Statistical physics approach to quantifying differences in myelinated nerve fibers

Machine learning enables non-Gaussian investigation of changes to peripheral nerves related to electrical stimulation

Electrical stimulation of the peripheral nervous system (PNS) is becoming increasingly important for the therapeutic treatment of numerous disorders. Thus, as peripheral nerves are increasingly the target of electrical stimulation, it is critical to determine how, and when, electrical stimulation results in anatomical changes in neural tissue. We introduce here a convolutional neural network and support vector machines for cell segmentation and analysis of histological samples of the sciatic nerve of rats stimulated with varying current intensities. We describe the methodologies and present results that highlight the validity of the approach: machine learning enabled highly efficient nerve measurement collection, while multivariate analysis revealed notable changes to nerves' anatomy, even when subjected to levels of stimulation thought to be safe according to the Shannon current limits.

Electrical Stimulation Induced Current Distribution in Peripheral Nerves Varies Significantly with the Extent of Nerve Damage: A Computational Study Utilizing Convolutional Neural Network and Realistic Nerve Models

Electrical stimulation of the peripheral nervous system is a promising therapeutic option for several conditions; however, its effects on tissue and the safety of the stimulation remain poorly understood. In order to devise stimulation protocols that enhance therapeutic efficacy without the risk of causing tissue damage, we constructed computational models of peripheral nerve and stimulation cuffs based on extremely high-resolution cross-sectional images of the nerves using the most recent advances in computing power and machine learning techniques. We developed nerve models using nonstimulated (healthy) and over-stimulated (damaged) rat sciatic nerves to explore how nerve damage affects the induced current density distribution. Using our in-house computational, quasi-static, platform, and the Admittance Method (AM), we estimated the induced current distribution within the nerves and compared it for healthy and damaged nerves. We also estimated the extent of localized cell damage in both healthy and damaged nerve samples. When the nerve is damaged, as demonstrated principally by the decreased nerve fiber packing, the current penetrates deeper into the over-stimulated nerve than in the healthy sample. As safety limits for electrical stimulation of peripheral nerves still refer to the Shannon criterion to distinguish between safe and unsafe stimulation, the capability this work demonstrated is an important step toward the development of safety criteria that are specific to peripheral nerve and make use of the latest advances in computational bioelectromagnetics and machine learning, such as Python-based AM and CNN-based nerve image segmentation.

Electrical Stimulation Induced Current Distribution in Peripheral Nerves Varies Significantly with the Extent of Nerve Damage: A Computational Study Utilizing Convolutional Neural Network and Realistic Nerve Models

Although electrical stimulation is an established treatment option for multiple central nervous and peripheral nervous system diseases, its effects on the tissue and subsequent safety of the stimulation are not well understood. Therefore, it is crucial to design stimulation protocols that maximize therapeutic efficacy while avoiding any potential tissue damage. Further, the stimulation levels need to be adjusted regularly to ensure that they are safe even with the changes to the nerve due to long-term stimulation. Using the latest advances in computing capabilities and machine learning approaches, we developed computational models of peripheral nerve stimulation based on very high-resolution cross-sectional images of the nerves. We generated nerve models constructed from non-stimulated (healthy) and over-stimulated (damaged) rat sciatic nerves to examine how the current density distribution is affected by nerve damage. Using our in-house numerical solver, the Admittance Method (AM), we computed the induced current distribution inside the nerves and compared the current penetration for healthy and damaged nerves. Our computational results indicate that when the nerve is damaged, primarily evidenced by the decreased nerve fiber packing, the current penetrates deeper inside the nerve than in the healthy case. As safety limits for electrical stimulation of biological tissue are still debated, we ultimately aim to utilize our computational models to determine refined safety criteria and help design safer and more efficacious electrical stimulation protocols.

