Modulation of Alcohol Use Disorder by Brain Stimulation.

Currently available therapeutic modalities for alcohol use disorder (AUD) produce limited effect sizes or long-term compliance. Recent methods that were developed to modulate brain activity represent potential novel treatment options. Various methods of brain stimulation, when applied repeatedly, can induce long-term neurobiological, behavioral, and cognitive modifications. Recent studies in alcoholic subjects indicate the potential of brain stimulation methods to reduce alcohol craving, consumption, and relapse. Specifically, deep brain stimulation (DBS) of the nucleus accumbens or non-surgical stimulation of the dorsolateral prefrontal cortex (PFC) or medial PFC and anterior cingulate cortex using transcranial magnetic stimulation (TMS) has shown clinical benefit. However, further preclinical and clinical research is needed to establish understanding of mechanisms and the treatment protocols of brain stimulation for AUD. While efforts to design comparable apparatus in rodents continue, preclinical studies can be used to examine targets for DBS protocols, or to administer temporal patterns of pulsus similar to those used for TMS, to more superficial targets through implanted electrodes. The clinical field will benefit from studies with larger sample sizes, higher numbers of stimulation sessions, maintenance sessions, and long follow-up periods. The effect of symptoms provocation before and during stimulation should be further studied. Larger studies may have the power to explore predictive factors for the clinical outcome and thereby to optimize patient selection and eventually even develop personalization of the stimulation parameters.

Neural consequences of 5-Hz transcranial alternating current stimulation over right hemisphere: An eLORETA EEG study.

INTRODUCTION: Transcranial alternating current stimulation (tACS) at 5-Hz to the right hemisphere can effectively alleviate anxiety symptoms. This study aimed to explore the neural mechanisms that drive the therapeutic benefits. METHODS: We collected electroencephalography (EEG) data from 24 participants with anxiety disorders before and after a tACS treatment session. tACS was applied over the right hemisphere, with 1.0 mA at F4, 1.0 mA at P4, and 2.0 mA at T8 (10-10 EEG convention). With eLORETA, we transformed the scalp signals into the current source density in the cortex. We then assessed the differences between post- and pre-treatment brain maps across multiple spectra (delta to low gamma) with non-parametric statistics. RESULTS: We observed a trend of heightened power in alpha and reduced power in mid-to-high beta and low gamma, in accord with the EEG markers of anxiolytic effects reported in previous studies. Additionally, we observed a consistent trend of de-synchronization at the stimulating sites across spectra. CONCLUSION: tACS 5-Hz over the right hemisphere demonstrated EEG markers of anxiety reduction. The after-effects of tACS on the brain are intricate and cannot be explained solely by the widely circulated entrainment theory. Rather, our results support the involvement of plasticity mechanisms in the offline effects of tACS.

Tripod transcranial alternating current stimulation at 5-Hz to alleviate anxiety symptoms: A preliminary report.

INTRODUCTION: One of the most common applications of transcranial electrical stimulation (tES) at low current intensity is to induce a relaxed state or reduce anxiety. With technical advancement, different waveforms, montages, and parameters can be incorporated into the treatment regimen. We developed a novel protocol to treat individuals with anxiety disorders by transcranial alternating current stimulation (tACS). METHODS: A total of 27 individuals with anxiety disorders underwent tACS treatment for 12 sessions, with each session lasting 25 min. tACS at 5 Hz was applied to F4 (1.0 mA), P4 (1.0 mA), and T8 (2.0 mA) EEG lead positions (tripod), with sinewave oscillation between T8 and F4/P4. We evaluated the primary and secondary outcomes using the Beck Anxiety Inventory (BAI) and neuropsychological assessments. RESULTS: Of the 27 patients, 19 (70.4 %) experienced a reduction in symptom severity >50 %, with an average reduction of BAI 58.5 %. All reported side effects were mild, with itching or tingling being the most common complaint. No significant differences were noted in attention, linguistic working memory, visuospatial working memory, or long-term memory in neuropsychological assessments. CONCLUSION: The results suggest the potential of this novel tripod tACS design as a rapid anxiety alleviator and the importance of a clinical trial to verify its efficacy.

