Conductance of porous media depends on external electric fields

In obstacle-filled media, such as extracellular or intracellular lumen of brain tissue, effective ion diffusion permeability is a key determinant of electrogenic reactions. Although this diffusion permeability is thought to depend entirely on structural features of the medium, such as porosity and tortuosity, brain tissue shows prominent non-ohmic properties, the origins of which remain poorly understood. Here, we explore Monte Carlo simulations of ion diffusion in a space filled with overlapping spheres, to predict that diffusion permeability of such media decreases with stronger external electric fields. This dependence increases with lower medium porosity while decreasing with radial (2D or 3D) compared to homogenous (1D) fields. We test our predictions empirically in an electrolyte chamber filled with microscopic glass spheres and find good correspondence with our predictions. A theoretical insight relates this phenomenon to a disproportionately increased dwell time of diffusing ions at potential barriers (or traps) representing geometric obstacles, when the field strength increases. The dependence of medium ion-diffusion permeability on electric field could be important for understanding conductivity properties of porous materials, in particular for the accurate interpretation of electric activity recordings in brain tissue

A unified model of electroporation and molecular transport

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, February 2011."February 2011." Cataloged from PDF version of thesis.Includes bibliographical references.Biological membranes form transient, conductive pores in response to elevated transmembrane voltage, a phenomenon termed electroporation. These pores facilitate electrical and molecular transport across cell membranes that are normally impermeable. By applying pulsed electric fields to cells, electroporation can be used to deliver nucleic acids, drugs, and other molecules into cells, making it a powerful research tool. Because of its widely demonstrated utility for in vitro applications, researchers are increasingly investigating related in vivo clinical applications of electroporation, such as gene delivery, drug delivery, and tissue ablation. In this thesis, we describe a quantitative, mechanistic model of electroporation and concomitant molecular transport that can be used for guiding and interpreting electroporation experiments and applications. The model comprises coupled mathematical descriptions of electrical transport, electrodiffusive molecular transport, and pore dynamics. Where possible, each of these components is independently validated against experimental results in the literature. We determine the response of a discretized cell system to an applied electric pulse by assembling the discretized transport relations into a large system of nonlinear differential equations that is efficiently solved and analyzed with MATLAB. We validate the model by replicating in silico two sets of experiments in the literature that measure electroporation-mediated transport of fluorescent probes. The model predictions of molecular uptake are in excellent agreement with these experimental measurements, for which the applied electric pulses collectively span nearly three orders of magnitude in pulse duration (50 ts -20 ms) and an order of magnitude in pulse magnitude (0.3 -3 kV/cm). The advantages of our theoretical approach are the ability to (1) analyze in silico the same quantities that are measured by experimental studies in vitro, (2) simulate electroporation dynamics that are difficult to assess experimentally, and (3) quickly screen a wide array of electric pulse waveforms for particular applications. We believe that our approach will contribute to a greater understanding of the mechanisms of electroporation and provide an in silico platform for guiding new experiments and applications.by Kyle Christopher Smith.Ph.D

The Application of Electric Fields in Biology and Medicine

We discuss a wide range of applications of electric fields in biology and medicine. For example, physiological strength (<500 V/m) fields are used to improve the healing of wounds, the stimulation of neurons, and the positioning and activation of cells on scaffolds for tissue engineering purposes. The brief, strong pulses used in electroporation are used to improve the insertion of drugs into tumors and DNA into cell nuclei. The references direct readers to detailed reviews of these applications. The mechanism by which cells detect physiological strength fields is not well understood. We also describe a field-transduction mechanism that shares features common to the detection of fluid shear by cells. We then provide some experimental evidence that supports our model

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

New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric permittivities show a contrast compared to the electric permittivity of the electrolyte phase. Our main result is the derivation of convenient low-dimensional equations, that is, of effective macroscopic porous media Poisson-Nernst-Planck equations, which reliably describe ionic transport. The contrast in the electric permittivities between liquid and solid phase and the heterogeneity of the porous medium induce strongly oscillating electric potentials (fields). In order to account for this special physical scenario, we introduce a modified asymptotic multiple-scale expansion which takes advantage of the nonlinearly coupled structure of the ionic transport equations. This allows for a systematic upscaling resulting in a new effective porous medium formulation which shows a new transport term on the macroscale. Solvability of all arising equations is rigorously verified. This emergence of a new transport term indicates promising physical insights into the influence of the microscale material properties on the macroscale. Hence, systematic upscaling strategies provide a source and a prospective tool to capitalize intrinsic scale effects for scientific, engineering, and industrial applications

