A Matlab library for solving quasi-static volume conduction problems using the boundary element method

A survey on integral equations for bioelectric modeling

Bioelectric modeling problems, such as electroencephalography, magnetoencephalography, transcranial electrical stimulation, deep brain stimulation, and transcranial magnetic stimulation, among others, can be approached through the formulation and resolution of integral equations of theboundary element method(BEM). Recently, it has been realized that thecharge-based formulationof the BEM is naturally well-suited for the application of thefast multipole method(FMM). The FMM is a powerful algorithm for the computation of many-body interactions and is widely applied in electromagnetic modeling problems. With the introduction of BEM-FMM in the context of bioelectromagnetism, the BEM can now compete with thefinite element method(FEM) in a number of application cases. This survey has two goals: first, to give a modern account of the main BEM formulations in the literature and their integration with FMM, directed to general researchers involved in development of BEM software for bioelectromagnetic applications. Second, to survey different techniques and available software, and to contrast different BEM and FEM approaches. As a new contribution, we showcase that the charge-based formulation is dual to the more common surface potential formulation.

Non-invasive localization of the ventricular excitation origin without patient-specific geometries using deep learning

Cardiovascular diseases account for 17 million deaths per year worldwide. Of these, 25% are categorized as sudden cardiac death, which can be related to ventricular tachycardia (VT). This type of arrhythmia can be caused by focal activation sources outside the sinus node. Catheter ablation of these foci is a curative treatment in order to inactivate the abnormal triggering activity. However, the localization procedure is usually time-consuming and requires an invasive procedure in the catheter lab. To facilitate and expedite the treatment, we present two novel localization support techniques based on convolutional neural networks (CNNs) that address these clinical needs. In contrast to existing methods, our approaches were designed to be independent of the patient-specific geometry and directly applicable to surface ECG signals, while also delivering a binary transmural position. Moreover, one of the method's outputs can be interpreted as several ranked solutions. The CNNs were trained on a dataset containing only simulated data and evaluated both on simulated test data and clinical data. On a novel large and open simulated dataset, the median test error was below 3 mm. The median localization error on the unseen clinical data ranged from 32 mm to 41 mm without optimizing the pre-processing and CNN to the clinical data. Interpreting the output of one of the approaches as ranked solutions, the best median error of the top-3 solutions decreased to 20 mm on the clinical data. The transmural position was correctly detected in up to 82% of all clinical cases. These results demonstrate a proof of principle to utilize CNNs to localize the activation source without the intrinsic need for patient-specific geometrical information. Furthermore, providing multiple solutions can assist physicians in identifying the true activation source amongst more than one possible location. With further optimization to clinical data, these methods have high potential to accelerate clinical interventions, replace certain steps within these procedures and consequently reduce procedural risk and improve VT patient outcomes.

MedalCare-XL: 16,900 healthy and pathological synthetic 12 lead ECGs from electrophysiological simulations

Mechanistic cardiac electrophysiology models allow for personalized simulations of the electrical activity in the heart and the ensuing electrocardiogram (ECG) on the body surface. As such, synthetic signals possess known ground truth labels of the underlying disease and can be employed for validation of machine learning ECG analysis tools in addition to clinical signals. Recently, synthetic ECGs were used to enrich sparse clinical data or even replace them completely during training leading to improved performance on real-world clinical test data. We thus generated a novel synthetic database comprising a total of 16,900 12 lead ECGs based on electrophysiological simulations equally distributed into healthy control and 7 pathology classes. The pathological case of myocardial infraction had 6 sub-classes. A comparison of extracted features between the virtual cohort and a publicly available clinical ECG database demonstrated that the synthetic signals represent clinical ECGs for healthy and pathological subpopulations with high fidelity. The ECG database is split into training, validation, and test folds for development and objective assessment of novel machine learning algorithms.

Targeted Modulation of Human Brain Interregional Effective Connectivity With Spike-Timing Dependent Plasticity

OBJECTIVE

The ability to selectively up- or downregulate interregional brain connectivity would be useful for research and clinical purposes. Toward this aim, cortico-cortical paired associative stimulation (ccPAS) protocols have been developed in which two areas are repeatedly stimulated with a millisecond-level asynchrony. However, ccPAS results in humans using bifocal transcranial magnetic stimulation (TMS) have been variable, and the mechanisms remain unproven. In this study, our goal was to test whether ccPAS mechanism is spike-timing-dependent plasticity (STDP).

MATERIALS AND METHODS

Eleven healthy participants received ccPAS to the left primary motor cortex (M1) → right M1 with three different asynchronies (5 milliseconds shorter, equal to, or 5 milliseconds longer than the 9-millisecond transcallosal conduction delay) in separate sessions. To observe the neurophysiological effects, single-pulse TMS was delivered to the left M1 before and after ccPAS while cortico-cortical evoked responses were extracted from the contralateral M1 using source-resolved electroencephalography.

RESULTS

Consistent with STDP mechanisms, the effects on synaptic strengths flipped depending on the asynchrony. Further implicating STDP, control experiments suggested that the effects were unidirectional and selective to the targeted connection.

CONCLUSION

The results support the idea that ccPAS induces STDP and may selectively up- or downregulate effective connectivity between targeted regions in the human brain.

Measurement of Frontal Midline Theta Oscillations using OPM-MEG

Optically pumped magnetometers (OPMs) are an emerging lightweight and compact sensor that can measure magnetic fields generated by the human brain. OPMs enable construction of wearable magnetoencephalography (MEG) systems, which offer advantages over conventional instrumentation. However, when trying to measure signals at low frequency, higher levels of inherent sensor noise, magnetic interference and movement artefact introduce a significant challenge. Accurate characterisation of low frequency brain signals is important for neuroscientific, clinical, and paediatric MEG applications and consequently, demonstrating the viability of OPMs in this area is critical. Here, we undertake measurement of theta band (4-8 Hz) neural oscillations and contrast a newly developed 174 channel triaxial wearable OPM-MEG system with conventional (cryogenic-MEG) instrumentation. Our results show that visual steady state responses at 4 Hz, 6 Hz and 8 Hz can be recorded using OPM-MEG with a signal-to-noise ratio (SNR) that is not significantly different to conventional MEG. Moreover, we measure frontal midline theta oscillations during a 2-back working memory task, again demonstrating comparable SNR for both systems. We show that individual differences in both the amplitude and spatial signature of induced frontal-midline theta responses are maintained across systems. Finally, we show that our OPM-MEG results could not have been achieved without a triaxial sensor array, or the use of postprocessing techniques. Our results demonstrate the viability of OPMs for characterising theta oscillations and add weight to the argument that OPMs can replace cryogenic sensors as the fundamental building block of MEG systems.

