Direct and Inverse Modeling for Stochastic Passive Microbead Rheology
The need in biology to understand the rheological properties of cells, tissues,
membranes, and biological liquids, has led to new techniques in microrheology, where
passive bead tracking is the fundamental probe of viscoelastic properties. We present
stochastic methods for direct and inverse characterization based on noisy time series
associated with either one or multiple beads, focusing on the distinctions in bead
statistics due to bead-bead hydrodynamic interactions versus the ratio of bead
separation distance and bead radii. Our modeling combines the seminal works of
Mason \& Weitz for single bead statistics and of Crocker-Levine-Lubensky for 2-bead
statistics, together with direct and inverse simulation tools for generalized Langevin equations.
The aim is to develop statistically accurate and fast direct simulation tools for
bead-bead fluctuations, and then inversion methods derived from maximum likelihood
methods and the Kalman filter. The application is to support experiments by R.
Superfine and D. Hill and for characterization and simulations of transport
mechanisms in lung airway surface liquids within the Virtual Lung Project at UNC Chapel Hill.