Enhancement of phonemic verbal fluency in multilingual young adults by transcranial random noise stimulation.

Several studies have analyzed the effects of transcranial direct current stimulation on verbal fluency tasks in non-clinical populations. Nevertheless, the reported effects on verbal fluency are inconsistent. In addition, the effect of other techniques such as transcranial random noise stimulation (tRNS) on verbal fluency enhancement has yet to be studied in healthy multilingual populations. This study aims to explore the effects of tRNS on verbal fluency in healthy multilingual individuals. Fifty healthy multilingual (Spanish, English and Basque) adults were randomly assigned to a tRNS or sham group. Electrodes were placed on the left dorsolateral prefrontal cortex and left inferior frontal gyrus. All participants performed phonemic and semantic verbal fluency tasks before, during (online assessment) and immediately after (offline assessment) stimulation in three different languages. The results showed significantly better performance by participants who received tRNS in the phonemic verbal fluency tasks in Spanish (in the online and offline assessment) and English (in the offline assessment). No differences between conditions were found in Basque nor semantic verbal fluency. These findings suggests that tRNS on the left prefrontal cortex could help improve phonemic, yet not semantic, fluency in healthy multilingual adults.

Lattice layout and optimizer effect analysis for generating optimal transcranial electrical stimulation (tES) montages through the metaheuristic L1L1 method.

Introduction: This study focuses on broadening the applicability of the metaheuristic L1-norm fitted and penalized (L1L1) optimization method in finding a current pattern for multichannel transcranial electrical stimulation (tES). The metaheuristic L1L1 optimization framework defines the tES montage via linear programming by maximizing or minimizing an objective function with respect to a pair of hyperparameters. Methods: In this study, we explore the computational performance and reliability of different optimization packages, algorithms, and search methods in combination with the L1L1 method. The solvers from Matlab R2020b, MOSEK 9.0, Gurobi Optimizer, CVX's SeDuMi 1.3.5, and SDPT3 4.0 were employed to produce feasible results through different linear programming techniques, including Interior-Point (IP), Primal-Simplex (PS), and Dual-Simplex (DS) methods. To solve the metaheuristic optimization task of L1L1, we implement an exhaustive and recursive search along with a well-known heuristic direct search as a reference algorithm. Results: Based on our results, and the given optimization task, Gurobi's IP was, overall, the preferable choice among Interior-Point while MOSEK's PS and DS packages were in the case of Simplex methods. These methods provided substantial computational time efficiency for solving the L1L1 method regardless of the applied search method. Discussion: While the best-performing solvers show that the L1L1 method is suitable for maximizing either focality and intensity, a few of these solvers could not find a bipolar configuration. Part of the discrepancies between these methods can be explained by a different sensitivity with respect to parameter variation or the resolution of the lattice provided.

Behavioral Validation of Individualized Low-Intensity Transcranial Electrical Stimulation (tES) Protocols.

Large interindividual variability in the effects of low-intensity transcranial electrical stimulation (tES) considerably limits its potential for clinical applications. It has been recently proposed that individualizing stimulation dose by accounting for interindividual anatomic differences would reduce the variability in electric fields (E-fields) over the targeted cortical site and therefore produce more consistent behavioral outcomes. However, improvement in behavioral outcomes following individualized dose tES has never been compared with that of conventional fixed dose tES. In this study, we aimed to empirically evaluate the effect of individualized dose tES on behavior and further compare it with the effects of sham and fixed dose stimulations. We conducted a single-blinded, sham-controlled, repeated-measures study to examine the impact of transcranial direct current stimulation on motor learning and that of transcranial alternating current stimulation on the working memory of 42 healthy adult individuals. Each participant underwent three sessions of tES, receiving fixed dose, individualized dose, or sham stimulation over the targeted brain region for the entire behavioral task. Our results showed that the individualized dose reduced the variability in E-fields at the targeted cortical surfaces. However, there was no significant effect of tES on behavioral outcomes. We argue that although the stimulation dose and E-field intensity at the targeted cortical site are linearly correlated, the effect of E-fields on behavior seems to be more complex. Effective optimization of tES protocols warrants further research considering both neuroanatomical and functional aspects of behavior.