EEG Beta functional connectivity decrease in the left amygdala correlates with the affective pain in fibromyalgia: A pilot study

Fibromyalgia (FM) is a major chronic pain disease with prominent affective disturbances, and pain-associated changes in neurotransmitters activity and in brain connectivity. However, correlates of affective pain dimension lack. The primary goal of this correlational cross-sectional case-control pilot study was to find electrophysiological correlates of the affective pain component in FM. We examined the resting-state EEG spectral power and imaginary coherence in the beta (β) band (supposedly indexing the GABAergic neurotransmission) in 16 female patients with FM and 11 age-adjusted female controls. FM patients displayed lower functional connectivity in the High β (Hβ, 20-30 Hz) sub-band than controls (p = 0.039) in the left basolateral complex of the amygdala (p = 0.039) within the left mesiotemporal area, in particular, in correlation with a higher affective pain component level (r = 0.50, p = 0.049). Patients showed higher Low β (Lβ, 13-20 Hz) relative power than controls in the left prefrontal cortex (p = 0.001), correlated with ongoing pain intensity (r = 0.54, p = 0.032). For the first time, GABA-related connectivity changes correlated with the affective pain component are shown in the amygdala, a region highly involved in the affective regulation of pain. The β power increase in the prefrontal cortex could be compensatory to pain-related GABAergic dysfunction.

Looking through the windows: a study about the dependency of phase-coupling estimates on the data length

OBJECTIVE

Being able to characterize functional connectivity (FC) state dynamics in a real-time setting, such as in brain-computer interface, neurofeedback or closed-loop neurostimulation frameworks, requires the rapid detection of the statistical dependencies that quantify FC in short windows of data. The aim of this study is to characterize, through extensive realistic simulations, the reliability of FC estimation as a function of the data length. In particular, we focused on FC as measured by phase-coupling (PC) of neuronal oscillations, one of the most functionally relevant neural coupling modes.

APPROACH

We generated synthetic data corresponding to different scenarios by varying the data length, the signal-to-noise ratio, the phase difference value, the spectral analysis approach (Hilbert or Fourier) and the fractional bandwidth. We compared seven PC metrics, i.e. imaginary part of phase locking value (PLV), PLV of orthogonalized signals, phase lag index (PLI), debiased weighted PLI, imaginary part of coherency, coherence of orthogonalized signals and lagged coherence.

MAIN RESULTS

Our findings show that, for a signal-to-noise-ratio of at least 10 dB, a data window that contains 5 to 8 cycles of the oscillation of interest (e.g. a 500-800ms window at 10Hz) is generally required to achieve reliable PC estimates. In general, Hilbert-based approaches were associated with higher performance than Fourier-based approaches. Furthermore, the results suggest that, when the analysis is performed in a narrow frequency range, a larger window is required.

SIGNIFICANCE

The achieved results pave the way to the introduction of best-practice guidelines to be followed when a real-time frequency-specific PC assessment is at target.

Closed-loop optimization of transcranial magnetic stimulation with electroencephalography feedback

Background

Transcranial magnetic stimulation (TMS) is widely used in brain research and treatment of various brain dysfunctions. However, the optimal way to target stimulation and administer TMS therapies, for example, where and in which electric field direction the stimuli should be given, is yet to be determined.

Objective

To develop an automated closed-loop system for adjusting TMS parameters (in this work, the stimulus orientation) online based on TMS-evoked brain activity measured with electroencephalography (EEG).

Methods

We developed an automated closed-loop TMS–EEG set-up. In this set-up, the stimulus parameters are electronically adjusted with multi-locus TMS. As a proof of concept, we developed an algorithm that automatically optimizes the stimulation orientation based on single-trial EEG responses. We applied the algorithm to determine the electric field orientation that maximizes the amplitude of the TMS–EEG responses. The validation of the algorithm was performed with six healthy volunteers, repeating the search twenty times for each subject.

Results

The validation demonstrated that the closed-loop control worked as desired despite the large variation in the single-trial EEG responses. We were often able to get close to the orientation that maximizes the EEG amplitude with only a few tens of pulses.

Conclusion

Optimizing stimulation with EEG feedback in a closed-loop manner is feasible and enables effective coupling to brain activity.

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Closed-loop set-up for guiding TMS with brain activity feedback.

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Automatic stimulus orientation optimization based on TMS-evoked EEG responses.

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Adjusting TMS parameters electronically allows fast and effortless procedures.

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TMS-evoked EEG responses depend on the stimulus orientation.

Spatial sampling of MEG and EEG based on generalized spatial-frequency analysis and optimal design

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We analyze spatial sampling of MEG and EEG using a realistic head model.

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On-scalp MEG may benefit from three times more samples than EEG and off-scalp MEG.

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We optimize sample positions to convey the most information from the brain.

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Optimized sampling can be useful when the sensor number is limited.

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The sample positions can be optimized to target a region of interest in the brain.

In this paper, we analyze spatial sampling of electro- (EEG) and magnetoencephalography (MEG), where the electric or magnetic field is typically sampled on a curved surface such as the scalp. By simulating fields originating from a representative adult-male head, we study the spatial-frequency content in EEG as well as in on- and off-scalp MEG. This analysis suggests that on-scalp MEG, off-scalp MEG and EEG can benefit from up to 280, 90 and 110 spatial samples, respectively. In addition, we suggest a new approach to obtain sensor locations that are optimal with respect to prior assumptions. The approach also allows to control, e.g., the uniformity of the sensor locations. Based on our simulations, we argue that for a low number of spatial samples, model-informed non-uniform sampling can be beneficial. For a large number of samples, uniform sampling grids yield nearly the same total information as the model-informed grids.

