The impact of artifact removal approaches on TMS-EEG signal.

Transcranial magnetic stimulation (TMS)-evoked potentials (TEPs) allow one to assess cortical excitability and effective connectivity in clinical and basic research. However, obtaining clean TEPs is challenging due to the various TMS-related artifacts that contaminate the electroencephalographic (EEG) signal when the TMS pulse is delivered. Different preprocessing approaches have been employed to remove the artifacts, but the degree of artifact reduction or signal distortion introduced in this phase of analysis is still unknown. Knowing and controlling this potential source of uncertainty will increase the inter-rater reliability of TEPs and improve the comparability between TMS-EEG studies. The goal of this study was to assess the variability in TEP waveforms due to of the use of different preprocessing pipelines. To accomplish this aim, we preprocessed the same TMS-EEG data with four different pipelines and compared the results. The dataset was obtained from 16 subjects in two identical recording sessions, each session consisting of both left dorsolateral prefrontal cortex and left inferior parietal lobule stimulation at 100% of the resting motor threshold. Considerable differences in TEP amplitudes and global mean field power (GMFP) were found between the preprocessing pipelines. Topographies of TEPs from the different pipelines were all highly correlated (ρ>0.8) at latencies over 100 ms. By contrast, waveforms at latencies under 100 ms showed a variable level of correlation, with ρ ranging between 0.2 and 0.9. Moreover, the test-retest reliability of TEPs depended on the preprocessing pipeline. Taken together, these results take us to suggest that the choice of the preprocessing approach has a marked impact on the final TEP, and that further studies are needed to understand advantages and disadvantages of the different approaches.

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

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.

Automated search of stimulation targets with closed-loop transcranial magnetic stimulation.

Transcranial magnetic stimulation (TMS) protocols often include a manual search of an optimal location and orientation of the coil or peak stimulating electric field to elicit motor responses in a target muscle. This target search is laborious, and the result is user-dependent. Here, we present a closed-loop search method that utilizes automatic electronic adjustment of the stimulation based on the previous responses. The electronic adjustment is achieved by multi-locus TMS, and the adaptive guiding of the stimulation is based on the principles of Bayesian optimization to minimize the number of stimuli (and time) needed in the search. We compared our target-search method with other methods, such as systematic sampling in a predefined cortical grid. Validation experiments on five healthy volunteers and further offline simulations showed that our adaptively guided search method needs only a relatively small number of stimuli to provide outcomes with good accuracy and precision. The automated method enables fast and user-independent optimization of stimulation parameters in research and clinical applications of TMS.

EEG Artifact Removal in TMS Studies of Cortical Speech Areas.

The combination of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) is commonly applied for studying the effective connectivity of neuronal circuits. The stimulation excites neurons, and the resulting TMS-evoked potentials (TEPs) are recorded with EEG. A serious obstacle in this method is the generation of large muscle artifacts from scalp muscles, especially when frontolateral and temporoparietal, such as speech, areas are stimulated. Here, TMS-EEG data were processed with the signal-space projection and source-informed reconstruction (SSP-SIR) artifact-removal methods to suppress these artifacts. SSP-SIR suppressed muscle artifacts according to the difference in frequency contents of neuronal signals and muscle activity. The effectiveness of SSP-SIR in rejecting muscle artifacts and the degree of excessive attenuation of brain EEG signals were investigated by comparing the processed versions of the recorded TMS-EEG data with simulated data. The calculated individual lead-field matrix describing how the brain signals spread on the cortex were used as simulated data. We conclude that SSP-SIR was effective in suppressing artifacts also when frontolateral and temporoparietal cortical sites were stimulated, but it may have suppressed also the brain signals near the stimulation site. Effective connectivity originating from the speech-related areas may be studied even when speech areas are stimulated at least on the contralateral hemisphere where the signals were not suppressed that much.

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.

Short-interval intracortical inhibition in human primary motor cortex: A multi-locus transcranial magnetic stimulation study.

Short-interval intracortical inhibition (SICI) has been studied with paired-pulse transcranial magnetic stimulation (TMS) by administering two pulses at a millisecond-scale interstimulus interval (ISI) to a single cortical target. It has, however, been difficult to study the interaction of nearby cortical targets with paired-pulse TMS. To overcome this limitation, we have developed a multi-locus TMS (mTMS) device, which allows controlling the stimulus location electronically. Here, we applied mTMS to study SICI in primary motor cortex with paired pulses targeted to adjacent locations, aiming to quantify the extent of the cortical region producing SICI in the location of a test stimulus. We varied the location and timing of the conditioning stimulus with respect to a test stimulus targeted to the cortical hotspot of the abductor pollicis brevis (APB) in order to study their effects on motor evoked potentials. We further applied a two-coil protocol with the conditioning stimulus given by an oval coil only to the surroundings of the APB hotspot, to which a subsequent test stimulus was administered with a figure-of-eight coil. The strongest SICI occurred at ISIs below 1 ms and at ISIs around 2.5 ms. These ISIs increased when the conditioning stimulus receded from the APB hotspot. Our two-coil paired-pulse TMS study suggests that SICI at ISIs of 0.5 and 2.5 ms originate from different mechanisms or neuronal elements.

