Abstract
The complexity of the biochemical and physical mechanisms involved in the development of a cancerous tumor and the specificity of its behavior according to the host tissue, significantly impedes the understanding of its structure and function. Recent scientific studies highlight the effect of mechanical properties of the surrounding tissue on the structure, shape and parameters of tumor growth, with emphasis on non-symmetric growth. In this PhD research proposal, we analyze a macroscopic mathematical model for the development of a benign cancerous tumor with an ellipsoid structure in a non-homogeneous field of pressure and nutrients, under the most widely accepted assumptions of tumor growth in this stage. We intend to investigate the conditions that allow the growth in this special anisotropic structure, the existence and stability of a stationary stage of the tumour’s evolution and its dependence on the ellipsoid’s eccentricities.
As the morphological instability in the structure of a quiescent tumor suggests a functional transition of the colony to malignant growth, this investigation is considered important for a deeper understanding of biological mechanisms and a possible therapeutic approach.
The ultimate goal of the proposed study is to determine critical conditions and parameters that indicate the transition of an ellipsoid cancerous tumor from stability to instability.
Advisory committee
Supervisor Kariotou Foteini, Assistant Prof. SST, HOU
Members: Hadjinicolaou Maria, Professor, SST, HOU
Stratis Ioannis, Professor, Mathematics department, National & Kapodistrian University of Athens