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

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.

A full-head model to investigate intra and extracochlear electric fields in cochlear implant stimulation

Objective.Despite the widespread use and technical improvement of cochlear implant (CI) devices over past decades, further research into the bioelectric bases of CI stimulation is still needed. Various stimulation modes implemented by different CI manufacturers coexist, but their true clinical benefit remains unclear, probably due to the high inter-subject variability reported, which makes the prediction of CI outcomes and the optimal fitting of stimulation parameters challenging. A highly detailed full-head model that includes a cochlea and an electrode array is developed in this study to emulate intracochlear voltages and extracochlear current pathways through the head in CI stimulation.Approach.Simulations based on the finite element method were conducted under monopolar, bipolar, tripolar (TP), and partial TP modes, as well as for apical, medial, and basal electrodes. Variables simulated included: intracochlear voltages, electric field (EF) decay, electric potentials at the scalp and extracochlear currents through the head. To better understand CI side effects such as facial nerve stimulation, caused by spurious current leakage out from the cochlea, special emphasis is given to the analysis of the EF over the facial nerve.Main results.The model reasonably predicts EF magnitudes and trends previously reported in CI users. New relevant extracochlear current pathways through the head and brain tissues have been identified. Simulated results also show differences in the magnitude and distribution of the EF through different segments of the facial nerve upon different stimulation modes and electrodes, dependent on nerve and bone tissue conductivities.Significance.Full-head models prove useful tools to model intra and extracochlear EFs in CI stimulation. Our findings could prove useful in the design of future experimental studies to contrast FNS mechanisms upon stimulation of different electrodes and CI modes. The full-head model developed is freely available for the CI community for further research and use.

Modification of brain conductivity in human focal epilepsy: A model-based estimation from stereoelectroencephalography

OBJECTIVE

We have developed a novel method for estimating brain tissue electrical conductivity using low-intensity pulse stereoelectroencephalography (SEEG) stimulation coupled with biophysical modeling. We evaluated the hypothesis that brain conductivity is correlated with the degree of epileptogenicity in patients with drug-resistant focal epilepsy.

METHODS

We used bipolar low-intensity biphasic pulse stimulation (.2 mA) followed by a postprocessing pipeline for estimating brain conductivity. This processing is based on biophysical modeling of the electrical potential induced in brain tissue between the stimulated contacts in response to pulse stimulation. We estimated the degree of epileptogenicity using a semi-automatic method quantifying the dynamic of fast discharge at seizure onset: the epileptogenicity index (EI). We also investigated how the location of stimulation within specific anatomical brain regions or within lesional tissue impacts brain conductivity.

RESULTS

We performed 1034 stimulations of 511 bipolar channels in 16 patients. We found that brain conductivity was lower in the epileptogenic zone (EZ; unpaired median difference = .064, p < .001) and inversely correlated with the epileptogenic index value (p < .001, Spearman rho = -.32). Conductivity values were also influenced by anatomical site, location within lesion, and delay between SEEG electrode implantation and stimulation, and had significant interpatient variability. Mixed model multivariate analysis showed that conductivity is significantly associated with EI (F = 13.45, p < .001), anatomical regions (F = 5.586, p < .001), delay since implantation (F = 14.71, p = .003), and age at SEEG (F = 6.591, p = .027), but not with the type of lesion (F = .372, p = .773) or the delay since last seizure (F = 1.592, p = .235).

SIGNIFICANCE

We provide a novel model-based method for estimating brain conductivity from SEEG low-intensity pulse stimulations. The brain tissue conductivity is lower in EZ as compared to non-EZ. Conductivity also varies significantly across anatomical brain regions. Involved pathophysiological processes may include changes in the extracellular space (especially volume or tortuosity) in epileptic tissue.

Towards a more accurate quasi-static approximation of the electric potential for neurostimulation with kilohertz-frequency sources. J Neural Eng 2023;20:10.1088/1741-2552/ad1612. [PMID: 38100821 PMCID: PMC10822676 DOI: 10.1088/1741-2552/ad1612]

Objective.Our goal was to determine the conditions for which a more precise calculation of the electric potential than the quasi-static approximation may be needed in models of electrical neurostimulation, particularly for signals with kilohertz-frequency components.Approach.We conducted a comprehensive quantitative study of the differences in nerve fiber activation and conduction block when using the quasi-static and Helmholtz approximations for the electric potential in a model of electrical neurostimulation.Main results.We first show that the potentials generated by sources of unbalanced pulses exhibit different transients as compared to those of charge-balanced pulses, and this is disregarded by the quasi-static assumption. Secondly, relative errors for current-distance curves were below 3%, while for strength-duration curves these ranged between 1%-17%, but could be improved to less than 3% across the range of pulse duration by providing a corrected quasi-static conductivity. Third, we extended our analysis to trains of pulses and reported a 'congruence area' below 700 Hz, where the fidelity of fiber responses is maximal for supra-threshold stimulation. Further examination of waveforms and polarities revealed similar fidelities in the congruence area, but significant differences were observed beyond this area. However, the spike-train distance revealed differences in activation patterns when comparing the response generated by each model. Finally, in simulations of conduction-block, we found that block thresholds exhibited errors above 20% for repetition rates above 10 kHz. Yet, employing a corrected value of the conductivity improved the agreement between models, with errors no greater than 8%.Significance.Our results emphasize that the quasi-static approximation cannot be naively extended to electrical stimulation with high-frequency components, and notable differences can be observed in activation patterns. As well, we introduce a methodology to obtain more precise model responses using the quasi-static approach, retaining its simplicity, which can be a valuable resource in computational neuroengineering.

Quasi-static pipeline in electroconvulsive therapy computational modeling

BACKGROUND

Computational models of current flow during Electroconvulsive Therapy (ECT) rely on the quasi-static assumption, yet tissue impedance during ECT may be frequency specific and change adaptively to local electric field intensity.

OBJECTIVES

We systematically consider the application of the quasi-static pipeline to ECT under conditions where 1) static impedance is measured before ECT and 2) during ECT when dynamic impedance is measured. We propose an update to ECT modeling accounting for frequency-dependent impedance.

METHODS

The frequency content on an ECT device output is analyzed. The ECT electrode-body impedance under low-current conditions is measured with an impedance analyzer. A framework for ECT modeling under quasi-static conditions based on a single device-specific frequency (e.g., 1 kHz) is proposed.

RESULTS

Impedance using ECT electrodes under low-current is frequency dependent and subject specific, and can be approximated at >100 Hz with a subject-specific lumped parameter circuit model but at <100 Hz increased non-linearly. The ECT device uses a 2 μA 800 Hz test signal and reports a static impedance that approximate 1 kHz impedance. Combined with prior evidence suggesting that conductivity does not vary significantly across ECT output frequencies at high-currents (800-900 mA), we update the adaptive pipeline for ECT modeling centered at 1 kHz frequency. Based on individual MRI and adaptive skin properties, models match static impedance (at 2 μA) and dynamic impedance (at 900 mA) of four ECT subjects.

CONCLUSIONS

By considering ECT modeling at a single representative frequency, ECT adaptive and non-adaptive modeling can be rationalized under a quasi-static pipeline.