The effect of experimental pain on short-interval intracortical inhibition with multi-locus transcranial magnetic stimulation.

Chronic neuropathic pain is known to alter the primary motor cortex (M1) function. Less is known about the normal, physiological effects of experimental neurogenic pain on M1. The objective of this study is to determine how short-interval intracortical inhibition (SICI) is altered in the M1 representation area of a muscle exposed to experimental pain compared to SICI of another muscle not exposed to pain. The cortical representation areas of the right abductor pollicis brevis (APB) and biceps brachii (BB) muscles of 11 subjects were stimulated with a multi-locus transcranial magnetic stimulation device while the resulting motor-evoked potentials (MEPs) were recorded with electromyography. Single- and paired-pulse TMS was administered in seven conditions, including one with the right hand placed in cold water. The stimulation intensity for the conditioning pulses in the paired-pulse examination was 80% of the resting motor threshold (RMT) of the stimulated site and 120% of RMT for both the test and single pulses. The paired-pulse MEP amplitudes were normalized with the mean amplitude of the single-pulse MEPs of the same condition and muscle. SICI was compared between conditions. After the cold pain, the normalized paired-pulse MEP amplitudes decreased in APB, but not in BB, indicating that SICI was potentially increased only in the cortical area of the muscle subjected to pain. These data suggest that SICI is increased in the M1 representation area of a hand muscle shortly after exposure to pain has ended, which implies that short-lasting pain can alter the inhibitory balance in M1.

["ConnectToBrain" : Synergy project for therapeutic closed-loop stimulation of brain network disorders]. / "ConnectToBrain" : Synergy-Projekt zur Closed-loop-Stimulationstherapie von Netzwerkerkrankungen des Gehirns.

Therapeutic non-invasive transcranial brain stimulation with previous treatment protocols showed at best moderate effect sizes and large interindividual variability with a substantial proportion of non-responders. A currently intensively discussed approach to address these problems is individualized closed-loop stimulation. ConnectToBrain is a synergy project funded by the European Research Council to develop noninvasive closed-loop therapeutic stimulation of network disorders of the human brain.It consists of three main pillars: (1) development of a multichannel transcranial magnetic stimulation (mTMS) coil array that covers nearly all of the cerebral cortex and enables highly precise electronic control of location, direction, intensity and timing of the induced electrical fields, (2) development of real-time analysis of activity and connectivity in brain networks using electroencephalography (EEG) for instantaneous spatial and temporal control of stimulation (brain state-dependent, closed-loop stimulation) and adaptive optimization of treatment effects by machine learning and (3) translation of these neurotechnological innovations into physiological and clinical studies.

Truncated RAP-MUSIC (TRAP-MUSIC) for MEG and EEG source localization.

Electrically active brain regions can be located applying MUltiple SIgnal Classification (MUSIC) on magneto- or electroencephalographic (MEG; EEG) data. We introduce a new MUSIC method, called truncated recursively-applied-and-projected MUSIC (TRAP-MUSIC). It corrects a hidden deficiency of the conventional RAP-MUSIC algorithm, which prevents estimation of the true number of brain-signal sources accurately. The correction is done by applying a sequential dimension reduction to the signal-subspace projection. We show that TRAP-MUSIC significantly improves the performance of MUSIC-type localization; in particular, it successfully and robustly locates active brain regions and estimates their number. We compare TRAP-MUSIC and RAP-MUSIC in simulations with varying key parameters, e.g., signal-to-noise ratio, correlation between source time-courses, and initial estimate for the dimension of the signal space. In addition, we validate TRAP-MUSIC with measured MEG data. We suggest that with the proposed TRAP-MUSIC method, MUSIC-type localization could become more reliable and suitable for various online and offline MEG and EEG applications.

Automatic and robust noise suppression in EEG and MEG: The SOUND algorithm.

