Quasi-static pipeline in electroconvulsive therapy computational modeling

Computational Optimization of Spinal Cord Stimulation for Dorsal Horn Interneuron Polarization

OBJECTIVES

The proposed mechanisms of spinal cord stimulation (SCS) follow the polarization of dorsal column axons; however, the development of subparesthesia SCS has encouraged the consideration of different targets. Given their relative proximity to the stimulation electrodes and their role in pain processing (eg, synaptic processing and gate control theory), spinal cord dorsal horn interneurons may be attractive stimulation targets.

MATERIALS AND METHODS

We developed a computational modeling pipeline termed "quasiuniform-mirror assumption" and applied it to predict polarization of dorsal horn interneuron cell types (islet type, central type, stellate/radial, vertical-like) to SCS. The quasiuniform-mirror assumption allows the prediction of the peak and directional axes of dendrite polarization for each cell type and location in the dorsal horn, in addition to the impact of the stimulation pulse width and electrode configuration.

RESULTS

For long pulses, the peak polarization per milliampere of SCS with a spaced bipolar configuration was islet type 3.5mV, central type 1.3mV, stellate/radial 1.4mV, and vertical-like 1.6mV. For stellate/radial, the peak dendrite polarization was dorsal-ventral, and for islet-type, the peak dendrite polarization was in the rostral-caudal axis. For islet type and central type cells, peak dendrite polarization was between stimulation electrodes, whereas for stellate/radial and vertical-like cells, peak dendrite polarization was under the stimulation electrodes. The impact of the pulse width depends on the membrane time constants. Assuming a 1-millisecond time constant, for a 1-millisecond or 100-μs pulse width, the peak dendrite polarization decreases (from direct current values) by approximately 33% and approximately 88%, respectively. Increasing the interelectrode distance beyond approximately 3 cm did not significantly increase the peak polarization but expanded the region of interneuron polarization.

CONCLUSIONS

Predicted maximum polarization of islet-cells in the superficial dorsal horn at locations between electrodes is 4.6mV for 2 mA, 1-millisecond pulse SCS. A polarization of a few millivolts is sufficient to modulate synaptic processing through subthreshold mechanisms. Our simulations provide support for SCS approaches optimized to modulate the dendrites of dorsal horn neurons.

Computational modeling of neuromuscular activation by transcutaneous electrical nerve stimulation to the lower back

Objectives.Transcutaneous Electrical Nerve Stimulation (TENS) to the lower back is an established electrical therapy for acute and chronic back pain. The efficacy and mechanisms of lower back TENS depend on the penetration depth of electrical current. We compare the intensity and spatial extent (depth) of current flow in the body during TENS with varied electrode positions/shapes on the human back.Materials and Methods.A high-resolution MRI-derived anatomical model of the back was developed, considering major tissue compartments, including skin and muscles. TENS with upper and lower back electrode positions and varied electrode shapes (square, circular, rectangular) were simulated. An exemplary 50 mA current was applied under quasistatic approximation and quasi-uniform electric field assumption of 6.15 V m-1(low), 12.3 V m-1(mid), and 24.6 V m-1(high) neuromuscular activation thresholds were considered.Results.Under all simulated TENS conditions (50 mA), electric fields at the skin exceed the high threshold (consistent with peripheral nerve activation) and at least some muscle regions exceed the mid threshold. Muscle activation was influenced by the anatomy of muscle in the medial-lateral direction and upper-lower back. The electrode shape had minimal effect on deep tissue current penetration.Conclusions.Our simulations indicate significant current penetration into back tissue (electric fields above low threshold) to >8 cm in all TENS conditions simulated, consistent with nerve and muscle activation.Significance.Anatomically precise models of upper and lower back TENS show current penetration to deep muscle, supporting direct muscle stimulation driving clinical benefits.

Computational Models of High-Definition Electroconvulsive Therapy for Focal or Multitargeting Treatment

ABSTRACT

Attempts to dissociate electroconvulsive therapy (ECT) therapeutic efficacy from cognitive side effects of ECT include modifying electrode placement, but traditional electrode placements employing 2 large electrodes are inherently nonfocal, limiting the ability to selectively engage targets associated with clinical benefit while avoiding nontargets associated with adverse side effects. Limited focality represents a technical limitation of conventional ECT, and there is growing evidence that the spatial distribution of the ECT electric fields induced in the brain drives efficacy and side effects. Computational models can be used to predict brain current flow patterns for existing and novel ECT montages. Using finite element method simulations (under quasi-static, nonadaptive assumptions, 800-mA total current), the electric fields generated in the superficial cortex and subcortical structures were predicted for the following traditional ECT montages (bilateral temporal, bifrontal, right unilateral) and experimental montages (focal electrically administered seizure therapy, lateralized high-definition [HD]-ECT, unilateral 4 × 1-ring HD-ECT, bilateral 4 × 1-ring HD-ECT, and a multipolar HD-ECT). Peak brain current density in regions of interest was quantified. Conventional montages (bilateral bifrontal, right unilateral) each produce distinct but diffuse and deep current flow. Focal electrically administered seizure therapy and lateralized HD-ECT produce unique, lateralized current flow, also impacting specific deep regions. A 4 × 1-ring HD-ECT restricts current flow to 1 (unilateral) or 2 (bilateral) cortical regions. Multipolar HD-ECT shows optimization to a specific target set. Future clinical trials are needed to determine whether enhanced control over current distribution is achieved with these experimental montages, and the resultant seizures, improve the risk/benefit ratio of ECT.

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.

Amplitude-determined seizure-threshold, electric field modeling, and electroconvulsive therapy antidepressant and cognitive outcomes

Electroconvulsive therapy (ECT) pulse amplitude, which dictates the induced electric field (E-field) magnitude in the brain, is presently fixed at 800 or 900 milliamperes (mA) without clinical or scientific rationale. We have previously demonstrated that increased E-field strength improves ECT's antidepressant effect but worsens cognitive outcomes. Amplitude-determined seizure titration may reduce the E-field variability relative to fixed amplitude ECT. In this investigation, we assessed the relationships among amplitude-determined seizure-threshold (STa), E-field magnitude, and clinical outcomes in older adults (age range 50 to 80 years) with depression. Subjects received brain imaging, depression assessment, and neuropsychological assessment pre-, mid-, and post-ECT. STa was determined during the first treatment with a Soterix Medical 4×1 High Definition ECT Multi-channel Stimulation Interface (Investigation Device Exemption: G200123). Subsequent treatments were completed with right unilateral electrode placement (RUL) and 800 mA. We calculated Ebrain defined as the 90th percentile of E-field magnitude in the whole brain for RUL electrode placement. Twenty-nine subjects were included in the final analyses. Ebrain per unit electrode current, Ebrain/I, was associated with STa. STa was associated with antidepressant outcomes at the mid-ECT assessment and bitemporal electrode placement switch. Ebrain/I was associated with changes in category fluency with a large effect size. The relationship between STa and Ebrain/I extends work from preclinical models and provides a validation step for ECT E-field modeling. ECT with individualized amplitude based on E-field modeling or STa has the potential to enhance neuroscience-based ECT parameter selection and improve clinical outcomes.

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.