Quasistatic approximation in neuromodulation.

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Exploring Motor Network Connectivity in State-Dependent Transcranial Magnetic Stimulation: A Proof-of-Concept Study.

State-dependent non-invasive brain stimulation (NIBS) informed by electroencephalography (EEG) has contributed to the understanding of NIBS inter-subject and inter-session variability. While these approaches focus on local EEG characteristics, it is acknowledged that the brain exhibits an intrinsic long-range dynamic organization in networks. This proof-of-concept study explores whether EEG connectivity of the primary motor cortex (M1) in the pre-stimulation period aligns with the Motor Network (MN) and how the MN state affects responses to the transcranial magnetic stimulation (TMS) of M1. One thousand suprathreshold TMS pulses were delivered to the left M1 in eight subjects at rest, with simultaneous EEG. Motor-evoked potentials (MEPs) were measured from the right hand. The source space functional connectivity of the left M1 to the whole brain was assessed using the imaginary part of the phase locking value at the frequency of the sensorimotor µ-rhythm in a 1 s window before the pulse. Group-level connectivity revealed functional links between the left M1, left supplementary motor area, and right M1. Also, pulses delivered at high MN connectivity states result in a greater MEP amplitude compared to low connectivity states. At the single-subject level, this relation is more highly expressed in subjects that feature an overall high cortico-spinal excitability. In conclusion, this study paves the way for MN connectivity-based NIBS.

A simulation study: comparing independent component analysis and signal-space projection - source-informed reconstruction for rejecting muscle artifacts evoked by transcranial magnetic stimulation.

Introduction: The combination of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) allows researchers to explore cortico-cortical connections. To study effective connections, the first few tens of milliseconds of the TMS-evoked potentials are the most critical. Yet, TMS-evoked artifacts complicate the interpretation of early-latency data. Data-processing strategies like independent component analysis (ICA) and the combined signal-space projection-source-informed reconstruction approach (SSP-SIR) are designed to mitigate artifacts, but their objective assessment is challenging because the true neuronal EEG responses under large-amplitude artifacts are generally unknown. Through simulations, we quantified how the spatiotemporal properties of the artifacts affect the cleaning performances of ICA and SSP-SIR. Methods: We simulated TMS-induced muscle artifacts and superposed them on pre-processed TMS-EEG data, serving as the ground truth. The simulated muscle artifacts were varied both in terms of their topography and temporal profiles. The signals were then cleaned using ICA and SSP-SIR, and subsequent comparisons were made with the ground truth data. Results: ICA performed better when the artifact time courses were highly variable across the trials, whereas the effectiveness of SSP-SIR depended on the congruence between the artifact and neuronal topographies, with the performance of SSP-SIR being better when difference between topographies was larger. Overall, SSP-SIR performed better than ICA across the tested conditions. Based on these simulations, SSP-SIR appears to be more effective in suppressing TMS-evoked muscle artifacts. These artifacts are shown to be highly time-locked to the TMS pulse and manifest in topographies that differ substantially from the patterns of neuronal potentials. Discussion: Selecting between ICA and SSP-SIR should be guided by the characteristics of the artifacts. SSP-SIR might be better equipped for suppressing time-locked artifacts, provided that their topographies are sufficiently different from the neuronal potential patterns of interest, and that the SSP-SIR algorithm can successfully find those artifact topographies from the high-pass-filtered data. ICA remains a powerful tool for rejecting artifacts that are not strongly time locked to the TMS pulse.

A bicoherence approach to analyze multi-dimensional cross-frequency coupling in EEG/MEG data.

We introduce a blockwise generalisation of the Antisymmetric Cross-Bicoherence (ACB), a statistical method based on bispectral analysis. The Multi-dimensional ACB (MACB) is an approach that aims at detecting quadratic lagged phase-interactions between vector time series in the frequency domain. Such a coupling can be empirically observed in functional neuroimaging data, e.g., in electro/magnetoencephalographic signals. MACB is invariant under orthogonal trasformations of the data, which makes it independent, e.g., on the choice of the physical coordinate system in the neuro-electromagnetic inverse procedure. In extensive synthetic experiments, we prove that MACB performance is significantly better than that obtained by ACB. Specifically, the shorter the data length, or the higher the dimension of the single data space, the larger the difference between the two methods.

Acoustic noise generated by TMS in typical environment and inside an MRI scanner.

