How does the electric field induced by tDCS influence motor-related connectivity? Model-guided perspectives

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.


Introduction
Non-invasive brain electrical stimulation has been studied extensively over the past two decades.Since the first experiments by Nitsche andPaulus in 2000 (Nitsche andPaulus 2000), many different protocols have been designed and carried out in health and disease, using transcutaneous direct current stimulation (tDCS) (Peterchev et al 2012).tDCS is one of the most common techniques applied due to its portability, low cost of devices and scarce reports of adverse effects.It uses weak direct (continuous) currents of typically 1-4 mA during 15-40 min delivered in the brain through electrodes placed over the scalp (Nitsche andPaulus 2000, Peterchev et al 2012).tDCS has been observed to modulate neuronal excitability in humans, similarly to long-term potentiation mechanisms of learning and memory related to neuroplasticity processes, and correlating with cognitive and motor function improvements in many psychiatric and neurological disorders (Lefaucheur et al 2017, Ruffini et al 2018).
Advances in imaging and neurophysiological techniques have demonstrated that brain connectivity patterns are usually present in neurological conditions such as stroke, Alzheimer, Parkinson and Amyotrophic Lateral Sclerosis (ALS) (Hallett et al 2020).Changes in brain communication between different cortical regions detected by functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) appear early in the onset of certain diseases.Functional connectivity (FC) patterns seem to have signatures for certain neurological conditions, and are considered potential biomarkers for early detection of disease onset and progression (Nasseroleslami et al 2019, Hallett et al 2020).
More recently, tDCS research has turned to investigate its therapeutic potential to repair, restore or delay abnormal FC patterns in dysfunctional neural networks (Ruffini et al 2018).Improvements in resting-state (rs) FC after tDCS delivery were observed in neurologic conditions with impact on movement, such as multiple sclerosis and post-stroke (Lefebvre et al 2017, Porcaro et al 2019, Chan and Han 2020).tDCS delivered at the primary sensory cortex (S1) of MS patients during 5 days resulted in reduction of fatigue perception, evaluated by the modified fatigue impact scale (mFIS).This reduction was explained by 48% of mFIS variance in the regression model by bilateral changes in resting-state (rs) connectivity in the sensorimotor cortex (SMC: S1 and primary motor cortex-M1 regions) measured by EEG (Porcaro et al 2019).Twenty-two chronic hemiparetic stroke patients participated in a randomised, placebo-controlled, double-blind, crossover study, where active/ sham tDCS was applied bilaterally, over left and right M1, in a single session during motor skill learning.rs-fMRI of patients acquired one week before active and sham interventions presented larger FC between the M1 and dorsal premotor cortex (PMC) of the non lesioned hemisphere.One week after active tDCS, larger FC occurred between M1 and dorsal PMC of the damaged hemisphere, indicating that tDCS combined with motor training can induce connectivity reshaping (Lefebvre et al 2017).Reported changes in FC induced by tDCS were observed to depend on the stimulation protocol characteristics (Ruffini et al 2018, Chan andHan 2020).
Computational modelling studies prove essential tools to understand the underlying biophysics of tDCS effects in neural networks.Electric field (EF) magnitude and distribution are strongly influenced by electrical tissue properties and by electrode placement, distance, design and size (Peterchev et al 2012, Miranda et al 2013, Saturnino et al 2015, Mencarelli et al 2020, Salvador et al 2021, Videira et al 2022), as well as by individual anatomy.Modelling studies have addressed the effect of individual characteristics such as age, sex, and anatomical morphology on the predicted EF.For example, Opitz et al explained 