The present study provides a comprehensive, anatomy-informed analysis of how individual variability in brain and skull features shapes the spatial distribution and intensity of tDCS-induced E-fields. By leveraging a large, demographically diverse cohort and advanced computational modeling, we demonstrate that both electrode montage and subject-specific anatomy critically determine the patterns and network-level E-field distribution of tDCS-induced fields. These findings have significant implications for the design and personalization of non-invasive brain stimulation protocols.

Our results demonstrate that both electrode placement and individual anatomical features strongly shape the spatial distribution and intensity of tDCS-induced E-fields, consistent with previous computational modeling studies [23, 24, 51]. Even when identical montages are applied, differences in skull thickness, CSF volume, cortical folding, and other structural factors substantially influence where and how strongly the current reaches the cortex, as supported by the distribution of the E-field maxima (figure 2).

The mechanisms underlying these effects are well-established in bioelectrics: current flow follows the path of least resistance through conductive tissues [46], meaning that individual variations in tissue geometry and conductivity create subject-specific current pathways [44]. For instance, thicker skulls attenuate current more strongly due to their low conductivity (0.01 S m−1), while enlarged CSF spaces can create conductive ‘shunts’ that divert current away from cortical targets [45, 48]. Similarly, cortical folding patterns influence current density distribution because gyri receive higher current density than sulci, creating focality that varies with individual gyrification patterns [42].

Consequently, the region receiving the highest E-field may not always align with the intended target of stimulation, a finding that has important implications for both research reproducibility and clinical efficacy [12, 23, 51]. Indeed, additional E-field maxima often appear beneath the cathode regardless of electrode configuration, suggesting that the simple anode-excitation/cathode-inhibition dichotomy does not fully capture the effects of stimulation. This spatial variability underscores the challenge of achieving precise and reproducible targeting with tDCS, even when using standardized electrode montages, and highlights the necessity of individualized modeling to account for subject-specific anatomy, as well as the potential for off-target effects in regions adjacent to the primary stimulation site. This observation suggests that standardized, ‘one-size-fits-all’ protocols provide only a coarse approximation of current flow and are unlikely to achieve consistent targeting across individuals. Not only can the location of peak stimulation vary, but also the current density reaching the cortex or intended target region can differ substantially between individuals, further amplifying variability in E-field magnitude at a given site. In some cases, a given montage may deliver sufficient E-field strength to the desired cortical area, whereas in others the same configuration may shift the peak of stimulation to adjacent or more distributed regions or deliver markedly different intensities.

Our network-level dosimetry analyses revealed that tDCS does not deliver E-fields to all brain systems equally but rather induces suprathreshold E-field magnitudes in certain functional networks more consistently than others. In particular, the executive and default mode networks exhibited the most consistently elevated E-field magnitudes above the physiological efficacy threshold, which is expected given that most montages targeted the DLPFC, a key hub within the executive control network. However, the E-field magnitude and spatial distribution were highly sensitive to both montage configuration and individual anatomy. Even when identical montages were applied, the extent to which different systems received suprathreshold E-fields varied, reflecting both the spatial distribution of induced fields and the underlying organization of large-scale connectivity.

The delivery of suprathreshold E-fields to multiple networks beyond the primary target raises important considerations for both therapeutic applications and experimental interpretation. For cognitive enhancement applications targeting working memory, the simultaneous stimulation of executive and default mode networks may be beneficial, as these systems work in concert during demanding cognitive tasks [84]. However, the direction of modulation (whether a network is facilitated or suppressed) is equally important and depends on factors beyond E-field magnitude alone, such as stimulation polarity, baseline neural activity, and network state [67]. Unintended delivery of suprathreshold E-fields to additional networks could introduce confounding effects or reduce the specificity of interventions. For instance, inadvertent stimulation of sensorimotor networks during cognitive protocols may complicate the interpretation of behavioral outcomes, while excessive E-field delivery to default mode regions during attention-demanding tasks could potentially interfere with performance depending on the polarity and functional state of the network [85].

Principal component and feature importance analyses further identified the anatomical and stimulation parameters most strongly driving these network-level effects, thereby providing actionable guidance for montage selection and highlighting the need to account for individual variability in systems-level interpretations of tDCS.

