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Wansbrough K, Marinovic W, Fujiyama H, Vallence AM. Beta tACS of varying intensities differentially affect resting-state and movement-related M1-M1 connectivity. Front Neurosci 2024; 18:1425527. [PMID: 39371612 PMCID: PMC11450697 DOI: 10.3389/fnins.2024.1425527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Accepted: 08/29/2024] [Indexed: 10/08/2024] Open
Abstract
Due to the interconnected nature of the brain, changes in one region are likely to affect other structurally and functionally connected regions. Emerging evidence indicates that single-site transcranial alternating current stimulation (tACS) can modulate functional connectivity between stimulated and interconnected unstimulated brain regions. However, our understanding of the network response to tACS is incomplete. Here, we investigated the effect of beta tACS of different intensities on phase-based connectivity between the left and right primary motor cortices in 21 healthy young adults (13 female; mean age 24.30 ± 4.84 years). Participants underwent four sessions of 20 min of 20 Hz tACS of varying intensities (sham, 0.5 mA, 1.0 mA, or 1.5 mA) applied to the left primary motor cortex at rest. We recorded resting-state and event-related electroencephalography (EEG) before and after tACS, analyzing changes in sensorimotor beta (13-30 Hz) imaginary coherence (ImCoh), an index of functional connectivity. Event-related EEG captured movement-related beta activity as participants performed self-paced button presses using their right index finger. For resting-state connectivity, we observed intensity-dependent changes in beta ImCoh: sham and 0.5 mA stimulation resulted in an increase in beta ImCoh, while 1.0 mA and 1.5 mA stimulation decreased beta ImCoh. For event-related connectivity, 1.5 mA stimulation decreased broadband ImCoh (4-90 Hz) during movement execution. None of the other stimulation intensities significantly modulated event-related ImCoh during movement preparation, execution, or termination. Interestingly, changes in ImCoh during movement preparation following 1.0 mA and 1.5 mA stimulation were significantly associated with participants' pre-tACS peak beta frequency, suggesting that the alignment of stimulation frequency and peak beta frequency affected the extent of neuromodulation. Collectively, these results suggest that beta tACS applied to a single site influences connectivity within the motor network in a manner that depends on the intensity and frequency of stimulation. These findings have significant implications for both research and clinical applications.
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Affiliation(s)
- Kym Wansbrough
- School of Psychology, College of Health and Education, Murdoch University, Perth, WA, Australia
- Centre for Healthy Ageing, Health Futures Institute, Murdoch University, Perth, WA, Australia
- Centre for Molecular Medicine and Innovative Therapeutics, Health Futures Institute, Murdoch University, Perth, WA, Australia
| | - Welber Marinovic
- School of Population Health, Curtin University, Perth, WA, Australia
| | - Hakuei Fujiyama
- School of Psychology, College of Health and Education, Murdoch University, Perth, WA, Australia
- Centre for Healthy Ageing, Health Futures Institute, Murdoch University, Perth, WA, Australia
- Centre for Molecular Medicine and Innovative Therapeutics, Health Futures Institute, Murdoch University, Perth, WA, Australia
| | - Ann-Maree Vallence
- School of Psychology, College of Health and Education, Murdoch University, Perth, WA, Australia
- Centre for Healthy Ageing, Health Futures Institute, Murdoch University, Perth, WA, Australia
- Centre for Molecular Medicine and Innovative Therapeutics, Health Futures Institute, Murdoch University, Perth, WA, Australia
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Sanchez-Romero R, Akyuz S, Krekelberg B. EFMouse: a Matlab toolbox to model electric fields in the mouse brain. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.07.25.605227. [PMID: 39091807 PMCID: PMC11291114 DOI: 10.1101/2024.07.25.605227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 08/04/2024]
Abstract
Compared to the rapidly growing literature on transcranial electrical stimulation (tES) in humans, research into the mechanisms underlying neuromodulation by tES using in-vivo animal models is growing but still relatively rare. Such research, however, is key to overcoming experimental limitations in humans and essential to build a detailed understanding of the in-vivo consequences of tES that can ultimately lead to development of targeted and effective therapeutic applications of noninvasive brain stimulation. The sheer difference in scale and geometry between animal models and the human brain contributes to the complexity of designing and interpreting animal studies. Here we extend previous approaches to model intracranial electric fields to generate predictions that can be tested with in-vivo intracranial recordings. Although the toolbox has general applicability and could be used to predict intracranial fields for any tES study using mice, we illustrate its usage by comparing fields in a high-density multi-electrode montage with a more traditional two electrode montage. Our simulations show that both montages can produce strong focal homogeneous electric fields in targeted areas. However, the high-density montage produces a field that is more perpendicular to the visual cortical surface, which is expected to result in larger changes in neuronal excitability. Highlights EFMouse is a novel, open-source, Matlab-based electric field simulator for the mouse brain.EFMouse quantifies field focality and homogeneity in regions of the Allen Mouse Brain Atlas.Focal and strong stimulation can be produced with two or five electrode montages.A high-density montage with a lumbar return generates fields perpendicular to the cortical surface.
