Paper List

Journal: ArXiv Preprint
Published: Unknown
BiophysicsMechanobiology

Tissue stress measurements with Bayesian Inversion Stress Microscopy

Institut Jacques Monod, CNRS, Université Paris Cité | Institut Curie, Paris Université Sciences et Lettres | Friedrich-Alexander Universität Erlangen-Nürnberg | Max-Planck-Zentrum für Physik und Medizin | Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris

Lucas Anger, Andreas Schoenit, Fanny Wodrascka, Carine Rossé, René-Marc Mège, Benoit Ladoux, Philippe Marcq
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The 30-Second View

IN SHORT: This paper addresses the core challenge of measuring absolute, tissue-scale mechanical stress without making assumptions about tissue rheology, which is crucial for understanding mechanobiology in complex, heterogeneous tissues.

Innovation (TL;DR)

  • Methodology Introduces Bayesian Inversion Stress Microscopy (BISM), a method that infers the complete 2D stress tensor (σ_xx, σ_yy, σ_xy) from traction force data by solving an underdetermined inverse problem using Bayesian inference, without requiring rheological assumptions.
  • Methodology Demonstrates robust applicability across diverse experimental geometries and boundary conditions, including confined tissues of arbitrary shape (e.g., star-shaped, elliptic) and systems with free boundaries (e.g., wound healing assays).
  • Biology Provides absolute stress measurements, enabling the testing of fundamental assumptions in tissue mechanics. For example, it shows that a fourfold increase in cell density does not necessarily lead to compressive stress (mean tension decreased by a factor of three but remained positive), challenging the simple density-stress paradigm.

Key conclusions

  • BISM provides absolute stress measurements validated against traction force moments. In a confined square MDCK monolayer, inferred mean isotropic stress (⟨σ_iso_inf⟩ = 7.76 kPa·μm) closely matched the calculated true value (⟨σ_iso_true⟩ = 7.77 kPa·μm), with a coefficient of determination R_t² = 1.0.
  • The method is geometry-agnostic. Applied to a star-shaped MDCK island, BISM inferred stresses (e.g., ⟨σ_iso_inf⟩ = 1.57 kPa·μm) that excellently agreed with traction force moments (⟨σ_iso_true⟩ = 1.56 kPa·μm), demonstrating reliability in arbitrary confined shapes.
  • BISM reveals a linear relationship between mean tissue tension and mean traction force amplitude (slope ~15.5 μm, on the order of a cell diameter), providing a quantitative link between external cell-substrate forces and internal tissue stress.
Background and Gap： Existing methods for tissue stress inference, such as Monolayer Stress Microscopy (MSM), rely on assumptions of linear elasticity and homogeneous tissue properties, limiting their application to complex, heterogeneous, or non-linear biological tissues. BISM fills this gap by providing a rheology-agnostic framework.

Abstract: Cells within biological tissue are constantly subjected to dynamic mechanical forces. Measuring the internal stress of tissues has proven crucial for our understanding of the role of mechanical forces in fundamental biological processes like morphogenesis, collective migration, cell division or cell elimination and death. Previously, we have introduced Bayesian Inversion Stress Microscopy (BISM), which is relying on measuring cell-generated traction forces in vitro and has proven particularly useful to measure absolute stresses in confined cell monolayers. We further demonstrate the applicability and robustness of BISM across various experimental settings with different boundary conditions, ranging from confined tissues of arbitrary shape to monolayers composed of different cell types. Importantly, BISM does not require assumptions on cell rheology. Therefore, it can be applied to complex heterogeneous tissues consisting of different cell types, as long as they can be grown on a flat substrate. Finally, we compare BISM to other common stress measurement techniques using a coherent experimental setup, followed by a discussion on its limitations and further perspectives.