Statistical physics approach to quantifying differences in myelinated nerve fibers

Abstract

We present a new method to quantify differences in myelinated nerve fibers. These differences range from morphologic characteristics of individual fibers to differences in macroscopic properties of collections of fibers. Our method uses statistical physics tools to improve on traditional measures, such as fiber size and packing density. As a case study, we analyze cross–sectional electron micrographs from the fornix of young and old rhesus monkeys using a semi-automatic detection algorithm to identify and characterize myelinated axons. We then apply a feature selection approach to identify the features that best distinguish between the young and old age groups, achieving a maximum accuracy of 94% when assigning samples to their age groups. This analysis shows that the best discrimination is obtained using the combination of two features: the fraction of occupied axon area and the effective local density. The latter is a modified calculation of axon density, which reflects how closely axons are packed. Our feature analysis approach can be applied to characterize differences that result from biological processes such as aging, damage from trauma or disease or developmental differences, as well as differences between anatomical regions such as the fornix and the cingulum bundle or corpus callosum.

Transient Anomalous Diffusion MRI in Excised Mouse Spinal Cord: Comparison Among Different Diffusion Metrics and Validation With Histology

“…Differently from the standard axonal density, which does not consider the various obstacles in the ECS not recognized as axons, ELD accounts for the area not occupied by axons. In a study involving rhesus monkeys, ELD was able to discriminate between youth and elderly based on the axonal density of white matter in the fornix (Comin et al, 2014).Unexpectedly, we did not observe any correlation between the α-metric parameters and ELD. Conversely, γ-metrics (in particular Mγ and γort) and QSI metrics (FWHM and Zics) showed strong negative correlations with ELD (Table 3).…”

“…Dens.) and effective local density (ELD) as extracted in Comin et al (2014) were estimated. The Ax Dens was derived from the ratio between the fraction of area occupied by axolemmas, and the area of an axon with average diameter computed over the ROI, and approximated to a circle.…”

“…A pixel-wise adaptive Wiener method based on statistics estimated from a local neighborhood of each pixel was applied prior to the segmentation. The mask associated to the ics component was polished through surface, circularity and uniformity thresholds, as described in literature (Comin et al, 2014): briefly, the algorithm discarded: those objects with an area smaller than a specific value defined by the user, presumably representing speckles and non-axons spots; the objects for which the ratio of the perimeter to the square root of the area was larger than 6.2, corresponding to elongated ellipses with b > 6a, with a and b the semi-minor and semi-major axes of the ellipse, respectively; the objects with a ratio σ/µ > 0.5 of the standard deviation σ and the mean intensity µ, assumed to contain debris or multiple tissue types. Six ROIs were manually drawn encompassing six WM tracts: funiculus gracilis (fg), dorsal-Corticospinal tract (dCST), rubrospinal tract (RST), spino-thalamic tract (STT), vestibulospinal tract (VST), reticulo-spinal tract (ReST) (Figure 3).…”

“…This work aims to elucidate and validate ( Jelescu and Budde, 2017 ) the image contrast and information obtained using the tAD model in white matter (WM) through a direct comparison between different diffusion metrics and histology. Due to the peculiar characteristics of complex tissue that the tAD could highlight, in addition to the conventional parameters describing the geometry of the tissue, such as the axons diameter and the axons density, we quantified some local parameters, such as the effective local density (ELD) that reflects how closely the axons are packed ( Comin et al, 2014 ).…”

Methods to Determine and Analyze the Cellular Spatial Distribution Extracted From Multiplex Immunofluorescence Data to Understand the Tumor Microenvironment

“…Depending on how the data are presented, the results generated can be different every time the algorithm is run, and the Euclidean distance can unequally weight factors and can be used only if the meaning is defined. In contrast, hierarchical clustering can be agglomerative when similar objects are grouped into clusters and into a set of clusters, where each cluster is distinct from the others and the objects within each cluster are broadly similar to each other (Comin et al, 2014;Lin et al, 2015) (Figure 15A). Divisive hierarchical clustering is done by initially grouping all observations into one cluster and then successively splitting these clusters, typically by sequentially merging similar clusters (Figure 15A).…”