PCA using Spearman correlations (to account for potential non-normality in anatomical features) revealed that the dominant axis of variability (PC1) is primarily driven by cortical geometry, particularly LGI (), with significant contributions from CTh (ρ = 0.24), skull thickness (ρ = 0.21), and CSF thickness (ρ = 0.16). Montage effects are most pronounced for bilateral parietal configurations (P3–P4, all electrode shapes). The strong negative association with gyrification indicates that individuals with less cortical folding tend to have higher PC1 scores, suggesting that more gyrified cortices create more complex current pathways that alter E-field distribution patterns. This finding aligns with biophysical principles where cortical folding creates variable tissue interfaces and distances between electrodes and cortical targets, with gyri receiving higher current density than sulci [42, 43].

The secondary contributions of skull thickness and CSF thickness to PC1 reflect their established roles as the primary resistive barrier and conductive shunt, respectively [44, 47]. The use of Spearman correlation revealed a stronger effect of gyrification and a weaker effect of CSF thickness compared to Pearson correlations, suggesting that the relationship between cortical folding and E-field variability is more robust when accounting for monotonic (rather than strictly linear) relationships, and that the CSF effect may be partially driven by extreme values.

The secondary axis (PC2) is shaped primarily by the conductive and resistive tissue layers, including CSF thickness (ρ = 0.33) and skull thickness (ρ = 0.19), along with sulcal depth (ρ = 0.13), LGI (), and skin thickness (). The prominence of CSF and skull thickness on PC2, combined with sulcal depth, likely reflects how these structural features jointly modulate current pathways, as thicker CSF spaces provide conductive ‘shunts’ while thicker skulls attenuate current, and deeper sulci create additional pathways through CSF pools that can bypass cortical targets [42, 44, 48]. This multifactorial nature underscores the complex interplay between tissue conductivities and geometric factors in determining E-field distributions [24, 86].

The tertiary axis (PC3, 7.3% of variance) provides complementary insight by capturing montage-specific variability that is independent of individual anatomical features. PC3 strongly differentiates frontal montages (all negatively associated, ) from bilateral parietal montages (positively associated, ρ ≈ 0.15), with no significant anatomical contributions. This anatomy-independent axis likely reflects intrinsic differences in current flow paths between anterior and posterior electrode positions that persist regardless of individual structural variation. The emergence of PC3 demonstrates that E-field variability arises from both subject-specific anatomy (PC1, PC2) and montage-specific factors (PC3), reinforcing the importance of considering both dimensions when optimizing stimulation protocols.

The dominance of parietal montages in driving variance patterns may reflect the greater anatomical heterogeneity in posterior brain regions, where complex sulcal patterns and variable CSF spaces create more diverse current pathways compared to the relatively uniform frontal cortex [38, 39]. Notably, bilateral parietal montages are the only configurations showing significant correlations with both PC1 and PC2, indicating that these montages are particularly sensitive to anatomical variability and may require special consideration in both research and clinical protocols. This pattern indicates that bilateral parietal montages are less effective in anatomically distinct regions characterized by lower gyrification, thicker cortex, thicker skull, thicker CSF, and deeper sulci, compared to the dominant variability patterns captured by the PCs.

Importantly, these variance patterns are driven by electrode position rather than electrode size or shape, suggesting distinct mechanistic roles rooted in fundamental principles of current flow. Electrode position determines how current flow interacts with individual anatomical features because different brain regions exhibit distinct tissue architecture and conductivity profiles [46]. For example, frontal placement encounters relatively uniform skull thickness and cortical folding, while parietal placement must navigate more complex sulcal patterns and variable CSF distributions [39]. In contrast, electrode size and shape primarily affect the spatial precision and location of E-field maxima by modulating current density at the scalp-electrode interface, with larger electrodes creating more diffuse fields and smaller electrodes producing more focal stimulation [50, 53]. This principle is empirically supported by the near-identical PCA correlation coefficients observed for C1 and C5 electrodes at matched positions (table 3), demonstrating that electrode diameter does not meaningfully alter the dominant patterns of E-field variability. However, FWHM analyses reveal that larger circular electrodes produce modestly increased spatial spread, with the bilateral DLPFC montage (F3–F4) showing the largest difference between electrode sizes (table 2). For practical montage selection, electrode position should be prioritized over electrode size when optimizing for consistent E-field delivery across individuals, though electrode size remains relevant for targeting precision in specific configurations.

These findings indicate that even subtle anatomical differences can substantially alter the spatial distribution and intensity of tDCS-induced fields, and that montage selection, particularly for parietal targets, should be informed by individual anatomy.