50% of the variability found for two head models subjected to the standard motor cortex montage as caused by differences in cerebrospinal fluid (CSF) thickness, skull thickness and gyral depth (Opitz et al 2015).Mosayebi-Samani et al also showed that individual anatomical factors such as local CSF thickness and electrode-to-cortex distance near the targeted brain region explained EF variability when using conventional large-pad electrodes (Mosayebi-Samani et al 2021).Antonenko et al found a significant interaction of EFs with head, skull, skin and CSF tissue volumes in subjects aged between 20 and 79 years using standard large-pad montages at different scalp locations.The effect of CSF volume was found to be lower in young compared with older adults, but irrespective of electrode position (Antonenko et al 2021).Bhatacharjee et al (2022) also detected sex differences in the predicted EF in the cortex, which differed for different age groups and electrode locations.Across all age groups, CSF and grey matter (GM) volumes remained significant predictors of EF dosed at the targeted regions of interest (ROIs).In line with these results, Kashyap et al also found that CSF volume at the regional level near the targeted ROI was the main parameter explaining variability in EF focality (Kashyap et al 2022).
Modelling studies have also highlighted that the influence of tDCS-induced EFs does not only depend on their intensity or focality but also on their relative direction to specific cortical targets (Rawji et al 2018, Hannah et al 2019, Laakso et al 2019).Callejón-Leblic and Miranda (2021) conducted a computational analysis of the distribution of both tangential and normal EF components on a representative parcellated atlas-based brain model for four large-pad tDCS montages.The simulations showed a dual EF pattern through the cortical surface, with the tangential component widely distributed over gyri and the normal component highly confined on sulci.Evans et al analysed interindividual variability in EF direction for three conventional tDCS montages and their simulations confirmed a high variability within 50%-150% across montages.They confirmed differences in the radial inward EF at different functional subregions of the motor cortex (Evans et al 2020(Evans et al , 2022)).
More recently, stimulation protocols based on simple large-pad two-electrode placements are being replaced by multi-electrode montages to target intra-and inter-hemispheric neural networks using multichannel/high-definition (HD) paradigms.These are predicted to influence the spatial distribution of the induced EF, aiming at improving focality over functionally connected targets.When analysing local EF deviation in the cortex, Mikkonen et al (2020) predicted an increase in EF intensity at the target for high-definition compared with conventional two-large pad electrode montages, but at a cost of higher inter-subject variability.
In summary, the relevance of computational models in the optimization of stimulation protocols at targeted cortical networks is evidenced.The design of robust montages able to alleviate the variability observed in terms of brain connectivity-related outcomes could considerably increase the efficacy of tDCS protocols.This study aims to investigate possible relations between FC changes induced by tDCS and the EF spatial distribution in the cortex, as predicted by computational models.To do so, studies that measured tDCS-induced changes in FC using different stimulation paradigms were selected, including standard large-pad two-electrode or high-definition (HD) montages.Our approach focuses on motor-related effects, since this study is integrated within a larger project aiming to identify non-invasive strategies for motor-related FC dysfunctions.The tDCS montages selected from literature were modelled using computational numerical methods and EF patterns were studied at the light of the motor-related FC reported.Realistic head models from five healthy volunteers were used to address the impact of inter-subject variability.

