Reduction of conductivity uncertainty propagations in the inverse problem of EEG source analysis

In computer simulations, the response of a system under study depends on the input parameters. Each of these parameters can be assigned a fixed value or a range of values within the input parameter space for system performance evaluations. Starting from values of the input parameters and a certain given model, the so-called forward problem can be solved that needs to approximate the output of the system. Starting from measurements related to the output of the system model it is possible to determine the state of the system by solving the so-called inverse problem. In the case of a non-linear inverse problem, non-linear minimization techniques need to be used where the forward model is iteratively evaluated for different input parameters. The accuracy of the solution in the inverse problem is however decreased due to the noise available in the measurements and due to uncertainties in the system model. Uncertainties are parameters for which their values are not exactly known and/or that can vary in time and/or depend on the environment. These uncertainties have, for given input parameter values, an influence on the forward problem solution. This forward uncertainty propagation leads then to errors in the inverse solutions because the forward model is iteratively evaluated for recovering the inverse solutions. Until now, it was assumed that the recovery errors could not be reduced. The only option was to either quantify the uncertain parameter values as accurate as possible or to reflect the uncertainty in the inverse solutions, i.e. determination of the region in parameter space wherein the inverse solution is likely to be situated. The overall aim of this thesis was to develop reduction techniques of inverse reconstruction errors so that the inverse problem is solved in a more robust and thus accurate way. Methodologies were specifically developed for electroencephalography (EEG) source analysis. EEG is a non-invasive technique that measures on the scalp of the head, the electric potentials induced by the neuronal activity. EEG has several applications in biomedical engineering and is an important diagnostic tool in clinical neurophysiology. In epilepsy, EEG is used to map brain areas and to receive source localization information that can be used prior to surgical operation. Starting from Maxwell’s equations in their quasi-static formulation and from a physical model of the head, the forward problem predicts the measurements that would be obtained for a given configuration of current sources. The used headmodels in this thesis are multi-layered spherical head models. The neural sources are parameterized by the location and orientation of electrical dipoles. In this thesis, a set of limited number of dipole sources is used as source model leading to a well posed inverse problem. The inverse problem starts from measured EEG data and recovers the locations and orientations of the electrical dipole sources. A loss in accuracy of the recovered neural sources occurs because of noise in the EEG measurements and uncertainties in the forward model. Especially the conductivity values of scalp, skull and brain are not well known since these values are difficult to measure. Moreover, these uncertainties can vary from person to person, in time, etc. In this thesis, novel numerical methods are developed so to provide new approaches in the improvement of spatial accuracy in EEG source analysis, taking into account model uncertainties. Nowadays, the localization of the electrical activity in the brain is still a current and challenging research topic due to the many difficulties arising e.g. in the process of modeling the head and dealing with the not well known conductivity values of its different tissues. Due to uncertainty in the conductivity value of the head tissues, high values of errors are introduced when solving the EEG inverse problem. In order to improve the accuracy of the solution of the inverse problem taking into account the uncertainty of the conductivity values, a new mathematical approach in the definition of the cost function is introduced and new techniques in the iterative scheme of the inverse reconstruction are proposed. The work in this thesis concerns three important phases. In a first stage, we developed a robust methodology for the reduction of errors when reconstructing a single electrical dipole in the case of a single uncertainty. This uncertainty concerns the skull to soft tissue conductivity ratio which is an important parameter in the forward model. This conductivity ratio is difficult to quantify and depends from person to person. The forward model that we employed is a three shell spherical head model where the forward potentials depend on the conductivity ratio. We reformulated the solution of the forward problem by using a Taylor expansion around an actual value of the conductivity ratio which led to a linear model of the solution for the simulated potentials. The introduction of this expanded forward model, led to a sensitivity analysis which provided relevant information for the reconstruction of the sources in EEG source analysis. In order to develop a technique for reducing the errors in inverse solutions, some challenging mathematical questions and computational problems needed to be tackled. We proposed in this thesis the Reduced Conductivity Dependence (RCD) method where we reformulate the traditional cost function and where we incorporated some changes with respect to the iterative scheme. More specifically, in each iteration we include an internal fitting procedure and we propose selection of sensors. The fitting procedure makes it possible to have an as accurate as possible forward model while the selection procedure eliminates the sensors which have the highest sensitivity to the uncertain skull to brain conductivity ratio. Using numerical experiments we showed that errors in reconstructed electrical dipoles are reduced using the RCD methodology in the case of no noise in measurements and in the case of noise in measurements. Moreover, the procedure for the selection of electrodes was thoroughly investigated as well as the influence of the use of different EEG caps (with different number of electrodes). When using traditional reconstruction methods, the number of electrodes has not a high influence on the spatial accuracy of the reconstructed single electrical dipole. However, we showed that when using the RCD methodology the spatial accuracy can be even more increased. This because of the selection procedure that is included within the RCD methodology. In a second stage, we proposed a RCD method that can be applied for the reconstruction of a limited number of dipoles in the case of a single uncertainty. The same ideas were applied onto the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) algorithm. The three shell spherical head model was employed with the skull to brain conductivity ratio as single uncertainty. We showed using numerical experiments that the spatial accuracy of each reconstructed dipole is increased, i.e. reduction of the conductivity dependence of the inverse solutions. Moreover, we illustrated that the use of the RCD-based subspace correlation cost function leads to a high efficiency even for high noise levels. Finally, in a third stage, we developed a RCD methodology for the reduction of errors in the case of multiple uncertainties. We used a five shell spherical head model where conductivity ratios with respect to skull, cerebrospinal fluid, and white matter were uncertain. The cost function as well as the fitting and selection procedure of the RCD method were extended. The numerical experiments showed reductions in the reconstructed electrical dipoles in comparison with the traditional methodology and also compared to the RCD methodology developed for dealing with a single uncertainty