Home-administered transcranial direct current stimulation with asynchronous remote supervision in the treatment of depression: feasibility, tolerability, and clinical effectiveness.

Introduction Background: Depression is an often chronic condition, characterized by wide-ranging physical, cognitive and psychosocial symptoms that can lead to disability, premature mortality or suicide. It affects 350 million people globally, yet up to 30% do not respond to traditional treatment, creating an urgent need for novel non-pharmacological treatments. This open-label naturalistic study assesses the practical feasibility, tolerability, and clinical effectiveness of home-administered transcranial direct current stimulation (tDCS) with asynchronous remote supervision, in the treatment of depression. Method: Over the course of 3 weeks, 40 patients with depression received psychotherapy and half of this group also received daily bi-frontal tDCS stimulation of the dorsolateral prefrontal cortex. These patients received tDCS for 30 min per session with the anode placed over F3 and the cathode over F4, at an intensity of 2 mA for 21 consecutive days. We measured patients' level of depression symptoms at four time points using the Beck Depression Inventory, before treatment and at 1-week intervals throughout the treatment period. We monitored practical feasibility such as daily protocol compliance and tolerability including side effects, with the PlatoScience cloud-based remote supervision platform. Results: Of the 20 patients in the tDCS group, 90% were able to comply with the protocol by not missing more than three of their assigned sessions, and none dropped out of the study. No serious adverse events were reported, with only 14 instances of mild to moderate side effects and two instances of scalp pain rated as severe, out of a total of 420 stimulation sessions. Patients in the tDCS group showed a significantly greater reduction in depression symptoms after 3 weeks of treatment, compared to the treatment as usual (TAU) group [t(57.2) = 2.268, p = 0.027]. The tDCS group also showed greater treatment response (50%) and depression remission rates (75%) compared to the TAU group (5 and 30%, respectively). Discussion Conclusion: These findings provide a possible indication of the clinical effectiveness of home-administered tDCS for the treatment of depression, and its feasibility and tolerability in combination with asynchronous supervision.

Outcome measures for electric field modeling in tES and TMS: A systematic review and large-scale modeling study.

BACKGROUND: Electric field (E-field) modeling is a potent tool to estimate the amount of transcranial magnetic and electrical stimulation (TMS and tES, respectively) that reaches the cortex and to address the variable behavioral effects observed in the field. However, outcome measures used to quantify E-fields vary considerably and a thorough comparison is missing. OBJECTIVES: This two-part study aimed to examine the different outcome measures used to report on tES and TMS induced E-fields, including volume- and surface-level gray matter, region of interest (ROI), whole brain, geometrical, structural, and percentile-based approaches. The study aimed to guide future research in informed selection of appropriate outcome measures. METHODS: Three electronic databases were searched for tES and/or TMS studies quantifying E-fields. The identified outcome measures were compared across volume- and surface-level E-field data in ten tES and TMS modalities targeting two common targets in 100 healthy individuals. RESULTS: In the systematic review, we extracted 308 outcome measures from 202 studies that adopted either a gray matter volume-level (n = 197) or surface-level (n = 111) approach. Volume-level results focused on E-field magnitude, while surface-level data encompassed E-field magnitude (n = 64) and normal/tangential E-field components (n = 47). E-fields were extracted in ROIs, such as brain structures and shapes (spheres, hexahedra and cylinders), or the whole brain. Percentiles or mean values were mostly used to quantify E-fields. Our modeling study, which involved 1,000 E-field models and > 1,000,000 extracted E-field values, revealed that different outcome measures yielded distinct E-field values, analyzed different brain regions, and did not always exhibit strong correlations in the same within-subject E-field model. CONCLUSIONS: Outcome measure selection significantly impacts the locations and intensities of extracted E-field data in both tES and TMS E-field models. The suitability of different outcome measures depends on the target region, TMS/tES modality, individual anatomy, the analyzed E-field component and the research question. To enhance the quality, rigor, and reproducibility in the E-field modeling domain, we suggest standard reporting practices across studies and provide four recommendations.

