Active rotational and translational microrheology beyond the linear spring regime

TL;DR

This paper introduces a new theoretical approach for active microrheology that accurately measures viscoelastic properties beyond the linear regime, especially useful for slowly changing microscopic systems like living cells.

Contribution

It presents a novel theory for determining complex shear modulus with non-linear driven particle motion and a variable transformation to improve measurement accuracy and efficiency.

Findings

The new theory accurately characterizes non-linear driven particle motion.

Variable transformation reduces low frequency drift and enhances signal strength.

Method enables faster measurements with reduced error in viscoelasticity.

Abstract

Active particle tracking microrheometers have the potential to perform accurate broad-band measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here which gives the complex shear modulus when the motion of a spherical particle is driven by non-linear forces. In some scenarios error can be further reduced by applying a variable transformation which linearises the equation of motion. This allows normalisation which eliminates low frequency drift in the particle's equilibrium position. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.