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Meinzer M, Shahbabaie A, Antonenko D, Blankenburg F, Fischer R, Hartwigsen G, Nitsche MA, Li SC, Thielscher A, Timmann D, Waltemath D, Abdelmotaleb M, Kocataş H, Caisachana Guevara LM, Batsikadze G, Grundei M, Cunha T, Hayek D, Turker S, Schlitt F, Shi Y, Khan A, Burke M, Riemann S, Niemann F, Flöel A. Investigating the neural mechanisms of transcranial direct current stimulation effects on human cognition: current issues and potential solutions. Front Neurosci 2024; 18:1389651. [PMID: 38957187 PMCID: PMC11218740 DOI: 10.3389/fnins.2024.1389651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Accepted: 05/15/2024] [Indexed: 07/04/2024] Open
Abstract
Transcranial direct current stimulation (tDCS) has been studied extensively for its potential to enhance human cognitive functions in healthy individuals and to treat cognitive impairment in various clinical populations. However, little is known about how tDCS modulates the neural networks supporting cognition and the complex interplay with mediating factors that may explain the frequently observed variability of stimulation effects within and between studies. Moreover, research in this field has been characterized by substantial methodological variability, frequent lack of rigorous experimental control and small sample sizes, thereby limiting the generalizability of findings and translational potential of tDCS. The present manuscript aims to delineate how these important issues can be addressed within a neuroimaging context, to reveal the neural underpinnings, predictors and mediators of tDCS-induced behavioral modulation. We will focus on functional magnetic resonance imaging (fMRI), because it allows the investigation of tDCS effects with excellent spatial precision and sufficient temporal resolution across the entire brain. Moreover, high resolution structural imaging data can be acquired for precise localization of stimulation effects, verification of electrode positions on the scalp and realistic current modeling based on individual head and brain anatomy. However, the general principles outlined in this review will also be applicable to other imaging modalities. Following an introduction to the overall state-of-the-art in this field, we will discuss in more detail the underlying causes of variability in previous tDCS studies. Moreover, we will elaborate on design considerations for tDCS-fMRI studies, optimization of tDCS and imaging protocols and how to assure high-level experimental control. Two additional sections address the pressing need for more systematic investigation of tDCS effects across the healthy human lifespan and implications for tDCS studies in age-associated disease, and potential benefits of establishing large-scale, multidisciplinary consortia for more coordinated tDCS research in the future. We hope that this review will contribute to more coordinated, methodologically sound, transparent and reproducible research in this field. Ultimately, our aim is to facilitate a better understanding of the underlying mechanisms by which tDCS modulates human cognitive functions and more effective and individually tailored translational and clinical applications of this technique in the future.