Reducing Line-of-block Artifacts in Cardiac Activation Maps Estimated Using ECG Imaging: A Comparison of Source Models and Estimation Methods

OBJECTIVE

To investigate cardiac activation maps estimated using electrocardiographic imaging and to find methods reducing line-of-block (LoB) artifacts, while preserving real LoBs.

METHODS

Body surface potentials were computed for 137 simulated ventricular excitations. Subsequently, the inverse problem was solved to obtain extracellular potentials (EP) and transmembrane voltages (TMV). From these, activation times (AT) were estimated using four methods and compared to the ground truth. This process was evaluated with two cardiac mesh resolutions. Factors contributing to LoB artifacts were identified by analyzing the impact of spatial and temporal smoothing on the morphology of source signals.

RESULTS

AT estimation using a spatiotemporal derivative performed better than using a temporal derivative. Compared to deflection-based AT estimation, correlation-based methods were less prone to LoB artifacts but performed worse in identifying real LoBs. Temporal smoothing could eliminate artifacts for TMVs but not for EPs, which could be linked to their temporal morphology. TMVs led to more accurate ATs on the septum than EPs. Mesh resolution had a negligible effect on inverse reconstructions, but small distances were important for cross-correlation-based estimation of AT delays.

CONCLUSION

LoB artifacts are mainly caused by the inherent spatial smoothing effect of the inverse reconstruction. Among the configurations evaluated, only deflection-based AT estimation in combination with TMVs and strong temporal smoothing can prevent LoB artifacts, while preserving real LoBs.

SIGNIFICANCE

Regions of slow conduction are of considerable clinical interest and LoB artifacts observed in non-invasive ATs can lead to misinterpretations. We addressed this problem by identifying factors causing such artifacts and methods to reduce them.

Sparse EEG source localization in frequency domain

This work presents an approach for EEG source localization when strong priors on predominant frequencies in the activities of the source are available. We describe the fundamentals of the used source reconstruction method based on a greedy approach, which can be applied indifferently in the time or frequency domain. The method is evaluated using simulated data reproducing realistic recorded activities in the context of fast periodic visual stimulation. In particular the advantage of reconstructing the source in the frequency domain against time domain is quantified in a realistic setup. Finally, the performances of the method are illustrated on real EEG signals recorded during a fast periodic visual stimulation task.

A bi-atrial statistical shape model for large-scale in silico studies of human atria: Model development and application to ECG simulations

Large-scale electrophysiological simulations to obtain electrocardiograms (ECG) carry the potential to produce extensive datasets for training of machine learning classifiers to, e.g., discriminate between different cardiac pathologies. The adoption of simulations for these purposes is limited due to a lack of ready-to-use models covering atrial anatomical variability. We built a bi-atrial statistical shape model (SSM) of the endocardial wall based on 47 segmented human CT and MRI datasets using Gaussian process morphable models. Generalization, specificity, and compactness metrics were evaluated. The SSM was applied to simulate atrial ECGs in 100 random volumetric instances. The first eigenmode of our SSM reflects a change of the total volume of both atria, the second the asymmetry between left vs. right atrial volume, the third a change in the prominence of the atrial appendages. The SSM is capable of generalizing well to unseen geometries and 95% of the total shape variance is covered by its first 24 eigenvectors. The P waves in the 12-lead ECG of 100 random instances showed a duration of 109.7±12.2 ms in accordance with large cohort studies. The novel bi-atrial SSM itself as well as 100 exemplary instances with rule-based augmentation of atrial wall thickness, fiber orientation, inter-atrial bridges and tags for anatomical structures have been made publicly available. This novel, openly available bi-atrial SSM can in future be employed to generate large sets of realistic atrial geometries as a basis for in silico big data approaches.

Feasibility of Reconstructing Source Functional Connectivity with Low-Density EEG

OBJECTIVES

Functional connectivity (FC) is increasingly used as target for neuromodulation and enhancement of performance. A reliable assessment of FC with electroencephalography (EEG) currently requires a laboratory environment with high-density montages and a long preparation time. This study investigated the feasibility of reconstructing source FC with a low-density EEG montage towards a usage in real life applications.

METHODS

Source FC was reconstructed with inverse solutions and quantified as node degree of absolute imaginary coherence in alpha frequencies. We used simulated coherent point sources as well as two real datasets to investigate the impact of electrode density (19 vs. 128 electrodes) and usage of template vs. individual MRI-based head models on localization accuracy. In addition, we checked whether low-density EEG is able to capture inter-individual variations in coherence strength.

RESULTS

In numerical simulations as well as real data, a reduction of the number of electrodes led to less reliable reconstructions of coherent sources and of coupling strength. Yet, when comparing different approaches to reconstructing FC from 19 electrodes, source FC obtained with beamformers outperformed sensor FC, FC computed after independent component analysis, and source FC obtained with sLORETA. In particular, only source FC based on beamformers was able to capture neural correlates of motor behavior.

CONCLUSION

Reconstructions of FC from low-density EEG is challenging, but may be feasible when using source reconstructions with beamformers.

A method for magnetocardiography functional localization based on boundary element method and Nelder-Mead simplex algorithm

BACKGROUND

The magnetocardiography (MCG) functional localization can transfer the biomagnetic signal to the electrical activity information inside the heart. The electrical activity is directly related to the physiological function of the heart.

METHODS

This study proposes a practical method for MCG functional localization based on the boundary element method (BEM) and the Nelder-Mead (NM) simplex algorithm. Single equivalent moving current dipole (SEMCD) is served as the equivalent cardiac source. The parameters of SEMCD are adapted using the NM simplex algorithm by fitting the measured MCG with the calculated MCG obtained based on BEM. The SEMCD parameters are solved in the sense that the difference between measured and calculated MCG is minimized.

RESULTS

The factors affecting the localization accuracy of this BEM-NM method were first explored with synthetic signals. Then, the results with real MCG signals show a good agreement between the SEMCD location and the region where ventricle depolarization starts, demonstrating the feasibility of this idea.

CONCLUSIONS

This is the first three-dimensional localization of the onset of ventricular depolarization with the BEM-NM method. The method is promising in the noninvasive localization of lesions for heart diseases.