Methods
Briefly, a literature search was first carried out to identify studies using tDCS for modulation of motor-related functional connectivity.Studies with different electrode montages were selected and then simulated in SimNIBS 3.2 software (https://simnibs.github.io/simnibs/)(Thielscher et al 2015), for five different head models obtained from magnetic resonance images (MRI).Mean values of the total electric field (EF) magnitude and of its components were determined at left and right primary motor cortices (M1), premotor cortices (PMC) and supplementary motor areas (SMA), main regions involved in motor programming, coordination and execution.Intra-and inter-hemispheric (IH) FC outcomes were identified in each study to address possible relations with the predicted EF magnitude and orientation at the aforementioned regions.The following sections will address the methods used in each of the steps described above.

Literature search
The studies included were selected as part of a literature review in progress and registered in PROSPERO database (CRD42021257099), carried out in January 2022 using the search sentence 'tDCS OR ((transcranial OR brain) AND (direct current) AND stimulation) AND (motor)) AND (connectivity)', in the internet databases ScienceDirect, PubMed, Web of Science.After full screening, 117 records were considered eligible for the literature review.From these records, 78 out of 87 studies used tDCS montages with only two electrodes.Montages with more than 2 electrodes (HD-tDCS) appeared only from 2017 onwards.We selected 7 studies for EF simulation that applied different tDCS protocols: 2 studies using 2 electrodes- Lang et al (2004) 1 present electrode placements and information on stimulation parameters.All studies selected reported FC outcomes measured at M1, PMC and SMA.Lang et al (2004) applied anodal tDCS at the left primary motor cortex (M1) using a two-electrode montage (UL montage, with anode on C3 and cathode on Fp2, positions of the EEG 10-10 system, see table 1).The aim was to determine effects in cortical regions distant from the site of stimulation, by measuring motor-evoked potentials (MEP) and transcallosal inhibition latency and duration (LTI, DTI) elicited in both hemispheres.Changes in MEP and DTI related only to modulation of pyramidal tract neurons (PTN) and interneurons (IN) from left M1, indicating effects of stimulation only in local circuits near the site of stimulation.Lindenberg et al (2013) applied the UL montage and also a bilateral montage (BL, table 1), by shifting the cathode position of Lang et al (2004) to the right M1.They addressed the differential impact of bihemispheric (BL) tDCS versus UL on motor system activity and fMRI-based connectivity at resting-state, during a finger tap task, a word semantic retrieval (cognitive) task and no-go condition.UL and BL both presented increased activation of the left hemisphere versus decreased activation of the right hemisphere, more pronounced in regions of the frontoparietal control network (M1 and prefrontal cortex, PFC) only for the tap condition.Correlation of laterality changes and fractional anisotropy obtained by diffusion tensor imaging (DTI), revealed that tDCS effects in M1 contralateral to the anode are mediated by transcallosal fibres.As UL only presented functional decoupling of motor-related regions, BL also presented changes in right operculum regions and in the left dorsal posterior cingulate cortex (dPCC), revealing more complex network modulations involving interhemispheric interactions and areas associated with motor control.
Ortiz et al (2020) investigated the effect of an asymmetric tDCS delivery by a 3-electrode placement (M3 montage, table 1) over EEG-based brain connectivity among hemispheres during a motor imagery (MI) task, for future applications in Brain-Computer Interface (BCI) applications in movement recovery after stroke.Increased connectivity interactions between central, left and right M1, SMA and PMC were identified in EEG alpha and beta bands, with a larger effect in the beta band.Thibaut et al (2019) aimed to study the feasibility of tDCS to reduce spasticity of upper limbs in patients with disorder of consciousness (DOC).tDCS was applied with a bilateral placement with 2 anodes x 2 cathodes, to target hemispheric imbalance activation associated with spasticity (M4 montage, table 1).Patients presenting reduced spasticity in finger flexors had increased connectivity between motor and frontal areas in beta band, associated with movement and decision making.Beta band also presented increased connectivity between frontal, prefrontal and frontopolar regions and increased power, related with movement preparation (priming).Increased power was also observed in the theta band, related with sensorimotor integration, probably due to changes in brain activity related to spasticity.
Baxter et al (2017) investigated the effects of anodal HD-tDCS over the left SMC in motor network connectivity during a one-dimensional EEG-based sensorimotor rhythm brain-computer interface task (anode at C3 and four cathodes placed at equal distances from the anode, montage M5a, table 1).Connectivity flow between similar cortical regions was differentially altered during left and right hand MI, with right MI involving the left PMC and motor network regions bilaterally, and left MI involving the left SMC and regions in the motor network.MI performance was also affected by inputs to left PMC and connectivity originated from the ipsilateral posterior parietal cortex (PC) to midline SMC.
Besson et al (2019) addressed the differential impact of online versus offline delivery of anodal HD-tDCS to M1 (montage M5b) in SMC activation during a motor task (finger opposition).Activation was measured by functional near-infrared spectroscopy (fNIRS).Online delivery of HD-tDCS resulted in higher activation of the SMC relative to sham, which is indicative that the time course of stimulation may influence local connectivity during task performance.
Mencarelli et al (2020) compared the effects of tDCS at the sensorimotor network (SMN) between the UL montage and a novel multi-electrode, network-targeted tDCS montage (net-tDCS, M8, table 1), optimised to increase excitability of the SMN, while inducing cathodal inhibition over the PFC and parietal brain regions.M8 induced greater FC increase over the SMN compared to UL, during and after stimulation.Negative connectivity between the SMN and prefrontal/parietal areas was also enhanced compared to UL, which shows the potential of net-tDCS as an alternative method to the UL approach, able to differentially modulate the interaction between networks.

Realistic human head models and tissue properties
Considering the need to provide personalised solutions for model-guided tDCS application for each individual in the clinical setting, inter-subject variability will be addressed using personalised human head models, obtained with the headreco pipeline from SimNIBS 3.2 (Thielscher et al 2015), which generates realistic human head models from individual MRIs.MRIs of the brain were acquired in four volunteers from the Otolaryngology Unit of the Virgen Macarena University Hospital (Seville, Spain).This research was conducted in accordance

Modelling tDCS montages
The studies selected presented large variability regarding electrodes' shapes and materials.We modelled the electrodes with the same shape used in the corresponding tDCS protocols, considering the same thickness for gel/saline and conductive layers, 2.5 and 1 mm, respectively.Default values from SimNIBS for the electrical conductivities of materials were used (σ conductive_layer = 29.4 S m −1 ; σ gel/saline = 1 S m −1 ).The top surface of each electrode was considered to be isopotential.Electrodes' positions were defined according to each experimental study using the EEG 10-10 system (figure 1 and table 1).