Feature importance analyses further showed that while the default mode and the executive control networks consistently receive the highest E-field magnitudes across montages, the magnitude and spatial extent of E-field distribution within these networks is shaped jointly by stimulation parameters and individual anatomical factors. As a result, although the identity of the networks receiving the strongest E-fields remains relatively consistent (reflecting the DLPFC targeting), the intensity and the spatial extent varies substantially based on the interaction between protocol design and subject-specific anatomy. This highlights the necessity of considering both dimensions when interpreting the systems-level dosimetry of tDCS.

Such variability complicates both experimental interpretation and translational applications of tDCS, emphasizing the importance of incorporating subject-specific modeling to better characterize and, where possible, account for these differences.

The clinical and practical implications of these findings are substantial. By quantifying the anatomical determinants of E-field variability, our results provide a robust framework for anatomy-informed montage selection. In particular, individuals with pronounced anatomical features, such as increased CSF thickness or deep sulci, may benefit from personalized modeling to optimize stimulation targeting and efficacy. Given that brain morphometry varies systematically across the lifespan [25], age-specific considerations become particularly important when selecting optimal montage configurations. As noted above, bilateral parietal montages are particularly sensitive to anatomical variability and require special consideration in both research and clinical protocols.

While individualized E-field modeling remains the gold standard for tailoring stimulation to anatomical features, it is not always feasible, such as when MRI data are unavailable due to clinical constraints or cost considerations. In such cases, anatomy-informed frameworks derived from large, demographically diverse cohorts can guide montage selection, providing a practical compromise between individual precision and population-level generalizability. Publicly accessible resources such as the BrainChart web application [25] facilitate this approach by providing age-specific normative values for key anatomical features, enabling researchers and clinicians to estimate expected brain morphometry without requiring individual scans. To translate our findings into practice, we provide a step-by-step workflow for anatomy-informed electrode selection (see subsection 4.3.1 below). The approach can be applied in two scenarios: (1) when MRI scans are available, key anatomical features can be extracted from individual scans and compared to our PCA-derived patterns of E-field variability; (2) when MRI is not available, normative brain morphometry databases (such as BrainChart [25]) can be consulted to estimate age-specific anatomical characteristics, which are then matched to PCA patterns using the loading vectors and population statistics provided in our Supplementary Material. In both cases, the workflow involves selecting montages that best match the subject’s anatomical profile and intended target, refining choices using feature importance maps, and optionally running individualized simulations for complex cases (when MRI data are available). Ultimately, our work supports a shift toward individualized, data-driven approaches in tDCS, with the potential to enhance both the precision and reproducibility of neuromodulation interventions.

A major contribution of this work is the development of a practical workflow for anatomy-informed montage selection. By mapping individual anatomical features to the principal axes of E-field variability, this framework enables clinicians and researchers to make evidence-based decisions for optimizing stimulation targeting. Importantly, the approach remains informative even when individual MRI data are unavailable, as existing normative brain morphometry databases (e.g. BrainChart [25]) can be consulted to obtain age-specific anatomical estimates that can then be matched to our population-derived loading vectors and feature importance patterns (provided in supplementary material). This framework thus moves the field beyond one-size-fits-all protocols and addresses a key source of variability that has long limited the reproducibility of tDCS research [9, 12].

Our findings suggest that personalized modeling, even using readily available MRI-derived features, can substantially improve the precision and efficacy of tDCS interventions. The proposed workflow is accessible to both technical and non-technical users, and could be further streamlined through integration with existing web-based tools for normative brain morphometry [25] or through the development of tDCS-specific lookup tables and decision support systems.

4.3.1. Practical guidance for anatomy-informed electrode selection

While individualized modeling remains the optimal choice for the accurate estimation of induced E-field, to help clinicians and researchers apply our findings in real-world settings, we outline a step-by-step approach for selecting the most appropriate tDCS electrode montage based on individual anatomy. This workflow is particularly useful when individual MR images are not available (not possible or of too low quality), but can also guide montage selection when MRI data are available. The workflow is designed to be accessible to both technical and non-technical users and addresses both dosing (achieving sufficient E-field strength) and targeting (achieving spatial precision) considerations:

1.  

Assess key anatomical features: For each new subject, assess the main anatomical features that influence current flow, such as CTh, skull thickness, CSF thickness, and sulcal depth. If MRI scans are available, these features can be extracted using standard neuroimaging tools (see methods). When MRI is not available, normative brain morphometry databases such as the BrainChart web application [25] (https://brainchart.shinyapps.io/brainchart) can be consulted to obtain age-specific normative reference values and centile calculations for key brain morphometry measures across the lifespan, enabling estimation of expected anatomical values based on the subject’s age and demographic characteristics. These age-derived estimates can then serve as proxy values for matching to our PCA patterns.

