Microrheology[1] is a technique used to measure the rheological properties of a medium, such as microviscosity, via the measurement of the trajectory of a flow tracer (a micrometre-sized particle).
Passive microrheology uses inherent thermal energy to move the tracers, whereas active microrheology uses externally applied forces, such as from a magnetic field or an optical tweezer, to do so.
[2] [3] Passive microrheology uses the thermal energy (kT) to move the tracers, although recent evidence suggests that active random forces inside cells may instead move the tracers in a diffusive-like manner.
[4] The trajectories of the tracers are measured optically either by microscopy, or alternatively by light scattering techniques.
Diffusing-wave spectroscopy (DWS) is a common choice that extends light scattering measurement techniques to account for multiple scattering events.
[5] From the mean squared displacement with respect to time (noted MSD or <Δr2> ), one can calculate the visco-elastic moduli G′(ω) and G″(ω) using the generalized Stokes–Einstein relation (GSER).
In a standard passive microrheology test, the movement of dozens of tracers is tracked in a single video frame.
The motivation is to average the movements of the tracers and calculate a robust MSD profile.
Observing the MSD for a wide range of integration time scales (or frequencies) gives information on the microstructure of the medium where are diffusing the tracers.
If the tracers are experiencing free diffusion in a purely viscous material, the MSD should grow linearly with sampling integration time:
If the tracers are moving in a spring-like fashion within a purely elastic material, the MSD should have no time dependence:
In most cases the tracers are presenting a sub-linear integration-time dependence, indicating the medium has intermediate viscoelastic properties.
Of course, the slope changes in different time scales, as the nature of the response from the material is frequency dependent.
Since the force involved is very weak (order of 10−15 N), microrheology is guaranteed to be in the so-called linear region of the strain/stress relationship.
The GSER is as follows: with A related method of passive microrheology involves the tracking positions of a particle at high frequency, often with a quadrant photodiode.
can be found, and then related to the real and imaginary parts of the response function,
[7] The response function leads directly to a calculation of the complex shear modulus,
via: Source:[8] There could be many artifacts that change the values measured by the passive microrheology tests, resulting in a disagreement between microrheology and normal rheology.
A different microrheological approach studies the cross-correlation of two tracers in the same sample.
Some studies has shown that this method is better in coming to agreement with standard rheological measurements (in the relevant frequencies and materials) Active microrheology may use a magnetic field ,[9][10][11][8][12] [13] optical tweezers[14] [15] [16] [17][18] or an atomic force microscope[19] to apply a force on the tracer and then find the stress/strain relation.
The response of the tracer is a factor of the matrix visco-elastic nature.
If a matrix is totally elastic (a solid), the response to the acting force should be immediate and the tracers should be observed moving by-
On the other hand, if the matrix is totally viscous (a liquid), there should be a phase shift of
in reality, as most materials are visco-elastic, the phase shift observed is
Given a measured response phase shift φ (sometimes noted as δ), this ratio applies:
Similar response phase analysis is used in regular rheology testing.
More recently, it has been developed into Force spectrum microscopy to measure contributions of random active motor proteins to diffusive motion in the cytoskeleton.