EF calculations
SimNIBS calculates the EF using the finite element method (FEM) with first order tetrahedral elements.It calculates the electric potential f by solving the homogeneous Laplace equation (∇•(σ∇f) = 0).The boundary conditions were applied according to Miranda et al (2013), considering the top surface of the electrodes as being isopotential.The current intensity was set at each anode and cathode according to the description of the tDCS protocol in each study (table 1).The EF and the current density (J) are determined by E = −∇f and J = σE, respectively.A total of seven simulations per subject were performed, each of them corresponding to each protocol listed in table 1.The solution time calculation was about 3-6 min per montage depending on the number of electrodes on a laptop with an Intel ® Core(TM) i7-8750H CPU processor clocked at 2.21 GHz and 16 GB of RAM.

Data analysis
The 99.9th, 99th and 95th percentiles of the EF magnitude were determined for all the tetrahedral elements in the GM volume mesh.The GM volumes with an EF magnitude above 50% and 75% of its maximum value (percentile 99.9) were also calculated as an approach to estimate a whole-brain measure for focality in each montage.All these values were provided by SimNIBS.We also used the map_to_fsavg function of SimNIBS to compute the normal (E_normal, nE) and tangential components (E_tangent, tE) of the EF at a surface located in the middle of the GM layer.Custom-made matlab scripts (matlab v17, https://www.mathworks.com)were adapted from SimNIBS tutorials to determine the values of the EF magnitude (E_norm), nE and tE components at M1, PMC and SMA at left and right hemispheres for each simulation and each subject.Values determined in each region were represented in violin plots using an open-source matlab function (Bechtold 2016).
Modelling studies in tDCS reported EF values larger than 0.15 V m −1 over the hand knob, when reproducing clinical settings with observed neuromodulatory effects (Miranda et al 2013, Nitsche andPaulus 2000).Therefore, montages will be assumed to have potential neuromodulatory effects whenever the EF exceeds this value.

Results
The spatial distribution of the electric field (EF) magnitude and of its tangential (tE) and normal (nE) components was determined for montages UL, BL, M3, M4, M5a, M5b and M8 using the realistic head models obtained with SimNIBS for subjects s1, s2, s3, s4, and s5.EF spatial profiles showed variations not only according to montage but also across individuals.The main findings are presented and discussed in the following subsections.

Distribution of the EF for each montage and subject
The spatial profiles of the EF in the GM of s1 are presented in figure 3 for each montage (see figures S.2 to S.5 for s2, s3, s4 and s5 in supplementary materials).The EF distribution varies with electrode placement: the EF spreads over a larger region for montages where the inter-electrode distance is larger, i.e.UL, M3 and M8.A larger size of the electrodes also contributes to EF spreading: M4 induces EF maxima between intra-hemispheric electrodes and less between hemispheres, compared to BL, which uses large-pad electrodes.
The 99.9th, 99th and 95th percentiles of the EF magnitude (EF (99.9%),EF (99%) and EF (95%), respectively) were estimated and presented in figure 4 for all subjects (values listed in table S1 in supplementary materials).Small variations can be seen across subjects, with differences spanning from 0.05 to 0.15 V m −1 .s3 and s5 present the largest values, especially in EF (99.9%) for montages M4, M5a, M5b and M8.Mean, standard deviation (STD) and coefficient of variation (CV) of values for each montage are presented in table 2. As previously explained, the focality for each montage was approximated as the volume of GM with EF magnitude above 75% and 50% of the maximum EF (calculated as the percentile 99.9%).The values for each subject and montage are presented in figure 5 (see values listed in table S2 in supplementary materials).Mean, STD and CV of values for each montage are presented in table 3. Montages are more focal montages when having less volume with EF magnitude above 50% or 75% of the maximum.

