Measuring forces and stresses in situ in living tissues

“Forces in tissues” workshop participants

doi:10.1101/016394

Abstract

Development, homeostasis and regeneration of tissues result from the interaction of genetics and mechanics. Kinematics and rheology are two main classes of measurements respectively providing deformations and mechanical properties of a material. They are now applied to living tissues and have contributed to the better understanding of their mechanics. Due to the complexity of living tissues, however, a third class of mechanical measurements, that of in situ forces and stresses, appears to be increasingly important to elaborate realistic models of tissue mechanics. We review here several emerging techniques of this class, their fields of applications, their advantages and limitations, and their validations. We argue that they will strongly impact on our understanding of developmental biology in the near future.

Glossary:

Deformation: relative change in size of an object. In one dimension, it is a dimensionless number: the fraction of change in the object length, whether positive (elongation) or negative (contraction). In two or three dimensions, elongation in one direction can coexist with contraction in another direction, so that the deformation is described by amplitudes in different directions (see “dilation” and “shear”). Also called “strain”.
Deformation rate: deformation per unit time, expressed as the inverse of a time. In one dimension, it can be for instance a change of a few percent per hour. In two or three dimensions, it is more complex (see “deformation”), and is equal to the symmetrical part of the velocity gradient.
Dilation: component of the deformation, which is isotropic, corresponding to a change of size.
Dynamics: description of a material evolution in reference to the forces which cause it.
Elastic deformation: reversible part of the deformation.
Elastic modulus: see “stiffness”.
Elasticity: capacity of a material to deform and store energy in response to an applied stress, and reversibly return to its initial rest shape after stress is removed.
Kinematics: visual description of motion, without reference to force
Liquid-like behaviour: behaviour of a material with a non-defined rest state, which can be continuously deformed by a very small shear stress.
Plastic deformation: irreversible part of the deformation.
Plastic material: material that undergoes irreversible deformation in response to an applied stress.
Plasticity: capacity of a material to be sculpted, i.e. acquire a new rest shape under an applied stress, and keep it when the stress is removed.
Purely elastic material: Material that responses immediately and elastically to applied stress.
Purely viscous material: material that flows in response to a shear stress and does not recover its initial shape after stress is removed.
Rheology: science of flow and deformation of materials.
Shear: component of the deformation that is purely anisotropic, that corresponds to a change of shape.
Solid-like behaviour: behaviour of a material with a defined rest state.
Stiffness: quantity which measures the resistance of an elastic solid in response to an applied stress. Also called “elastic modulus” or “rigidity”.
Strain: see “deformation”.
Stress: here mechanical stress, i.e. forces internal to the tissue, exerted by a tissue region onto a neighbour tissue region. It is a more coarse-grained notion than force, and is expressed as a force per unit size of tissue boundary.
Tension: force internal to an object, tending to decrease its size. The “surface tension” of an aggregate or a piece of 3D tissue tends to decrease its surface area, and is expressed in Newtons per meter. A one-dimensional object like a cell-cell adherens junction has a “line tension”, tending to decrease its length, and expressed in Newtons.
Viscosity: (1) tendency of a material to resist gradual deformation and flow in response to an applied stress; (2) quantity which measures this property (see “viscous modulus”).
Viscous modulus: quantity which measures the resistance of a viscous liquid in response to an applied stress. Usually called “viscosity” for short.
Yield: here, defines the transition between the elastic behaviour and the plastic behaviour.

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