Changes in Brain Resting-state Functional Connectivity Associated with Peripheral Nerve Block: A Pilot Study.

BACKGROUND: Limited information exists on the effects of temporary functional deafferentation (TFD) on brain activity after peripheral nerve block (PNB) in healthy humans. Increasingly, resting-state functional connectivity (RSFC) is being used to study brain activity and organization. The purpose of this study was to test the hypothesis that TFD through PNB will influence changes in RSFC plasticity in central sensorimotor functional brain networks in healthy human participants. METHODS: The authors achieved TFD using a supraclavicular PNB model with 10 healthy human participants undergoing functional connectivity magnetic resonance imaging before PNB, during active PNB, and during PNB recovery. RSFC differences among study conditions were determined by multiple-comparison-corrected (false discovery rate-corrected P value less than 0.05) random-effects, between-condition, and seed-to-voxel analyses using the left and right manual motor regions. RESULTS: The results of this pilot study demonstrated disruption of interhemispheric left-to-right manual motor region RSFC (e.g., mean Fisher-transformed z [effect size] at pre-PNB 1.05 vs. 0.55 during PNB) but preservation of intrahemispheric RSFC of these regions during PNB. Additionally, there was increased RSFC between the left motor region of interest (PNB-affected area) and bilateral higher order visual cortex regions after clinical PNB resolution (e.g., Fisher z between left motor region of interest and right and left lingual gyrus regions during PNB, -0.1 and -0.6 vs. 0.22 and 0.18 after PNB resolution, respectively). CONCLUSIONS: This pilot study provides evidence that PNB has features consistent with other models of deafferentation, making it a potentially useful approach to investigate brain plasticity. The findings provide insight into RSFC of sensorimotor functional brain networks during PNB and PNB recovery and support modulation of the sensory-motor integration feedback loop as a mechanism for explaining the behavioral correlates of peripherally induced TFD through PNB.

Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.