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Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

Author

Listed:
  • Martin Lysy
  • Natesh S. Pillai
  • David B. Hill
  • M. Gregory Forest
  • John W. R. Mellnik
  • Paula A. Vasquez
  • Scott A. McKinley

Abstract

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 μm 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-sec paths of 1 μm 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. Supplementary materials for this article are available online.

Suggested Citation

  • Martin Lysy & Natesh S. Pillai & David B. Hill & M. Gregory Forest & John W. R. Mellnik & Paula A. Vasquez & Scott A. McKinley, 2016. "Model Comparison and Assessment for Single Particle Tracking in Biological Fluids," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1413-1426, October.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:516:p:1413-1426
    DOI: 10.1080/01621459.2016.1158716
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6334 is not listed on IDEAS
    2. Gustavo Didier & Scott A. McKinley & David B. Hill & John Fricks, 2012. "Statistical challenges in microrheology," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(5), pages 724-743, September.
    3. David Lunn & Jessica Barrett & Michael Sweeting & Simon Thompson, 2013. "Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 551-572, August.
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    Citations

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    Cited by:

    1. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    2. Gustavo Didier & Kui Zhang, 2017. "The Asymptotic Distribution of The Pathwise Mean Squared Displacement in Single Particle Tracking Experiments," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 395-416, May.
    3. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Muszkieta, Monika & Janczura, Joanna, 2023. "A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment," Applied Mathematics and Computation, Elsevier, vol. 446(C).

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