nE and tE in M1, SMA and PMC
The values of nE and tE were determined in all subjects and montages in an intermediate surface in the GM, using the map_to_fsavg function in SimNIBS.Tables 4 and 5 summarise the regions where absolute values of nE and tE are higher than 0.15 V m −1 .Values in the M1, PMC and SMA regions of both cortices are presented in the violin plots in figure 6 for s1 (violin plots of the other subjects are presented in figures S7 to S10 of supplementary materials).
The effect of the EF is larger in the neuron components (dendrites, axon, axon terminals) that are oriented parallel to the field (Peterchev et al 2012, Reato et al 2019).Pyramidal tract neurons from layers 2 and 5, involved in motor processing, are usually oriented radially to the GM surface (McColgan et al 2020), thus the nE will be the component with the largest influence.It can be oriented towards the interior of the GM (positive) or towards the exterior (negative), which can result in depolarization or hyperpolarization of neurons' soma, respectively  (Reato et al 2019).Some regions in figure 6 have negative and positive nE, thus the two polarisation effects can occur.M3 was applied with a small current intensity (0.5 mA), originating a smaller EF compared with the other montages.M4 did not induce a sufficient value of nE: compared to BL, M4 has two more electrodes that divide the current, thus inducing a smaller EF and decreasing its components.M5a has the smallest inter-electrode    • BL at left M1 and SMA at both hemispheres.
The tangential component will have the most impact in fibres oriented tangentially to cortical layers, which are mostly collateral axons of pyramidal tract neurons and interneurons responsible for communication between regions for motor selection and coordination.From table 5, the montages that may induce tE-related modulation are:  • UL, M5b in left M1 and PMC; • M5a in left PMC; • BL, M8 in all regions, stronger in right PMC.
Similarly to nE, M3 and M4 did not reach values of tE above 0.15 V m −1 in most regions.BL and M8 are the montages that most favour values of tE, which may be due to a distributed placement of electrodes along a line between the two cortices.
From tables 4 and 5, we can also observe variability across subjects in terms of nE and tE values in each selected region.For instance, s3 presents larger values of these components in M3 and M4 montages, which seemed not to be viable for the other subjects.

Functional connectivity outcomes measured and relation with the EF
One of the main acute effects of tDCS is to transiently change the polarisation of neurons according to their orientation to the induced EF.How and if this impacts FC connectivity is still unknown.We can hypothesise that (2) indirect effect, by making these regions more responsive to communication with other regions (Lang et al 2004).
Modelling results from sections (3.1) and (3.2) predict EF patterns that vary with electrode number, placement and distance.The experimental studies corresponding to each one of the montages modelled (table 1) also resulted in different effects on FC.Table 6 summarises main EF characteristics identified in the previous sections for each montage and the respective FC outcomes observed.
BL and M8 montages showed the largest values of nE and tE, which is indicative that these montages may modulate responses directly and indirectly by changing the polarisation of neurons and of its collateral fibres, thus facilitating intra and inter-hemispheric communication.From table 6, these two montages are the ones that present inter-hemispheric connectivity (IH-FC) enhancement in the sensorimotor (SMN) network, which encompasses the regions addressed in this study, plus cingulate and primary sensory cortices (Chenji et al 2016).Curiously, M5a also presents IH-FC outcomes that do not seem consistent with the EF spatial distribution predicted.However, this study measures FC with motor imagery (MI), which is seen to enhance FC of the SMN (Zhang et al 2014).Since M5a has a very localised EF distribution, its direct activation may also increase the effect (2) of our hypothesis, making the left M1 more responsive with the other regions of the SMN during the MI task.The same probably applies to UL and M5b.M3 and M4 montages also presented FC outcomes, despite the lower nE and tE values predicted by computational models.Considering that, at least in the case of M4, s3 presented higher values of the EF than the other subjects, the modelling results cannot exclude the modulatory potential of these montages.However, it must be noticed that direct comparison between EF characteristics and FC outcomes reported is not straightforward, due to the high variability of FC assessment methods-MEP/TI (Lang et al 2004), fMRI (Lindenberg et al 2013, Mencarelli et al 2020), EEG (Baxter et al 2017, Thibaut et al 2019, Ortiz et al 2020) and fNIRS (Besson et al 2019).In the light of this, our results should be only considered as preliminary yet informative perspectives on how the EF magnitude and orientation may have contributed to the connectivity observed.

Discussion
This research aimed at investigating potential relations between EF spatial patterns predicted by realistic computational models and FC outcomes reported in the literature for seven tDCS montages, with varying number and size of electrodes and inter-electrode distances.Simulations were performed for five head models obtained from MRIs of volunteers, in order to identify which montages are more susceptible to inter-subject variability.Our results confirmed that: (i) EF magnitude and spread are dependent on electrode montage and anatomical variability, with multi-electrode montages leading to higher EF peak values, however at a cost of larger interindividual variability; (ii) focality can be improved in montages with intra-hemispheric placements or with smaller inter-electrode distances, but it is also susceptible to individual anatomical variations, (iii) electrode montages may lead to differentiated oriented tangential and normal EF-based neuromodulation mechanisms, probably modulated by individual brain morphology; and (iv) EF predicted by computational models can be related and used to guide tDCS FC outcomes.Further discussion on these findings is provided below.

