Effects of spatial smoothing on functional brain networks

1 Introduction

• Preprocessing effects on functional brain-network structure were not well understood, although spatial smoothing was commonly used and could affect network properties.Smoothing averages each voxel’s signal with those of its neighbors; its rationale outside the GLM paradigm was less evident.Source: §1 · p. 2
• Earlier work reported smoothing-related changes in seed-based connectivity and local-connectivity reliability, motivating investigation of region-level networks.Source: §1 · p. 2
• The effects of spatial smoothing on the structure and properties of region-level functional brain networks had not been investigated in detail.Source: §1 · p. 2
• Spatial smoothing changes hub identities and largest-component structure, decreases inter-subject variation, and makes different subjects’ networks more similar.The authors advise against smoothing ROI-level functional brain networks.Source: §1 · p. 2

2.1 Subjects

• The in-house sample comprised 13 healthy, right-handed volunteers, with a mean age of 25.1 ± 3.9 years.There were 11 females and 2 males; all reported normal or corrected-to-normal vision and no neurological or psychiatric history.Source: §2.1 · p. 2

2.2 Data acquisition

• The study used approximately six minutes of resting-state fMRI data, comprising 215 time points, and also acquired structural T1-weighted images.Participants rested with eyes open, fixating on a gray background; only resting-state data were used.Source: §2.2 · p. 3

2.3 Preprocessing of the data

• Preprocessing included removal of the first three frames, motion correction, tissue-signal regression, spatial registration, and detrending.Motion-related signals were regressed out; all subjects were below the 0.5 mm framewise-displacement threshold, so no scrubbing was performed.Source: §2.3 · p. 3

2.4 Spatial smoothing

• Spatial smoothing redefines each voxel’s time series as a kernel-weighted average of neighboring voxel time series.The study applied Gaussian kernels of 5, 8, and 12 mm FWHM, using unsmoothed data as the 0 mm reference.Source: §2.4 · p. 3

2.5 Regions of Interest (ROIs)

• The analysis used non-overlapping cortical ROIs from the Harvard-Oxford atlas at a 30% probability level.The cortex was divided into 96 ROIs; cerebellar and subcortical areas were excluded to follow commonly adopted connectomics pipelines.Source: §2.5 · pp. 3–4
• Each ROI time series was the average of its voxel time series; ROI sizes ranged from 5 to 857 voxels.Mean ROI size was 141.58 ± 147.46 voxels, and the median was 88.Source: §2.5 · p. 4

2.6 Network extraction

• Pearson correlations between ROI time series formed a symmetric adjacency matrix, with self-links set to zero.Link physical length was defined as the Euclidean distance between connected ROIs’ centroids.Source: §2.6 · p. 4
• Networks were binarized by retaining links above a weight percentile threshold; centrality analyses used 10% density and largest-component analyses used 3%.Results for centrality were qualitatively similar across densities from 5% to 10%; the selected densities yielded 456 and 137 links, respectively.Source: §2.6 · p. 4

2.7 Averaging and comparison of correlation coefficients

• Correlation coefficients were Fisher Z-transformed before averaging across subjects or subtracting two coefficients, then inverse-transformed after averaging.The authors note that Z-transformation decreases bias when averaging correlation coefficients.Source: §2.7 · p. 4

2.8 Centrality measures

• Degree counts a node’s direct neighbors and serves as a simple estimate of its centrality and hub status.The paper also uses eigenvector centrality to identify hubs.Source: §2.8 · p. 5
• Degree rank orders ROIs by degree and reveals changes in each ROI’s hubness relative to the rest of the network.The authors compare both degree values and degree ranks to assess smoothing effects.Source: §2.8 · p. 5
• Eigenvector centrality accounts recursively for neighbors’ degrees, emphasizing nodes central to the network globally.It emphasizes central clusters in functional brain networks.Source: §2.8 · p. 5
• The authors calculate degree and eigenvector centrality using an in-house Python script with NetworkX.Source: §2.8 · p. 5

2.9 Largest connected component

• The LCC is the network component with the most nodes; the authors identify it per subject and calculate each node’s share of subjects’ LCCs.In sparse networks, separate components limit which nodes can reach one another.Source: §2.9 · p. 5

