Optimization of focality and direction in dense electrode array transcranial direct current stimulation (tDCS)

Abstract

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.

Skull Modeling Effects in Conductivity Estimates Using Parametric Electrical Impedance Tomography

“…The skull models can be improved even further, for example by mapping the skull porosity derived from the CT Hounsfield units to electrical conductivity [9]. This mapping is parametric, with a low number of unknowns and bEIT can be used to estimate them in a similar way as shown in the present work.…”

Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation

“…Indeed, when using a single set of values (median) we find similar performance (r = 0.78 ± 0.10). Estimating spatial distribution of field magnitudes is important if one intends to use models to select the best electrode configuration to stimulate a particular brain region (Dmochowski et al, 2011;Ruffini et al, 2014;Guler et al, 2016). Many clinical trials and cognitive neuroscience experiments with TES aim to target a specific brain region, and many of the inferences that are drawn from such trials are predicated on having an accurate understanding of which areas are maximally stimulated, what polarity the stimulation has in specific sulci, and which areas are not significantly affected with a specific electrode montage.…”

“…Targeting aims to select the electrode configuration that achieves highest intensity in one location while perhaps minimizing stimulation intensity elsewhere in the brain (Dmochowski et al, 2011;Ruffini et al, 2014;Guler et al, 2016). We attempted to provide error bars on the estimated electric fields by comparing repeated measures over an interval of approximately 15-30 min.…”

Optimization of interferential stimulation of the human brain with electrode arrays

“…These non-zero values can additionally implement a relative weighting for different locations (say, to compensate for uneven sampling in the FEM mesh, or to emphasize some regions more than others, although we do not do this here). A few comments are in order here: As pointed out by Guler et al (2016), this quadratic criterion can be evaluated efficiently as, s T Qs ≤ P max , which is fast to compute because, Q = A T Γ 2 A, is a compact M × M matrix.…”

“…We also provide a mathematical proof that the solution of max-intensity stimulation can be obtained directly from the forward model for TES, as first proposed by Fernandez-Corazza et al (2019). Motivated by Guler et al (2016) and Fernandez-Corazza et al (2019), we convert the computationally intractable max-focality optimization for IFS into a max-intensity problem with constraint on the energy in the nontarget area. This non-convex optimization is treated as a goal attainment problem (Gembicki and Haimes, 1975) and then solved by sequential quadratic programming (Brayton et al, 1979).…”