Interplay between electrode placement and anatomical variability
Our results demonstrate that the effect of individual anatomy and electrode montage on the tDCS-induced EF may be mediated by an intricate interplay relationship.Intuitively, inter-electrode distance determines EF spreading.For instance, in our simulations, M5a and M5b were the most focal montages, followed by M4 and M8, thus smaller inter-electrode distances and/or intra-hemispheric placements may be better choices to induce a more focal EF.However, more focal montages showed higher variability among subjects in EF local maxima.M5a and M5b montages presented the highest variations among subjects, with CV > 0.25 in the 99.9th and 99th percentiles (table 2).These results agree with those reported by Mikkonen et al (2020), who found that the inter-subject variability of the simulated EFs systematically increased towards more focal montages with decreasing stimulation electrode size.Thus, smaller electrode sizes and distances may increase the influence of the individual anatomy immediately below the stimulating electrodes, in EF maximum values.These authors also reported a higher effect of skin and skull on EF magnitude as the inter-electrode distance of HD montages decreased, probably due to shunting effects through these first tissue layers.Focality can also be affected by anatomical variability among subjects: M3 and M8 showed the largest CV values from 0.29 to 0.42 (table 3).These two montages cover larger parts of the brain with longer inter-electrode distances, which inherently decreases the focality (or equivalently increases the spreading) of the EF.For these types of montages, in line with (Mikkonen et al 2020), our results showed that the variability increases for smaller electrode sizes, compared with large-pad electrode montages such as UL and BL (see figure 5).
Although lower, inter-individual variability still exists for such large-pad electrode montages (e.g. with CV values of 0.11 for EF magnitude and 0.14-0.19for focality in UL and BL montages, respectively).In this sense, Antonenko et al (2021) demonstrated that 79%-94% of the variability observed for large-pad electrode montages could be explained by general anatomical factors such as total head, skin, skull and CSF volumes.However, these associations were not found for focality, thus probably suggesting that regional characteristics such as intra and extra-cranial volumes and cortical morphology may have a role in the EF spread induced by each electrode montage.
Thus, we conclude that despite the general trends observed in EF patterns may be determined by electrode montage and inter-electrode distances, nuances exist, with outcome variability due to specific montages being also affected by individual characteristics.

Possible relations between EF magnitude and orientation and FC outcomes
tDCS is known by its effects on neuronal facilitation/inhibition, which strongly depend on the relative orientation of the EF respective to the neural target.A systematic review of Chan and Han (2020) provides perspectives on current evidence of tDCS modulation of aberrant resting-state connectivity in patients with neurological disorders, however, due to the heterogeneity in analytical methods of FC measurement and tDCS protocols applied, a meta-analysis was not conducted by Chan et al to determine a definite relation (Chan and Han 2020).In the same way, our study does not aim to find direct relations between tDCS-induced EFs and FC outcomes, rather provide some perspectives of how the EF characteristics can modify tDCS targets to induce favourable conditions for FC enhancement.
We have identified three main perspectives on tDCS effects that can provide indirect modulation that may impact FC: (A) Montages with larger EF spreading have the potential to modulate distant networks -UL and M8 induce EF patterns with higher nE and tE that can polarise PTN, axon collaterals and INs at stimulated targets, easing their communication with distant network targets that are functionally related, such as the SMN and the frontoparietal network; (B) Bihemispheric montages generate tangential EF patterns that may modulate collaterals and influence their response to interhemispheric connectivity -BL montage is predicted to induce a high tE, which may have polarisation effects of IN and collaterals involved in IH pathways of the SMN; (C) Focal montages seem to impact more on local networks, which is consistent with a high nE, however, the modulation of these can have repercussions on their connectivity with other areas, as seen in M5a montage.
M3 and M4 montages can also provide effects in motor-related connectivity, however the EF patterns induced seem to be less consistent across subjects.Delivering a larger dose will probably increase the probability for M3 and M4 induced EFs to reach individual thresholds and thus to obtain consistent results, however, careful considerations should be done regarding subjects' tolerability.
Thus, tDCS has the potential to indirectly influence intra-and inter-hemispheric connectivity by modulating neural components of motor-related networks.Optimization of tDCS using computational models can thus be essential for adequate dosing delivery in specific networks related to clinically relevant connectivity outcomes.From the studies selected, the study from Mencarelli et al (2020), using the M8 montage, also estimates the normal component of the EF through computational modelling.The authors used a model based on the Colin27 and the Stimweaver algorithm (Ruffini et al 2014) to determine the optimal position of the electrodes and injected currents to induce a normal EF of 0.25 V m −1 over the targeted sensorimotor region using the M8 montage (table 1).According to our simulations, the normal EF component was above 0.15 V m −1 in the right M1, PMC and SMA regions for all subjects and below this value in the left regions for all subjects, except for s3 and s1 (see table 4).Also, M8 showed a high variability in terms of focality across subjects, showing the largest CV values from 0.29 to 0.42 (see table 3).Therefore, our results suggest that more optimised and accurate results could have been achieved in Mencarelli et al (2020).if the electrode positions and currents would have been personalised using individual EF models instead of the single-brain Colin27 atlas.As observed in our results and in line with Mikkonen et al (2020), this is especially relevant in multielectrode-channel montages, for which higher EFs are obtained, albeit at a cost of higher inter-subject variability.Moreover, in our study, we have also simulated the tangential EF component and found that this was higher than 0.15 V m −1 in all right and left hemispheric regions for all the subjects.Indeed, M8 was the montage that most favoured the values of tE, which may be due to a distributed placement of electrodes along a line between the two cortices.The tangential component may have more impact in fibres oriented tangentially to cortical layers, which are collateral axons of pyramidal tract neurons and interneurons, responsible for communication between regions for motor selection and coordination.This way, our study raises the hypothesis that tE-mediated neuromodulation may also have an impact and partly explain the greater FC outcomes observed over SMN as well as the negative connectivity found with other prefrontal/parietal regions under this montage.This highlights the importance of combining modelling and experimental studies to identify EF direction-based mechanisms and stimulation outcomes at distinct neural segments (Callejón-Leblic and Miranda 2021).

