Speaker
Description
Poromechanics provides a unified theoretical framework to describe the strong coupling between fluid transport, solid deformation, and evolving microstructure in heterogeneous porous media. While originally developed for geophysical and engineering applications, this framework can be systematically extended to living matter, where fluid–structure interactions, growth-induced deformation, and transport limitations play a central regulatory role. In this contribution, we present a multiscale poromechanical formulation for biological tissues.
We first introduce the governing balance laws for mass and momentum of the solid and fluid phases constituting the tissue, together with constitutive relations accounting for compressibility, porosity evolution, growth, and transport–reaction mechanisms. Particular attention is paid to the coupling terms linking pore pressure, effective stress, deformation, and permeability, which are essential to capture nonlinear feedback mechanisms between flow and mechanics.
At the scale of multicellular aggregates (≈100–200 μm), cell assemblies are modeled as active poroelastic media in which oxygen transport, interstitial fluid pressure, and mechanically induced stresses jointly regulate growth and structural organization. Experimental validation is achieved through biophysical experiments based on the Cellular Capsule Technology, with quantitative agreement between simulations and experiments for capsule deformation, aggregate size, viable rim thickness, and necrotic core development. Sensitivity analyses reveal that, under confined conditions, a critical inhibitory pressure threshold becomes the dominant parameter controlling growth, in contrast to free growth conditions where proliferation kinetics and oxygen consumption prevail.
At the tissue scale, we introduce a reactive bi-compartment poromechanical formulation that explicitly couples vascular perfusion, interstitial transport, and tissue deformation. This framework captures key features of evolving porous media, including spatially heterogeneous and strain-dependent permeability, source–sink terms associated with vascular exchange, and strong chemo-mechanical coupling. Applied to glioblastoma, the model demonstrates how altered transport properties and growth-induced stresses interact to drive tumor progression. Image-informed simulations allow to qualitatively demonstrate the reliability of the mathematical model.
Overall, this work highlights how poromechanics offers a rigorous and extensible theoretical framework for coupled flow–deformation processes in living porous media opening new perspectives for quantitative modeling in biological and biomedical systems.
| Country | France |
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