Electroencephalography (EEG) and magnetoencephalography (MEG) often suffer from noise- and artifact-contaminated channels and trials. Conventionally, EEG and MEG data are inspected visually and cleaned accordingly, e.g., by identifying and rejecting the so-called "bad" channels. This approach has several shortcomings: data inspection is laborious, the rejection criteria are subjective, and the process does not fully utilize all the information in the collected data. Here, we present noise-cleaning methods based on modeling the multi-sensor and multi-trial data. These approaches offer objective, automatic, and robust removal of noise and disturbances by taking into account the sensor- or trial-specific signal-to-noise ratios. We introduce a method called the source-estimate-utilizing noise-discarding algorithm (the SOUND algorithm). SOUND employs anatomical information of the head to cross-validate the data between the sensors. As a result, we are able to identify and suppress noise and artifacts in EEG and MEG. Furthermore, we discuss the theoretical background of SOUND and show that it is a special case of the well-known Wiener estimators. We explain how a completely data-driven Wiener estimator (DDWiener) can be used when no anatomical information is available. DDWiener is easily applicable to any linear multivariate problem; as a demonstrative example, we show how DDWiener can be utilized when estimating event-related EEG/MEG responses. We validated the performance of SOUND with simulations and by applying SOUND to multiple EEG and MEG datasets. SOUND considerably improved the data quality, exceeding the performance of the widely used channel-rejection and interpolation scheme. SOUND also helped in localizing the underlying neural activity by preventing noise from contaminating the source estimates. SOUND can be used to detect and reject noise in functional brain data, enabling improved identification of active brain areas.

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.

Minimum-Norm Estimation of Motor Representations in Navigated TMS Mappings.

Navigated transcranial magnetic stimulation (nTMS) can be applied to locate and outline cortical motor representations. This may be important, e.g., when planning neurosurgery or focused nTMS therapy, or when assessing plastic changes during neurorehabilitation. Conventionally, a cortical location is considered to belong to the motor cortex if the maximum electric field (E-field) targeted there evokes a motor-evoked potential in a muscle. However, the cortex is affected by a broad E-field distribution, which tends to broaden estimates of representation areas by stimulating also the neighboring areas in addition to the maximum E-field location. Our aim was to improve the estimation of nTMS-based motor maps by taking into account the E-field distribution of the stimulation pulse. The effect of the E-field distribution was considered by calculating the minimum-norm estimate (MNE) of the motor representation area. We tested the method on simulated data and then applied it to recordings from six healthy volunteers and one stroke patient. We compared the motor representation areas obtained with the MNE method and a previously introduced interpolation method. The MNE hotspots and centers of gravity were close to those obtained with the interpolation method. The areas of the maps, however, depend on the thresholds used for outlining the areas. The MNE method may improve the definition of cortical motor areas, but its accuracy should be validated by comparing the results with maps obtained with direct cortical stimulation of the cortex where the E-field distribution can be better focused.

Visual deviant stimuli produce mismatch responses in the amplitude dynamics of neuronal oscillations.

OBJECTIVES: Auditory and visual deviant stimuli evoke mismatch negativity (MMN) responses, which can be recorded with electroencephalography (EEG) and magnetoencephalography (MEG). However, little is known about the role of neuronal oscillations in encoding of rare stimuli. We aimed at verifying the existence of a mechanism for the detection of deviant visual stimuli on the basis of oscillatory responses, so-called visual mismatch oscillatory response (vMOR). METHODS: Peripheral visual stimuli in an oddball paradigm, standard vs. deviant (7:1), were presented to twenty healthy subjects. The oscillatory responses to an infrequent change in the direction of moving peripheral stimuli were recorded with a 60-channel EEG system. In order to enhance the detection of oscillatory responses, we used the common spatial pattern (CSP) algorithm, designed for the optimal extraction of changes in the amplitude of oscillations. RESULTS: Both standard and deviant visual stimuli produced Event-Related Desynchronization (ERD) and Synchronization (ERS) primarily in the occipito-parietal cortical areas. ERD and ERS had overlapping time-courses and peaked at about 500-730 ms. These oscillatory responses, however, were significantly stronger for the deviant than for the standard stimuli. A difference between the oscillatory responses to deviant and standard stimuli thus reflects the presence of vMOR. CONCLUSIONS: The present study shows that the detection of visual deviant stimuli can be reflected in both synchronization and desynchronization of neuronal oscillations. This broadens our knowledge about the brain mechanisms encoding deviant sensory stimuli.

Recovering TMS-evoked EEG responses masked by muscle artifacts.