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

Neural tissue is a hierarchical multiscale system with intracellular and extracellular diffusion compartments at different length scales. The normal diffusion of bulk water in tissues is not able to detect the specific features of a complex system, providing nonlocal, diffusion measurement averaged on a 10-20 μm length scale. Being able to probe tissues with sub-micrometric diffusion length and quantify new local parameters, transient anomalous diffusion (tAD) would dramatically increase the diagnostic potential of diffusion MRI (DMRI) in detecting collective and sub-micro architectural changes of human tissues due to pathological damage. In DMRI, the use of tAD parameters quantified using specific DMRI acquisition protocols and their interpretation has often aroused skepticism. Although the derived formulas may accurately fit experimental diffusion-weighted data, the relationships between the postulated dynamical feature and the underlying geometrical structure remains elusive, or at most only suggestive. This work aimed to elucidate and validate the image contrast and information that can be obtained using the tAD model in white matter (WM) through a direct comparison between different diffusion metrics and histology. Towards this goal, we compared tAD metrics extracted from pure subdiffusion (α-imaging) and super-pseudodiffusion (γ-imaging) in excised mouse spinal cord WM, together with T2 and T2* relaxometry, conventional (normal diffusion-based) diffusion tensor imaging (DTI) and q-space imaging (QSI), with morphologic measures obtained by optical microscopy, to determine which structural and topological characteristics of myelinated axons influenced tAD contrast. Axon diameter (AxDiam), the standard deviation of diameters (SD_ax.diam), axonal density (AxDens) and effective local density (ELD) were extracted from optical images in several WM tracts. Among all the diffusion parameters obtained at 9.4 T, γ-metrics confirmed a strong dependence on magnetic in-homogeneities quantified by R2* = 1/T2* and showed the strongest associations with AxDiam and ELD. On the other hand, α-metrics showed strong associations with SD_ax.diam and was significantly related to AxDens, suggesting its ability to quantify local heterogeneity degree in neural tissue. These results elucidate the biophysical mechanism underpinning tAD parameters and show the clinical potential of tAD-imaging, considering that both physiologic and pathologic neurodegeneration translate into alterations of WM morphometry and topology.

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

Image analysis using multiplex immunofluorescence (mIF) to detect different proteins in a single tissue section has revolutionized immunohistochemical methods in recent years. With mIF, individual cell phenotypes, as well as different cell subpopulations and even rare cell populations, can be identified with extraordinary fidelity according to the expression of antibodies in an mIF panel. This technology therefore has an important role in translational oncology studies and probably will be incorporated in the clinic. The expression of different biomarkers of interest can be examined at the tissue or individual cell level using mIF, providing information about cell phenotypes, distribution of cells, and cell biological processes in tumor samples. At present, the main challenge in spatial analysis is choosing the most appropriate method for extracting meaningful information about cell distribution from mIF images for analysis. Thus, knowing how the spatial interaction between cells in the tumor encodes clinical information is important. Exploratory analysis of the location of the cell phenotypes using point patterns of distribution is used to calculate metrics summarizing the distances at which cells are processed and the interpretation of those distances. Various methods can be used to analyze cellular distribution in an mIF image, and several mathematical functions can be applied to identify the most elemental relationships between the spatial analysis of cells in the image and established patterns of cellular distribution in tumor samples. The aim of this review is to describe the characteristics of mIF image analysis at different levels, including spatial distribution of cell populations and cellular distribution patterns, that can increase understanding of the tumor microenvironment.

Significance tests for analyzing gene expression data with small sample sizes

MOTIVATION

Under two biologically different conditions, we are often interested in identifying differentially expressed genes. It is usually the case that the assumption of equal variances on the two groups is violated for many genes where a large number of them are required to be filtered or ranked. In these cases, exact tests are unavailable and the Welch's approximate test is most reliable one. The Welch's test involves two layers of approximations: approximating the distribution of the statistic by a t-distribution, which in turn depends on approximate degrees of freedom. This study attempts to improve upon Welch's approximate test by avoiding one layer of approximation.

RESULTS

We introduce a new distribution that generalizes the t-distribution and propose a Monte Carlo based test that uses only one layer of approximation for statistical inferences. Experimental results based on extensive simulation studies show that the Monte Carol based tests enhance the statistical power and performs better than Welch's t-approximation, especially when the equal variance assumption is not met and the sample size of the sample with a larger variance is smaller. We analyzed two gene-expression datasets, namely the childhood acute lymphoblastic leukemia gene-expression dataset with 22 283 genes and Golden Spike dataset produced by a controlled experiment with 13 966 genes. The new test identified additional genes of interest in both datasets. Some of these genes have been proven to play important roles in medical literature.

AVAILABILITY AND IMPLEMENTATION

R scripts and the R package mcBFtest is available in CRAN and to reproduce all reported results are available at the GitHub repository, https://github.com/iullah1980/MCTcodes.

SUPPLEMENTARY INFORMATION

Supplementary data is available at Bioinformatics online.