1 research outputs found
Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift
Volume limitations and low yield thresholds of biological fluids have led to
widespread use of passive microparticle rheology. The mean-squared-displacement
(MSD) statistics of bead position time series (bead paths) are either applied
directly to determine the creep compliance [Xu et al (1998)] or transformed to
determine dynamic storage and loss moduli [Mason & Weitz (1995)]. A prevalent
hurdle arises when there is a non-diffusive experimental drift in the data.
Commensurate with the magnitude of drift relative to diffusive mobility,
quantified by a P\'eclet number, the MSD statistics are distorted, and thus the
path data must be "corrected" for drift. The standard approach is to estimate
and subtract the drift from particle paths, and then calculate MSD statistics.
We present an alternative, parametric approach using maximum likelihood
estimation that simultaneously fits drift and diffusive model parameters from
the path data; the MSD statistics (and consequently the compliance and dynamic
moduli) then follow directly from the best-fit model. We illustrate and compare
both methods on simulated path data over a range of P\'eclet numbers, where
exact answers are known. We choose fractional Brownian motion as the numerical
model because it affords tunable, sub-diffusive MSD statistics consistent with
typical 30 second long, experimental observations of microbeads in several
biological fluids. Finally, we apply and compare both methods on data from
human bronchial epithelial cell culture mucus.Comment: 29 pages, 12 figure