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Affiliation(s)
- Marcus Meinzer
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Alireza Shahbabaie
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Daria Antonenko
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Felix Blankenburg
- Neurocomputation and Neuroimaging Unit, Department of Education and Psychology, Freie Universität Berlin, Berlin, Germany
| | - Rico Fischer
- Department of Psychology, University of Greifswald, Greifswald, Germany
| | - Gesa Hartwigsen
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Wilhelm Wundt Institute for Psychology, Leipzig University, Leipzig, Germany
| | - Michael A. Nitsche
- Department of Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors at TU Dortmund, Dortmund, Germany
- German Center for Mental Health (DZPG), Bochum, Germany
- Bielefeld University, University Hospital OWL, Protestant Hospital of Bethel Foundation, University Clinic of Psychiatry and Psychotherapy, Bielefeld, Germany
| | - Shu-Chen Li
- Chair of Lifespan Developmental Neuroscience, Faculty of Psychology, Technische Universität Dresden, Dresden, Germany
| | - Axel Thielscher
- Section for Magnetic Resonance, Department of Health Technology, Technical University of Denmark, Kongens Lyngby, Denmark
- Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Amager and Hvidovre, Copenhagen, Denmark
| | - Dagmar Timmann
- Department of Neurology and Center for Translational Neuro- and Behavioral Sciences (C-TNBS), Essen University Hospital, University of Duisburg-Essen, Essen, Germany
| | - Dagmar Waltemath
- Core Unit Data Integration Center, University Medicine Greifswald, Greifswald, Germany
| | | | - Harun Kocataş
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | | | - Giorgi Batsikadze
- Department of Neurology and Center for Translational Neuro- and Behavioral Sciences (C-TNBS), Essen University Hospital, University of Duisburg-Essen, Essen, Germany
| | - Miro Grundei
- Neurocomputation and Neuroimaging Unit, Department of Education and Psychology, Freie Universität Berlin, Berlin, Germany
| | - Teresa Cunha
- Section for Magnetic Resonance, Department of Health Technology, Technical University of Denmark, Kongens Lyngby, Denmark
| | - Dayana Hayek
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Sabrina Turker
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Wilhelm Wundt Institute for Psychology, Leipzig University, Leipzig, Germany
| | - Frederik Schlitt
- Department of Neurology and Center for Translational Neuro- and Behavioral Sciences (C-TNBS), Essen University Hospital, University of Duisburg-Essen, Essen, Germany
| | - Yiquan Shi
- Chair of Lifespan Developmental Neuroscience, Faculty of Psychology, Technische Universität Dresden, Dresden, Germany
| | - Asad Khan
- Department of Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors at TU Dortmund, Dortmund, Germany
| | - Michael Burke
- Department of Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors at TU Dortmund, Dortmund, Germany
| | - Steffen Riemann
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Filip Niemann
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
| | - Agnes Flöel
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
- German Center for Neurodegenerative Diseases (DZNE Site Greifswald), Greifswald, Germany
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Niemann F, Riemann S, Hubert AK, Antonenko D, Thielscher A, Martin AK, Unger N, Flöel A, Meinzer M. Electrode positioning errors reduce current dose for focal tDCS set-ups: Evidence from individualized electric field mapping. Clin Neurophysiol 2024; 162:201-209. [PMID: 38643613 DOI: 10.1016/j.clinph.2024.03.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Revised: 01/29/2024] [Accepted: 03/26/2024] [Indexed: 04/23/2024]
Abstract
OBJECTIVE Electrode positioning errors contribute to variability of transcranial direct current stimulation (tDCS) effects. We investigated the impact of electrode positioning errors on current flow for tDCS set-ups with different focality. METHODS Deviations from planned electrode positions were determined using data acquired in an experimental study (N = 240 datasets) that administered conventional and focal tDCS during magnetic resonance imaging (MRI). Comparison of individualized electric field modeling for planned and empirically derived "actual" electrode positions was conducted to quantify the impact of positioning errors on the electric field dose in target regions for tDCS. RESULTS Planned electrode positions resulted in higher current dose in the target regions for focal compared to conventional montages (7-12%). Deviations from planned positions significantly reduced current flow in the target regions, selectively for focal set-ups (26-30%). Dose reductions were significantly larger for focal compared to conventional set-ups (29-43%). CONCLUSIONS Precise positioning is crucial when using focal tDCS set-ups to avoid significant reductions of current dose in the intended target regions. SIGNIFICANCE Our results highlight the urgent need to routinely implement methods for improving electrode positioning, minimization of electrode drift, verification of electrode positions before and/or after tDCS and also to consider positioning errors when investigating dose-response relationships, especially for focal set-ups.
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Affiliation(s)
- Filip Niemann
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany
| | - Steffen Riemann
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany
| | - Ann-Kathrin Hubert
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany
| | - Daria Antonenko
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany
| | - Axel Thielscher
- Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Amager and Hvidovre, Hvidovre, Denmark; Technical University of Denmark, Department of Health Technology, Kongens Lyngby, Denmark
| | - Andrew K Martin
- Kent University, School of Psychology, Canterbury, United Kingdom
| | - Nina Unger
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany
| | - Agnes Flöel
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany; German Center for Neurodegenerative Diseases (DZNE Site Greifswald), Greifswald, Germany
| | - Marcus Meinzer
- University Medicine Greifswald, Department of Neurology, Greifswald, Germany.