Methodological considerations
We assumed the default conductivities of SimNIBS for all montages, which considers the electrode as represented by a layer of conductive rubber and a layer of saline-soaked sponge.This case applied to studies Lang et al (2004) When using these values in 'ernie' model, EF predictions differ by less than 3.5%, corresponding to differences in EF magnitude of the order of 0.01 V m -1 .which are below the typical values predicted to induce neuromodulation (Miranda et al 2013), thus this difference does not impact significantly the main findings of this research.
The use of more accurate models in the future is recommended, due to the different contributions of the many tissues existing in the brain.The models generated by the headreco pipeline are not as detailed as other models available in literature, such as the MIDA model, which includes over 50 different tissues in a full headneck model (Iacono et al 2015).Also, models obtained by headreco do not discriminate stratification of extracerebral tissues, which impact the dielectric properties assigned to the skin and consequently the EF distribution predicted in the brain (Colella et al 2021).On the other hand, individual specific anatomical characteristics influence the current flow and thus the EF induced by tDCS, which reflects in variable outcomes from subject to subject (Hunold et al 2023).Modulation of brain networks with non-invasive techniques such as tDCS, are strongly subject-dependent, thus precision medicine approaches are more and more recommended, guided by personalised models (Antal et al 2022).Considering this, we decided to address inter-subject variability with realistic and personalised head models generated directly by each individual MRIs, instead of using already available and detailed literature models, such as MIDA (Iacono et al 2015).However, considering the impact of tissue stratification on the EF characteristics, future studies in this context should include more detailed models with tissue stratification towards more accurate predictions (Colella et al 2021).
On the other hand, our study defines focality as a whole-brain metric based on the volume of GM with EF magnitude above 75% and 50% of the maximum EF (99.9th percentile), an intuitive and wider use metric in the tDCS field (Mikkonen et al 2020, Antonenko et al 2021, Van Hoornweder et al 2023), which has allowed us to quantify a global effect of change across subjects and montages (see figure 5).However, we acknowledge that other measures, such as the dose-target determination index (DTDI) proposed in Kashyap et al (2021).could provide more in-depth and accurate estimates when used in parcellated ROI-based analysis.

What lies ahead in FC modulation with tDCS
This study aims to qualitatively relate EF characteristics predicted by tDCS modelling with FC outcomes observed in stimulation protocols.The next step would be to analyse how the EF patterns will impact responses at network and neuronal levels.Direct and indirect effects should be addressed, which implies modelling not only effects of the EF on neuronal responses, such as latency and neuron activation threshold, but also how synaptic responses are affected by the EF, since direct activation may also impact IH-FC outcomes, as seen in the case of M5a montage.The next step for tDCS modelling will thus be the development of computational models at different scales, from cortex to neurons' scales, determining how to convert EF effects for each scale level.
One main limitation of this study is the low sample size analysed, which only allowed us to perform a qualitative analysis.Even so, we were able to detect variability in the EF spatial profiles for different montages across the five subjects.Future studies should quantify the sensitivity of EF spatial profiles induced by different montages to anatomical/morphological differences of subjects.This quantification can be used to guide on the selection of montages to apply in pilot studies where samples are small, and thus more sensitive to individual responses.We also highlight that the EF value of 0.15 V m −1 considered as a threshold for neuromodulation effects is not definitive.Threshold for neuromodulation in tDCS is most likely variable across subjects and taskdependent.Future studies should combine experimental and modelling protocols to infer on what could be the best estimates of the EF required for tDCS effects to occur.Non-invasive brain stimulation techniques, such as tDCS, have increasing evidence of effects in brain connectivity, which is altered in many neurological diseases and conditions.Results are variable and depend on the FC-related measures investigated.Experimental protocols informed by computational modelling studies can help to select the montages that induce an EF with the most favourable pattern for network activation and FC enhancement, as well as with less variability across subjects.This is especially relevant in a clinical context, where personalization of treatments may be more difficult to address.Searching for solutions with less variability can result in more uniformity in tDCS-induced connectivity outcomes, contributing to the definition of gold standards according to FC-related targets.