Combined transcranial magnetic stimulation (TMS) and electroencephalography (EEG) often suffers from large muscle artifacts. Muscle artifacts can be removed using signal-space projection (SSP), but this can make the visual interpretation of the remaining EEG data difficult. We suggest to use an additional step after SSP that we call source-informed reconstruction (SIR). SSP-SIR improves substantially the signal quality of artifactual TMS-EEG data, causing minimal distortion in the neuronal signal components. In the SSP-SIR approach, we first project out the muscle artifact using SSP. Utilizing an anatomical model and the remaining signal, we estimate an equivalent source distribution in the brain. Finally, we map the obtained source estimate onto the original signal space, again using anatomical information. This approach restores the neuronal signals in the sensor space and interpolates EEG traces onto the completely rejected channels. The introduced algorithm efficiently suppresses TMS-related muscle artifacts in EEG while retaining well the neuronal EEG topographies and signals. With the presented method, we can remove muscle artifacts from TMS-EEG data and recover the underlying brain responses without compromising the readability of the signals of interest.

Rotary scanning acquisition in ultra-low-field MRI.

PURPOSE: To develop a method of achieving large field of view (FOV) imaging with a smaller amount of data in ultra-low-field (ULF) MRI. THEORY: In rotary scanning acquisition (RSA), data from the imaging object is acquired at multiple angles by rotating the object or the scanner. RSA is similar to radial-trajectory acquisition but simplifies the measurement and image reconstruction when concomitant fields are nonnegligible. METHODS: RSA was implemented to achieve large FOV with only three localized superconductive quantum interference device (SQUID) sensors at the ULF-MRI field of 50 µT. RESULTS: Simulations suggest benefits of RSA, including reduced concomitant field artifacts, large FOV imaging, and SNR improvement. Experimental data demonstrate the feasibility of reconstructing large FOV images using only three SQUID sensors with 33% of the amount of data collected using a Cartesian trajectory. CONCLUSION: RSA can be useful in low-field, low-weight, or portable MRI to generate large FOV images with only a few sensors. Magn Reson Med 75:2255-2264, 2016. © 2015 Wiley Periodicals, Inc.

Transcutaneous vagus nerve stimulation modulates tinnitus-related beta- and gamma-band activity.

OBJECTIVES: The ability of a treatment method to interfere with tinnitus-related neural activity patterns, such as cortical gamma rhythms, has been suggested to indicate its potential in relieving tinnitus. Therapeutic modulation of gamma-band oscillations with vagus nerve stimulation has been recently reported in epileptic patients. The aim of this study was to investigate the effects of transcutaneous vagus nerve stimulation (tVNS) on neural oscillatory patterns. DESIGN: We calculated the power spectral density and synchrony of magnetoencephalography recordings during auditory stimulation in seven tinnitus patients and eight normal-hearing control subjects. Comparisons between subject groups were performed to reveal electrophysiological markers of tinnitus. tVNS-specific effects within each group were studied by comparing recording blocks with and without tVNS. We also investigated the correlation of each measure with individual ratings of tinnitus distress, as measured by the tinnitus handicap inventory questionnaire. RESULTS: Tinnitus patients differed from controls in the baseline condition (no tVNS applied), measured by both cortical oscillatory power and synchronization, particularly at beta and gamma frequencies. Importantly, we found tVNS-induced changes in synchrony, correlating strongly with tinnitus handicap inventory scores, at whole-head beta-band (r = -0.857, p = 0.007), whole-head gamma-band (r = -0.952, p = 0.0003), and frontal gamma-band (r = -0.952, p = 0.0003). CONCLUSIONS: We conclude that tVNS was successful in modulating tinnitus-related beta- and gamma-band activity and thus could have potential as a treatment method for tinnitus.

Efficient concomitant and remanence field artifact reduction in ultra-low-field MRI using a frequency-space formulation.

PURPOSE: For ultra-low-field MRI, the spatial-encoding magnetic fields generated by gradient coils can have strong concomitant fields leading to prominent image distortion. Additionally, using superconducting magnet to pre-polarize magnetization can improve the signal-to-noise ratio of ultra-low-field MRI. Yet the spatially inhomogeneous remanence field due to the permanently trapped flux inside a superconducting pre-polarizing coil modulates magnetization and causes further image distortion. METHOD: We propose a two-stage frequency-space (f-x) formulation to accurately describe the dynamics of spatially-encoded magnetization under the influence of concomitant and remanence fields, which allows for correcting image distortion due to concomitant and remanence fields. RESULTS: Our method is computationally efficient as it uses a combination of the fast Fourier transform algorithm and a linear equation solver. With sufficiently dense discretization in solving the linear equation, the performance of this f-x method was found to be stable among different choices of the regularization parameter and the regularization matrix. CONCLUSION: We present this method together with numerical simulations and experimental data to demonstrate how concomitant and remanence field artifacts in ultra-low-field MRI can be corrected efficiently.

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.

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.