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Table of contents
I Introduction
I.1 Cells and Tissues
I.1.1 Tissues
I.1.2 Cell monolayers
I.1.3 Forces
I.2 Measurement of physical quantities
I.2.1 Single cell measurements
I.2.2 External force measurements: traction force microscopy
I.2.3 Internal force measurements
I.2.4 Velocity measurements
I.2.5 Rheological models
I.2.6 Variability and probability distribution functions
I.3 Theoretical methods
I.3.1 Stochastic calculus
I.3.2 Bayesian inversion
I.3.3 Hyperparameter selection
I.3.4 Likelihood and model selection
I.3.5 Kalman filter
I.4 Outline
II Stochastic wound healing
II.1 Motivation
II.2 Summary of « Tissue fusion over nonadhering surfaces »
II.3 Discussion
II.3.1 Model selection
II.3.2 HaCaT experiments
II.3.3 Perspectives
IIIBayesian Inversion Stress Microscopy (BISM)
III.1 Motivation
III.1.1 Inference from cell geometry
III.1.2 Inference from TFM
III.2 Summary of « Inference of Internal Stress in a Cell Monolayer »
III.3 Discussion
III.3.1 Additional validations
III.3.2 Defects
III.3.3 Distribution of traction forces and internal stresses
III.3.4 Extension to 3D
IV Kalman Inversion Stress Microscopy (KISM)
IV.1 Statistical model
IV.1.1 Observation and evolution models
IV.1.2 Kalman filter
IV.1.3 Hyperparameter values
IV.2 Numerical validation
IV.2.1 Numerical simulation
IV.2.2 Validation
IV.3 Experimental application
IV.3.1 Quasi-1D monolayer in a ring
IV.3.2 2D monolayer in a square domain
IV.4 Summary and perspectives
V Bayesian Inversion Stress Microscopy from substrate displacement (BISMu)
V.1 Traction force measurements on a soft gel
V.1.1 Boundary Element Method
V.1.2 Fourier Transform Traction Cytometry
V.1.3 Other methods
V.2 Statistical models
V.2.1 Real space: BISMu
V.2.2 Fourier space: BISMuf
V.3 Numerical validation
V.3.1 Numerical simulation
V.3.2 Real space
V.3.3 Fourier space
V.3.4 Summary
V.4 Application to experimental data
VI Perspectives
VI.1 Model selection applied to constitutive equations
VI.2 Rotating ring
VI.3 Magnetized aggregate
Résumé en français
A Univariate probability distributions
B Code BISM/ KISM
C Experimental data
C.1 Wound healing on nonadhesive substrate (Guillaume Duclos, Maxime Deforet)
C.2 Rotating ring (Shreyansh Jain)
C.3 Defect (Thuan Beng Saw)
C.4 Square (Grégoire Peyret)
C.5 Magnetized aggregate (François Mazuel)
D Topological defects in epithelia govern the extrusion of dead cells
Bibliography
