Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective

Al Mudarra, M. M. and Ramírez-Torres, A. (2024) Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241230269) (Early Online Publication)

Abstract

This study investigates the growth of an avascular tumour described through the interchange of mass among its constituents and the production of inelastic distortions induced by growth itself. A key contribution of this research examines the role of non-local diffusion arising from the complex and heterogeneous tumour micro-environment. In our context, the non-local diffusion is enhanced by a variable-order fractional operator that incorporates crucial information about regions of limited nutrient availability within the tissue. Our research also focuses on the identification of an evolution law for the growth-induced inelastic distortions recast through the identification of non-conventional forces dual to suitable kinematic descriptors associated with the growth tensor. The establishment of such evolution law stems from examining the dissipation inequality and subsequently determining a posteriori connections between the inelastic distortions and the source/sink terms in the mass balance laws. To gain insights into the dynamics of tumour growth and its response to the proposed modelling framework, we first study how the variables governing the tissue evolution are affected by the introduction of the new growth law. Second, we investigate how regions of limited diffusion within the tumour, encoded into a fractional operator of variable-order, influence its growth.

• Item Type: Articles
• Additional Information: M.A.M.is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445).
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ramirez Torres, Dr Ariel and Al Mudarra, Mariam Mubarak N
• Authors: Al Mudarra, M. M., and Ramírez-Torres, A.
• College/School: College of Science and Engineering; College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematics and Mechanics of Solids
• Publisher: SAGE
• ISSN: 1081-2865
• ISSN (Online): 1741-3028
• Published Online: 28 February 2024
• Copyright Holders: Copyright: © The Author(s) 2024
• First Published: First published in Mathematics and Mechanics of Solids 2024
• Publisher Policy: Reproduced under a Creative Commons licence