Ανάλυση της ευστάθειας κατά την ανάπτυξη ελλειψοειδών καρκινικών όγκων

Abstract

The mathematical analysis of the tumour growth attracted a lot of interest in thelast two decades. However, as of today no generally accepted model for tumourgrowth exists. This is due partially to the incomplete understanding of the relatedpathology as well as the extremely complicated procedure that guides the evolutionof a tumour. Moreover, the growth of a tumour does depend on the available tissuesurrounding the tumour and therefore it represents a physical case which is realisticallymodelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidalshape is that it represents the sphere of the anisotropic space. It provides the appropriategeometrical model for any direction dependent physical quantity. In thepresent work we analyze the stability of a spherical tumour for four continuous modelsof an avascular tumour and the stability study of an ellipsoidal tumour. For allve models, conditions for the stability are stated and the results are implementedThe mathematical analysis of the tumour growth attracted a lot of interest in thelast two decades. However, as of today no generally accepted model for tumourgrowth exists. This is due partially to the incomplete understanding of the relatedpathology as well as the extremely complicated procedure that guides the evolutionof a tumour. Moreover, the growth of a tumour does depend on the available tissuesurrounding the tumour and therefore it represents a physical case which is realisticallymodelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidalshape is that it represents the sphere of the anisotropic space. It provides the appropriategeometrical model for any direction dependent physical quantity. In thepresent work we analyze the stability of a spherical tumour for four continuous modelsof an avascular tumour and the stability study of an ellipsoidal tumour. For allve models, conditions for the stability are stated and the results are implemented numerically. For the spherical cases, it is observed that the steady state radii thatsecure the stability of the tumour are dierent for each of the four models, and thatresults to dierences in the stable and unstable modes. As for the ellipsoidal model,it is shown that, in contrast to the highly symmetric spherical case, where stabilityis possible to be achieved, there are no conditions that secure the stability of anellipsoidal tumour. Hence, as in many physical cases, the observed instability is aconsequence of the lack of symmetry.