Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

Lysy, Martin; Pillai, Natesh S.; Hill, David B.; Forest, M. Gregory; Mellnik, John; Vasquez, Paula A.; McKinley, Scott A.

doi:10.1080/01621459.2016.1158716

Cited by 49 publications

(57 citation statements)

References 75 publications

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“…These kernels are candidates along with fractional Brownian motion for best fit to particle paths in mucus and other biological fluids. The determination of which models fit the data more accurately is an open challenge currently being explored in collaboration with S. McKinley, J. Mellnik, N. Pillai, and M. Lysy [164].…”

Section: F(t)f(s) = K B T K(|t − S|)mentioning

confidence: 99%

Complex Fluids and Soft Structures in the Human Body

Vasquez¹,

Forest²

2014

Complex Fluids in Biological Systems

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The human body is a composite of diverse materials able to perform specific functions. Few of these materials are simple liquids or solids; rather they share both liquid-like and solid-like properties. The material world between liquids and solids is unlimited and exploited by Nature to form complex fluids and soft structures with properties that are tuned to perform highly specialized functions. This chapter will briefly summarize the diversity of materials in the human body, and then drill deeper into one complex fluid (mucus, which coats every organ in the body) and one soft structure (an individual cell), and their remarkable properties. Some progress in characterizing these materials and modeling their functional properties, by others and our research group, will be presented with the take home message that we are in the early stages of interpreting experimental data and building predictive models and simulations of biological materials.

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Section: F(t)f(s) = K B T K(|t − S|)mentioning

confidence: 99%

Complex Fluids and Soft Structures in the Human Body

Vasquez¹,

Forest²

2014

Complex Fluids in Biological Systems

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“…One of our main goals in this paper is to devise and study new homogenization procedures that yield reduced models retaining essential features of a more general class of models. This program is of importance for identification, parameter inference and uncertainty quantification of stochastic systems [61,25,45,38] arising in the studies of anomalous diffusion [49,51], climate modeling [22,47] and molecular systems [10], among others. There is increasing amount of effort striving to implement this or related programs, starting from microscopic models [60], using various techniques [20,57,7,19,26], for different systems of interest in the literature.…”

Section: Goals Organization and Summary Of Results Of The Papermentioning

confidence: 99%

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

Lim

Wehr

Lewenstein

2020

Ann. Henri Poincaré

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We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations (SDEs) for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

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“…In the best case scenario, there are rigorous theoretical models derived from detailed molecular-scale knowledge of the physical and chemical properties of the soft matter system and the interaction of the embedded probes with the molecular structure. In such a scenario, one has candidate models to choose from, and model selection methods can be applied 11,12 to yield a best-fit model. The classical example is simple Brownian motion for diffusion in a viscous fluid, where there is a unique model and model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…A rigorous protocol for model selection is beyond the scope of this paper, and will be presented elsewhere. 12 …”

Section: Introductionmentioning

confidence: 99%

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Micro-heterogeneity metrics for diffusion in soft matter

et al. 2014

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Passive particle tracking of diffusive paths in soft matter, coupled with analysis of the path data, is firmly established as a fundamental methodology for characterization of both diffusive transport properties (the focus here) and linear viscoelasticity. For either focus, particle time series are typically analyzed by ensemble averaging over paths, a perfectly natural protocol for homogeneous materials or for applications where mean properties are sufficient. Many biological materials, however, are heterogeneous over length scales above the probe diameter, and the implications of heterogeneity for biologically relevant transport properties (e.g. diffusive passage times through a complex fluid layer) motivate this paper. Our goals are three-fold: first, to detect heterogeneity as reflected by the ensemble path data; second, to further decompose the ensemble of particle paths into statistically distinct clusters; and third, to fit the path data in each cluster to a model for the underlying stochastic process. After reviewing current best practices for detection and assessment of heterogeneity in diffusive processes, we introduce our strategy toward the first two goals with methods from the statistics and machine learning literature that have not found application thus far to passive particle tracking data. We apply an analysis based solely on the path data that detects heterogeneity and yields a decomposition of particle paths into statistically distinct clusters. After these two goals are achieved, one can then pursue model-fitting. We illustrate these heterogeneity metrics on diverse datasets: for numerically generated and experimental particle paths, with tunable and unknown heterogeneity, on numerical models for simple diffusion and anomalous sub-diffusion, and experimentally on sucrose, hyaluronic acid, agarose, and human lung culture mucus solutions.

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Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

Cited by 49 publications

References 75 publications

Complex Fluids and Soft Structures in the Human Body

Complex Fluids and Soft Structures in the Human Body

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

Micro-heterogeneity metrics for diffusion in soft matter

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