Conclusion
In this study, we provide modelling-based perspectives aimed at investigating potential relations between the EF spatial patterns predicted by computational models and the FC outcomes reported in the literature.Our main findings encompass: (i) EF magnitude and distribution intricately depend on the interplay between electrode montage and anatomical variability.Generally, multi-electrode montages lead to higher EF peak values at a cost of larger interindividual variability; (ii) focality can be improved in montages with intra-hemispheric placements or smaller inter-electrode distances, but it also shows a dependence on individual anatomy, (iii) electrode montages may be designed to lead to differentiated oriented tangential and normal EF-based neuromodulation mechanisms, however they are also modulated by individual brain morphology.In conclusion, our study demonstrates that EF predicted by computational models can be related and used to guide tDCS FC outcomes.Future combined experimental-modelling research in FC modulation will be an essential approach towards more optimised and reliable tDCS protocols in the clinical context of brain connectivity dysfunctions.
Figure 1 and table

Figure 1 .
Figure 1.Electrode montages considered for tDCS simulations in SimNIBS (anodes and cathodes in red and black, respectively).Positions are according to the EEG 10-10 system.
with the principles embodied in the Declaration of Helsinki and in accordance with local statutory requirements.All participants gave written informed consent to participate in the study and to use all data collected for the study and for publication.The study was approved by the Ethics Committee of the Virgen Macarena and Virgen del Rocío University Hospitals, Seville, Spain (code number C.P. SIMBIOTIC_2021_23-C.I. 0175-N-21).T1 and T2-weighted images were obtained and used for segmentation of tissues using the headreco function from SimNIBS(Thielscher et al 2015).The example dataset ernie was also included.Five head models were obtained (s1, s2, s3, s4 and ernie-s5) each one with six tissues (figure2): scalp; skull; cerebrospinal fluid (CSF); cortical grey matter (GM); cortical white matter (WM); eyes.These tissues were assembled in a volume conductor mesh with approximately 5 × 10 6 tetrahedral elements.We considered the default values of electrical conductivity of tissues of SimNIBS(Thielscher et al 2015): σ scalp = 0.465 S m −1 ; σ skull = 0.010 S m −1 ; σ CSF = 1.654 S m −1 ; σ GM = 0.275 S m −1 ; σ WM = 0.126 S m −1 ; σ eyes = 0.500 S m −1 .

Figure 3 .
Figure 3. EF spatial profiles in the GM for s1.Columns: montages; rows, from top to bottom: superior, left, and right views.The last row contains colour scales of the electrodes' current (left) and EF magnitude (right) normalized to maximum values.

Figure 6 .
Figure 6.Violin plots of values of nE (top 3 rows) and tE (bottom 3 rows) in left and right M1, PMC and SMA for s1.lh: left hemisphere; rh: right hemisphere.

Table 2 .
Mean, standard deviation (STD) and coefficients of variation (CV) of EF magnitude percentiles in each montage.

Table 3 .
Mean, STD and CV of the volume in cm 3 with EF values above 75% and 50% of 99.9th percentile in each montage.
distance, which favours shunt effects in the scalp, thus allowing less penetration of current inside the brain, resulting in lower nE values.From table 4, we can observe that the montages that may have nE-induced neuromodulatory effects in all subjects are:• UL, M5b at left M1 and M5b at left PMC;• M8 at right regions;

Table 4 .
Motor-related regions with absolute value of nE > 0.15 V m −1 in each subject and each montage.

Table 5 .
Motor-related regions with tE > 0.15 V m −1 in each subject and each montage.

Table 6 .
EF main characteristics and FC outcomes of tDCS protocols.