Disrupted resting-state EEG alpha-band interactions as a novel marker for the severity of visual field deficits after brain lesion

OBJECTIVE

Homonymous visual field deficits (HFVDs) are frequent following brain lesions. Current restoration treatments aim at activating areas of residual vision through numerous stimuli, but show limited effect. Recent findings suggest that spontaneous neural α-band coupling is more efficient for enabling visual perception in healthy humans than task-induced activations. Here, we evaluated whether it is also associated with the severity of HFVD.

METHODS

Ten patients with HFVDs after brain damage in the subacute to chronic stage and ten matched healthy controls underwent visual stimulation with alternating checkerboards and electroencephalography recordings of stimulation-induced power changes and of spontaneous neural interactions during rest.

RESULTS

Visual areas of the affected hemisphere showed reduced event-related power decrease in α and β frequency bands, but also reduced spontaneous α-band interactions during rest, as compared to contralesional areas and healthy controls. A multivariate stepwise regression retained the degree of disruption of spontaneous interactions, but not the reduced task-induced power changes as predictor for the severity of the visual deficit.

CONCLUSIONS

Spontaneous α-band interactions of visual areas appear as a better marker for the severity of HFVDs than task-induced activations.

SIGNIFICANCE

Treatment attempts of HFVDs should try to enhance spontaneous α-band coupling of structurally intact ipsilesional areas.

Spontaneous Network Coupling Enables Efficient Task Performance without Local Task-Induced Activations

Neurobehavioral studies in humans have long concentrated on changes in local activity levels during repetitive executions of a task. Spontaneous neural coupling within extended networks has latterly been found to also influence performance. Here, we intend to uncover the underlying mechanisms, the relative importance, and the interaction between spontaneous coupling and task-induced activations. To do so, we recorded two groups of healthy participants (male and female) during rest and while they performed either a visual perception or a motor sequence task. We demonstrate that, for both tasks, stronger activations during the task as well as greater network coupling through spontaneous α rhythms at rest predict performance. However, high performers present an absence of classical task-induced activations and, instead, stronger spontaneous network coupling. Activations were thus a compensation mechanism needed only in subjects with lower spontaneous network interactions. This challenges classical models of neural processing and calls for new strategies in attempts to train and enhance performance.SIGNIFICANCE STATEMENT Our findings challenge the widely accepted notion that task-induced activations are of paramount importance for behavior. This will have an important impact on interpretations of human neurobehavioral research. They further link the widely used techniques of quantifying network communication in the brain with classical neuroscience methods and demonstrate possible ways of how network communication influences human behavior. Traditional training methods attempt to enhance neural activations through task repetitions. Our findings suggest a more efficient neural target for learning: enhancing spontaneous neural interactions. This will be of major interest for a large variety of scientific fields with very broad applications in schools, work, and others.

Individual head models for estimating the TMS-induced electric field in rat brain

In transcranial magnetic stimulation (TMS), the initial cortical activation due to stimulation is determined by the state of the brain and the magnitude, waveform, and direction of the induced electric field (E-field) in the cortex. The E-field distribution depends on the conductivity geometry of the head. The effects of deviations from a spherically symmetric conductivity profile have been studied in detail in humans. In small mammals, such as rats, these effects are more pronounced due to their less spherical head, proportionally much thicker neck region, and overall much smaller size compared to the TMS coils. In this study, we describe a simple method for building individual realistically shaped head models for rats from high-resolution X-ray tomography images. We computed the TMS-induced E-field with the boundary element method and assessed the effect of head-model simplifications on the estimated E-field. The deviations from spherical symmetry have large, non-trivial effects on the E-field distribution: for some coil orientations, the strongest stimulation is in the brainstem even when the coil is over the motor cortex. With modelling prior to an experiment, such problematic coil orientations can be avoided for more accurate targeting.

NUTMEG: Open Source Software for M/EEG Source Reconstruction

Neurodynamic Utility Toolbox for Magnetoencephalo- and Electroencephalography (NUTMEG) is an open-source MATLAB-based toolbox for the analysis and reconstruction of magnetoencephalography/electroencephalography data in source space. NUTMEG includes a variety of options for the user in data import, preprocessing, source reconstruction, and functional connectivity. A group analysis toolbox allows the user to run a variety of inferential statistics on their data in an easy-to-use GUI-driven format. Importantly, NUTMEG features an interactive five-dimensional data visualization platform. A key feature of NUTMEG is the availability of a large menu of interference cancelation and source reconstruction algorithms. Each NUTMEG operation acts as a stand-alone MATLAB function, allowing the package to be easily adaptable and scripted for the more advanced user for interoperability with other software toolboxes. Therefore, NUTMEG enables a wide range of users access to a complete "sensor-to- source-statistics" analysis pipeline.

Concurrent electrophysiological and hemodynamic measurements of evoked neural oscillations in human visual cortex using sparsely interleaved fast fMRI and EEG

Electroencephalography (EEG) concurrently collected with functional magnetic resonance imaging (fMRI) is heavily distorted by the repetitive gradient coil switching during the fMRI acquisition. The performance of the typical template-based gradient artifact suppression method can be suboptimal because the artifact changes over time. Gradient artifact residuals also impede the subsequent suppression of ballistocardiography artifacts. Here we propose recording continuous EEG with temporally sparse fast fMRI (fast fMRI-EEG) to minimize the EEG artifacts caused by MRI gradient coil switching without significantly compromising the field-of-view and spatiotemporal resolution of fMRI. Using simultaneous multi-slice inverse imaging to achieve whole-brain fMRI with isotropic 5-mm resolution in 0.1 ​s, and performing these acquisitions once every 2 ​s, we have 95% of the duty cycle available to record EEG with substantially less gradient artifact. We found that the standard deviation of EEG signals over the entire acquisition period in fast fMRI-EEG was reduced to 54% of that in conventional concurrent echo-planar imaging (EPI) and EEG recordings (EPI-EEG) across participants. When measuring 15-Hz steady-state visual evoked potentials (SSVEPs), the baseline-normalized oscillatory neural response in fast fMRI-EEG was 2.5-fold of that in EPI-EEG. The functional MRI responses associated with the SSVEP delineated by EPI and fast fMRI were similar in the spatial distribution, the elicited waveform, and detection power. Sparsely interleaved fast fMRI-EEG provides high-quality EEG without substantially compromising the quality of fMRI in evoked response measurements, and has the potential utility for applications where the onset of the target stimulus cannot be precisely determined, such as epilepsy.