Stimulated brains and meditative minds: A systematic review on combining low intensity transcranial electrical stimulation and meditation in humans

Background: Low intensity transcranial electrical stimulation (tES) and meditation are two promising, yet variable, non-pharmacological interventions. Growing research is investigating combined effects of both techniques on one's cognitive, emotional, and physical health. Objective: This article reviews the current research that combines tES and meditation interventions in healthy and diseased participants. The review considers the intervention parameters and their effects in a well-organized manner. Method: A systematic search for clinical and experimental published studies was conducted in the PubMed, Cochrane, and transcranial direct current stimulation (tDCS) databases using common keywords for tES and for meditation techniques well defined by previous studies. Unpublished ongoing studies were identified with the ClinicalTrials.gov and DRKS.de clinical trial websites. Results: 20 published studies and 13 ongoing studies were included for qualitative analysis. 13 published articles studied patients with chronic pain, psychological disorders, cognitive impairment, and movement disorders. Anodal tDCS was the only tES technique while mindfulness meditation was the most common meditation type. Eight studies had a main group effect, with outcome improvement in the active combined intervention. However, most published studies showed improvements after at least one combined intervention with variable effects. Conclusion: Pairing anodal tDCS with meditation shows promising improvements of the physical, mental, and emotional aspects of daily life. Further studies are required to confirm the relevance of this combination in the clinic. (AU)

Multi-objective optimization via evolutionary algorithm (MOVEA) for high-definition transcranial electrical stimulation of the human brain.

Designing a transcranial electrical stimulation (tES) strategy requires considering multiple objectives, such as intensity in the target area, focality, stimulation depth, and avoidance zone. These objectives are often mutually exclusive. In this paper, we propose a general framework, called multi-objective optimization via evolutionary algorithm (MOVEA), which solves the non-convex optimization problem in designing tES strategies without a predefined direction. MOVEA enables simultaneous optimization of multiple targets through Pareto optimization, generating a Pareto front after a single run without manual weight adjustment and allowing easy expansion to more targets. This Pareto front consists of optimal solutions that meet various requirements while respecting trade-off relationships between conflicting objectives such as intensity and focality. MOVEA is versatile and suitable for both transcranial alternating current stimulation (tACS) and transcranial temporal interference stimulation (tTIS) based on high definition (HD) and two-pair systems. We comprehensively compared tACS and tTIS in terms of intensity, focality, and steerability for targets at different depths. Our findings reveal that tTIS enhances focality by reducing activated volume outside the target by 60%. HD-tTIS and HD-tDCS can achieve equivalent maximum intensities, surpassing those of two-pair tTIS, such as 0.51 V/m under HD-tACS/HD-tTIS and 0.42 V/m under two-pair tTIS for the motor area as a target. Analysis of variance in eight subjects highlights individual differences in both optimal stimulation policies and outcomes for tACS and tTIS, emphasizing the need for personalized stimulation protocols. These findings provide guidance for designing appropriate stimulation strategies for tACS and tTIS. MOVEA facilitates the optimization of tES based on specific objectives and constraints, advancing tTIS and tACS-based neuromodulation in understanding the causal relationship between brain regions and cognitive functions and treating diseases. The code for MOVEA is available at https://github.com/ncclabsustech/MOVEA.