EEG inverse problem solution with minimal influence of the conductivity

In this paper, we propose a novel method that improves the accuracy of the estimation of neural electrical dipoles when solving the EEG inverse problem. A spherical head model is used where we limit the influence of the unknown conductivity brain-skull ratio on the inverse problem.We redefine the cost function that is used in the EEG problem where only useful information is used as input in the inverse problem. In contrast to previous approaches, weighting factors are used where the electrodes are strategically chosen so to reduce the error made on EEG dipole source localization. The proposed method enhances the source localization accuracy from approximately 9mm to 1mm for dipoles near the edge and from 2.1mm to 0.4mm for dipoles near the center of the brain

Precision near-infrared radial velocity instrumentation II: Non-Circular Core Fiber Scrambler

We have built and commissioned a prototype agitated non-circular core fiber scrambler for precision spectroscopic radial velocity measurements in the near-infrared H band. We have collected the first on-sky performance and modal noise tests of these novel fibers in the near-infrared at H and K bands using the CSHELL spectrograph at the NASA InfraRed Telescope Facility (IRTF). We discuss the design behind our novel reverse injection of a red laser for co-alignment of star-light with the fiber tip via a corner cube and visible camera. We summarize the practical details involved in the construction of the fiber scrambler, and the mechanical agitation of the fiber at the telescope. We present radial velocity measurements of a bright standard star taken with and without the fiber scrambler to quantify the relative improvement in the obtainable blaze function stability, the line spread function stability, and the resulting radial velocity precision. We assess the feasibility of applying this illumination stabilization technique to the next generation of near-infrared spectrographs such as iSHELL on IRTF and an upgraded NIRSPEC at Keck. Our results may also be applied in the visible for smaller core diameter fibers where fiber modal noise is a significant factor, such as behind an adaptive optics system or on a small < 1 meter class telescope such as is being pursued by the MINERVA and LCOGT collaborations.Comment: Proceedings of the SPIE Optics and Photonics Conference "Techniques and Instrumentation for Detection of Exoplanets VI" held in San Diego, CA, August 25-29, 201

Retrieval of Precise Radial Velocities from Near-Infrared High Resolution Spectra of Low Mass Stars

Given that low-mass stars have intrinsically low luminosities at optical wavelengths and a propensity for stellar activity, it is advantageous for radial velocity (RV) surveys of these objects to use near-infrared (NIR) wavelengths. In this work we describe and test a novel RV extraction pipeline dedicated to retrieving RVs from low mass stars using NIR spectra taken by the CSHELL spectrograph at the NASA Infrared Telescope Facility, where a methane isotopologue gas cell is used for wavelength calibration. The pipeline minimizes the residuals between the observations and a spectral model composed of templates for the target star, the gas cell, and atmospheric telluric absorption; models of the line spread function, continuum curvature, and sinusoidal fringing; and a parameterization of the wavelength solution. The stellar template is derived iteratively from the science observations themselves without a need for separate observations dedicated to retrieving it. Despite limitations from CSHELL's narrow wavelength range and instrumental systematics, we are able to (1) obtain an RV precision of 35 m/s for the RV standard star GJ 15 A over a time baseline of 817 days, reaching the photon noise limit for our attained SNR, (2) achieve ~3 m/s RV precision for the M giant SV Peg over a baseline of several days and confirm its long-term RV trend due to stellar pulsations, as well as obtain nightly noise floors of ~2 - 6 m/s, and (3) show that our data are consistent with the known masses, periods, and orbital eccentricities of the two most massive planets orbiting GJ 876. Future applications of our pipeline to RV surveys using the next generation of NIR spectrographs, such as iSHELL, will enable the potential detection of Super-Earths and Mini-Neptunes in the habitable zones of M dwarfs.Comment: 64 pages, 28 figures, 5 tables. Accepted for publication in PAS