Using a Spatio-Temporal Basis for ECG Imaging of Ventricular Pacings: Insights From Simulations and First Application to Clinical Data

ECG imaging estimates the cardiac electrical activity from body surface potentials. As this involves solving a severly ill-posed problem, additional information is required to get a unique and stable solution. Recent progress is based on introducing more problem-specific information by exploiting the structure of cardiac excitation. However, added information must be either certain or general enough to not impair the solution. We have recently developed a method that uses a spatio-temporal basis to restrict the solution space. In the present work, we analyzed this method with respect to one of the most fundamental assumptions made during basis creation: cardiac (an)isotropy. We tested the reconstruction using simulations of ventricular pacings and then applied it to clinical data. In simulations, the overall median localization error was smallest with a basis including fiber orientation. For the clinical data, however, the overall error was smallest with an isotropic basis. This observation suggests that modeling priors should be introduced with care, whereby further work is needed.

A unified weighted minimum norm solution for the reference inverse problem in EEG

A well known problem in EEG recordings deals with the unknown potential of the reference electrode. In the last years several authors presented comparisons among the most popular solutions, the global conclusion being that the traditional Average Reference (AR) and the Reference Standardization Technique (REST) are the best approximations (Nunez, 2010; Kayser and Tenke, 2010; Liu et al., 2015; Chella et al., 2016). In this work we do not aim to further compare these techniques but to support the fact that both solutions can be derived from a general inverse problem formalism for reference estimation (Hu et al., 2019; Hu et al., 2018; Salido-Ruiz et al., 2011). Using the alternative approach of least squares, our findings are consistent with the theoretical findings in Hu et al. (2019) and Hu et al. (2018) showing that the AR is the minimum norm solution, while REST is a weighted minimum norm including some approximate propagation model. AR is thus a particular case of REST, which itself uses a particular formulation of the source estimation inverse problem. With a different derivation, we provide the additional powerful evidences to reinforce the cited findings.

The impact of improved MEG-MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5-10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI-MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis. We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0-15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality). We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis. We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS)

OBJECTIVE

A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics.

APPROACH

We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB^® 2018a environment.

MAIN RESULTS

In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used.

SIGNIFICANCE

This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

Modulating functional connectivity after stroke with neurofeedback: Effect on motor deficits in a controlled cross-over study

Synchronization of neural activity as measured with functional connectivity (FC) is increasingly used to study the neural basis of brain disease and to develop new treatment targets. However, solid evidence for a causal role of FC in disease and therapy is lacking. Here, we manipulated FC of the ipsilesional primary motor cortex in ten chronic human stroke patients through brain-computer interface technology with visual neurofeedback. We conducted a double-blind controlled crossover study to test whether manipulation of FC through neurofeedback had a behavioral effect on motor performance. Patients succeeded in increasing FC in the motor cortex. This led to improvement in motor function that was significantly greater than during neurofeedback training of a control brain area and proportional to the degree of FC enhancement. This result provides evidence that FC has a causal role in neurological function and that it can be effectively targeted with therapy.

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Stroke patients participated in clinical trial on neurofeedback of functional connectivity.

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Patients learned to enhance synchrony of neural activity in their motor cortex.

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This led to reduced motor impairment.

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Evidence for a causal role of neural synchrony in neurological deficits and recovery.

Prefrontal Cortex Stimulation Enhances Fear Extinction Memory in Humans

BACKGROUND

Animal fear conditioning studies have illuminated neuronal mechanisms of learned associations between sensory stimuli and fear responses. In rats, brief electrical stimulation of the infralimbic cortex has been shown to reduce conditioned freezing during recall of extinction memory. Here, we translated this finding to humans with magnetic resonance imaging-navigated transcranial magnetic stimulation (TMS).

METHODS

Subjects (N = 28) were aversively conditioned to two different cues (day 1). During extinction learning (day 2), TMS was paired with one of the conditioned cues but not the other. TMS parameters were similar to those used in rat infralimbic cortex: brief pulse trains (300 ms at 20 Hz) starting 100 ms after cue onset, total of four trains (28 TMS pulses). TMS was applied to one of two targets in the left frontal cortex, one functionally connected (target 1) and the other unconnected (target 2, control) with a human homologue of infralimbic cortex in the ventromedial prefrontal cortex. Skin conductance responses were used as an index of conditioned fear.

RESULTS

During extinction recall (day 3), the cue paired with TMS to target 1 showed significantly reduced skin conductance responses, whereas TMS to target 2 had no effect. Further, we built group-level maps that weighted TMS-induced electric fields and diffusion magnetic resonance imaging connectivity estimates with fear level. These maps revealed distinct cortical regions and large-scale networks associated with reduced versus increased fear.

CONCLUSIONS

The results showed that spatiotemporally focused TMS may enhance extinction learning and/or consolidation of extinction memory and suggested novel cortical areas and large-scale networks for targeting in future studies.

A Quasi-Static Boundary Element Approach With Fast Multipole Acceleration for High-Resolution Bioelectromagnetic Models

OBJECTIVE

We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals.

RESULTS

The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case.

SIGNIFICANCE

At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement.

CONCLUSIONS

Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.

Noninvasive extraction of microsecond-scale dynamics from human motor cortex

State-of-the-art noninvasive electromagnetic recording techniques allow observing neuronal dynamics down to the millisecond scale. Direct measurement of faster events has been limited to in vitro or invasive recordings. To overcome this limitation, we introduce a new paradigm for transcranial magnetic stimulation. We adjusted the stimulation waveform on the microsecond scale, by varying the duration between the positive and negative phase of the induced electric field, and studied corresponding changes in the elicited motor responses. The magnitude of the electric field needed for given motor-evoked potential amplitude decreased exponentially as a function of this duration with a time constant of 17 µs. Our indirect noninvasive measurement paradigm allows studying neuronal kinetics on the microsecond scale in vivo.

