Optimal design of on-scalp electromagnetic sensor arrays for brain source localisation

Optically pumped magnetometers (OPMs) are quickly widening the scopes of noninvasive neurophysiological imaging. The possibility of placing these magnetic field sensors on the scalp allows not only to acquire signals from people in movement, but also to reduce the distance between the sensors and the brain, with a consequent gain in the signal-to-noise ratio. These advantages make the technique particularly attractive to characterise sources of brain activity in demanding populations, such as children and patients with epilepsy. However, the technology is currently in an early stage, presenting new design challenges around the optimal sensor arrangement and their complementarity with other techniques as electroencephalography (EEG). In this article, we present an optimal array design strategy focussed on minimising the brain source localisation error. The methodology is based on the Cramér-Rao bound, which provides lower error bounds on the estimation of source parameters regardless of the algorithm used. We utilise this framework to compare whole head OPM arrays with commercially available electro/magnetoencephalography (E/MEG) systems for localising brain signal generators. In addition, we study the complementarity between EEG and OPM-based MEG, and design optimal whole head systems based on OPMs only and a combination of OPMs and EEG electrodes for characterising deep and superficial sources alike. Finally, we show the usefulness of the approach to find the nearly optimal sensor positions minimising the estimation error bound in a given cortical region when a limited number of OPMs are available. This is of special interest for maximising the performance of small scale systems to ad hoc neurophysiological experiments, a common situation arising in most OPM labs

Shrinkage approach for spatiotemporal EEG covariance matrix estimation

The characterization of the background activity in electroencephalography (EEG) is of interest in many problems, such as in the study of the brain rhythms and in the solution of the inverse problem for source localization. In most cases the background activity is modeled as a random process, and a basic characterization is done via the second order moments of the process, i.e., the spatiotemporal covariance. The general spatiotemporal covariance matrix of the background activity in EEG is extremely large. To reduce its dimensionality it is generally decomposed as a Kronecker product of a spatial and a temporal covariance matrices. They are generally estimated from the data using sample estimators, which have numerical and statistical problems when the number of trials is small. We present a shrinkage estimator for both EEG spatial and temporal covariance matrices of the background activity. We show that this estimator outperforms the commonly used ones when the quantity of available data is low. We find sufficient conditions for the consistency of the shrinkage estimator and present some results concerning its numerical stability. We compare several shrinkage approaches and show how to improve the estimator by incorporating known structure in the covariance matrix based on background activity models. Results using simulated and real EEG data support our approach

Electrode and brain modelling in stereo-EEG

Objective To quantify the perturbation due to the presence of a measuring depth electrode on the intracranial electric potential distribution, and to study the effect of the heterogeneity and anisotropy of the brain tissues’ electric conductivity. Methods The governing differential equations are solved with the Boundary Elements Method to compute the perturbation on the electric potential distribution caused by the presence of the measuring electrode, and with the Finite Elements Method to simulate measurements in an heterogeneous anisotropic brain model. Results The perturbation on the measured electric potential is negligible if the source of electric activity is located more than approximately 1 mm away from the electrode. The error induced by this perturbation in the estimation of the source position is below 1 mm in all tested situations. The results hold for different sizes of the electrode’s contacts. The effect of the brain’s heterogeneity and anisotropy is more important. In a particular example simulated dipolar sources in the gray matter show localization differences of up to 5 mm between homogeneous isotropic and heterogeneous anisotropic brain models. Conclusions It is not necessary to include detailed electrode models in order to solve the stereo-EEG (sEEG) forward and inverse problems. The heterogeneity and anisotropy of the brain electric conductivity should be modeled if possible. The effect of using an homogeneous isotropic brain model approximation should be studied in a case by case basis, since it depends on the electrode positions, the subject’s electric conductivity map, and the source configuration. Significance This simulation study is helpful for interpreting the sEEG measurements, and for choosing appropriate electrode and brain models; a necessary first step in any attempt to solve the sEEG inverse problem

General bounds for electrode mislocation on the EEG inverse problem

We analyze the effect of electrode mislocation on the electroencephalography (EEG) inverse problem using the Cramér–Rao bound (CRB) for single dipolar source parameters. We adopt a realistic head shape model, and solve the forward problem using the Boundary Element Method; the use of the CRB allows us to obtain general results which do not depend on the algorithm used for solving the inverse problem. We consider two possible causes for the electrode mislocation, errors in the measurement of the electrode positions and an imperfect registration between the electrodes and the scalp surfaces. For 120 electrodes placed in the scalp according to the 10–20 standard, and errors on the electrode location with a standard deviation of 5 mm, the lower bound on the standard deviation in the source depth estimation is approximately 1 mm in the worst case. Therefore, we conclude that errors in the electrode location may be tolerated since their effect on the EEG inverse problem are negligible from a practical point of view

General bounds for electrode mislocation on the EEG inverse problem

We analyze the effect of electrode mislocation on the electroencephalography (EEG) inverse problem using the Cramér–Rao bound (CRB) for single dipolar source parameters. We adopt a realistic head shape model, and solve the forward problem using the Boundary Element Method; the use of the CRB allows us to obtain general results which do not depend on the algorithm used for solving the inverse problem. We consider two possible causes for the electrode mislocation, errors in the measurement of the electrode positions and an imperfect registration between the electrodes and the scalp surfaces. For 120 electrodes placed in the scalp according to the 10–20 standard, and errors on the electrode location with a standard deviation of 5 mm, the lower bound on the standard deviation in the source depth estimation is approximately 1 mm in the worst case. Therefore, we conclude that errors in the electrode location may be tolerated since their effect on the EEG inverse problem are negligible from a practical point of view

DeepIED: An epileptic discharge detector for EEG-fMRI based on deep learning

Presurgical evaluation that can precisely delineate the epileptogenic zone (EZ) is one important step for successful surgical resection treatment of refractory epilepsy patients. The noninvasive EEG-fMRI recording technique combined with general linear model (GLM) analysis is considered an important tool for estimating the EZ. However, the manual marking of interictal epileptic discharges (IEDs) needed in this analysis is challenging and time-consuming because the quality of the EEG recorded inside the scanner is greatly deteriorated compared to the usual EEG obtained outside the scanner. This is one of main impediments to the widespread use of EEG-fMRI in epilepsy. We propose a deep learning based semi-automatic IED detector that can find the candidate IEDs in the EEG recorded inside the scanner which resemble sample IEDs marked in the EEG recorded outside the scanner. The manual marking burden is greatly reduced as the expert need only edit candidate IEDs. The model is trained on data from 30 patients. Validation of IEDs detection accuracy on another 37 consecutive patients shows our method can improve the median sensitivity from 50.0% for the previously proposed template-based method to 84.2%, with false positive rate as 5 events/min. Reproducibility validation on 15 patients is applied to evaluate if our method can produce similar hemodynamic response maps compared with the manual marking ground truth results. We explore the concordance between the maximum hemodynamic response and the intracerebral EEG defined EZ and find that both methods produce similar percentage of concordance (76.9%, 10 out of 13 patients, electrode was absent in the maximum hemodynamic response in two patients). This tool will make EEG-fMRI analysis more practical for clinical usage. Keywords: EEG-fMRI, Deep learning, IED detection, GLM, Epileps