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.

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.

Quasi-static approximation error of electric field analysis for transcranial current stimulation.

Objective.Numerical modeling of electric fields induced by transcranial alternating current stimulation (tACS) is currently a part of the standard procedure to predict and understand neural response. Quasi-static approximation (QSA) for electric field calculations is generally applied to reduce the computational cost. Here, we aimed to analyze and quantify the validity of the approximation over a broad frequency range.Approach.We performed electromagnetic modeling studies using an anatomical head model and considered approximations assuming either a purely ohmic medium (i.e. static formulation) or a lossy dielectric medium (QS formulation). The results were compared with the solution of Maxwell's equations in the cases of harmonic and pulsed signals. Finally, we analyzed the effect of electrode positioning on these errors.Main results.Our findings demonstrate that the QSA is valid and produces a relative error below 1% up to 1.43 MHz. The largest error is introduced in the static case, where the error is over 1% across the entire considered spectrum and as high as 20% in the brain at 10 Hz. We also highlight the special importance of considering the capacitive effect of tissues for pulsed waveforms, which prevents signal distortion induced by the purely ohmic approximation. At the neuron level, the results point a difference of sense electric field as high as 22% at focusing point, impacting pyramidal cells firing times.Significance.QSA remains valid in the frequency range currently used for tACS. However, neglecting permittivity (static formulation) introduces significant error for both harmonic and non-harmonic signals. It points out that reliable low frequency dielectric data are needed for accurate transcranial current stimulation numerical modeling.

No Evidence of Attentional Modulation of the Neural Response to the Temporal Fine Structure of Continuous Musical Pieces.

Speech and music are spectrotemporally complex acoustic signals that are highly relevant for humans. Both contain a temporal fine structure that is encoded in the neural responses of subcortical and cortical processing centers. The subcortical response to the temporal fine structure of speech has recently been shown to be modulated by selective attention to one of two competing voices. Music similarly often consists of several simultaneous melodic lines, and a listener can selectively attend to a particular one at a time. However, the neural mechanisms that enable such selective attention remain largely enigmatic, not least since most investigations to date have focused on short and simplified musical stimuli. Here, we studied the neural encoding of classical musical pieces in human volunteers, using scalp EEG recordings. We presented volunteers with continuous musical pieces composed of one or two instruments. In the latter case, the participants were asked to selectively attend to one of the two competing instruments and to perform a vibrato identification task. We used linear encoding and decoding models to relate the recorded EEG activity to the stimulus waveform. We show that we can measure neural responses to the temporal fine structure of melodic lines played by one single instrument, at the population level as well as for most individual participants. The neural response peaks at a latency of 7.6 msec and is not measurable past 15 msec. When analyzing the neural responses to the temporal fine structure elicited by competing instruments, we found no evidence of attentional modulation. We observed, however, that low-frequency neural activity exhibited a modulation consistent with the behavioral task at latencies from 100 to 160 msec, in a similar manner to the attentional modulation observed in continuous speech (N100). Our results show that, much like speech, the temporal fine structure of music is tracked by neural activity. In contrast to speech, however, this response appears unaffected by selective attention in the context of our experiment.

Inhibitory control dysfunction in parkinsonian impulse control disorders.

Impulse control disorders (ICDs) in Parkinson's disease have been associated with dysfunctions in the control of value- or reward-based responding (choice impulsivity) and abnormalities in mesocorticolimbic circuits. The hypothesis that dysfunctions in the control of response inhibition (action impulsivity) also play a role in Parkinson's disease ICDs has recently been raised, but the underlying neural mechanisms have not been probed directly. We used high-resolution EEG recordings from 41 patients with Parkinson's disease with and without ICDs to track the spectral and dynamical signatures of different mechanisms involved in inhibitory control in a simple visuomotor task involving no selection between competing responses and no reward to avoid potential confounds with reward-based decision. Behaviourally, patients with Parkinson's disease with ICDs proved to be more impulsive than those without ICDs. This was associated with decreased beta activity in the precuneus and in a region of the medial frontal cortex centred on the supplementary motor area. The underlying dynamical patterns pinpointed dysfunction of proactive inhibitory control, an executive mechanism intended to gate motor responses in anticipation of stimulation in uncertain contexts. The alteration of the cortical drive of proactive response inhibition in Parkinson's disease ICDs pinpoints the neglected role the precuneus might play in higher order executive functions in coordination with the supplementary motor area, specifically for switching between executive settings. Clinical perspectives are discussed in the light of the non-dopaminergic basis of this function.