Longitudinal Structural and Functional Differences Between Proportional and Poor Motor Recovery After Stroke

BACKGROUND

Evolution of motor function during the first months after stroke is stereotypically bifurcated, consisting of either recovery to about 70% of maximum possible improvement ("proportional recovery, PROP") or in little to no improvement ("poor recovery, POOR"). There is currently no evidence that any rehabilitation treatment will prevent POOR and favor PROP.

OBJECTIVE

To perform a longitudinal and multimodal assessment of functional and structural changes in brain organization associated with PROP.

METHODS

Fugl-Meyer Assessments of the upper extremity and high-density electroencephalography (EEG) were obtained from 63 patients, diffusion tensor imaging from 46 patients, at 2 and 4 weeks (T0) and at 3 months (T1) after stroke onset.

RESULTS

We confirmed the presence of 2 distinct recovery patterns (PROP and POOR) in our sample. At T0, PROP patients had greater integrity of the corticospinal tract (CST) and greater EEG functional connectivity (FC) between the affected hemisphere and rest of the brain, in particular between the ventral premotor and the primary motor cortex. POOR patients suffered from degradation of corticocortical and corticofugal fiber tracts in the affected hemisphere between T0 and T1, which was not observed in PROP patients. Better initial CST integrity correlated with greater initial global FC, which was in turn associated with less white matter degradation between T0 and T1.

CONCLUSIONS

These findings suggest links between initial CST integrity, systems-level cortical network plasticity, reduction of white matter atrophy, and clinical motor recovery after stroke. This identifies candidate treatment targets.

Measuring MEG closer to the brain: Performance of on-scalp sensor arrays

Optically-pumped magnetometers (OPMs) have recently reached sensitivity levels required for magnetoencephalography (MEG). OPMs do not need cryogenics and can thus be placed within millimetres from the scalp into an array that adapts to the individual head size and shape, thereby reducing the distance from cortical sources to the sensors. Here, we quantified the improvement in recording MEG with hypothetical on-scalp OPM arrays compared to a 306-channel state-of-the-art SQUID array (102 magnetometers and 204 planar gradiometers). We simulated OPM arrays that measured either normal (nOPM; 102 sensors), tangential (tOPM; 204 sensors), or all components (aOPM; 306 sensors) of the magnetic field. We built forward models based on magnetic resonance images of 10 adult heads; we employed a three-compartment boundary element model and distributed current dipoles evenly across the cortical mantle. Compared to the SQUID magnetometers, nOPM and tOPM yielded 7.5 and 5.3 times higher signal power, while the correlations between the field patterns of source dipoles were reduced by factors of 2.8 and 3.6, respectively. Values of the field-pattern correlations were similar across nOPM, tOPM and SQUID gradiometers. Volume currents reduced the signals of primary currents on average by 10%, 72% and 15% in nOPM, tOPM and SQUID magnetometers, respectively. The information capacities of the OPM arrays were clearly higher than that of the SQUID array. The dipole-localization accuracies of the arrays were similar while the minimum-norm-based point-spread functions were on average 2.4 and 2.5 times more spread for the SQUID array compared to nOPM and tOPM arrays, respectively.

Integral equations and boundary-element solution for static potential in a general piece-wise homogeneous volume conductor

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.

Incorporating and Compensating Cerebrospinal Fluid in Surface-Based Forward Models of Magneto- and Electroencephalography

MEG/EEG source imaging is usually done using a three-shell (3-S) or a simpler head model. Such models omit cerebrospinal fluid (CSF) that strongly affects the volume currents. We present a four-compartment (4-C) boundary-element (BEM) model that incorporates the CSF and is computationally efficient and straightforward to build using freely available software. We propose a way for compensating the omission of CSF by decreasing the skull conductivity of the 3-S model, and study the robustness of the 4-C and 3-S models to errors in skull conductivity. We generated dense boundary meshes using MRI datasets and automated SimNIBS pipeline. Then, we built a dense 4-C reference model using Galerkin BEM, and 4-C and 3-S test models using coarser meshes and both Galerkin and collocation BEMs. We compared field topographies of cortical sources, applying various skull conductivities and fitting conductivities that minimized the relative error in 4-C and 3-S models. When the CSF was left out from the EEG model, our compensated, unbiased approach improved the accuracy of the 3-S model considerably compared to the conventional approach, where CSF is neglected without any compensation (mean relative error < 20% vs. > 40%). The error due to the omission of CSF was of the same order in MEG and compensated EEG. EEG has, however, large overall error due to uncertain skull conductivity. Our results show that a realistic 4-C MEG/EEG model can be implemented using standard tools and basic BEM, without excessive workload or computational burden. If the CSF is omitted, compensated skull conductivity should be used in EEG.

Computational modeling in melanoma for novel drug discovery

INTRODUCTION

There is a growing body of evidence highlighting the applications of computational modeling in the field of biomedicine. It has recently been applied to the in silico analysis of cancer dynamics. In the era of precision medicine, this analysis may allow the discovery of new molecular targets useful for the design of novel therapies and for overcoming resistance to anticancer drugs. According to its molecular behavior, melanoma represents an interesting tumor model in which computational modeling can be applied. Melanoma is an aggressive tumor of the skin with a poor prognosis for patients with advanced disease as it is resistant to current therapeutic approaches.

AREAS COVERED

This review discusses the basics of computational modeling in melanoma drug discovery and development. Discussion includes the in silico discovery of novel molecular drug targets, the optimization of immunotherapies and personalized medicine trials.

EXPERT OPINION

Mathematical and computational models are gradually being used to help understand biomedical data produced by high-throughput analysis. The use of advanced computer models allowing the simulation of complex biological processes provides hypotheses and supports experimental design. The research in fighting aggressive cancers, such as melanoma, is making great strides. Computational models represent the key component to complement these efforts. Due to the combinatorial complexity of new drug discovery, a systematic approach based only on experimentation is not possible. Computational and mathematical models are necessary for bringing cancer drug discovery into the era of omics, big data and personalized medicine.

Analysis and visualization of intracardiac electrograms in diagnosis and research: Concept and application of KaPAVIE

BACKGROUND AND OBJECTIVE

Progress in biomedical engineering has improved the hardware available for diagnosis and treatment of cardiac arrhythmias. But although huge amounts of intracardiac electrograms (EGMs) can be acquired during electrophysiological examinations, there is still a lack of software aiding diagnosis. The development of novel algorithms for the automated analysis of EGMs has proven difficult, due to the highly interdisciplinary nature of this task and hampered data access in clinical systems. Thus we developed a software platform, which allows rapid implementation of new algorithms, verification of their functionality and suitable visualization for discussion in the clinical environment.