2.  

Compare to study patterns: Our analysis used PCA to identify which anatomical features most affect how E-fields are distributed in the brain. We provide loading vectors (directions of greatest variability) that show which features matter most for each electrode montage.

3.  

Montage recommendation: For a given subject, look for the montage(s) whose loading vectors best match the subject’s anatomical profile and the intended brain target. In practical terms, if a subject has a thicker skull or deeper sulci, choose the montage that our results show is less affected by those features, or that maximizes the E-field in the desired network. When MRI data are available, the subject’s position in the PCA space can be estimated by projecting their parcel-level anatomical features through the trained PCA model (standardized and rotated using the population-derived loadings). Note that this detailed PCA projection approach requires MRI scans and is not part of the non-MRI workflow path. Loading vectors, population-level morphological statistics, subject IDs, and detailed calculation steps (including the subject_correlations.r R script) can be found in the supplementary material, section S1.

4.  

Refine with feature importance: Use the feature importance heatmaps (figure 4) to further guide your choice. These maps indicate which anatomical features and montages have the strongest impact on the E-field distribution. Select montages that are either robust (less variable across people for consistent dosing) or highly sensitive (for personalized targeting), depending on your clinical or research goal. Consider the 0.15 Vm−1 efficacy threshold for dosing and FWHM metrics for targeting precision (see Results, table 2).

5.  

Optional: individualized modeling: For complex cases or when high precision is needed, consider running a personalized E-field simulation using the subject’s MRI data and the selected montage. This step is more technical but can provide additional confidence in the montage choice.

Despite the strengths of our approach, several limitations warrant consideration. First, our simulations assume homogeneous tissue conductivities and do not account for dynamic physiological states or inter-session variability [33]. Second, while the HCP-A cohort provides a robust sample of older adults (36–80 years), generalizability to younger or clinical populations remains to be established. The age range of our sample captures important adult aging trajectories but does not encompass the full lifespan trajectories of brain development and aging documented in normative studies [25]. Third, our analyses focus on E-field distributions rather than direct behavioral or neurophysiological outcomes; thus, the translation of field strength to functional effects should be interpreted with caution [19, 21]. Finally, for small electrodes that are often used with conductive gel, we modeled the contact medium as saline sponge (1 S m−1); conductive gels typically have higher conductivities (approximately 1.5–2 S m−1 or higher depending on formulation) [53]. This assumption primarily affects absolute E-field magnitude through electrode-medium conductivity and contact impedance, with higher gel conductivity potentially leading to increased E-field magnitudes in the cortex, though the spatial distribution of fields is expected to remain largely unchanged [53]. Future work should include sensitivity analyses varying electrode medium and layer thickness.

Additionally, while we employed rigorous quality control and sensitivity analyses, some degree of error is inevitable due to MRI preprocessing, mesh generation, and registration steps. Future work should aim to validate these findings using empirical measurements such as EEG during tDCS to assess cortical activity changes, TMS-evoked potentials to measure cortical excitability, or behavioral outcomes that correlate with predicted E-field distributions. Previous work has demonstrated the feasibility of such validation through intracranial measurements in epilepsy patients [52]. As technology progresses reduced model digital-twins can be built that accelerate the validation process [87]. Validation should also be extended to diverse populations beyond the cohort of this work.

While this work focuses on tDCS as a representative case, many of the anatomical considerations and methodological recommendations discussed here are also relevant to other non-invasive electrical stimulation techniques, such as transcranial alternating current stimulation (tACS) [88] and transcranial temporal interference stimulation (tTIS) [89].

An important limitation of the current workflow is that while it can be applied with or without MRI data, the montage space explored in this study is limited to a subset of commonly used electrode combinations. To create a more comprehensive matching space that enables selection of more realistic and diverse montage combinations, future derivative work should expand the analysis to include a broader range of electrode positions, configurations, and geometries. Such expansion would enhance the practical utility of the framework by providing a richer database of montage-anatomy interactions from which to select optimal configurations.

In summary, this study underscores the critical role of individual anatomy in shaping the effects of tDCS and provides a robust, evidence-based framework for personalized stimulation. By integrating anatomical data into protocol design, we can enhance the precision, reproducibility, and ultimately the clinical utility of non-invasive brain stimulation. These advances pave the way for more effective, individualized neuromodulation therapies and set a new standard for rigor in the field.