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

Spatial filtering in electrical impedance tomography

We propose a new method to localize electrical conductivity changes in the human head using Electrical Impedance Tomography (EIT). In EIT, a localized conductivity change produces a change in the electric potential distribution which is equivalent to a potential generated by a dipole at the same location. We propose to estimate the location of conductivity changes with the same techniques used to solve the Electroencephalography source localization problem. In particular, we show an adaptation of the Linear Constrain Minimum Variance Beamforming technique to perform this estimation. We simulate a localized 10% conductivity change in a realistic model of the human head to apply the method. Results show that depending on the noise level, the method can accurately localize the conductivity change.Laboratorio de Electrónica Industrial, Control e InstrumentaciónFacultad de Ingenierí

A Bayesian Technique for Real and Integer Parameters Estimation in Linear Models and its Application to GNSS High Precision Positioning

A novel Bayesian technique for the joint estimation of real and integer parameters in a linear measurement model is presented. The integer parameters take values on a finite set, and the real ones are assumed to be a Gaussian random vector. The posterior distribution of these parameters is sequentially determined as new measurements are incorporated. This is a mixed distribution with a Gaussian continuous part and a discrete one. Estimators for the integer and real parameters are derived from this posterior distribution. A Maximum A Posteriori (MAP) estimator modified with the addition of a confidence threshold is used for the integer part and a Minimum Mean Squared Error (MMSE) is used for the real parameters. Two different cases are addressed: i) both real and integer parameters are time invariant and ii) the integer parameters are time invariant but the real ones are time varying. Our technique is applied to the GNSS carrier phase ambiguity resolution problem, that is key for high precision positioning applications. The good performance of the proposed technique is illustrated through simulations in different scenarios where different kind of measurements as well as different satellite visibility conditions are considered. Comparisons with state-of-the-art ambiguity solving algorithms confirm performance improvement. The new method is shown to be useful not only in the estimation stage but also for validating the estimates ensuring a predefined success rate through proper threshold selection.Facultad de Ingenierí

A robust orthogonal adaptive approach to SISO deconvolution

This paper formulates in a common framework some results from the fields of robust filtering, function approximation with orthogonal basis, and adaptive filtering, and applies them for the design of a general deconvolution processor for SISO systems. The processor is designed to be robust to small parametric uncertainties in the system model, with a partially adaptive orthogonal structure. A simple gradient type of adaptive algorithm is applied to update the coefficients that linearly combine the fixed robust basis functions used to represent the deconvolver. The advantages of the design are inherited from the mentioned fields: low sensitivity to parameter uncertainty in the system model, good numerical and structural behaviour, and the capability of tracking changes in the systems dynamics. The linear equalization of a simple ADSL channel model is presented as an example including comparisons between the optimal nominal, adaptive FIR, and the proposed design.Facultad de IngenieríaComisión de Investigaciones Científicas de la provincia de Buenos Aire

Estimation of electrical conductivity of a layered spherical head model using electrical impedance tomography

Electrical Impedance Tomography (EIT) is a non-invasive method that aims to create an electrical conductivity map of a volume. In particular, it can be applied to study the human head. The method consists on the injection of an unperceptive and known current through two electrodes attached to the scalp, and the measurement of the resulting electric potential distribution at an array of sensors also placed on the scalp. In this work, we propose a parametric estimation of the brain, scalp and skull conductivities using EIT over an spherical model of the head. The forward problem involves the computation of the electric potential on the surface, for given the conductivities and the injection electrode positions, while the inverse problem consists on estimating the conductivities given the sensor measurements. In this study, the analytical solution to the forward problem based on a three layer spherical model is first described. Then, some measurements are simulated adding white noise to the solutions and the inverse problem is solved in order to estimate the brain, skull and scalp conductivity relations. This is done with a least squares approach and the Nelder-Mead multidimensional unconstrained nonlinear minimization method.Facultad de Ingenierí

Estimation of electrical conductivity of a layered spherical head model using electrical impedance tomography

