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.

Pareto optimization for electrodes placement: compromises between electrophysiological and practical aspects.

Wearable electronics and sensors are increasingly popular for personal health monitoring, including smart shirts containing electrocardiography (ECG) electrodes. Optimal electrode performance requires careful selection of the electrode position. On top of the electrophysiological aspects, practical aspects must be considered due to the dynamic recording environment. We propose a new method to obtain optimal electrode placement by considering multiple dimensions. The electrophysiological aspects were represented by P-, R-, and T-peak of ECG waveform, while the shirt-skin gap, shirt movement, and regional sweat rate represented the practical aspects. This study employed a secondary data set and simulations for the electrophysiological and practical aspects, respectively. Typically, there is no ideal solution that maximizes satisfaction degrees of multiple electrophysiological and practical aspects simultaneously; a compromise is the most appropriate approach. Instead of combining both aspects-which are independent of each other-into a single-objective optimization, we used multi-objective optimization to obtain a Pareto set, which contains predominant solutions. These solutions may facilitate the decision-makers to decide the preferred electrode locations based on application-specific criteria. Our proposed approach may aid manufacturers in making decisions regarding the placement of electrodes within smart shirts.

SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

Magnetic nanoparticle imaging by random and maximum length sequences of inhomogeneous activation fields.

Biomedical applications of magnetic nanoparticles require a precise knowledge of their biodistribution. From multi-channel magnetorelaxometry measurements, this distribution can be determined by means of inverse methods. It was recently shown that the combination of sequential inhomogeneous excitation fields in these measurements is favorable regarding the reconstruction accuracy when compared to homogeneous activation . In this paper, approaches for the determination of activation sequences for these measurements are investigated. Therefor, consecutive activation of single coils, random activation patterns and families of m-sequences are examined in computer simulations involving a sample measurement setup and compared with respect to the relative condition number of the system matrix. We obtain that the values of this condition number decrease with larger number of measurement samples for all approaches. Random sequences and m-sequences reveal similar results with a significant reduction of the required number of samples. We conclude that the application of pseudo-random sequences for sequential activation in the magnetorelaxometry imaging of magnetic nanoparticles considerably reduces the number of required sequences while preserving the relevant measurement information.

Adapting source grid parameters to improve the condition of the magnetostatic linear inverse problem of estimating nanoparticle distributions.

The problem of estimating magnetic nanoparticle distributions from magnetorelaxometric measurements is addressed here. The objective of this work was to identify source grid parameters that provide a good condition for the related linear inverse problem. The parameters investigated here were the number of sources, the extension of the source grid, and the source direction. A new measure of the condition, the ratio between the largest and mean singular value of the lead field matrix, is proposed. Our results indicated that the source grids should be larger than the sensor area. The sources and, consequently, the magnetic excitation field, should be directed toward the Z-direction. For underdetermined linear inverse problems, such as in our application, the number of sources affects the condition to a relatively small degree. Overdetermined magnetostatic linear inverse problems, however, benefit from a reduction in the number of sources, which considerably improves the condition. The adapted source grids proposed here were used to estimate the magnetostatic dipole from simulated data; the L2-norm, residual, and distances between the estimated and simulated sources were significantly reduced.

Tangential and radial epileptic spike activity: different sensitivity in EEG and MEG.

OBJECTIVE: Observations in epileptic patients show that interictal spikes are sometimes only visible in electroencephalography (EEG) and sometimes only in magnetoencephalography (MEG). This observation cannot readily be explained by the theoretical sensitivities of EEG and MEG based on analytical models. In this context, we aimed to study the directional sensitivity of radial and tangential spike activity in numerical simulations using realistic head models. METHODS: We calculated the signal-to-noise ratio (SNR) of simulated spikes at varying orientations and with varying background activity in 12 brain regions in 4 volunteers. Different levels of background activity were modeled by adjusting the amplitudes of several thousand dipoles distributed in the cortex. RESULTS: For a fixed realistic background activity, we found a higher SNR for MEG spikes for spike orientations that deviated not > 30° from the tangential direction. In contrast, we found a higher SNR for EEG spikes that deviated not > 45° from the radial direction. When the radial background activity was selectively increased, the sensitivity of EEG for radially oriented spikes decreased; when the tangential background activity selectively increased, the sensitivity of MEG for tangentially oriented spikes was decreased. CONCLUSIONS: Our simulations provide a possible explanation for the clinically observed differences in epileptic spike detection between EEG and MEG. Epileptic spike detection can be improved by analyzing a combination of EEG and MEG data.

Reconstruction of multiple neuromagnetic sources using augmented evolution strategies-- a comparative study.

The localization of dipolar sources in the brain based on electroencephalography (EEG) or magnetoencephalography (MEG) data is a frequent problem in the neurosciences. Deterministic standard approaches such as the Levenberg-Marquardt (LM) method often have problems in finding the global optimum of the associated nonlinear optimization function, when two or more dipoles are to be reconstructed. In such cases, probabilistic approaches turned out to be superior, but their applicability in neuromagnetic source localizations is not yet satisfactory. The objective of this study was to find probabilistic optimization strategies that perform better in such applications. Thus, hybrid and nested evolution strategies (NES) which both realize a combination of global and local search by means of multilevel optimizations were newly designed. The new methods were benchmarked and compared to the established evolution strategies (ES), to fast evolution strategies (FES), and to the deterministic LM method by conducting a two-dipole fit with MEG data sets from neuropsychological experiments. The best results were achieved with NES.