cells surrounding a core of quiescent cells. A biomimetic experiment of swelling gel with a similar geometry as avascular growth of melonama in the epidermis is presented to show that this instability has an elastic origin due to the growth process itself. Then I will present an adaptation of the mixture model to melanoma growth and show that this model exhibits travelling wave solutions in one dimension carrying a transverse perturbation of finite amplitude. In radial, we have found the same spatial instability for radially growing tumour with constant velocity. We establish a criterion for shape bifurcation in function of the biomechanical parameters of the skin and tumour cell properties that we compare to clinical data.

Joint work with: C. Chatelain, P. Ciarletta and Julien Dervaux