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

Generalized Volterra-Wiener and surrogate data methods for complex time series analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 133-150).This thesis describes the current state-of-the-art in nonlinear time series analysis, bringing together approaches from a broad range of disciplines including the non-linear dynamical systems, nonlinear modeling theory, time-series hypothesis testing, information theory, and self-similarity. We stress mathematical and qualitative relationships between key algorithms in the respective disciplines in addition to describing new robust approaches to solving classically intractable problems. Part I presents a comprehensive review of various classical approaches to time series analysis from both deterministic and stochastic points of view. We focus on using these classical methods for quantification of complexity in addition to proposing a unified approach to complexity quantification encapsulating several previous approaches. Part II presents robust modern tools for time series analysis including surrogate data and Volterra-Wiener modeling. We describe new algorithms converging the two approaches that provide both a sensitive test for nonlinear dynamics and a noise-robust metric for chaos intensity.by Akhil Shashidhar.M.Eng

Nonlinear, multiple-input modeling of cerebral autoregulation using Volterra Kernel estimation

Autoregulation refers to the automatic adjustment of blood flow to supply the required oxygen and glucose and remove waste, in proportion to the tissue’s requirement at any instant of time. For the brain, cerebral autoregulation is an active process by which cerebral blood flow is controlled at an approximately steady level despite changes in the arterial blood pressure. Robust assessment of the cerebral autoregulation by a model that characterizes this system has been the goal of many studies, searching for techniques that can be used in clinical scenarios to detect potentially dangerous impairment of control. Multiple input, single output (MISO) models can be used to assess autoregulation, and system parameters can be estimated from spontaneous beat-to-beat variations in arterial blood pressure (ABP) and breath-by-breath end-tidal carbon dioxide (PETCO2) as inputs, and cerebral blood flow velocity (CBFV) as the output .In this study a non-linear, multivariate approach, based on Volterra-type kernel estimation models is employed. The results are compared with linear models as well as nonlinear single-input single-output (SISO) models. The normalized mean squared error was used as the criteria of performance of each model in assessing cerebral autoregulation. Our simulation results indicate that for relatively short signals (around 300 sec), nonlinear, multiple-input models based on Volterra systems performed best, though the benefit varied considerably between subjects. When using a fixed model for all recordings, a linear SISO model with ABP as input provided the smallest average modeling error.Keywords- Cerebral Autoregulation, Non-linear analysis, physiological systems, Blood pressure, CO2, Blood flow, Volterra Kernel Models, Laguerre- Volterra networks (LVNs)

Nanoscale Nonlinear Dynamic Characterization of the Neuron-Electrode Junction

Extracellular recordings from neurons using microelectrode and field effect transistor arrays suffer from many problems including low signal to noise ratio, signal attenuation due to counter-ion diffusion from the bulk extracellular medium and a modification of the shape of the cell-generated potentials due to the presence of a highly dispersive dielectric medium in the cell-electrode cleft. Attempts to date to study the neuron-electrode interface have focused on point or area contact linear-equivalent-circuit models. We present here the results obtained from a \u27data-true\u27 nonlinear dynamic characterization of the neuron-electrode junction using Volterra-Wiener modeling. For the characterization, NG108-15 cells were cultured on microelectrode arrays and stimulated with broadband Gaussian white noise under voltage clamp mode. A Volterra-Wiener model was then estimated using the input signal and the extracellular signal recorded on the microelectrode. The existence of the second order Wiener kernel confirmed that the recorded extracellular signal had a nonlinear component. The verification of the estimated model was carried out by employing the intracellular action potential as an input to the Volterra-Wiener model and comparing the predicted extracellular response with the corresponding extracellular signal recorded on the microelectrode. We believe that a \u27data-true\u27 Volterra-Wiener model of the neuron-electrode junction shall not only facilitate a direct insight into the physicochemical processes taking place at the interface during signal transduction but will also allow one to evolve strategies for engineering the neuron-electrode interface using surface chemical modification of the microelectrodes

Nanoscale Nonlinear Dynamic Characterization Of The Neuron-Electrode Junction

Extracellular recordings from neurons using microelectrode and field effect transistor arrays suffer from many problems including low signal to noise ratio, signal attenuation due to counter-ion diffusion from the bulk extracellular medium and a modification of the shape of the cell-generated potentials due to the presence of a highly dispersive dielectric medium in the cell-electrode cleft. Attempts to date to study the neuron-electrode interface have focused on point or area contact linear-equivalent-circuit models. We present here the results obtained from a \u27data-true\u27 nonlinear dynamic characterization of the neuron-electrode junction using Volterra-Wiener modeling. For the characterization, NG108-15 cells were cultured on microelectrode arrays and stimulated with broadband Gaussian white noise under voltage clamp mode. A Volterra-Wiener model was then estimated using the input signal and the extracellular signal recorded on the microelectrode. The existence of the second order Wiener kernel confirmed that the recorded extracellular signal had a nonlinear component. The verification of the estimated model was carried out by employing the intracellular action potential as an input to the Volterra-Wiener model and comparing the predicted extracellular response with the corresponding extracellular signal recorded on the microelectrode. We believe that a \u27data-true\u27 Volterra-Wiener model of the neuron-electrode junction shall not only facilitate a direct insight into the physicochemical processes taking place at the interface during signal transduction but will also allow one to evolve strategies for engineering the neuron-electrode interface using surface chemical modification of the microelectrodes. Copyright © 2008 American Scientific Publishers All rights reserved