Unified approach in TES and IES optimization applied to realistic head models

SERGEI TUROVETS; COLLAVINI S.; MARIANO FERNÁNDEZ CORAZZA; C. H. MURAVCHIK

Montreal (Virtual)

Conferencia; 2020 OHBM ANNUAL MEETING; 2020

OHBM

Introduction:Transcranial Electrical Stimulation (TES) is a fast-growing therapeutic method to potentially treat different neurological disorders. In multiple-electrode TES, a current injection pattern is applied to the electrode array to stimulate some brain region of interest (ROI). In a recent work, we proved that many pattern optimization methods proposed so far, are in fact specific solutions of the same mathematical formulation [1]. There, we focused in showing and proving the theoretical links, but illustrated our findings in an atlas head model. The novelty of the current work is the application of the same approach to detailed head models and realistic targets of clinical interest. Moreover, we apply it to intracranial electrical stimulation (IES) with depth electrodes in the context of epilepsy pre-surgical planning, where optimal targeting has not been fully explored.Methods:Head models: Based on structural MRI and CT images we built three realistic head models, two for TES and one for IES. For the TES models, we used BrainK [2] to segment the tissues and iso2mesh [3] to mesh the volumes. The electromagnetic problem was solved using our in-house tetrahedral FEM solver [4]. For the IES model, Simnibs [5] was used to segment and iElectrodes [6] to determine the depth-electrode positions. In IES, a unique ROI marked by a specialist.Optimization methods: The constrained maximizing intensity method [7] can be stated as follows: maximize the directional current density at the ROI subject to: (i) non-ROI brain energy is limited to α; (ii) total injected current is limited; (iii) injected current per electrode is limited. In our previous work [1], we showed that by varying α, a continuous set of optimal solutions can be obtained with two extreme solutions: the maximum intensity (lowest focality), which is equivalent to the reciprocity optimization method [8], and the maximum focality (lowest intensity), which is equivalent to the weighted least squares (WLS) solution [9]. We defined intensity as the mean ROI normal-to-cortex electric field, and the focality as the intensity over the square root of α [1].Results:The maximum intensity maps (Fig. 1A,C) show the maximum possible directional intensity at each point of the cortex (each element of the cortex is assumed as the ROI at a time), whereas the maximum focality maps (Fig. 1B,D) shows the maximum possible focality for each cortical element. These figures provide a clear visualization of which cortical regions can be targeted with stronger intensity (or better focality) than others. Fig. 1E shows, the focality-intensity trade-off curves for four representative targets located at deep structures of interest. Even the better focality solutions have a focality 10 times lower than cortical targets (compared to Fig. 1B), although the intensity of the maximum intensity solutions (Fig. 1E) are around 3-4 times lower (compared to Fig. 1A). These curves allow to determine, for a specific target, an optimal solution based on its focality-intensity values.For IES, Fig. 3A shows the resulting intensity-focality trade-off curve for the ROI, whereas Figs. 3B and 3C show some current injection patterns (Fig. 3B) and current density distributions (Fig. 3B). Note how the WLS solution (left) is less sparse than the reciprocity solution (right) that only engages two electrodes, following the results found shown in [1] for TES.Conclusions:Larger intensities can be produced at the walls of cortical sulci, whereas most focal solutions can be obtained when targeting the tips of the gyri. Some deep sources can be targeted with good intensity compared to cortical ROIs, but the focality decreases more strongly for deep targets.The unified approach can also be applied to IES. The whole range of optimal solutions can be obtained if current injection through contacts from different electrodes is allowed, which is not typically done in clinical practice yet.Figures:Fig 1: Simulations on realistic head models. Maximum intensity (A) and (C) and maximum focality (B) and (D) maps for the two realistic head models. (E) Focality-intensity trade-off curves for the different optimal solutions to four representative deep-ROI examples. Each point of the curverepresents a different optimal solution for a different value of α. The curves are built by varying the non-ROI energy constraint in the optimization problem as in [1].Fig 2: (A) Focality-intensity trade-off curve for all optimal solutions assuming a ROI being stimulated using depth electrodes. (B) Evolution of the optimal current injection pattern for six examples marked with a red circle in (A), with the ROI is superimposed in gray. (C) Resulting electric field intensity [V/m] on a slice of the brain produced by the injection patterns in B.