Sergei Turovets

EEG source localization: Sensor density and head surface coverage

BACKGROUND The accuracy of EEG source localization depends on a sufficient sampling of the surface potential field, an accurate conducting volume estimation (head model), and a suitable and well-understood inverse technique. The goal of the present study is to examine the effect of sampling density and coverage on the ability to accurately localize sources, using common linear inverse weight techniques, at different depths. Several inverse methods are examined, using the popular head conductivity. NEW METHOD Simulation studies were employed to examine the effect of spatial sampling of the potential field at the head surface, in terms of sensor density and coverage of the inferior and superior head regions. In addition, the effects of sensor density and coverage are investigated in the source localization of epileptiform EEG. RESULTS Greater sensor density improves source localization accuracy. Moreover, across all sampling density and inverse methods, adding samples on the inferior surface improves the accuracy of source estimates at all depths. COMPARISON WITH EXISTING METHODS More accurate source localization of EEG data can be achieved with high spatial sampling of the head surface electrodes. CONCLUSIONS The most accurate source localization is obtained when the voltage surface is densely sampled over both the superior and inferior surfaces.

Ermakov Hamiltonian systems in nonlinear optics of elliptic Gaussian beams

Abstract It is shown that the systems of equations describing the propagation of elliptic Gaussian beams in a nonlinear medium are Ermakov Hamiltonian systems. It is demonstrated that these systems are completely integrable. The condition under which any Ermakov system is also a Hamiltonian system is determined.

Computational modeling of human head conductivity

The computational environment for estimation of unknown regional electrical conductivities of the human head, based on realistic geometry from segmented MRI up to 2563 resolution, is described. A finite difference alternating direction implicit (ADI) algorithm, parallelized using OpenMP, is used to solve the forward problem describing the electrical field distribution throughout the head given known electrical sources. A simplex search in the multi-dimensional parameter space of tissue conductivities is conducted in parallel using a distributed system of heterogeneous computational resources. The theoretical and computational formulation of the problem is presented. Results from test studies are provided, comparing retrieved conductivities to known solutions from simulation. Performance statistics are also given showing both the scaling of the forward problem and the performance dynamics of the distributed search.

Conductivity Analysis for High-Resolution EEG

We describe a technique for noninvasive conductivity estimation of the human head tissues in vivo. It is based on the bounded electrical impedance tomography (bEIT) measurements procedure and realistically shaped high-resolution finite difference model (FDM) of the human head geometry composed from the subject specific co-registered CT and MRI. The first experimental results with two subjects demonstrate feasibility of such technology.

Optimization of focality and direction in dense electrode array transcranial direct current stimulation (tDCS)

OBJECTIVE Transcranial direct current stimulation (tDCS) aims to alter brain function non-invasively via electrodes placed on the scalp. Conventional tDCS uses two relatively large patch electrodes to deliver electrical current to the brain region of interest (ROI). Recent studies have shown that using dense arrays containing up to 512 smaller electrodes may increase the precision of targeting ROIs. However, this creates a need for methods to determine effective and safe stimulus patterns as the number of degrees of freedom is much higher with such arrays. Several approaches to this problem have appeared in the literature. In this paper, we describe a new method for calculating optimal electrode stimulus patterns for targeted and directional modulation in dense array tDCS which differs in some important aspects with methods reported to date. APPROACH We optimize stimulus pattern of dense arrays with fixed electrode placement to maximize the current density in a particular direction in the ROI. We impose a flexible set of safety constraints on the current power in the brain, individual electrode currents, and total injected current, to protect subject safety. The proposed optimization problem is convex and thus efficiently solved using existing optimization software to find unique and globally optimal electrode stimulus patterns. MAIN RESULTS Solutions for four anatomical ROIs based on a realistic head model are shown as exemplary results. To illustrate the differences between our approach and previously introduced methods, we compare our method with two of the other leading methods in the literature. We also report on extensive simulations that show the effect of the values chosen for each proposed safety constraint bound on the optimized stimulus patterns. SIGNIFICANCE The proposed optimization approach employs volume based ROIs, easily adapts to different sets of safety constraints, and takes negligible time to compute. An in-depth comparison study gives insight into the relationship between different objective criteria and optimized stimulus patterns. In addition, the analysis of the interaction between optimized stimulus patterns and safety constraint bounds suggests that more precise current localization in the ROI, with improved safety criterion, may be achieved by careful selection of the constraint bounds.