BACKGROUND: The operation of a transcranial magnetic stimulation (TMS) coil produces high-intensity impulse sounds. In TMS, a magnetic field is generated by a short-duration pulse in the range of thousands of amperes in the TMS coil. When placed in a strong magnetic field, such as inside a magnetic resonance imaging (MRI) bore, the interaction of the magnetic field and the current in the TMS coil can cause strong forces on the coil casing. The strengths of these forces depend on the coil orientation in the main magnetic field (B0). Part of the energy in this process is dissipated in the form of acoustic noise. OBJECTIVE: Our objective was to measure the sound pressure levels (SPL) of TMS "click" sounds created by commercial TMS stimulators and coils in a typical environment and inside a 3-T MRI scanner and advance the knowledge of the acoustic behaviour of TMS to safely conduct TMS alone as well as concurrently with functional MRI (fMRI). METHODS: We report SPL measurements of two commercial MRI-compatible TMS systems in the 3-T B0 field of an MRI scanner and in the earth's magnetic field. Also, we present the acoustic noise measurements of four commercial TMS stimulators and three different TMS coils in a typical operational environment without the B0 field. RESULTS: The maximum peak SPL measured was 158 dB(C) inside the 3-T MRI scanner. Outside the scanner, the maximum peak SPL was 117 dB(C). Inside the scanner, the peak SPL increased by 21-45 dB(C) depending on the stimulator and the orientation of the electric field relative to the B field. CONCLUSIONS: Hearing protection is obligatory during concurrent TMS-fMRI experiments and highly recommended during any TMS experiment. The manufacturing of quieter TMS systems is encouraged to reduce the risk of hearing damage and other unwanted effects.

Quasistatic approximation in neuromodulation.

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuro-modulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g., Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Measuring the accuracy of ICA-based artifact removal from TMS-evoked potentials.

BACKGROUND: The analysis and interpretation of transcranial magnetic stimulation (TMS)-evoked potentials (TEPs) relies on successful cleaning of the artifacts, which typically mask the early (0-30 ms) TEPs. Independent component analysis (ICA) is possibly the single most utilized methodology to clean these signals. OBJECTIVE: ICA-based cleaning is reliable provided that the input data are composed of independent components. Differently, in case the underlying components are to some extent dependent, ICA algorithms may yield erroneous estimates of the components, resulting in incorrectly cleaned data. We aim to ascertain whether TEP signals are suited for ICA. METHODS: We present a systematic analysis of how the properties of simulated artifacts imposed on measured artifact-free TEPs affect the ICA results. The variability of the artifact waveform over the recorded trials is varied from deterministic to stochastic. We measure the accuracy of ICA-based cleaning for each level of variability. RESULTS: Our findings indicate that, when the trial-to-trial variability of an artifact component is small, which can result in dependencies between underlying components, ICA-based cleaning biases towards eliminating also non-artifactual TEP data. We also show that the variability can be measured using the ICA-derived components, which in turn allows us to estimate the cleaning accuracy. CONCLUSION: As TEP artifacts tend to have small trial-to-trial variability, one should be aware of the possibility of eliminating brain-derived EEG when applying ICA-based cleaning strategies. In practice, after ICA, the artifact component variability can be measured, and it predicts to some extent the cleaning reliability, even when not knowing the clean ground-truth data.

DELMEP: a deep learning algorithm for automated annotation of motor evoked potential latencies.

The analysis of motor evoked potentials (MEPs) generated by transcranial magnetic stimulation (TMS) is crucial in research and clinical medical practice. MEPs are characterized by their latency and the treatment of a single patient may require the characterization of thousands of MEPs. Given the difficulty of developing reliable and accurate algorithms, currently the assessment of MEPs is performed with visual inspection and manual annotation by a medical expert; making it a time-consuming, inaccurate, and error-prone process. In this study, we developed DELMEP, a deep learning-based algorithm to automate the estimation of MEP latency. Our algorithm resulted in a mean absolute error of about 0.5 ms and an accuracy that was practically independent of the MEP amplitude. The low computational cost of the DELMEP algorithm allows employing it in on-the-fly characterization of MEPs for brain-state-dependent and closed-loop brain stimulation protocols. Moreover, its learning ability makes it a particularly promising option for artificial-intelligence-based personalized clinical applications.

MarLe: Markerless estimation of head pose for navigated transcranial magnetic stimulation.

Navigated transcranial magnetic stimulation (nTMS) is a valuable tool for non-invasive brain stimulation. Currently, nTMS requires fixing of markers on the patient's head. Head marker displacements lead to changes in coil placement and brain stimulation inaccuracy. A markerless neuronavigation method is needed to increase the reliability of nTMS and simplify the nTMS protocol. In this study, we introduce and release MarLe, a Python markerless head tracker neuronavigation software for TMS. This novel software uses computer-vision techniques combined with low-cost cameras to estimate the head pose for neuronavigation. A coregistration algorithm, based on a closed-form solution, was designed to track the patient's head and the TMS coil referenced to the individual's brain image. We show that MarLe can estimate head pose based on real-time video processing. An intuitive pipeline was developed to connect the MarLe and nTMS neuronavigation software. MarLe achieved acceptable accuracy and stability in a mockup nTMS experiment. MarLe allows real-time tracking of the patient's head without any markers. The combination of face detection and a coregistration algorithm can overcome nTMS head marker displacement concerns. MarLe can improve reliability, simplify, and reduce the protocol time of brain intervention techniques such as nTMS.