Effects of Transcranial Electrical Stimulation on Gambling and Gaming: A Systematic Review of Studies on Healthy Controls, Participants with Gambling/Gaming Disorder, and Substance Use Disorder.

Gambling disorder (GD) and internet gaming disorder (IGD) are formally recognized behavioral addictions with a rapidly growing prevalence and limited treatment options. Recently, transcranial electrical stimulation (tES) techniques have emerged as potentially promising interventions for improving treatment outcomes by ameliorating cognitive functions implicated in addictive behaviors. To systematize the current state of evidence and better understand whether and how tES can influence gambling and gaming-related cognitive processes, we conducted a PRISMA-guided systematic review of the literature, focusing on tES effects on gaming and gambling in a diverse range of population samples, including healthy participants, participants with GD and IGD, as well as participants with substance abuse addictions. Following the literature search in three bibliographic databases (PubMed, Web of Science, and Scopus), 40 publications were included in this review, with 26 conducted on healthy participants, 6 focusing on GD and IGD patients, and 8 including participants with other addictions. Most of the studies targeted the dorsolateral prefrontal cortex, using transcranial direct current stimulation (tDCS), and assessed the effects on cognition, using gaming and gambling computerized cognitive tasks measuring risk taking and decision making, e.g., balloon analogue risk task, Iowa gambling task, Cambridge gambling task, etc. The results indicated that tES could change gambling and gaming task performances and positively influence GD and IGD symptoms, with 70% of studies showing neuromodulatory effects. However, the results varied considerably depending on the stimulation parameters, sample characteristics, as well as outcome measures used. We discuss the sources of this variability and provide further directions for the use of tES in the context of GD and IGD treatment.

Stimulated brains and meditative minds: A systematic review on combining low intensity transcranial electrical stimulation and meditation in humans.

Background: Low intensity transcranial electrical stimulation (tES) and meditation are two promising, yet variable, non-pharmacological interventions. Growing research is investigating combined effects of both techniques on one's cognitive, emotional, and physical health. Objective: This article reviews the current research that combines tES and meditation interventions in healthy and diseased participants. The review considers the intervention parameters and their effects in a well-organized manner. Method: A systematic search for clinical and experimental published studies was conducted in the PubMed, Cochrane, and transcranial direct current stimulation (tDCS) databases using common keywords for tES and for meditation techniques well defined by previous studies. Unpublished ongoing studies were identified with the ClinicalTrials.gov and DRKS.de clinical trial websites. Results: 20 published studies and 13 ongoing studies were included for qualitative analysis. 13 published articles studied patients with chronic pain, psychological disorders, cognitive impairment, and movement disorders. Anodal tDCS was the only tES technique while mindfulness meditation was the most common meditation type. Eight studies had a main group effect, with outcome improvement in the active combined intervention. However, most published studies showed improvements after at least one combined intervention with variable effects. Conclusion: Pairing anodal tDCS with meditation shows promising improvements of the physical, mental, and emotional aspects of daily life. Further studies are required to confirm the relevance of this combination in the clinic.

Multiple functions of the angular gyrus at high temporal resolution.

Here, the functions of the angular gyrus (AG) are evaluated in the light of current evidence from transcranial magnetic/electric stimulation (TMS/TES) and EEG/MEG studies. 65 TMS/TES and 52 EEG/MEG studies were examined in this review. TMS/TES literature points to a causal role in semantic processing, word and number processing, attention and visual search, self-guided movement, memory, and self-processing. EEG/MEG studies reported AG effects at latencies varying between 32 and 800 ms in a wide range of domains, with a high probability to detect an effect at 300-350 ms post-stimulus onset. A three-phase unifying model revolving around the process of sensemaking is then suggested: (1) early AG involvement in defining the current context, within the first 200 ms, with a bias toward the right hemisphere; (2) attention re-orientation and retrieval of relevant information within 200-500 ms; and (3) cross-modal integration at late latencies with a bias toward the left hemisphere. This sensemaking process can favour accuracy (e.g. for word and number processing) or plausibility (e.g. for comprehension and social cognition). Such functions of the AG depend on the status of other connected regions. The much-debated semantic role is also discussed as follows: (1) there is a strong TMS/TES evidence for a causal semantic role, (2) current EEG/MEG evidence is however weak, but (3) the existing arguments against a semantic role for the AG are not strong. Some outstanding questions for future research are proposed. This review recognizes that cracking the role(s) of the AG in cognition is possible only when its exact contributions within the default mode network are teased apart.

