Mathematical modeling of anisotropic avascular tumor growth. (October 2015)

• Record Type: Journal Article
• Authors: Ramírez-Torres, A.; Rodríguez-Ramos, R.; Merodio, J.; Bravo-Castillero, J.; Guinovart-Díaz, R.; Alfonso, J.C.L.
• Is Part Of: Mechanics research communications. Volume 69(2015:Oct.)
• Page Start: 8
• Page End: 14
• Publication Date: 2015-10
• Subjects: Growth of avascular tumor spheroids -- Anisotropic growth deformation tensor -- Mixture theory -- Multiple natural configurations; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2015.06.002
• Languages: English
• ISSNs: 0093-6413

Abstract

Abstract : Highlights: We provide a theoretical framework in the context of continuum mechanics to investigate the growth of avascular tumor spheroids. Anisotropic growth is considered. Mixtures theory and the notion of multiple natural configurations are used to develop a single phase mathematical model of avascular solid tumor growth. Mechanical modulation of growing tumors in a rigid surrounding tissue is investigated. Numerical results are compared with experimental data previously reported in the literature. Abstract: Cancer represents one the most challenging problems in medicine and biology nowadays, and is being actively addressed by many researchers from different areas of knowledge. The increasing development of sophisticated mathematical models and computer-based procedures has had a positive impact on our understanding of cancer-related mechanisms and the design of anticancer treatment strategies. However, further investigation and experimentation are still required to completely elucidate the tumor-associated mechanical responses, as well as the effect of mechanical forces on the net tumor growth. In this work we develop a theoretical framework in the context of continuum mechanics to investigate the anisotropic growth of avascular tumor spheroids. To that end, a specific anisotropic growth deformation tensor is considered, which also describes an isotropic growth law as a particular case. Mixtures theory and the notion of multiple natural configurations are then used to formulate a mathematical model of avascular tumor growth. More precisely, mass, momentum balance and nutrients diffusion equations are derived, where solid tumors are assumed as hyperelastic and compressible materials. Moreover, mechanical interactions with a rigid extracellular matrix (ECM) are considered, and the mechanical modulation of growing tumors in a rigid surrounding tissue is investigated by means of numerical simulations. Finally, the model results are compared with experimental data previously reported in the literature.