A novel stress-induced anisotropic growth model driven by nutrient diffusion

Theory, FEM implementation and applications in bio-mechanical problems

authored by: Meisam Soleimani, Nikhil Muthyala, Michele Marino, Peter Wriggers
Abstract: In this paper, a novel physically-motivated anisotropic model for growth driven by nutrient diffusion is proposed and the mathematical framework is extensively presented. Growth phenomena usually occur in living tissues under different mechanobiological stimuli. Here the growth is driven by the diffusion of a chemical substance which reflects, in fact, the extent of nutrients availability or other growth factors at the cellular level. Due to its simplicity, a commonly used assumption is the isotropy of the growth tensor. In other words, the magnitude of the growth is determined by the nutrient diffusion without incorporating the effect of a preferred direction for cell growth. Since the macroscopic volumetric growth is the resultant of mitosis (binary fission) at cellular scale, it makes sense to confer directionality to the growth tensor. This will render the growth tensor anisotropic and consequently more complex. In this work, the anisotropy of the growth tensor is dictated by the principal directions of the stress tensor in an intuitive and physically motivated fashion. One can imagine that the growth is powered by nutrient diffusion while it is steered by the stress. A fully implicit and monolithic scheme is implemented for this coupled and multiphysics problem in an FEM framework. Several numerical examples are presented to demonstrate the applicability and versatility of the proposed model for reproducing biofilm growth in confined geometries; tumor growth within the brain in the avascular stage; and bone ingrowth in the vicinity of a rough implant surface.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Tor Vergata University of Rome
Type: Article
Journal: Journal of the Mechanics and Physics of Solids
Volume: 144
ISSN: 0022-5096
Publication date: 11.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.jmps.2020.104097 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b781659db6e649f395867e725f1668ff,
title = "A novel stress-induced anisotropic growth model driven by nutrient diffusion: Theory, FEM implementation and applications in bio-mechanical problems",
abstract = "In this paper, a novel physically-motivated anisotropic model for growth driven by nutrient diffusion is proposed and the mathematical framework is extensively presented. Growth phenomena usually occur in living tissues under different mechanobiological stimuli. Here the growth is driven by the diffusion of a chemical substance which reflects, in fact, the extent of nutrients availability or other growth factors at the cellular level. Due to its simplicity, a commonly used assumption is the isotropy of the growth tensor. In other words, the magnitude of the growth is determined by the nutrient diffusion without incorporating the effect of a preferred direction for cell growth. Since the macroscopic volumetric growth is the resultant of mitosis (binary fission) at cellular scale, it makes sense to confer directionality to the growth tensor. This will render the growth tensor anisotropic and consequently more complex. In this work, the anisotropy of the growth tensor is dictated by the principal directions of the stress tensor in an intuitive and physically motivated fashion. One can imagine that the growth is powered by nutrient diffusion while it is steered by the stress. A fully implicit and monolithic scheme is implemented for this coupled and multiphysics problem in an FEM framework. Several numerical examples are presented to demonstrate the applicability and versatility of the proposed model for reproducing biofilm growth in confined geometries; tumor growth within the brain in the avascular stage; and bone ingrowth in the vicinity of a rough implant surface.",
keywords = "Anisotropic growth, Biofilm growth, Bone ingrowth, Finite strain, Nutrient diffusion, Tumor growth",
author = "Meisam Soleimani and Nikhil Muthyala and Michele Marino and Peter Wriggers",
note = "Funding Information: This project was funded by the Ministry of Science and Culture (MWK) of Lower Saxony, Germany within the framework of the SMARTBIOTECS alliance between the Technical University of Braunschweig and the Leibniz University of Hannover. The authors acknowledge this support. Moreover, Michele Marino appreciates the support of the ministry of education, university and research (Italy) through the Rita Levi Montalcini program for young researchers. Meisam Soleimani extends his particular gratitude to Prof. Joze Korelc in University of Ljubljana for a short but extremely fruitful discussion with him. ",
year = "2020",
month = nov,
doi = "10.1016/j.jmps.2020.104097",
language = "English",
volume = "144",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Ltd.",
}