arXiv subjects

Sham Tlili

Publications and source records attributed to Sham Tlili.

4 recordsLinked to original sources

arXiv2026

Viscous vertex model for active epithelial tissues

We present a rotationally invariant viscous vertex model that accounts for both cortical and bulk dissipation of cells. The vanishing substrate-friction limit is enforced via Lagrange multipliers, which also provides a framework for implementing various boundary conditions, such as fixed boundaries and prescribed tractions. Building on this formulation, we introduce a slab-shear rheology protocol to extract an effective, coarse-grained tissue shear viscosity. Under polar or nematic activity, viscosity regulates the formation of elongated, spatially correlated cell-shape textures and stabilizes well-defined topological defects. Because the model remains well-posed at zero substrate friction, it is naturally suited to describing free-floating epithelia and organoids.

physics.bio-ph↗

arXiv2025

Noninvasive rheological inference from stable flows in confined tissues

Quantifying the in-plane rheology of epithelial monolayers remains challenging due to the difficulty of imposing controlled shear. We introduce a self-driven, rheometer-like assay in which collective migration generates stationary shear flows, allowing rheological parameters to be inferred directly from image sequences. The assay relies on two sets of ring-shaped fibronectin patches, micropatterned in arrays for high-throughput imaging. Within isolated rings, the epithelial tissue exhibits persistent rotation, from which we infer active migration stresses and substrate friction. Within partially overlapping rings, the tissue exhibits sustained shear, from which we infer the elastic and viscous responses of the cells. The emergence of a Maxwell-like viscoelastic relation -- characterized by a linear relationship between mean cell deformation and neighbor-exchange rate -- is specifically recapitulated within a wet vertex-model framework, which reproduces experimental measurements only when intercellular viscous dissipation is included alongside substrate friction. We apply our method to discriminate the respective roles of two myosin~II isoforms in tissue mechanics. Overall, by harnessing self-generated stresses instead of externally imposed ones, we propose a noninvasive route to rheological inference in migrating epithelial tissues and, more generally, in actively flowing granular materials.

cond-mat.soft↗

arXiv2025

Inferring viscoplastic models from velocity fields: a physics-informed neural network approach

Fluid-like materials are ubiquitous, spanning from living biological tissues to geological formations, and across scales ranging from micrometers to kilometers. Inferring their rheological properties remains a major challenge, particularly when traditional rheometry fails to capture their complex, three-dimensional, and often heterogeneous behavior. This difficulty is exacerbated by system size, boundary conditions, and other material-specific physical, chemical, or thermal constraints. In this work, we explore whether rheological laws can be inferred directly from flow observations. We propose a physics-informed neural network (PINN) framework designed to learn constitutive viscoplastic laws from velocity field data alone. Our method uses a neural network to interpolate the velocity field, enabling the computation of velocity gradients via automatic differentiation. These gradients are used to estimate the residuals of the governing conservation laws, which implicitly depend on the unknown rheology. We jointly optimize both the constitutive model and the velocity field representation by minimizing the physical residuals and discrepancies from observed data. We validate our approach on synthetic velocity fields generated from numerical simulations using Herschel-Bulkley, Carreau and Panastasiou models under various flow conditions. The algorithm reliably infers rheological parameters, even in the presence of significant noise. We analyze the dependence of inference performance on flow geometry and sampling, highlighting the importance of shear rate distribution in the dataset. Finally, we explore preliminary strategies for model-agnostic inference via embedded model selection, demonstrating the potential of PINNs for identifying the most suitable rheological law from candidate models.

physics.flu-dyn↗

arXiv2015

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.

physics.bio-ph↗