Virtual lesions in MEG reveal increasing vulnerability of the language network from early childhood through adolescence

Functional outcomes after pediatric brain injury often show an inverse relationship with age (Kennard Principle), with a well-established pediatric advantage in language. Early in childhood, language is supported by a bilateral and diffuse network that becomes increasingly left-lateralized and focal through adolescence. These observations suggest that extensive representation and/or topological redundancy may confer robustness in younger children. Brain networks can be modeled as graphs, and in silico attacks (iterated node removal) can simulate lesion impact to assay network robustness. Classical robustness metrics focus on the largest connected component and define a percolation point at disintegration; however, in finite systems like brain networks, the largest component only reaches size zero when all nodes are removed, limiting utility. An alternative is to define percolation by the peak size of the second largest connected component, capturing redundancy that may subsume workload after damage. A further challenge is optimal thresholding: many topological parameters are density-dependent, and typical fixed-threshold approaches or data-driven schemes (MST, percolation) still require density selection, introducing multiple-comparisons or power issues. Functional Data Analysis (FDA) provides a framework to model network metrics as functions across densities, avoiding arbitrary threshold selection and multiple-comparison burdens. The current study aimed to determine developmental differences in percolation point from early childhood through adolescence, hypothesizing an inverse relationship between percolation point and age (greater robustness in younger children).

The study builds on literature indicating a pediatric advantage in language outcomes after brain injury and developmental changes from bilateral, diffuse to left-lateralized, focal language networks. Redundancy in neural circuits is a ubiquitous trait that supports robustness and adaptability, potentially conferring early developmental resilience. Graph-theoretic analyses and in silico lesion models have been used to assess network robustness, with centrality measures (eigenvector, betweenness) highlighting nodes important for network function. Prior work also underscores challenges of thresholding in brain network analyses due to density dependence, with approaches like MST or percolation-based filtering still requiring initial density choices. FDA has been proposed to model functions (e.g., metrics across densities) rather than single scalars, offering a way to address thresholding and multiple-comparison issues. Conceptually, distinctions between connector (domain-general) and provincial (domain-specific) hubs are important for understanding network organization and vulnerability, and developmental pruning of short-range with increasing long-range connections influences efficiency and potential vulnerability.

Participants: 82 typically-developing, native English-speaking children/adolescents (45 female), ages 4.0 to 18.7 years, with high-quality MEG and MRI, recruited at Cincinnati Children's Hospital Medical Center (2014–2020). Exclusion: neurological/hearing impairments, speech/language deficits, learning disability (family report). Consent/assent obtained; IRB/REB approvals in place. Data acquisition: MEG stories listening paradigm on a 275-channel whole-head system (CTF; 1200 Hz sampling). Participants supine; continuous head localization. Stimuli: 48 child-friendly stories (2–3 s sentences) and 48 matched speech-shaped noise trials, delivered binaurally via calibrated system. Structural MRI (3D T1-weighted, 1 mm isotropic) acquired at 3T (Philips Achieva or Ingenia Elition) after MEG, with fiducial markers for coregistration. Network definition: Whole-brain nodes derived from a 200-unit random parcellation (yielding 194 nodes). Language network defined using NeuroSynth (May 1, 2022; search term "language"), uniformity test map (FDRq=0.01) based on 1101 studies; parcellation parcels with at least 10% overlap with the binarized map were included (89/194 parcels; 52 left hemisphere). MEG preprocessing and source localization: FieldTrip (MATLAB) used. Continuous data bandpass-filtered 0.1–100 Hz; 60 Hz notch applied. ICA performed; stereotypical ocular/cardiac components (0–9; mean 3.82) rejected. Data epoched 0–2000 ms relative to stimulus onset. Single-shell sourcemodels from segmented T1 images. Node positions warped from template to individual space (SPM12). Stories and noise trials concatenated for covariance and common spatial filter construction. Source activity estimated with LCMV beamformer (0.1% regularization). Only stories trials used for connectivity and attack analyses. Functional connectivity: Connectivity assessed in narrow frequency bins to retain spectrally focused effects. Trial-wise Fourier representations computed for 0.5–100 Hz in 0.5 Hz steps with ±2 Hz DPSS multitapers. Pairwise connectivity quantified via weighted phase lag index (wPLI) for each frequency bin; aggregated using L2 norm to estimate total cross-spectral coupling. Adjacency matrices constructed for whole-brain and language networks. Mean Euclidean inter-node distance computed and included as a covariate to account for potential field spread differences related to brain size across ages. Attack analyses: Networks proportionally thresholded over densities from 100% to 0.25% in 0.25% steps. At each density, nodes were removed randomly, or targeted by descending eigenvector centrality (EC) or betweenness centrality (BC). Graph metrics computed using Brain Connectivity Toolbox. With each node removal, sizes of the largest and second largest connected components were computed. Percolation point defined as the fraction of nodes removed at which the second largest component peaked. Attacks iterated 100 times to estimate mean percolation point per density (ties in targeted attacks resolved randomly among maximally central nodes). Functional Data Analysis (FDA): Preprocessing removed outliers showing spikes at the lowest density (0.25%) based on z-scores of the last function value (>2). Percolation point-by-density functions were initially represented by 4th-order B-splines (402 basis functions), trimmed based on the first derivative of the mean group function to focus on the precipitous decline region. Each function was smoothed with a penalty on the second derivative; smoothing parameter selected by minimizing GCV over an exponential range. Outliers were further identified via sum of squared residuals from smoothed fits. Modeling: Function-on-scalar regression (penalized flexible functional regression, PFFR) modeled percolation point as a function of density, with predictors age, sex, handedness, and mean Euclidean node distance (nuisance). Unsmoothened response functions were used; appropriate smoothing chosen during regression. Beta functions for predictors allowed to vary with density and were smoothed using 5 cubic P-splines with first-order difference penalty. Model diagnostics included Q-Q, residual checks, response vs fitted, and k-basis dimension checks. Hypothesis testing and variance explained: Overall model significance assessed via Likelihood Ratio tests comparing the full model to a model with beta estimates constrained constant across the function. Adjusted R2 and functional R2 reported for full model and each predictor. Semi-partial correlations computed from R2 differences. Pointwise 95% CIs for beta estimates obtained via bootstrap resampling (1000 iterations) to address dependency/heteroskedasticity across densities. Significance for a predictor at a given density range required: significant overall model (LR test), significant predictor in the model, and 95% CI excluding zero. A conservative p-value threshold of 0.001 was used for overall and partial effects. Analyses were performed for random, EC-, and BC-based attacks at whole-brain and language network levels.

