Preliminaries for a new mathematical framework for modelling tumour growth using stress state decomposition technique

• Autores: Di Rado, Héctor Ariel; Beneyto, Pablo Alejandro; Mroginski, Javier Luis
• Año de publicación: 2020
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Journal of Biosciences and Medicine, 2020, vol. 8, p. 73-81.
• Materia: Cancer; Tumour growth; Mathematical modelling; Stress state decomposition technique
• Institución: Universidad Nacional del Nordeste

Fil: Di Rado, Héctor Ariel. Universidad Nacional del Nordeste. Facultad de Ingeniería; Argentina.
Fil: Beneyto, Pablo Alejandro. Universidad Nacional del Nordeste. Facultad de Ingeniería; Argentina.
Fil: Mroginski, Javier Luis. Universidad Nacional del Nordeste. Facultad de Ingeniería; Argentina.
The main goal of the present paper is to present a mathematical framework for modelling tumour growth based on stress state decomposition technique (SSDT). This is a straightforward extension of the model for multi-phase non- saturated soil consolidation with pollutant transport presented by the authors and may be regarded as an alternative to classical frameworks based on TCAT theory. In this preliminary work, the Representative Volume Element (RVE) for tumour is proposed along with its comparison with the corresponding one for soils modelling developed formerly by the authors. Equations stand- ing for tumour phase are flawlessly brought into correspondence with those of gaseous phase in the soil problem showing that a similar task may be car- ried out for the remainders phases taking part in both RVEs. Furthermore, stresses induced by nonlinear saturation and permeability dependence on suction for soil interstitial fluids transport finds its counterpart on the contact between the cancer cell membrane and interstitial fluids rendering a higher primary variables coupling degree than what was attained in TCAT theory. From these preliminaries assessments, it may be put forward that likewise the stress state decomposition procedure stands for an alternative for modelling multi-phase nonsaturated soil consolidation with pollutant transport; it does for modelling cancer as well.