Mathematical modeling of the interplay between stress and anisotropic growth of avascular tumors

Valdés-Ravelo, F., Ramírez-Torres, A. , Rodríguez-Ramos, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Penta, R. , Conci, A., Sabina, F. J. and García-Reimbert, C. (2018) Mathematical modeling of the interplay between stress and anisotropic growth of avascular tumors. Journal of Mechanics in Medicine and Biology, 18(1), 1850006. (doi: 10.1142/s0219519418500069)

Abstract

In this work, we propose a new mathematical framework for the study of the mutual interplay between anisotropic growth and stresses of an avascular tumor surrounded by an external medium. The mechanical response of the tumor is dictated by anisotropic growth, and reduces to that of an elastic, isotropic, and incompressible material when the latter is not taking place. Both proliferation and death of tumor cells are in turn assumed to depend on the stresses. We perform a parametric analysis in terms of key parameters representing growth anisotropy and the influence of stresses on tumor growth in order to determine how these effects affect tumor progression. We observe that tumor progression is enhanced when anisotropic growth is considered, and that mechanical stresses play a major role in limiting tumor growth.

• Item Type: Articles
• Keywords: Avascular tumor, linear elasticity, anisotropic growth, stress-driven growth.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo and Ramirez Torres, Dr Ariel
• Authors: Valdés-Ravelo, F., Ramírez-Torres, A., Rodríguez-Ramos, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Penta, R., Conci, A., Sabina, F. J., and García-Reimbert, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Mechanics in Medicine and Biology
• Publisher: World Scientific Publishing
• ISSN: 0219-5194
• ISSN (Online): 1793-6810
• Published Online: 08 February 2018
• Copyright Holders: Copyright © 2018 World Scientific Publishing
• First Published: First published in Journal of Mechanics in Medicine and Biology 18(1):1850006
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher