SCI Publications

OBJECTIVE: The growing clinical acceptance of neurostimulation technology has highlighted the need to accurately predict neural activation as a function of stimulation parameters and electrode design. In this study we evaluate the effects of the tissue and electrode capacitance on the volume of tissue activated (VTA) during deep brain stimulation (DBS).

METHODS: We use a Fourier finite element method (Fourier FEM) to calculate the potential distribution in the tissue medium as a function of time and space simultaneously for a range of stimulus waveforms. The extracellular voltages are then applied to detailed multi-compartment cable models of myelinated axons to determine neural activation. Neural activation volumes are calculated as a function of the stimulation parameters and magnitude of the capacitive components of the electrode-tissue interface.

RESULTS: Inclusion of either electrode or tissue capacitance reduces the VTA compared to electrostatic simulations in a manner dependent on the capacitance magnitude and the stimulation parameters (amplitude and pulse width). Electrostatic simulations with typical DBS parameter settings (-3 V or -3 mA, 90 micros, 130 Hz) overestimate the VTA by approximately 20\% for voltage- or current-controlled stimulation. In addition, strength-duration time constants decrease and more closely match clinical measurements when explicitly accounting for the effects of voltage-controlled stimulation.

CONCLUSIONS: Attempts to quantify the VTA from clinical neurostimulation devices should account for the effects of electrode and tissue capacitance.

SIGNIFICANCE: DBS has rapidly emerged as an effective treatment for movement disorders; however, little is known about the VTA during therapeutic stimulation. In addition, the influence of tissue and electrode capacitance has been largely ignored in previous models of neural stimulation. The results and methodology of this study provide the foundation for the quantitative analysis of the VTA during clinical neurostimulation.

Keywords: Algorithms, Axons, Axons: physiology, Computer Simulation, Deep Brain Stimulation, Electric Capacitance, Electrodes, Extracellular Space, Extracellular Space: physiology, Finite Element Analysis, Implanted, Models, Myelinated, Myelinated: physiology, Nerve Fibers, Neurological, Neurons, Neurons: physiology, Poisson Distribution, Statistical

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component n-dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.

A quantum chemistry–based force field for molecular dynamics simulations of energetic dinitro compounds has been developed, based on intermolecular binding energies, molecular geometries, molecular electrostatic potentials, and conformational energies obtained from quantum chemistry calculations on model compounds. Nonbonded parameters were determined by fitting experimental densities and heats of vaporizations of model compounds. Torsional parameters were parameterized to reproduce accurately the relative conformational energy minima and barriers in 2,2-dinitropropane, di-methoxy di-methyl ether, 2,2-dinitro-3-methoxypropane, and bis(2,2-dinitropropyl)formal. Molecular dynamics simulations using the developed force field accurately reproduce thermodynamic and transport properties of 1,1-dinitroethane, 2,2-dinitropropane, and a eutectic mixture of bis(2,2-dinitropropyl)formal and bis(2,2-dinitropropyl)acetal.

The simulation of pool fires involving complex hydrocarbon fuels requires the development of a simplified surrogate with a limited number of compounds having known oxidation mechanisms. A series of six-component surrogates was developed for the simulation of JP-8 pool fires, and experiments were carried out with a 30-cm-diameter pool fire to allow comparison of the surrogate fuel behavior to that of the jet fuel. The surrogate was shown to simulate the burning rate, radiant heat flux, and sooting tendency of jet fuel under steady-state pool fire conditions. This study also illustrated the transient nature of batch pool fire experiments and highlighted the difficulties associated with formulating an appropriate surrogate to mimic jet fuel behavior over the lifetime of a batch pool fire. These difficulties were shown to arise from fuel compositional changes, with preferential destruction of lighter components and accumulation of heavier components during the course of the fire.

This paper provides a multiscale analytical study of steady incompressible turbulent flow through a channel of either Couette or pressure-driven Poiseuille type. Mathematically, the paper’s two most novel features are that (1) the analysis begins with an underdetermined singular perturbation problem, namely the Reynolds averaged mean momentum balance equation, and (2) it leads to the existence of an infinite number of length scales. (These two features are probably linked, but the linkage will not be pursued.) The paper develops a credible assumption of a mathematical nature which, when added to the initial underdetermined problem, results in a knowledge of almost the complete layer (scaling) structure of the mean velocity and Reynolds stress profiles. This structure in turn provides a lot of other important information about those profiles. The possibility of almost-logarithmic sections of the mean velocity profile is given special attention. The sense in which the length scales are asymptotically proportional to the distance from the wall is determined. Most traditional theoretical analyses of these wall-bounded flows are based ultimately on either the classical overlap hypothesis, mixing length concepts, or similarity arguments. The present paper avoids those approaches and their attendant assumptions. Empirical data are also not used, except that the Reynolds stress takes on positive values. Instead, reasonable criteria are proposed for recognizing scaling layers in the flow, and they are then used to determine the scaling structure and much more information.

Steady Couette and pressure-driven turbulent channel flows have large regions in which the gradients of the viscous and Reynolds stresses are approximately in balance (stress gradient balance regions). In the case of Couette flow, this region occupies the entire channel. Moreover, the relevant features of pressure-driven channel flow throughout the channel can be obtained from those of Couette flow by a simple transformation. It is shown that stress gradient balance regions are characterized by an intrinsic hierarchy of ‘scaling layers’ (analogous to the inner and outer domains), filling out the stress gradient balance region except for locations near the wall. The spatial extent of each scaling layer is found asymptotically to be proportional to its distance from the wall.

There is a rigorous connection between the scaling hierarchy and the mean velocity profile. This connection is through a certain function A(y⁺) defined in terms of the hierarchy, which remains O(1) for all y+. The mean velocity satisfies an exact logarithmic growth law in an interval of the hierarchy if and only if A is constant. Although A is generally not constant in any such interval, it is arguably almost constant under certain circumstances in some regions. These results are obtained completely independently of classical inner/outer/overlap scaling arguments, which require more restrictive assumptions.

The possible physical implications of these theoretical results are discussed.