Modeling cell and tissue electroporation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 201-213).Large, pulsed electric fields are becoming an increasingly important tool in drug delivery, gene delivery, and apoptosis induction. Nonetheless, much remains unknown about the fundamental mechanisms by which large electric fields interact with cells and tissue, in part because many critical features of the cell and tissue responses occur on time and length scales that are difficult to assess experimentally. Therefore, sophisticated models are needed to further understanding of the basic mechanisms of interaction. Electroporation, in which transient, aqueous pores form in lipid bilayers, is one fundamental mechanism by which large electric fields may alter biological systems. Here cell and tissue electroporation models are presented that are based on the asymptotic model of electroporation and the new mesh transport network method (MTNM), which utilizes equivalent circuit networks to simulate nonlinear, coupled transport phenomena. The cell system simulations show that small magnitude (0.1 MV/m), long duration (100 [mu]s) pulses result in conventional electroporation, in which pores form in only the plasma membrane, while large magnitude (10 MV/m), short duration (10 ns) pulses result in supra-electroporation, in which pores form in the plasma membrane and organelle membranes.(cont.) The organelle membrane electroporation may be a primary mechanism by which large magnitude, short duration pulses lead to complex, experimentally observed responses, including apoptosis. The tissue system simulations show that dynamic spatial shifts in the electric field accompany electroporation. For certain pulses, the shifting electric field can lead to quite spatially extensive tissue electroporation. The models presented here offer new insights into the dynamic electrical responses of cells and tissue to pulses of widely varying strength and duration and will contribute to the development of new therapies and biotechnologies based on electroporation.by Kile Christopher Smith.S.M

Impact of brain tissue filtering on neurostimulation fields: A modeling study

Electrical neurostimulation techniques, such as deep brain stimulation (DBS) and transcranial magnetic stimulation (TMS), are increasingly used in the neurosciences, e.g., for studying brain function, and for neurotherapeutics, e.g., for treating depression, epilepsy, and Parkinson's disease. The characterization of electrical properties of brain tissue has guided our fundamental understanding and application of these methods, from electrophysiologic theory to clinical dosing-metrics. Nonetheless, prior computational models have primarily relied on ex-vivo impedance measurements. We recorded the in-vivo impedances of brain tissues during neurosurgical procedures and used these results to construct MRI guided computational models of TMS and DBS neurostimulatory fields and conductance-based models of neurons exposed to stimulation. We demonstrated that tissues carry neurostimulation currents through frequency dependent resistive and capacitive properties not typically accounted for by past neurostimulation modeling work. We show that these fundamental brain tissue properties can have significant effects on the neurostimulatory-fields (capacitive and resistive current composition and spatial/temporal dynamics) and neural responses (stimulation threshold, ionic currents, and membrane dynamics). These findings highlight the importance of tissue impedance properties on neurostimulation and impact our understanding of the biological mechanisms and technological potential of neurostimulatory methods.United States. Defense Advanced Research Projects Agency (Contract W31P4Q-09-C-0117)National Institute of Neurological Disorders and Stroke (U.S.) (Award R43NS062530)National Institute of Neurological Disorders and Stroke (U.S.) (Award 1R44NS080632

Quartz-mems: Wet chemical etching assisted by electromagnetic energy sources for the development of quartz crystal to be used for microelectromechanical systems

Quartz crystal resonators have been the most commonly used timing devices to date. Today\u27s timing market requires devices to be as small as possible and consume smaller amounts of energy. Because of the market demand, many startup companies have formed to develop silicon resonators as timing devices. Silicon resonators have poor noise and temperature performance (due to its linear temperature versus frequency coefficient). At the moment the only advantage that silicon resonators have over quartz crystal resonators is a small form factor. The photolithography processing method currently being used in industry is a very tedious task, requiring multiple etching steps and a final frequency trimming step for each individual resonator. The goal of this research was to find a process that could increase the etch rate of quartz crystals beyond the current methods available. This dissertation reports the first results on x-rays assisting the electrochemical etching of quartz crystals in the development of quartz resonators. This process has shown the ability to increase the etch rate of quartz by 27%. The second method explored in this work involves the use of lasers to rapidly etch quartz crystals during the wet etching process. The etch rate with the laser setup can be varied from 3.8 μm/hr to 278 μm/hr. These processes were integrated with a control system used to measure the resonant frequency of each individual resonator to an accuracy of +/- 10ppm. Using two lasers incorporated with the control system allowed for a total etching accuracy of +/- 50ppm for two resonators on the same die