arXiv subjects

David B. Hill

Publications and source records attributed to David B. Hill.

6 recordsLinked to original sources

arXiv2019

Measurement Error Correction in Particle Tracking Microrheology

In diverse biological applications, particle tracking of passive microscopic species has become the experimental measurement of choice -- when either the materials are of limited volume, or so soft as to deform uncontrollably when manipulated by traditional instruments. In a wide range of particle tracking experiments, a ubiquitous finding is that the mean squared displacement (MSD) of particle positions exhibits a power-law signature, the parameters of which reveal valuable information about the viscous and elastic properties of various biomaterials. However, MSD measurements are typically contaminated by complex and interacting sources of instrumental noise. As these often affect the high-frequency bandwidth to which MSD estimates are particularly sensitive, inadequate error correction can lead to severe bias in power law estimation and thereby, the inferred viscoelastic properties. In this article, we propose a novel strategy to filter high-frequency noise from particle tracking measurements. Our filters are shown theoretically to cover a broad spectrum of high-frequency noises, and lead to a parametric estimator of MSD power-law coefficients for which an efficient computational implementation is presented. Based on numerous analyses of experimental and simulated data, results suggest our methods perform very well compared to other denoising procedures.

stat.AP↗

arXiv2018

Evidence that self-similar microrheology of highly entangled polymeric solutions scales robustly with, and is tunable by, polymer concentration

We report observations of a remarkable scaling behavior with respect to concentration in the passive microbead rheology of two highly entangled polymeric solutions, polyethylene oxide (PEO) and hyaluronic acid (HA). This behavior was reported previously [Hill et al., PLOS ONE (2014)] for human lung mucus, a complex biological hydrogel, motivating the current study for synthetic polymeric solutions PEO and HA. The strategy is to identify, and focus within, a wide range of lag times $τ$ for which passive micron diameter beads exhibit self-similar (fractional, power law) mean-squared-displacement (MSD) statistics. For lung mucus, PEO at three different molecular weights (Mw), and HA at one Mw, we find ensemble-averaged MSDs of the form ${\langle}Δr^{2}(τ){\rangle} = 4D_ατ^α$, all within a common band, [1/60 sec, 3 sec], of lag times $τ$. We employ the MSD power law parameters $(D_α,α)$ to classify each polymeric solution over a range of highly entangled concentrations. By the generalized Stokes-Einstein relation, power law MSD implies power law elastic $G'(ω)$ and viscous $G''(ω)$ moduli for frequencies $1/τ$, [0.33 sec$^{-1}$, 60 sec$^{-1}$]. A natural question surrounds the polymeric properties that dictate $D_α$ and $α$, e.g. polymer concentration c, Mw, and stiffness (persistence length). In [Hill et al., PLOS ONE (2014)], we showed the MSD exponent $α$ varies linearly, while the pre-factor $D_α$ varies exponentially, with concentration, i.e. the semi-log plot, $(log(D_α),α)(c)$ of the classifier data is collinear. Here we show the same result for three distinct Mw PEO and HA at a single Mw. Future studies are required to explore the generality of these results for polymeric solutions, and to understand this scaling behavior with polymer concentration.

cond-mat.soft↗

arXiv2018

Fluid heterogeneity detection based on the asymptotic distribution of the time-averaged mean squared displacement in single particle tracking experiments

A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $σ^2 t^α$ as a function of time $t$ for some constant $σ^2$, where the diffusion exponent satisfies $α\neq 1$. In this article, we use recent results on the asymptotic distribution of the time-averaged mean squared displacement (Didier and Zhang (2017)) to construct statistical tests for detecting physical heterogeneity in viscoelastic fluid samples starting from one or multiple observed anomalously diffusive paths. The methods are asymptotically valid for the range $0 < α< 3/2$ and involve a mathematical characterization of time-averaged mean squared displacement bias and the effect of correlated disturbance errors. The assumptions on particle motion cover a broad family of fractional Gaussian processes, including fractional Brownian motion and many fractional instances of the generalized Langevin equation framework. We apply the proposed methods in experimental data from treated $P.\ aeruginosa$ biofilms generated by the collaboration of the Hill and Schoenfisch Labs at UNC-Chapel Hill.

cond-mat.soft↗

arXiv2016

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 Péclet 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 Péclet 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.

cond-mat.soft↗

arXiv2015

Model comparison and assessment for single particle tracking in biological fluids

State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. For particles on the order of 1 micron diameter, these paths are generally inconsistent with simple Brownian motion. Yet, despite an abundance of data confirming these findings and their wide-ranging scientific implications, stochastic modeling of the complex particle motion has received comparatively little attention. Even among posited models, there is virtually no literature on likelihood-based inference, model comparisons, and other quantitative assessments. In this article, we develop a rigorous and computationally efficient Bayesian methodology to address this gap. We analyze two of the most prevalent candidate models for 30 second paths of 1 micron diameter tracer particles in human lung mucus: fractional Brownian motion (fBM) and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory. Our model comparisons distinctly favor GLE over fBM, with the former describing the data remarkably well up to the timescales for which we have reliable information.

stat.AP↗

arXiv2012

Statistical Challenges in Microrheology

Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical properties of biological fluids, of the material properties of membranes or the cytoplasm of cells, or of the entire cell. The theoretical underpinning of microrheology was given in Mason and Weitz (Physical Review Letters; 1995), who introduced a framework for the use of path data of diffusing particles to infer viscoelastic properties of its fluid environment. The multi-particle tracking techniques that were subsequently developed have presented numerous challenges for experimentalists and theoreticians. This paper describes some specific challenges that await the attention of statisticians and applied probabilists. We describe relevant aspects of the physical theory, current inferential efforts and simulation aspects of a central model for the dynamics of nano-scale particles in viscoelastic fluids, the generalized Langevin equation.

stat.ME↗