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September 2022 Measurement error correction in particle tracking microrheology
Yun Ling, Martin Lysy, Ian Seim, Jay Newby, David B. Hill, Jeremy Cribb, M. Gregory Forest
Author Affiliations +
Ann. Appl. Stat. 16(3): 1747-1773 (September 2022). DOI: 10.1214/21-AOAS1565


In diverse biological applications, single-particle tracking (SPT) 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 SPT experiments, a ubiquitous finding is that of long-range dependence in the particles’ motion. This is characterized by a power-law signature in the mean squared displacement (MSD) of particle positions as a function of time, 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 SPT 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.

Funding Statement

This work was supported by NSERC Grants RGPIN-2020-04364 (Lysy) and RGPIN-2019-06435 (Newby), Cystic Fibrosis Foundation grants HILL19G0 and HILL20Y2-OUT (Hill), NIH grants 5P30DK065988-17 (Hill) and 5P41EB002025 (Cribb), and NSF grants DMS-1664645 and CISE-1931516 (Forest).


The corresponding author for this work is Martin Lysy. Additional author affiliations are Department of Biology, University of North Carolina at Chapel Hill (Seim), and Department of Applied Physical Sciences and Department of Biomedical Engineering, University of North Carolina at Chapel Hill (Forest). The authors would like to thank the referees, the Associate Editor, and the Editor for the constructive feedback which greatly improved this work.


Download Citation

Yun Ling. Martin Lysy. Ian Seim. Jay Newby. David B. Hill. Jeremy Cribb. M. Gregory Forest. "Measurement error correction in particle tracking microrheology." Ann. Appl. Stat. 16 (3) 1747 - 1773, September 2022.


Received: 1 November 2019; Revised: 1 July 2021; Published: September 2022
First available in Project Euclid: 19 July 2022

Digital Object Identifier: 10.1214/21-AOAS1565

Keywords: high-frequency filtering , measurement error , Single-particle tracking , subdiffusion

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 3 • September 2022
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