Performance of optimal transcranial electrical stimulation limiting the number of active electrodes

FERNANDEZ CORAZZA, MARIANO; COLLAVINI, SANTIAGO; LUU, PHAN; MURAVCHIK, CARLOS; TUCKER, DON

Glasgow

Conferencia; OHBM 2022; 2022

Introduction:Transcranial electricalstimulation (TES) is a fast-growing therapeutic method to potentially treat differentneurological disorders. In multiple-electrode TES, a current injection patternis applied to the electrode array to stimulate some brain region of interest (ROI).In a recent work [1], we proved that many pattern optimizationmethods proposed so far are in fact specific solutions of the same mathematicalformulation, the constrained directional maximization (CDM) approach [2]. Moreover, we showed that there is a smoothtransition between the most focal, least intense, and least sparse solution (weightedleast squares [3]) to the most intense, most sparse, and leastfocal solution (reciprocity-based [4]). These optimal solutions can be arranged in asmooth focality versus intensity trade-off curve. In our previous work [1], we assumed an unlimited number of independentelectrical current sources. In the present work, we add the constraint on thenumber of active sources to the CDM and we assess the focality versus intensityperformance of optimized TES with and without this additional constraint. Methods:Head model: Based on structural magnetic resonance (MR) and computed tomographyimages we built a realistic head model using BrainK [5] to segment the head into seven tissues (scalp,skull, cerebrospinal fluid, eyeballs, gray matter, white matter and internalair) and assigned to them literature conductivity values (0.35, 0.01, 1.79,1.55, 0.33, 0.25 and 0 S/m, respectively). BrainK was also used to parcellatethe cortical surface into 2400 oriented dipoles and to corregister a sensor netwith 129 electrodes. The electromagnetic problem was solved using BEL’s hexahedralfinite element method (FEM) solver HexaFEM, generating a transfer matrixwith the resulting current density at each dipole of applying 128 independentcurrent injection patterns. Optimizationmethods: The constrained maximizing intensity method [2] can be stated as follows: maximize thedirectional current density at a region of interest (ROI) subject to presetlimits in: (i) non-ROI brain energy (α) thatcontrols the focality versus intensity ratio; (ii) total injected current; and (iii)injected current per electrode. We defined intensity and focality as in ourprevious work [1].Constraining thenumber of active electrodes: The number of activeelectrodes might surpass the number of available current generators for a givenhardware (HW), particularly in the large focality solutions. We incorporated tothe CDM approach the constraint number (iv): the maximum number of activeelectrodes. We adapted the branch and bound technique to the CDM problem,similarly to what was done in another work but applied to the least squaresapproach [6]. Results:We selected twodifferent dipoles as representative examples of target ROIs, one shallowlocated at the primary sensory region, and one deep located at theparahippocampal gyrus, and computed the whole range of optimal solutionswithout constraining the number of active electrodes and constraining thenumber of active electrodes to 6. Figs. 1 and 2 show the results for the shallowand deep targets respectively. For a wide range of optimal solutions (graybackground), the obtained focality versus intensity curves of the unconstrainedand the constrained solutions overlap (see plots A), but the constrainedsolutions use a much lesser number of active electrodes (see plots B). On theright of this gray area both solutions are identical because the most intensesolutions become sparser, requiring fewer active electrodes than the imposedlimitation of 6. On the left of this gray area, the most focal solutions havelower performance when constraining the number of active electrodes. Conclusions:It is possible to use few active electrodes andstill obtain the same quality of stimulation (i.e., the same focality-intensityratio) for a wide range of optimized TES solutions when including the number ofactive electrode constraint. Significance: HW specifications can be relaxed toa low number of active sources, without a significant loss in performance. Thecountereffect is that the optimizations are much slower to compute.