The detection of a strong episignature for Chung–Jansen syndrome, partially overlapping with Börjeson–Forssman–Lehmann and White–Kernohan syndromes

Chung-Jansen syndrome is a neurodevelopmental disorder characterized by intellectual disability, behavioral problems, obesity and dysmorphic features. It is caused by pathogenic variants in the PHIP gene that encodes for the Pleckstrin homology domain-interacting protein, which is part of an epigenetic modifier protein complex. Therefore, we hypothesized that PHIP haploinsufficiency may impact genome-wide DNA methylation (DNAm). We assessed the DNAm profiles of affected individuals with pathogenic and likely pathogenic PHIP variants with Infinium Methylation EPIC arrays and report a specific and sensitive DNAm episignature biomarker for Chung–Jansen syndrome. In addition, we observed similarities between the methylation profile of Chung–Jansen syndrome and that of functionally related and clinically partially overlapping genetic disorders, White–Kernohan syndrome (caused by variants in DDB1 gene) and Börjeson–Forssman–Lehmann syndrome (caused by variants in PHF6 gene). Based on these observations we also proceeded to develop a common episignature biomarker for these disorders. These newly defined episignatures can be used as part of a multiclass episignature classifier for screening of affected individuals with rare disorders and interpretation of genetic variants of unknown clinical significance, and provide further insights into the common molecular pathophysiology of the clinically-related Chung–Jansen, Börjeson–Forssman–Lehmann and White–Kernohan syndromes.</p

A planet within the debris disk around the pre-main-sequence star AU Microscopii

AU Microscopii (AU Mic) is the second closest pre main sequence star, at a distance of 9.79 parsecs and with an age of 22 million years. AU Mic possesses a relatively rare and spatially resolved3 edge-on debris disk extending from about 35 to 210 astronomical units from the star, and with clumps exhibiting non-Keplerian motion. Detection of newly formed planets around such a star is challenged by the presence of spots, plage, flares and other manifestations of magnetic activity on the star. Here we report observations of a planet transiting AU Mic. The transiting planet, AU Mic b, has an orbital period of 8.46 days, an orbital distance of 0.07 astronomical units, a radius of 0.4 Jupiter radii, and a mass of less than 0.18 Jupiter masses at 3 sigma confidence. Our observations of a planet co-existing with a debris disk offer the opportunity to test the predictions of current models of planet formation and evolution.Comment: Nature, published June 24th [author spelling name fix

A high-precision near-infrared survey for radial velocity variable low-mass stars using CSHELL and a methane gas cell

We present the results of a precise near-infrared (NIR) radial velocity (RV) survey of 32 low-mass stars with spectral types K2-M4 using CSHELL at the NASA InfraRed Telescope Facility in the K band with an isotopologue methane gas cell to achieve wavelength calibration and a novel, iterative RV extraction method. We surveyed 14 members of young (≈25-150 Myr) moving groups, the young field star ϵ Eridani, and 18 nearby (&lt;25 pc) low-mass stars and achieved typical single-measurement precisions of 8-15 m s-1with a long-term stability of 15-50 m s-1 over longer baselines. We obtain the best NIR RV constraints to date on 27 targets in our sample, 19 of which were never followed by high-precision RV surveys. Our results indicate that very active stars can display long-term RV variations as low as ∼25-50 m s-1 at ≈2.3125 μm, thus constraining the effect of jitter at these wavelengths. We provide the first multiwavelength confirmation of GJ 876 bc and independently retrieve orbital parameters consistent with previous studies. We recovered RV variabilities for HD 160934 AB and GJ 725 AB that are consistent with their known binary orbits, and nine other targets are candidate RV variables with a statistical significance of 3σ-5σ. Our method, combined with the new iSHELL spectrograph, will yield long-term RV precisions of ≲5 m s-1 in the NIR, which will allow the detection of super-Earths near the habitable zone of mid-M dwarfs