METHODS

A software for visualization was developed in Qt5 and C++ utilizing the class library of VTK. The algorithms for signal analysis were implemented in MATLAB. Clinical data for analysis was exported from electroanatomical mapping systems.

RESULTS

The visualization software KaPAVIE (Karlsruhe Platform for Analysis and Visualization of Intracardiac Electrograms) was implemented and tested on several clinical datasets. Both common and novel algorithms were implemented which address important clinical questions in diagnosis of different arrhythmias. It proved useful in discussions with clinicians due to its interactive and user-friendly design. Time after export from the clinical mapping system to visualization is below 5min.

CONCLUSION

KaPAVIE(2) is a powerful platform for the development of novel algorithms in the clinical environment. Simultaneous and interactive visualization of measured EGM data and the results of analysis will aid diagnosis and help understanding the underlying mechanisms of complex arrhythmias like atrial fibrillation.

Direct neural current imaging in an intact cerebellum with magnetic resonance imaging

The ability to detect neuronal currents with high spatiotemporal resolution using magnetic resonance imaging (MRI) is important for studying human brain function in both health and disease. While significant progress has been made, we still lack evidence showing that it is possible to measure an MR signal time-locked to neuronal currents with a temporal waveform matching concurrently recorded local field potentials (LFPs). Also lacking is evidence that such MR data can be used to image current distribution in active tissue. Since these two results are lacking even in vitro, we obtained these data in an intact isolated whole cerebellum of turtle during slow neuronal activity mediated by metabotropic glutamate receptors using a gradient-echo EPI sequence (TR=100ms) at 4.7T. Our results show that it is possible (1) to reliably detect an MR phase shift time course matching that of the concurrently measured LFP evoked by stimulation of a cerebellar peduncle, (2) to detect the signal in single voxels of 0.1mm(3), (3) to determine the spatial phase map matching the magnetic field distribution predicted by the LFP map, (4) to estimate the distribution of neuronal current in the active tissue from a group-average phase map, and (5) to provide a quantitatively accurate theoretical account of the measured phase shifts. The peak values of the detected MR phase shifts were 0.27-0.37°, corresponding to local magnetic field changes of 0.67-0.93nT (for TE=26ms). Our work provides an empirical basis for future extensions to in vivo imaging of neuronal currents.

Sparse cortical source localization using spatio-temporal atoms

This paper addresses the problem of sparse localization of cortical sources from scalp EEG recordings. Localization algorithms use propagation model under spatial and/or temporal constraints, but their performance highly depends on the data signal-to-noise ratio (SNR). In this work we propose a dictionary based sparse localization method which uses a data driven spatio-temporal dictionary to reconstruct the measurements using Single Best Replacement (SBR) and Continuation Single Best Replacement (CSBR) algorithms. We tested and compared our methods with the well-known MUSIC and RAP-MUSIC algorithms on simulated realistic data. Tests were carried out for different noise levels. The results show that our method has a strong advantage over MUSIC-type methods in case of synchronized sources.

A Space-Time-Frequency Dictionary for Sparse Cortical Source Localization

OBJECTIVE

Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions.

METHODS

In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary.

RESULTS

We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio.

CONCLUSION

Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. From a computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time.

SIGNIFICANCE

The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.

Investigations of sensitivity and resolution of ECG and MCG in a realistically shaped thorax model

Solving the inverse problem of electrocardiography (ECG) and magnetocardiography (MCG) is often referred to as cardiac source imaging. Spatial properties of ECG and MCG as imaging systems are, however, not well known. In this modelling study, we investigate the sensitivity and point-spread function (PSF) of ECG, MCG, and combined ECG+MCG as a function of source position and orientation, globally around the ventricles: signal topographies are modelled using a realistically-shaped volume conductor model, and the inverse problem is solved using a distributed source model and linear source estimation with minimal use of prior information. The results show that the sensitivity depends not only on the modality but also on the location and orientation of the source and that the sensitivity distribution is clearly reflected in the PSF. MCG can better characterize tangential anterior sources (with respect to the heart surface), while ECG excels with normally-oriented and posterior sources. Compared to either modality used alone, the sensitivity of combined ECG+MCG is less dependent on source orientation per source location, leading to better source estimates. Thus, for maximal sensitivity and optimal source estimation, the electric and magnetic measurements should be combined.

Two intrinsic coupling types for resting-state integration in the human brain

Recent findings indicate that synchronous neural activity at rest influences human performance in subsequent tasks. Synchronization can occur in form of phase coupling or amplitude correlation. It is unknown whether these coupling types have differing behavioral significance at rest. To address this, we performed resting-state electroencephalography (EEG) and source connectivity analysis in several populations of healthy subjects and patients with brain lesions. We systematically compared different types and frequencies of neural synchronization and investigated their association with behavioral performance in verbal and spatial attention tasks. Behavioral performance could be consistently predicted by two distinct resting-state coupling patterns: (1) amplitude envelope correlation of beta activity between homologous areas of both hemispheres, (2) lagged phase synchronization in EEG alpha activity between a brain area and the entire cortex. A disruption of these coupling patterns was also associated with neurological deficits in patients with stroke lesions. This suggests the existence of two distinct network systems responsible for resting-state integration. Lagged phase synchronization in the alpha band is associated with global interaction across networks while amplitude envelope correlation seems to be behaviorally relevant for interactions within networks and between hemispheres. These two coupling types may therefore provide complementary insights on brain physiology and pathology.

Evidence for distinct human auditory cortex regions for sound location versus identity processing

Neurophysiological animal models suggest that anterior auditory cortex (AC) areas process sound-identity information, whereas posterior ACs specialize in sound location processing. In humans, inconsistent neuroimaging results and insufficient causal evidence have challenged the existence of such parallel AC organization. Here we transiently inhibit bilateral anterior or posterior AC areas using MRI-guided paired-pulse transcranial magnetic stimulation (TMS) while subjects listen to Reference/Probe sound pairs and perform either sound location or identity discrimination tasks. The targeting of TMS pulses, delivered 55–145 ms after Probes, is confirmed with individual-level cortical electric-field estimates. Our data show that TMS to posterior AC regions delays reaction times (RT) significantly more during sound location than identity discrimination, whereas TMS to anterior AC regions delays RTs significantly more during sound identity than location discrimination. This double dissociation provides direct causal support for parallel processing of sound identity features in anterior AC and sound location in posterior AC.