Concurrency in electrical neuroinformatics: parallel computation for studying the volume conduction of brain electrical fields in human head tissues

Advances in human brain neuroimaging for high‐temporal and high‐spatial resolutions will depend on localization of electroencephalography (EEG) signals to their cortex sources. The source localization inverse problem is inherently ill‐posed and depends critically on the modeling of human head electromagnetics. We present a systematic methodology to analyze the main factors and parameters that affect the EEG source‐mapping accuracy. These factors are not independent, and their effect must be evaluated in a unified way. To do so requires significant computational capabilities to explore the problem landscape, quantify uncertainty effects, and evaluate alternative algorithms. Bringing high‐performance computing to this domain is necessary to open new avenues for neuroinformatics research. The head electromagnetics forward problem is the heart of the source localization inverse. We present two parallel algorithms to address tissue inhomogeneity and impedance anisotropy. Highly accurate head modeling environments will enable new research and clinical neuroimaging applications. Cortex‐localized dense‐array EEG analysis is the next‐step in neuroimaging domains such as early childhood reading, understanding of resting‐state brain networks, and models of full brain function. Therapeutic treatments based on neurostimulation will also depend significantly on high‐performance computing integration. Copyright

Instrumentation for low frequency EIT studies of the human head and its validation in phantom experiments

We describe instrumentation for low frequency (< 500 Hz) EIT studies of the human head and its calibration, testing and validation in the phantom experiments. Our EIT system prototype is based on a 256 channel commercial EEG system complimented by the current injection module and lock-in detection software. We have designed and built two types of head phantoms: i) a resistor network and ii) a cylinder tank filled with saline and gel insertions with chemically targeted conductivity values. We have developed a technology for fabricating, handling and storage of agar TX151 gel insertions. Independent and direct conductivity measurements of gel samples have been performed using a HP LCR meter in a four electrode conductivity cell specifically designed and built for this purpose. Measurements of saline conductivity were done with commercially available salinity / conductivity meters. Our inverse conductivity estimates in the phantom experiments with EIDORS and in-house software cross-validate the viability of the EIT-EEG system.

Use of Parallel Simulated Annealing for Computational Modeling of Human Head Conductivity

We present a parallel computational environment used to determine conductivity properties of human head tissues when the effects of skull inhomogeneities are modeled. The environment employs a parallel simulated annealing algorithm to overcome poor convergence rates of the simplex method for larger numbers of head tissues required for accurate modeling of electromagnetic dynamics of brain function. To properly account for skull inhomogeneities, parcellation of skull parts is necessary. The multi-level parallel simulated annealing algorithm is described and performance results presented. Significant improvements in both convergence rate and speedup are achieved. The simulated annealing algorithm was successful in extracting conductivity values for up to thirteen head tissues without showing computational deficiency.

Anatomically Constrained Conductivity Estimation of the Human Head Tissues in Vivo: Computational Procedure and Preliminary Experiments

We have shown that using parameterized EIT measurements procedure and realistically shaped highresolution finite difference models (FDM) of the human head based on the subject specific co-registered CT and MRI scans, it was possible to extract up to 13 head tissues conductivities in simulations with synthetic data. We have used the multi-start downhill simplex and simulated annealing algorithms depending on the number of unknowns in inverse search. The procedure describes parcellation of a skull into 10–12 anatomically relevant bone plates and provides the skull conductivity inhomogeneities information in the forward solver for the EEG inverse problem. The preliminary results of the first experiments performed on a human subject are also reported.

Induced superradiance in a thin film of two-level atoms

Abstract The transmission and reflection of a thin film of inverted two-level atoms is investigated numerically and analytically. The case of normal incidence of rectangular and secanthyperbolic-shape pulses is considered. It is shown, that the induced superradiance effect occurs due to the initial excited-state atoms. The time dependence of the transmitted and reflected pulses has been found.