Keshavanarayana, P. orcid.org/0000-0002-8147-363X, Ruess, M. orcid.org/0000-0002-8503-6541 and de Borst, R. orcid.org/0000-0002-3457-3574 (2018) On the monolithic and staggered solution of cell contractility and focal adhesion growth. International Journal for Numerical Methods in Biomedical Engineering. e3138. ISSN 2040-7939
Abstract
The mechanical response of cells to stimuli tightly couples biochemical and biomechanical processes, which describe fundamental properties such as cell growth and reorientation. Cells interact continuously with their external surroundings, the extracellular matrix (ECM), by establishing a bond between cell and ECM through the formation of focal adhesions. Focal adhesions are made up of integrins, which are mechanosensitive proteins and responsible for the communication between the cell and the ECM. The governing biochemomechanical processes can be modeled by means of a continuum approach considering mechanical and thermodynamic equilibrium to describe cell contractility and focal adhesion growth. The immanent multiphysical character of cell mechanics involves important aspects such as the coupling of fields of different scales and corresponding interface conditions that are sensitive to the solution of the governing numerical problem. These aspects become even more relevant when considering a feedback loop among the multiphysical solutions fields. In this contribution, we consider solution properties and sensitivity aspects of a nonlinear mechanical continuum model for the prognosis of stress fiber growth and reorientation incorporating a mechanosensitive feedback loop. We provide the governing equations of a Hill model-based stress fiber growth, which is coupled to a thermodynamical approach modeling the focal adhesions. Furthermore, a variational formulation including the algebraic equations is derived for staggered and monolithic solution approaches and the reaction-diffusion equation that models the feedback mechanism. We test both schemes with regard to reliability, accuracy, and numerical efficiency for different model parameters and loading scenarios. We present algorithmic aspects of the considered solution schemes and reveal their robustness with regard to model refinement in space and time and finally provide an assessment of their overall solution performance for multiphysics problems in the context of cell mechanics.
Metadata
Authors/Creators: |
|
---|---|
Copyright, Publisher and Additional Information: | This is the peer reviewed version of the following article: Keshavanarayana P, Ruess M, de Borst R. On the monolithic and staggered solution of cell contractility and focal adhesion growth. Int J Numer Meth Biomed Engng. 2018;e3138, which has been published in final form at https://doi.org/10.1002/cnm.3138. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. |
Keywords: | biochemomechanics; coupled equations; monolithic and staggered solution; nonlinear continuum model; stress fiber model |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Sep 2018 11:12 |
Last Modified: | 20 Aug 2019 00:41 |
Published Version: | https://doi.org/10.1002/cnm.3138 |
Status: | Published online |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1002/cnm.3138 |
Related URLs: |