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Gomez-Tames J, Fernández-Corazza M. Perspectives on Optimized Transcranial Electrical Stimulation Based on Spatial Electric Field Modeling in Humans. J Clin Med 2024; 13:3084. [PMID: 38892794 PMCID: PMC11172989 DOI: 10.3390/jcm13113084] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 05/20/2024] [Accepted: 05/22/2024] [Indexed: 06/21/2024] Open
Abstract
Background: Transcranial electrical stimulation (tES) generates an electric field (or current density) in the brain through surface electrodes attached to the scalp. Clinical significance has been demonstrated, although with moderate and heterogeneous results partly due to a lack of control of the delivered electric currents. In the last decade, computational electric field analysis has allowed the estimation and optimization of the electric field using accurate anatomical head models. This review examines recent tES computational studies, providing a comprehensive background on the technical aspects of adopting computational electric field analysis as a standardized procedure in medical applications. Methods: Specific search strategies were designed to retrieve papers from the Web of Science database. The papers were initially screened based on the soundness of the title and abstract and then on their full contents, resulting in a total of 57 studies. Results: Recent trends were identified in individual- and population-level analysis of the electric field, including head models from non-neurotypical individuals. Advanced optimization techniques that allow a high degree of control with the required focality and direction of the electric field were also summarized. There is also growing evidence of a correlation between the computationally estimated electric field and the observed responses in real experiments. Conclusions: Computational pipelines and optimization algorithms have reached a degree of maturity that provides a rationale to improve tES experimental design and a posteriori analysis of the responses for supporting clinical studies.
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Affiliation(s)
- Jose Gomez-Tames
- Department of Medical Engineering, Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan
- Center for Frontier Medical Engineering, Chiba University, Chiba 263-8522, Japan
| | - Mariano Fernández-Corazza
- LEICI Institute of Research in Electronics, Control and Signal Processing, National University of La Plata, La Plata 1900, Argentina
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Yatsuda K, Yu W, Gomez-Tames J. Population-level insights into temporal interference for focused deep brain neuromodulation. Front Hum Neurosci 2024; 18:1308549. [PMID: 38708141 PMCID: PMC11066208 DOI: 10.3389/fnhum.2024.1308549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 04/09/2024] [Indexed: 05/07/2024] Open
Abstract
The ability to stimulate deep brain regions in a focal manner brings new opportunities for treating brain disorders. Temporal interference (TI) stimulation has been suggested as a method to achieve focused stimulation in deep brain targets. Individual-level knowledge of the interferential currents has permitted personalizing TI montage via subject-specific digital human head models, facilitating the estimation of interferential electric currents in the brain. While this individual approach offers a high degree of personalization, the significant intra-and inter-individual variability among specific head models poses challenges when comparing electric-field doses. Furthermore, MRI acquisition to develop a personalized head model, followed by precise methods for placing the optimized electrode positions, is complex and not always available in various clinical settings. Instead, the registration of individual electric fields into brain templates has offered insights into population-level effects and enabled montage optimization using common scalp landmarks. However, population-level knowledge of the interferential currents remains scarce. This work aimed to investigate the effectiveness of targeting deep brain areas using TI in different populations. The results showed a trade-off between deep stimulation and unwanted cortical neuromodulation, which is target-dependent at the group level. A consistent modulated electric field appeared in the deep brain target when the same montage was applied in different populations. However, the performance in terms of focality and variability varied when the same montage was used among populations. Also, group-level TI exhibited greater focality than tACS, reducing unwanted neuromodulation volume in the cortical part by at least 1.5 times, albeit with higher variability. These results provide valuable population-level insights when considering TI montage selection.