Review of individualized current flow modeling studies for transcranial electrical stimulation.

There is substantial intersubject variability of behavioral and neurophysiological responses to transcranial electrical stimulation (tES), which represents one of the most important limitations of tES. Many tES protocols utilize a fixed experimental parameter set disregarding individual anatomical and physiological properties. This one-size-fits-all approach might be one reason for the observed interindividual response variability. Simulation of current flow applying head models based on available anatomical data can help to individualize stimulation parameters and contribute to the understanding of the causes of this response variability. Current flow modeling can be used to retrospectively investigate the characteristics of tES effectivity. Previous studies examined, for example, the impact of skull defects and lesions on the modulation of current flow and demonstrated effective stimulation intensities in different age groups. Furthermore, uncertainty analysis of electrical conductivities in current flow modeling indicated the most influential tissue compartments. Current flow modeling, when used in prospective study planning, can potentially guide stimulation configurations resulting in individually effective tES. Specifically, current flow modeling using individual or matched head models can be employed by clinicians and scientists to, for example, plan dosage in tES protocols for individuals or groups of participants. We review studies that show a relationship between the presence of behavioral/neurophysiological responses and features derived from individualized current flow models. We highlight the potential benefits of individualized current flow modeling.

Effects of transcranial electrical stimulation techniques on foreign vocabulary learning.

Although the use of transcranial electrical stimulation (tES) techniques on healthy population has been linked to facilitating language learning, studies on their effects on foreign language learning processes are scarce and results remain unclear. The objective of this study was to analyze whether tES enhances foreign language learning processes. Sixty-four healthy native Spanish-speaking participants were randomly assigned to four groups (transcranial direct current, transcranial random noise, tDCS-tRNS stimulation, or sham). They completed two intervention sessions with a two-week gap in between. During the first session the participants received stimulation (1.5 mA) while learning new English words and then performed recall and recognition tasks. Learning was assessed at follow-up, two weeks later. No differences in learning between groups were observed in the first session (F(1,61)= .86; p = .36). At follow-up, significantly higher learning accuracy was observed after tRNS compared to sham (p = .037). These results suggest that tRNS could be helpful in improving the processes involved in foreign language vocabulary learning.

Transcranial versus direct electrical stimulation for intraoperative motor-evoked potential monitoring: Prognostic value comparison in asleep brain tumor surgery.