Whole-brain analyses: - Random attacks: Overall model significant (F=5.99, p<0.0001; R2=0.947; functional R2=1.3%). Age showed a significant negative effect on percolation point at densities below 15% (F=31.44, p<0.0001), indicating decreasing robustness with age; sex and handedness not significant. - BC-based attacks: Overall model significant (F=6.82, p<0.0001; R2=0.934; functional R2=8.20%). Age had a significant negative effect across all densities (F=126.38, p<0.0001); sex and handedness not significant. - EC-based attacks: No significant effects of age, sex, or handedness at any densities. - Visualization (5% density): Younger participants (1st age quartile) showed more consistently removed regions (group-level hubs) prior to network failure, with more distributed posterior (occipital/parietal) hubs; older participants (4th quartile) showed more focal distributions and greater heterogeneity among neighboring regions. Stories (language) network analyses: - Random attacks: Overall model significant (F=13.39, p<0.0001; R2=0.965; functional R2=2.7%). Age had a significant negative effect from 1–15% density (F=44.51, p<0.0001); sex and handedness not significant. - BC-based attacks: Overall model significant (F=6.75, p<0.0001; R2=0.915; functional R2=5.7%). Age had a significant negative effect across all densities (F=86.25, p<0.0001); sex and handedness not significant. - EC-based attacks: No significant effects of age, sex, or handedness at any densities. - Visualization (5% density): Younger children had more consistently removed regions across subjects (group-level hubs), whereas older participants had fewer such regions. Overall: Across whole-brain and language networks, age-related increases in vulnerability (lower percolation point with increasing age) were observed for random and BC-based attacks, but not for EC-based attacks. EC-based attacks dismantled networks earlier overall, but their effectiveness did not vary with age.

The density-independent FDA framework revealed that brain network vulnerability increases from childhood through adolescence, aligning with the pediatric advantage literature. The strongest developmental effect emerged for BC-based attacks, implicating nodes that bridge information flow (connector roles) as increasingly critical with age. In contrast, EC-based attacks—targeting nodes with high popularity/embeddedness—were equally effective across ages, suggesting that domain-general connector hubs remain relatively stable developmentally, whereas domain-specific hubs (more aligned with high betweenness) gain relative importance in older participants. Developmental pruning of short-range connections with increasing long-range connections likely enhances efficiency but increases vulnerability, reflected in older cohorts' greater susceptibility to BC-based dismantling. Spatial visualizations support a shift from bilateral, distributed critical hubs in younger children to more focal, heterogeneous distributions in older adolescents. Clinically, these findings support a network-based perspective for pediatric neurosurgical planning, emphasizing assessment of plastic potential (capacity for residual tissue to subsume function) and downstream network impacts of focal resections at developmentally specific stages.

This study introduces a percolation-based, density-independent (FDA) framework to assess developmental changes in brain network robustness using MEG-derived functional connectivity. Findings demonstrate increasing vulnerability of whole-brain and language networks with age for random and betweenness centrality-based attacks, while eigenvector centrality-based vulnerability remains stable across childhood and adolescence. The results suggest that developmental reorganization toward more efficient, long-range connectivity entails heightened susceptibility, with domain-specific hubs becoming increasingly critical. Future research should extend these methods to single-subject mapping of critical hubs for specific functions to guide individualized, developmentally informed clinical interventions, and further test task-specific strategies (e.g., visualization reliance) and longitudinal trajectories.

- Percolation point definition in finite networks is theoretically challenging when based on the largest connected component; the study addressed this by using the peak of the second largest component, but this choice may capture different aspects of redundancy than traditional definitions. - Thresholding of brain networks is a known confound; while the FDA approach mitigates arbitrary density selection, residual dependencies on density-specific features and smoothing choices remain. - Connectivity estimates relied on MEG source-space wPLI and L2 spectral aggregation; despite measures to reduce field spread and bias (e.g., wPLI, inclusion of mean Euclidean distance as covariate), MEG connectivity is susceptible to methodological limitations (e.g., ghost interactions), which may influence graph topology. - Visualizations suggested younger participants may rely more on posterior regions for the language task, but this interpretation was not experimentally tested. - The study focused on typically-developing children and adolescents performing a stories listening task; generalization to other tasks, modalities, or clinical populations was not assessed within this work.