Nonlinear Dynamic Modeling, Simulation And Characterization Of The Mesoscale Neuron-electrode Interface

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signalto-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently iv proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the v planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research

Study of microvascular blood flow modulated by electroosmosis

An analytical study of microvascular non-Newtonian blood flow is conducted incorporating the electro-osmosis phenomenon. Blood is considered as a Bingham rheological aqueous ionic solution. An externally applied static axial electrical field is imposed on the system. The Poisson-Boltzmann equation for electrical potential distribution is implemented to accommodate the electrical double layer (EDL) in the microvascular regime. With long wavelength, lubrication and Debye-Hückel approximations, the boundary value problem is rendered non-dimensional. Analytical solutions are derived for the axial velocity, volumetric flow rate, pressure gradient, volumetric flow rate, averaged volumetric flow rate along one time-period, pressure rise along one wavelength and stream function. A plug width is featured in the solutions. Via symbolic software (MathematicaTM), graphical plots are generated for the influence of Bingham plug flow width parameter, electrical Debye length (thickness) and Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) on the key hydrodynamic variables. An increase in plug flow width is observed to accelerate the axial flow, enhance volumetric flow rate and has a varied influence on the pressure rise depending on whether the flow is in the free pumping or pumping region. Increasing electrical Debye length consistently enhances axial flow, volumetric flow rate and also pressure rise (at any value of volumetric flow rate)

Effectiveness of flow obstructions in enhancing electro-osmotic flow

In this paper the influence of obstructions on micro-channel electroosmotic flow is investigated for the first time. To carry out such a study, regular obstructions are introduced into micro-channels and flow rates are numerically calculated. The effect of channel width on flow rates is analysed on both free and obstructed channels. The solid material considered for channel walls and obstructions is silicon and the electrolyte is de-ionised water. The parameters studied include channel width, obstruction size and effective porosity of the channel. The effective porosity is varied between 0.4 and 0.8 depending on other chosen parameters. The results clearly demonstrate that, under the analysed conditions, introduction of obstructions into channels wider than100 micro meters enhances the flow rate induced by electro-osmosis

Modelling electro-osmotic flow in porous media: a review

PurposeThis paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.Design/methodology/approachModelling electro-osmosis in fluid systems without solid particles has been firstly introduced. Then, after a brief description of the existing approaches for porous media modelling, EOF in porous media has been considered by analysing the main contributions to the development of this topic.FindingsThe analysis of literature has highlighted the absence of an universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.Originality/valueFor the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed in order to provide detailed indications for future works concerning this topic

Simulations of charged droplet collisions in shear flow

Acknowledgments This research has been enabled by the use of computing resources provided by WestGrid, the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca), and Compute/Calcul Canada. O.S. thanks NSERC for an Alexander Graham Bell Canada Graduate Scholarship.Peer reviewedPostprin

Charge relaxation dynamics of an electrolytic nanocapacitor

Understanding ion relaxation dynamics in overlapping electric double layers (EDLs) is critical for the development of efficient nanotechnology based electrochemical energy storage, electrochemomechanical energy conversion and bioelectrochemical sensing devices as well as controlled synthesis of nanostructured materials. Here, a Lattice Boltzmann (LB) method is employed to simulate an electrolytic nanocapacitor subjected to a step potential at t = 0 for various degrees of EDL overlap, solvent viscosities, ratios of cation to anion diffusivity and electrode separations. The use of a novel, continuously varying and Galilean invariant, molecular speed dependent relaxation time (MSDRT) with the LB equation recovers a correct microscopic description of the molecular collision phenomena and enhances the stability of the LB algorithm. Results for large EDL overlaps indicated oscillatory behavior for the ionic current density in contrast to monotonic relaxation to equilibrium for low EDL overlaps. Further, at low solvent viscosities and large EDL overlaps, anomalous plasma-like spatial oscillations of the electric field were observed that appeared to be purely an effect of nanoscale confinement. Employing MSDRT in our simulations enabled a modeling of the fundamental physics of the transient charge relaxation dynamics in electrochemical systems operating away from equilibrium wherein Nernst-Einstein relation is known to be violated.Comment: Accepted for publication in the Journal of Physical Chemistry C on October 30 2014. Supplementary info available free of charge via the Internet at http://pubs.acs.org. Revised version includes more details on the computation of the molecular speed dependent relaxation time (MSDRT) and emphasizes the Galilean invariance of the computed MSDR