The influence of anisotropic growth and geometry on the stress of solid tumors

Ramírez-Torres, A. , Rodríguez-Ramos, R., Merodio, J., Penta, R. , Bravo-Castillero, J., Guinovart-Díaz, R., Sabina, F. J., García-Reimbert, C., Sevostianov, I. and Conci, A. (2017) The influence of anisotropic growth and geometry on the stress of solid tumors. International Journal of Engineering Science, 119, pp. 40-49. (doi: 10.1016/j.ijengsci.2017.06.011)

Abstract

Solid stresses can affect tumor patho-physiology in at least two ways: directly, by compressing cancer and stromal cells, and indirectly, by deforming blood and lymphatic vessels. In this work, we model the tumor mass as a growing hyperelastic material. We enforce a multiplicative decomposition of the deformation gradient to study the role of anisotropic tumor growth on the evolution and spatial distribution of stresses. Specifically, we exploit radial symmetry and analyze the response of circumferential and radial stresses to (a) degree of anisotropy, (b) geometry of the tumor mass (cylindrical versus spherical shape), and (c) different tumor types (in terms of mechanical properties). According to our results, both radial and circumferential stresses are compressive in the tumor inner regions, whereas circumferential stresses are tensile at the periphery. Furthermore, we show that the growth rate is inversely correlated with the stresses’ magnitudes. These qualitative trends are consistent with experimental results. Our findings therefore elucidate the role of anisotropic growth on the tumor stress state. The potential of stress-alleviation strategies working together with anticancer therapies can result in better treatments.

• Item Type: Articles
• Additional Information: AR gratefully acknowledges the Program of Postdoctoral Scholarships of DGAPA from UNAM, Mexico. From February 2017 AR is financially supported by INdAM. JM and RP acknowledge support from the Ministry of Economy in Spain under the project reference DPI2014-58885-R. Thanks to the Project (7515) Métodos Físico-Matemáticos para el estudio de nuevos materiales y la propagación de ondas. Aplicaciones. Also, we thanks to Departamento de Matemáticas y Mecánica IIMASUNAM for their support and Ramiro Chávez Tovar and Ana Pérez Arteaga for computational assistance. A.C. is grateful to CNPq (Projects INCT-MACC and 303240/2015-6).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo and Ramirez Torres, Dr Ariel
• Authors: Ramírez-Torres, A., Rodríguez-Ramos, R., Merodio, J., Penta, R., Bravo-Castillero, J., Guinovart-Díaz, R., Sabina, F. J., García-Reimbert, C., Sevostianov, I., and Conci, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Journal of Engineering Science
• Publisher: Elsevier
• ISSN: 0020-7225
• ISSN (Online): 1879-2197
• Published Online: 13 June 2017
• Copyright Holders: Copyright © 2017 Elsevier, Ltd.
• First Published: First published in International Journal of Engineering Science 119:40-49
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.