Electrical Impedance Tomography (EIT) is a non-invasive method that aims to create an electrical conductivity map of a volume. In particular, it can be applied to study the human head. The method consists on the injection of an unperceptive and known current through two electrodes attached to the scalp, and the measurement of the resulting electric potential distribution at an array of sensors also placed on the scalp. In this work, we propose a parametric estimation of the brain, scalp and skull conductivities using EIT over an spherical model of the head. The forward problem involves the computation of the electric potential on the surface, for given the conductivities and the injection electrode positions, while the inverse problem consists on estimating the conductivities given the sensor measurements. In this study, the analytical solution to the forward problem based on a three layer spherical model is first described. Then, some measurements are simulated adding white noise to the solutions and the inverse problem is solved in order to estimate the brain, skull and scalp conductivity relations. This is done with a least squares approach and the Nelder-Mead multidimensional unconstrained nonlinear minimization method.Facultad de Ingenierí

Digital DS-CDMA detection in impulsive noise: base band vs. band-pass nonlinear processing

In the context of DS-CDMA detection, a digital base-band model for the received signal after chip-matched filtering, is often adopted. Nonlinear treatment of these samples for robust detection in impulsive environments has been already proposed. In this paper we study the advantages of band-pass nonlinear detection schemes for DS-CDMA receivers, over those in base-band. We consider for both schemes i) an impulsive noise model with independent α-stable distributed sequences and ii) a hard-limiter as memoryless nonlinearity. Probability of error and asymptotic relative efficiency expressions are given, with simulations that validate them. Results shown that band-pass nonlinear detection is preferable.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Spatial filtering in electrical impedance tomography

We propose a new method to localize electrical conductivity changes in the human head using Electrical Impedance Tomography (EIT). In EIT, a localized conductivity change produces a change in the electric potential distribution which is equivalent to a potential generated by a dipole at the same location. We propose to estimate the location of conductivity changes with the same techniques used to solve the Electroencephalography source localization problem. In particular, we show an adaptation of the Linear Constrain Minimum Variance Beamforming technique to perform this estimation. We simulate a localized 10% conductivity change in a realistic model of the human head to apply the method. Results show that depending on the noise level, the method can accurately localize the conductivity change.Laboratorio de Electrónica Industrial, Control e InstrumentaciónFacultad de Ingenierí

A Bayesian Technique for Real and Integer Parameters Estimation in Linear Models and its Application to GNSS High Precision Positioning

A novel Bayesian technique for the joint estimation of real and integer parameters in a linear measurement model is presented. The integer parameters take values on a finite set, and the real ones are assumed to be a Gaussian random vector. The posterior distribution of these parameters is sequentially determined as new measurements are incorporated. This is a mixed distribution with a Gaussian continuous part and a discrete one. Estimators for the integer and real parameters are derived from this posterior distribution. A Maximum A Posteriori (MAP) estimator modified with the addition of a confidence threshold is used for the integer part and a Minimum Mean Squared Error (MMSE) is used for the real parameters. Two different cases are addressed: i) both real and integer parameters are time invariant and ii) the integer parameters are time invariant but the real ones are time varying. Our technique is applied to the GNSS carrier phase ambiguity resolution problem, that is key for high precision positioning applications. The good performance of the proposed technique is illustrated through simulations in different scenarios where different kind of measurements as well as different satellite visibility conditions are considered. Comparisons with state-of-the-art ambiguity solving algorithms confirm performance improvement. The new method is shown to be useful not only in the estimation stage but also for validating the estimates ensuring a predefined success rate through proper threshold selection

A Bayesian Technique for Real and Integer Parameters Estimation in Linear Models and its Application to GNSS High Precision Positioning

A novel Bayesian technique for the joint estimation of real and integer parameters in a linear measurement model is presented. The integer parameters take values on a finite set, and the real ones are assumed to be a Gaussian random vector. The posterior distribution of these parameters is sequentially determined as new measurements are incorporated. This is a mixed distribution with a Gaussian continuous part and a discrete one. Estimators for the integer and real parameters are derived from this posterior distribution. A Maximum A Posteriori (MAP) estimator modified with the addition of a confidence threshold is used for the integer part and a Minimum Mean Squared Error (MMSE) is used for the real parameters. Two different cases are addressed: i) both real and integer parameters are time invariant and ii) the integer parameters are time invariant but the real ones are time varying. Our technique is applied to the GNSS carrier phase ambiguity resolution problem, that is key for high precision positioning applications. The good performance of the proposed technique is illustrated through simulations in different scenarios where different kind of measurements as well as different satellite visibility conditions are considered. Comparisons with state-of-the-art ambiguity solving algorithms confirm performance improvement. The new method is shown to be useful not only in the estimation stage but also for validating the estimates ensuring a predefined success rate through proper threshold selection.Facultad de Ingenierí