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Micro-heterogeneity metrics for diffusion in soft matter.

ABSTRACT: 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.

SUBMITTER: Mellnik J

PROVIDER: S-EPMC4186960 | biostudies-literature | 2014 Oct

REPOSITORIES: biostudies-literature

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Micro-heterogeneity metrics for diffusion in soft matter.

Mellnik John J Vasquez Paula A PA McKinley Scott A SA Witten Jacob J Hill David B DB Forest M Gregory MG

Soft matter 20140821 39

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 ...[more]

PMID: 25144347

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Project description:BackgroundAlthough diffusion tensor imaging has been a major research focus for Alzheimer's disease in recent years, it remains unclear whether it has sufficient stability to have biomarker potential. To date, frequently inconsistent results have been reported, though lack of standardisation in acquisition and analysis make such discrepancies difficult to interpret. There is also, at present, little knowledge of how the biometric properties of diffusion tensor imaging might evolve in the course of Alzheimer's disease.MethodsThe biomarker question was addressed in this study by adopting a standardised protocol both for the whole brain (tract-based spatial statistics), and for a region of interest: the midline corpus callosum. In order to study the evolution of tensor changes, cross-sectional data from very mild (N?=?21) and mild (N?=?22) Alzheimer's disease patients were examined as well as a longitudinal cohort (N?=?16) that had been rescanned at 12 months.Findings and significanceThe results revealed that increased axial and mean diffusivity are the first abnormalities to occur and that the first region to develop such significant differences was mesial parietal/splenial white matter; these metrics, however, remained relatively static with advancing disease indicating they are suitable as 'state-specific' markers. In contrast, increased radial diffusivity, and therefore decreased fractional anisotropy-though less detectable early-became increasingly abnormal with disease progression, and, in the splenium of the corpus callosum, correlated significantly with dementia severity; these metrics therefore appear 'stage-specific' and would be ideal for monitoring disease progression. In addition, the cross-sectional and longitudinal analyses showed that the progressive abnormalities in radial diffusivity and fractional anisotropy always occurred in areas that had first shown an increase in axial and mean diffusivity. Given that the former two metrics correlate with dementia severity, but the latter two did not, it would appear that increased axial diffusivity represents an upstream event that precedes neuronal loss.

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Micro-heterogeneity metrics for diffusion in soft matter.

Publications

Micro-heterogeneity metrics for diffusion in soft matter.

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