Unification of optimal targeting methods in transcranial electrical stimulation

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how ?optimality? is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.Fil: Fernandez Corazza, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; ArgentinaFil: Turovets, Sergei. University of Oregon; Estados UnidosFil: Muravchik, Carlos Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentin

A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seventissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.Laboratorio de Electrónica Industrial, Control e Instrumentación (LEICI

Main resonances in directly modulated semiconductor lasers: effect of spontaneous emission and gain saturation

Boundaries for the primary saddle-node bifurcations related to the main resonances in pump--modulated laser diodes are obtained via numerical simulation. Our model contains explicitly the gain saturation and spontaneous emission terms and we focus on the effect that these terms have on the large signal modulation regime. We find that the spontaneous emission term strongly modifies the qualitative behavior of the instabilities boundaries, while the gain saturation factor manifests itself in the damping of relaxation oscillations and leads to a simple quantitative shift of boundaries.We acknowledge financial support from DGES (Spain) projects PB97-0141-C02-01, BMF 2000-1 108 and TIC 99-0645. S.I. Turovets acknowledges the fellowship from MEC (Spain).Peer reviewe

Spatial sensitivity of the optimal dose in TES to the skull and scalp conductivity specifications

Introduction:Electrical impedance tomography (EIT) is a non-invasivetechnique that can be used to estimate the scalp and skull conductivityvalues. These values are required for modelling transcranial electricalstimulation (TES) to estimate the current density dose on the brain. Wepreviously found individual EIT estimates for four subjects using detailedhead models [1]. The question we address here is: what?s the impact in TESof using individual EIT estimates versus typical literature values?Methods:Usingfinite element simulations, we computed the maximumpossible TES dose for each element of the grey matter (GM) along itsnormal-to-cortex orientation, assuming afixed current budget of 1mA.Optimal current injection patterns where obtained using the reciprocityoptimization method [2]. The same procedure was followed for modelsusing bEIT estimated (Table I in [1]) and literature (scalp: 300mS/m, skull:8mS/m) conductivity values.Results:At each GM location, we computed the normalized differencebetween the maximum doses obtained with both conductivity specifica-tions. It is known that some deep regions can also get stimulated with TESat intensities of the same order as shallow targets due to the brain ge-ometry and the highly-conductive CSF paths (e.g. [2]). Despite this fact, wefound that TES dose on shallow brain regions, i.e. regions closer to theskull, were more sensitive (~70% difference) to scalp and skull conductivityspecifications than deeper regions (<20%).Discussion:Our results suggest that to estimate TES dose on shallowtargets, it is highly recommended to use scalp and skull conductivity es-timates as accurate as possible. On the other hand, deeper targets - nomatter if their doses are large or small - are less sensitive to scalp and skullconductivity mis-specifications.Fil: Fernandez Corazza, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; ArgentinaFil: Turovets, Sergei. University of Oregon; Estados UnidosFil: Muravchik, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina3rd International Brain Stimulation ConferenceCanadáElsevie

Theory of Main Resonances in Directly Modulated Diode Lasers

Domains of existence of the main resonances in directly modulated semiconductor lasers are obtained by application of quasi-conservative theory. The predictions are compared with numerical results coming from a direct integration of the model equations and with experimental observations reported by other groups. In both cases we find a qualitative good agreement. We consider a model that contains explicitly the gain saturation and spontaneous emission terms. We find that the spontaneous emission strongly modifies the qualitative behavior of the instabilities boundaries, while the gain saturation leads to a simple quantitative shift of boundaries