Advanced Pipeline for Designing Multi-Locus TMS Coils With Current Density Constraints.

OBJECTIVE: This work aims for a method to design manufacturable windings for transcranial magnetic stimulation (TMS) coils with fine control over the induced electric field (E-field) distributions. Such TMS coils are required for multi-locus TMS (mTMS). METHODS: We introduce a new mTMS coil design workflow with increased flexibility in target E-field definition and faster computations compared to our previous method. We also incorporate custom current density and E-field fidelity constraints to ensure that the target E-fields are accurately reproduced with feasible winding densities in the resulting coil designs. We validated the method by designing, manufacturing, and characterizing a 2-coil mTMS transducer for focal rat brain stimulation. RESULTS: Applying the constraints reduced the computed maximum surface current densities from 15.4 and 6.6 kA/mm to the target value 4.7 kA/mm, yielding winding paths suitable for a 1.5-mm-diameter wire with 7-kA maximum currents while still replicating the target E-fields with the predefined 2.8% maximum error in the FOV. The optimization time was reduced by two thirds compared to our previous method. CONCLUSION: The developed method allowed us to design a manufacturable, focal 2-coil mTMS transducer for rat TMS impossible to attain with our previous design workflow. SIGNIFICANCE: The presented workflow enables considerably faster design and manufacturing of previously unattainable mTMS transducers with increased control over the induced E-field distribution and winding density, opening new possibilities for brain research and clinical TMS.

TMS-Induced Modulation of EEG Functional Connectivity Is Affected by the E-Field Orientation.

Coregistration of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) allows non-invasive probing of brain circuits: TMS induces brain activation due to the generation of a properly oriented focused electric field (E-field) using a coil placed on a selected position over the scalp, while EEG captures the effects of the stimulation on brain electrical activity. Moreover, the combination of these techniques allows the investigation of several brain properties, including brain functional connectivity. The choice of E-field parameters, such as intensity, orientation, and position, is crucial for eliciting cortex-specific effects. Here, we evaluated whether and how the spatial pattern, i.e., topography and strength of functional connectivity, is modulated by the stimulus orientation. We systematically altered the E-field orientation when stimulating the left pre-supplementary motor area and showed an increase of functional connectivity in areas associated with the primary motor cortex and an E-field orientation-specific modulation of functional connectivity intensity.

Effective Intracerebral Connectivity in Acute Stroke: A TMS-EEG Study.

Stroke is a major cause of disability because of its motor and cognitive sequelae even when the acute phase of stabilization of vital parameters is overcome. The most important improvements occur in the first 8-12 weeks after stroke, indicating that it is crucial to improve our understanding of the dynamics of phenomena occurring in this time window to prospectively target rehabilitation procedures from the earliest stages after the event. Here, we studied the intracortical excitability properties of delivering transcranial magnetic stimulation (TMS) to the primary motor cortex (M1) of left and right hemispheres in 17 stroke patients who suffered a mono-lateral left hemispheric stroke, excluding pure cortical damage. All patients were studied within 10 days of symptom onset. TMS-evoked potentials (TEPs) were collected via a TMS-compatible electroencephalogram system (TMS-EEG) concurrently with motor-evoked responses (MEPs) induced in the contralateral first dorsal interosseous muscle. Comparison with age-matched healthy volunteers was made by collecting the same bilateral-stimulation data in nine healthy volunteers as controls. Excitability in the acute phase revealed relevant changes in the relationship between left lesioned and contralesionally right hemispheric homologous areas both for TEPs and MEPs. While the paretic hand displayed reduced MEPs compared to the non-paretic hand and to healthy volunteers, TEPs revealed an overexcitable lesioned hemisphere with respect to both healthy volunteers and the contra-lesion side. Our quantitative results advance the understanding of the impairment of intracortical inhibitory networks. The neuronal dysfunction most probably changes the excitatory/inhibitory on-center off-surround organization that supports already acquired learning and reorganization phenomena that support recovery from stroke sequelae.

TMS combined with EEG: Recommendations and open issues for data collection and analysis.