Comparison of minimum-norm estimation and beamforming in electrocardiography with acute ischemia

In the electrocardiographic (ECG) inverse problem, the electrical activity of the heart is estimated from measured electrocardiogram. A model of thorax conductivities and a model of the cardiac generator is required for the ECG inverse problem. Limitations and errors in methods, models, and data will lead to errors in the estimates. However, in experimental applications, the use of limited or erroneous models is often inevitable due to necessary model simplifications and the difficulty of obtaining accurate 3D anatomical imaging data. In this work, we focus on two methods for solving the inverse problem of ECG in the case of acute ischemia: minimum-norm (MN) estimation and linearly constrained minimum-variance beamforming. We study how these methods perform with different sizes of ischemia and with erroneous conductivity models. The results indicate that the beamformer can localize small ischemia given an accurate model, but it cannot be used for estimating the size of ischemia. The MN estimator is tolerant to geometry errors and excels in estimating the size of ischemia, although the beamformer performs better with accurate model and small ischemia.

Comparison of three-shell and simplified volume conductor models in magnetoencephalography

Experimental MEG source imaging studies have typically been carried out with either a spherically symmetric head model or a single-shell boundary-element (BEM) model that is shaped according to the inner skull surface. The concepts and comparisons behind these simplified models have led to misunderstandings regarding the role of skull and scalp in MEG. In this work, we assess the forward-model errors due to different skull/scalp approximations and due to differences and errors in model geometries. We built five anatomical models of a volunteer using a set of T1-weighted MR scans and three common toolboxes. Three of the models represented typical models in experimental MEG, one was manually constructed, and one contained a major segmentation error at the skull base. For these anatomical models, we built forward models using four simplified approaches and a three-shell BEM approach that has been used as reference in previous studies. Our reference model contained in addition the skull fine-structure (spongy bone). We computed signal topographies for cortically constrained sources in the left hemisphere and compared the topographies using relative error and correlation metrics. The results show that the spongy bone has a minimal effect on MEG topographies, and thus the skull approximation of the three-shell model is justified. The three-shell model performed best, followed by the corrected-sphere and single-shell models, whereas the local-spheres and single-sphere models were clearly worse. The three-shell model was the most robust against the introduced segmentation error. In contrast to earlier claims, there was no noteworthy difference in the computation times between the realistically-shaped and sphere-based models, and the manual effort of building a three-shell model and a simplified model is comparable. We thus recommend the realistically-shaped three-shell model for experimental MEG work. In cases where this is not possible, we recommend a realistically-shaped corrected-sphere or single-shell model.

Dipolar estimates of the cortical map

Various methods based on anatomical or mathematical models have been developed to estimate cortical potentials. Among them, the most popular are the surface Laplacians (SL) and the Electrical Source Imaging (ESI) approaches. In this paper, we develop an informed method named dipolar cortical mapping (DCM), aiming to find a balance between ESI methods based on anatomical models and methods without strong anatomical priors, such as surface Laplacians. Our method only uses easily available information on the electrode position and is based on a physiologically parametrized family of interpolating functions. Simulation results show that DCM competes with previously proposed surface Laplacians and with the model based Minimum Norm Estimates (MNE) computed with a Boundary Element Model (BEM).

Comparison of spherical and realistically shaped boundary element head models for transcranial magnetic stimulation navigation

OBJECTIVE

MRI-guided real-time transcranial magnetic stimulation (TMS) navigators that apply electromagnetic modeling have improved the utility of TMS. However, their accuracy and speed depends on the assumed volume conductor geometry. Spherical models found in present navigators are computationally fast but may be inaccurate in some areas. Realistically shaped boundary-element models (BEMs) could increase accuracy at a moderate computational cost, but it is unknown which model features have the largest influence on accuracy. Thus, we compared different types of spherical models and BEMs.

METHODS

Globally and locally fitted spherical models and different BEMs with either one or three compartments and with different skull-to-brain conductivity ratios (1/1-1/80) were compared against a reference BEM.

RESULTS

The one-compartment BEM at inner skull surface was almost as accurate as the reference BEM. Skull/brain conductivity ratio in the range 1/10-1/80 had only a minor influence. BEMs were superior to spherical models especially in frontal and temporal areas (up to 20mm localization and 40% intensity improvement); in motor cortex all models provided similar results.

CONCLUSIONS

One-compartment BEMs offer a good balance between accuracy and computational cost.

SIGNIFICANCE

Realistically shaped BEMs may increase TMS navigation accuracy in several brain areas, such as in prefrontal regions often targeted in clinical applications.

Uncovering neural independent components from highly artifactual TMS-evoked EEG data

Transcranial magnetic stimulation (TMS) combined with electroencephalography (EEG) is a powerful tool for studying cortical excitability and connectivity. To enhance the EEG interpretation, independent component analysis (ICA) has been used to separate the data into independent components (ICs). However, TMS can evoke large artifacts in EEG, which may greatly distort the ICA separation. The removal of such artifactual EEG from the data is a difficult task. In this paper we study how badly the large artifacts distort the ICA separation, and whether the distortions could be avoided without removing the artifacts. We first show that, in the ICA separation, the time courses of the ICs are not affected by the large artifacts, but their topographies could be greatly distorted. Next, we show how this distortion can be circumvented. We introduce a novel technique of suppression, by which the EEG data are modified so that the ICA separation of the suppressed data becomes reliable. The suppression, instead of removing the artifactual EEG, rescales all the data to about the same magnitude as the neural EEG. For the suppressed data, ICA returns the original time courses, but instead of the original topographies, it returns modified ones, which can be used, e.g., for the source localization. We present three suppression methods based on principal component analysis, wavelet analysis, and whitening of the data matrix, respectively. We test the methods with numerical simulations. The results show that the suppression improves the source localization.