The most accurate source localization is obtained when the voltage surface is densely sampled over both the superior and inferior surfaces.

Objective Transcranial direct current stimulation (tDCS) aims to alter brain function noninvasively via electrodes placed on the scalp. Conventional tDCS uses two relatively large patch electrodes to deliver electrical currents to the brain region of interest (ROI). Recent studies have shown that using dense arrays containing up to 512 smaller electrodes may increase the precision of targeting ROIs. However, this creates a need for methods to determine effective and safe stimulus patterns as the degrees of freedom is much higher with such arrays. Several approaches to this problem have appeared in the literature. In this paper, we describe a new method for calculating optimal electrode stimulus pattern for targeted and directional modulation in dense array tDCS which differs in some important aspects with methods reported to date. Approach We optimize stimulus pattern of dense arrays with fixed electrode placement to maximize the current density in a particular direction in the ROI. We impose a flexible set of safety constraints on the current power in the brain, individual electrode currents, and total injected current, to protect subject safety. The proposed optimization problem is convex and thus efficiently solved using existing optimization software to find unique and globally optimal electrode stimulus patterns. Main results Solutions for four anatomical ROIs based on a realistic head model are shown as exemplary results. To illustrate the differences between our approach and previously introduced methods, we compare our method with two of the other leading methods in the literature. We also report on extensive simulations that show the effect of the values chosen for each proposed safety constraint bound on the optimized stimulus patterns. Significance The proposed optimization approach employs volume based ROIs, easily adapts to different sets of safety constraints, and takes negligible time to compute. In-depth comparison study gives insight into the relationship between different objective criteria and optimized stimulus patterns. In addition, the analysis of the interaction between optimized stimulus patterns and safety constraint bounds suggests that more precise current localization in the ROI, with supposably improved safety criterion, may be achieved by careful selection of the constraint bounds.

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

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In pain management as well as other clinical applications of neuromodulation, it is important to consider the timing parameters influencing activity-dependent plasticity, including pulsed versus sustained currents, as well as the spatial action of electrical currents as they polarize the complex convolutions of the cortical mantle. These factors are of course related; studying temporal factors is not possible when the spatial resolution of current delivery to the cortex is so uncertain to make it unclear whether excitability is increased or decreased with anodal vs. cathodal current flow. In the present study we attempted to improve the targeting of specific cortical locations by applying current through flexible source-sink configurations of 256 electrodes in a geodesic array. We constructed a precision electric head model for 12 healthy individuals. Extraction of the individual’s cortical surface allowed computation of the component of the induced current that is normal to the target cortical surface. In an effort to replicate the long-term depression (LTD) induced with pulsed protocols in invasive animal research and transcranial magnetic stimulation studies, we applied 100 ms pulses at 1.9 s intervals either in cortical-surface-anodal or cortical-surface-cathodal directions, with a placebo (sham) control. The results showed significant LTD of the motor evoked potential as a result of the cortical-surface-cathodal pulses in contrast to the placebo control, with a smaller but similar LTD effect for anodal pulses. The cathodal LTD after-effect was sustained over 90 min following current injection. These results support the feasibility of pulsed protocols with low total charge in non-invasive neuromodulation when the precision of targeting is improved with a dense electrode array and accurate head modeling.

Abstract-Objective: To estimate scalp, skull, compact bone and marrow bone electrical conductivity values based on Electrical Impedance Tomography (EIT) measurements, and to determine the influence of skull modeling details on the estimates. Methods: We collected EIT data with 62 current injection pairs and built five 6-8 million finite element (FE) head models with different grades of skull simplifications for four subjects, including three whose head models serve as Atlas in the scientific literature and in commercial equipment (Colin27 and EGI's Geosource atlases). We estimated electrical conductivity of the scalp, skull, marrow bone and compact bone tissues for each current injection pair, each model, and each subject. We also provide subject specific conductivity estimates for widely used Atlas head models.

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