Transcranial magnetic stimulation (TMS) evokes neuronal activity in the targeted cortex and connected brain regions. The evoked brain response can be measured with electroencephalography (EEG). TMS combined with simultaneous EEG (TMS-EEG) is widely used for studying cortical reactivity and connectivity at high spatiotemporal resolution. Methodologically, the combination of TMS with EEG is challenging, and there are many open questions in the field. Different TMS-EEG equipment and approaches for data collection and analysis are used. The lack of standardization may affect reproducibility and limit the comparability of results produced in different research laboratories. In addition, there is controversy about the extent to which auditory and somatosensory inputs contribute to transcranially evoked EEG. This review provides a guide for researchers who wish to use TMS-EEG to study the reactivity of the human cortex. A worldwide panel of experts working on TMS-EEG covered all aspects that should be considered in TMS-EEG experiments, providing methodological recommendations (when possible) for effective TMS-EEG recordings and analysis. The panel identified and discussed the challenges of the technique, particularly regarding recording procedures, artifact correction, analysis, and interpretation of the transcranial evoked potentials (TEPs). Therefore, this work offers an extensive overview of TMS-EEG methodology and thus may promote standardization of experimental and computational procedures across groups.

Accuracy and precision of navigated transcranial magnetic stimulation.

Objective.Transcranial magnetic stimulation (TMS) induces an electric field (E-field) in the cortex. To facilitate stimulation targeting, image-guided neuronavigation systems have been introduced. Such systems track the placement of the coil with respect to the head and visualize the estimated cortical stimulation location on an anatomical brain image in real time. The accuracy and precision of the neuronavigation is affected by multiple factors. Our aim was to analyze how different factors in TMS neuronavigation affect the accuracy and precision of the coil-head coregistration and the estimated E-field.Approach.By performing simulations, we estimated navigation errors due to distortions in magnetic resonance images (MRIs), head-to-MRI registration (landmark- and surface-based registrations), localization and movement of the head tracker, and localization of the coil tracker. We analyzed the effect of these errors on coil and head coregistration and on the induced E-field as determined with simplistic and realistic head models.Main results.Average total coregistration accuracies were in the range of 2.2-3.6 mm and 1°; precision values were about half of the accuracy values. The coregistration errors were mainly due to head-to-MRI registration with average accuracies 1.5-1.9 mm/0.2-0.4° and precisions 0.5-0.8 mm/0.1-0.2° better with surface-based registration. The other major source of error was the movement of the head tracker with average accuracy of 1.5 mm and precision of 1.1 mm. When assessed within an E-field method, the average accuracies of the peak E-field location, orientation, and magnitude ranged between 1.5 and 5.0 mm, 0.9 and 4.8°, and 4.4 and 8.5% across the E-field models studied. The largest errors were obtained with the landmark-based registration. When computing another accuracy measure with the most realistic E-field model as a reference, the accuracies tended to improve from about 10 mm/15°/25% to about 2 mm/2°/5% when increasing realism of the E-field model.Significance.The results of this comprehensive analysis help TMS operators to recognize the main sources of error in TMS navigation and that the coregistration errors and their effect in the E-field estimation depend on the methods applied. To ensure reliable TMS navigation, we recommend surface-based head-to-MRI registration and realistic models for E-field computations.

Source-based artifact-rejection techniques for TMS-EEG.

Neuronal electroencephalography (EEG) signals arise from the cortical postsynaptic currents. Due to the conductive properties of the head, these neuronal sources produce relatively smeared spatial patterns in EEG. We can model these topographies to deduce which signals reflect genuine TMS-evoked cortical activity and which data components are merely noise and artifacts. This review will concentrate on two source-based artifact-rejection techniques developed for TMS-EEG data analysis, signal-space-projection-source-informed reconstruction (SSP-SIR), and the source-estimate-utilizing noise-discarding algorithm (SOUND). The former method was designed for rejecting TMS-evoked muscle artifacts, while the latter was developed to suppress noise signals from EEG and magnetoencephalography (MEG) in general. We shall cover the theoretical background for both methods, but most importantly, we will describe some essential practical perspectives for using these techniques effectively. We demonstrate and explain what approaches produce the most reliable inverse estimates after cleaning the data or how to perform non-biased comparisons between cleaned datasets. All noise-cleaning algorithms compromise the signals of interest to a degree. We elaborate on how the source-based methods allow objective quantification of the overcorrection. Finally, we consider possible future directions. While this article concentrates on TMS-EEG data analysis, many theoretical and practical aspects, presented here, can be readily applied in other EEG/MEG applications. Overall, the source-based cleaning methods provide a valuable set of TMS-EEG preprocessing tools. We can objectively evaluate their performance regarding possible overcorrection. Furthermore, the overcorrection can always be taken into account to compare cleaned datasets reliably. The described methods are based on current electrophysiological and anatomical understanding of the head and the EEG generators; strong assumptions of the statistical properties of the noise and artifact signals, such as independence, are not needed.