An analytical framework for 3D microrheology measurements using an optical trap

Abstract

Microrheology with optical tweezers (MOT) is an all-optical technique that allows for viscoelastic properties to be probed at microscopic scales, and is particularly useful for materials that feature complex microstructures, such as biological samples. MOT is increasingly being employed alongside 3D imaging systems and particle tracking methods to allow for the 3D mapping of the viscoelastic properties of materials. The inherently anisotropic nature of the optical trap strength in 3D allows viscoelastic properties to be probed over a wider range of frequencies, as the weaker trap strength in the axial direction will extend the range of low frequency/long time measurements. However, it has been shown that such anisotropy can also result in a significant overestimation of the material viscosity. In this work a new analytical method is demonstrated to overcome this artefact. This is achieved by resampling 3D MOT data over a wide range of solid angles and making some basic assumptions with regards the shape of the optical trap. This approach is applied to simulated data where the anisotropy induced maximum error in viscosity is reduced from ~ 150% to < 5% for a Newtonian fluid. The effectiveness of the method is further confirmed by experimental MOT measurements performed with water and gelatine solutions showing that viscosity can be extracted reliably across a wide frequency range. This work opens a new route to full 3D mapping of the viscoelastic properties of soft materials over a broad frequency range.