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Affiliation(s)
- Kanata Yatsuda
- Department of Medical Engineering, Graduate School of Engineering, Chiba University, Chiba, Japan
| | - Wenwei Yu
- Center for Frontier Medical Engineering, Chiba University, Chiba, Japan
| | - Jose Gomez-Tames
- Center for Frontier Medical Engineering, Chiba University, Chiba, Japan
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Carè M, Chiappalone M, Cota VR. Personalized strategies of neurostimulation: from static biomarkers to dynamic closed-loop assessment of neural function. Front Neurosci 2024; 18:1363128. [PMID: 38516316 PMCID: PMC10954825 DOI: 10.3389/fnins.2024.1363128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2023] [Accepted: 02/22/2024] [Indexed: 03/23/2024] Open
Abstract
Despite considerable advancement of first choice treatment (pharmacological, physical therapy, etc.) over many decades, neurological disorders still represent a major portion of the worldwide disease burden. Particularly concerning, the trend is that this scenario will worsen given an ever expanding and aging population. The many different methods of brain stimulation (electrical, magnetic, etc.) are, on the other hand, one of the most promising alternatives to mitigate the suffering of patients and families when conventional treatment fall short of delivering efficacious treatment. With applications in virtually all neurological conditions, neurostimulation has seen considerable success in providing relief of symptoms. On the other hand, a large variability of therapeutic outcomes has also been observed, particularly in the usage of non-invasive brain stimulation (NIBS) modalities. Borrowing inspiration and concepts from its pharmacological counterpart and empowered by unprecedented neurotechnological advancement, the neurostimulation field has seen in recent years a widespread of methods aimed at the personalization of its parameters, based on biomarkers of the individuals being treated. The rationale is that, by taking into account important factors influencing the outcome, personalized stimulation can yield a much-improved therapy. Here, we review the literature to delineate the state-of-the-art of personalized stimulation, while also considering the important aspects of the type of informing parameter (anatomy, function, hybrid), invasiveness, and level of development (pre-clinical experimentation versus clinical trials). Moreover, by reviewing relevant literature on closed loop neuroengineering solutions in general and on activity dependent stimulation method in particular, we put forward the idea that improved personalization may be achieved when the method is able to track in real time brain dynamics and adjust its stimulation parameters accordingly. We conclude that such approaches have great potential of promoting the recovery of lost functions and enhance the quality of life for patients.
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Affiliation(s)
- Marta Carè
- IRCCS Ospedale Policlinico San Martino, Genova, Italy
| | - Michela Chiappalone
- Department of Informatics, Bioengineering, Robotics System Engineering (DIBRIS), University of Genova, Genova, Italy
- Rehab Technologies Lab, Istituto Italiano di Tecnologia, Genova, Italy
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Fernandes SR, Callejón-Leblic MA, Ferreira HA. How does the electric field induced by tDCS influence motor-related connectivity? Model-guided perspectives. Phys Med Biol 2024; 69:055007. [PMID: 38266295 DOI: 10.1088/1361-6560/ad222d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 01/24/2024] [Indexed: 01/26/2024]
Abstract
Over the last decade, transcranial direct current stimulation (tDCS) has been applied not only to modulate local cortical activation, but also to address communication between functionally-related brain areas. Stimulation protocols based on simple two-electrode placements are being replaced by multi-electrode montages to target intra- and inter-hemispheric neural networks using multichannel/high definition paradigms.Objective. This study aims to investigate the characteristics of electric field (EF) patterns originated by tDCS experiments addressing changes in functional brain connectivity.Methods. A previous selection of tDCS experimental studies aiming to modulate motor-related connectivity in health and disease was conducted. Simulations of the EF induced in the cortex were then performed for each protocol selected. The EF magnitude and orientation are determined and analysed in motor-related cortical regions for five different head models to account for inter-subject variability. Functional connectivity outcomes obtained are qualitatively analysed at the light of the simulated EF and protocol characteristics, such as electrode position, number and stimulation dosing.Main findings. The EF magnitude and orientation predicted by computational models can be related with the ability of tDCS to modulate brain functional connectivity. Regional differences in EF distributions across subjects can inform electrode placements more susceptible to inter-subject variability in terms of brain connectivity-related outcomes.Significance. Neuronal facilitation/inhibition induced by tDCS fields may indirectly influence intra and inter-hemispheric connectivity by modulating neural components of motor-related networks. Optimization of tDCS using computational models is essential for adequate dosing delivery in specific networks related to clinically relevant connectivity outcomes.
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Affiliation(s)
- Sofia Rita Fernandes
- Instituto de Biofísica e Engenharia Biomédica, Faculdade de Ciências, Universidade de Lisboa, Portugal
| | - M Amparo Callejón-Leblic
- Oticon Medical, Madrid, Spain
- Grupo de Ingeniería Biomédica, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Spain
- Servicio de Otorrinolaringología, Hospital Universitario Virgen Macarena, Sevilla, Spain
| | - Hugo Alexandre Ferreira
- Instituto de Biofísica e Engenharia Biomédica, Faculdade de Ciências, Universidade de Lisboa, Portugal
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