Speaker
Description
Biological tissues are often subjected to forces, and modeling their response is crucial in cases like tumor growth or skin contraction to improve therapies. Linear elasticity is the simplest constitutive law, allowing superposition and fundamental solutions to analyze multiple force points, as illustrated by the immersed interface method \cite{roy2020immersed}. We discuss this principle in terms of convergence using singularity removal \cite{Gjerde_2019}.
However, real tissues are porous and contain moisture, and microstructures change due to cellular activity. To capture this, we use a morpho-visco-poroelastic framework \cite{Hall_2008}, which accounts for elasticity, porosity, and microstructural evolution. This framework is analyzed for stability around equilibria \cite{Sabia2025}. To address spurious oscillations in numerical solutions, we provide monotonicity conditions and propose a numerical stabilization method.
Bibliography
@book{roy2020immersed,
author = "Roy, Somnath and De, Ashoke and Balaras, Elias",
title = "Immersed boundary method",
publisher = "Springer",
year = "2020",
series = "Computational Methods in Engineering $\&$ the Sciences",
address = "Singapore",
DOI = "https://doi.org/10.1007/978-981-15-3940-4"
}
@article{Gjerde_2019,
author = {Gjerde, Ingeborg G. and Kumar, Kundan and Nordbotten, Jan M.},
doi = {10.1007/s10596-019-09899-4},
issn = {1573-1499},
journal = {Comput. Geosci.},
month = {December},
number = {2},
pages = {443–457},
publisher = {Springer Science and Business Media LLC},
title = {A singularity removal method for coupled 1D–3D flow models},
url = {http://dx.doi.org/10.1007/s10596-019-09899-4},
volume = {24},
year = {2019}
}
@phdthesis{Hall_2008,
author = {Hall, C L},
title = { Modelling of some biological materials using continuum mechanics},
school ={Queensland University of Technology},
year = {2008}
}
@InProceedings{Sabia2025,
author={Asghar, Sabia and Vermolen, Fred J},
editor={Sequeira, Ad{\'e}lia
and Silvestre, Ana
and Valtchev, Svilen S.
and Janela, Jo{\~a}o},
title={Stability of Equilibria in a One Dimensional Model for Morpho--Poroelasticity for Soft Tissues},
booktitle={Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2},
year={2025},
publisher={Springer Nature Switzerland},
address={Cham},
pages={468--476},
isbn={978-3-031-86169-7},
doi={10.1007/978-3-031-86169-7_48}
}