Objective: Safe resection of gliomas involving motor pathways in asleep-anesthesia requires the combination of brain mapping, to identify and spare essential motor sites, and continuous monitoring of motor-evoked potentials (MEPs), to detect possible vascular damage to the corticospinal tract (CST). MEP monitoring, according to intraoperative neurophysiology societies, is generally recommended by transcranial electrodes (TES), and no clear indications of direct cortical stimulation (DCS) or the preferential use of one of the two techniques based on the clinical context is available. The main aim of the study was to identify the best technique(s) based on different clinical conditions, evaluating the efficacy and prognostic value of both methodologies. Methods: A retrospective series of patients with tumors involving the motor pathways who underwent surgical resection with the aid of brain mapping and combined MEP monitoring via TES and DCS was evaluated. Irreversible MEP amplitude reduction (>50% compared to baseline) was used as an intraoperative warning and correlated to the postoperative motor outcome. Selectivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were computed for both techniques. Results: Four hundred sixty-two patients were retrospectively analyzed, and only 1.9% showed a long-term motor impairment. Both TES and DCS obtained high specificity and NPV for the acute and 1-month motor deficit. Sensitivity was rather low for the acute deficit but excellent considering the 1-month follow-up for both techniques. DCS was extremely reliable in predicting a postoperative motor decline (PPV of 100% and 90% for acute and long-term deficit, respectively). Conversely, TES produced a high number of false-positive results, especially for long-term deficits (65, 87.8% of all warnings) therefore obtaining poor PPV values (18% and 12% for acute and 1-month deficits, respectively). TES false-positive results were significantly associated with parietal tumors and lateral patient positioning. Conclusions: Data support the use of mapping and combined monitoring via TES and DCS. The sole TES monitoring is reliable in most procedures but not in parietal tumors or those requiring lateral positioning. Although no indications are available in international guidelines, DCS should be recommended, particularly for cases approached by a lateral position.

Addressing transcranial electrical stimulation variability through prospective individualized dosing of electric field strength in 300 participants across two samples: the 2-SPED approach.

Objective. Transcranial electrical stimulation (tES) is a promising method for modulating brain activity and excitability with variable results to date. To minimize electric (E-)field strength variability, we introduce the 2-sample prospective E-field dosing (2-SPED) approach, which uses E-field strengths induced by tES in a first population to individualize stimulation intensity in a second population.Approach. We performed E-field modeling of three common tES montages in 300 healthy younger adults. First, permutation analyses identified the sample size required to obtain a stable group average E-field in the primary motor cortex (M1), with stability being defined as the number of participants where all group-average E-field strengths ± standard deviation did not leave the population's 5-95 percentile range. Second, this stable group average was used to individualize tES intensity in a second independent population (n = 100). The impact of individualized versus fixed intensity tES on E-field strength variability was analyzed.Main results. In the first population, stable group average E-field strengths (V/m) in M1 were achieved at 74-85 participants, depending on the tES montage. Individualizing the stimulation intensity (mA) in the second population resulted in uniform M1 E-field strength (all p < 0.001) and significantly diminished peak cortical E-field strength variability (all p < 0.01), across all montages.Significance. 2-SPED is a feasible way to prospectively induce more uniform E-field strengths in a region of interest. Future studies might apply 2-SPED to investigate whether decreased E-field strength variability also results in decreased physiological and behavioral variability in response to tES.

L1-norm vs. L2-norm fitting in optimizing focal multi-channel tES stimulation: linear and semidefinite programming vs. weighted least squares.

BACKGROUND AND OBJECTIVE: This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce a mathematical formulation for finding a current pattern that optimizes an L1-norm fit between a given focal target distribution and volumetric current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates. METHODS: We present a linear programming approach that performs L1-norm fitting and penalization of the current pattern (L1L1) to control the number of non-zero currents. The optimizer filters a large set of candidate solutions using a two-stage metaheuristic search from a pre-filtered set of candidates. RESULTS: The numerical simulation results obtained with both 8- and 20-channel electrode montages suggest that our hypothesis on the benefits of L1-norm data fitting is valid. Compared to an L1-norm regularized L2-norm fitting (L1L2) via semidefinite programming and weighted Tikhonov least-squares method (TLS), the L1L1 results were overall preferable for maximizing the focused current density at the target position, and the ratio between focused and nuisance current magnitudes. CONCLUSIONS: We propose the metaheuristic L1L1 optimization approach as a potential technique to obtain a well-localized stimulus with a controllable magnitude at a given target position. L1L1 finds a current pattern with a steep contrast between the anodal and cathodal electrodes while suppressing the nuisance currents in the brain, hence, providing a potential alternative to modulate the effects of the stimulation, e.g., the sensation experienced by the subject.