2.10 Network visualizations

• Network metrics are visualized using projected ROI centroid coordinates, slightly adjusted to reduce overlap while retaining approximate anatomical positions.Source: §2.10 · p. 5

2.11 ABIDE data

• To test whether findings generalize beyond the in-house data, the authors repeat all analyses on ABIDE I resting-state fMRI from 28 healthy controls.Source: §2.11 · p. 5

3.1 Spatial smoothing increases weights of short links

• Smoothing most strongly increases weights of short links, altering link-length distributions in networks thresholded to retain the strongest connections.The authors attribute the effect to signal mixing across nearby ROI boundaries, limited by kernel width.Source: §3.1 · p. 6, Figure 1 · p. 7

3.2 Spatial smoothing increases the degrees of small ROIs

• At 10% density, ROI size and degree change were negatively correlated for FWHM5 (r = −0.55), FWHM8 (r = −0.53), and FWHM12 (r = −0.57).Degrees of small ROIs increased while those of larger ROIs decreased; the fixed link count constrains the total degree.Source: §3.2 · p. 6, Figure 2 · p. 7

3.3 Network centrality measures are distorted by spatial smoothing

• At fixed 10% density, smoothing increases maximum and minimum degrees but decreases the median, increasing degree-distribution skewness.The largest changes occur in some temporal-lobe ROIs and nearby areas, while connections weaken or disappear between most other areas.Source: §3.3 · pp. 6, 8
• Smoothing shifts degree ranks across ROIs, with some temporal, frontal, and parietal ranks rising and some occipital, midline, and frontal-pole ranks falling.Degree and eigenvector centrality remain strongly correlated across smoothing levels (r = 0.90–0.91); changed hub rankings may alter interpretations of ROI roles.Source: §3.3 · p. 8

3.4 Smoothing may disconnect brain areas in the functional networks

• At 3% density, smoothing reduces variation in LCC membership across subjects; at FWHM 12 mm, nearly all participants’ LCCs include temporal and neighboring ROIs, while some occipital and frontal ROIs drop out.At higher densities, almost all nodes belong to the LCC, so smoothing affects connection strength instead of membership.Source: §3.4 · p. 8

4.1 Spatial smoothing changes the identity of hubs of the functional brain network

• Smoothing significantly alters HarvardOxford ROI networks, producing parameter-dependent artifacts and potentially changing which nodes are identified as hubs.The authors report increased degree and eigenvector centrality in small ROIs.Source: §4.1 · pp. 8, 13
• Degree and centrality changes are concentrated around temporal-lobe ROIs, while smoothing also disconnects frontal and occipital ROIs from the LCC.Small ROIs are especially affected because their boundary area is large relative to volume, making their signals more exposed to cross-ROI mixing.Source: Figure 3 · p. 9, Figure 5 · p. 11, Figure 6 · p. 12

4.2 Spatial smoothing changes the structure of functional brain networks

• At constant network density, smoothing strengthens short links more than long ones, increasing local segregation while weakening integration between clusters.Longer, weaker inter-cluster links are downplayed, although the paper describes them as important for effective information processing.Source: §4.2 · p. 13

4.3 Spatial smoothing decreases inter-subject variation

• Smoothing makes subjects’ largest connected components more similar, reducing inter-subject variation and potentially making ROI membership reflect smoothing side effects rather than true centrality.This reduction may also diminish differences between groups intended to differ, potentially biasing comparisons of network modular structure.Source: §4.3 · p. 13

4.5 Conclusion

• Because ROI construction already averages signals without mixing signals across ROIs, the authors conclude there is no specific reason to apply additional spatial smoothing.They caution that smoothing can over-emphasize strong short-range links, change hub identity, and reduce inter-subject variation.Source: §4.4 · p. 13, §4.5 · p. 14

• ABIDE means Autism Brain Imaging Data Exhange.Source: Abbreviations · p. 14
• BOLD means blood-oxygen-level dependent.Source: Abbreviations · p. 14
• fMRI means functional magnetic resonance imaging.Source: Abbreviations · p. 14
• FWHM means full width at half maximum.Source: Abbreviations · p. 14
• LCC means largest connected component.Source: Abbreviations · p. 14
• SNR means signal-to-noise ratio.Source: Abbreviations · p. 14

1.1 Iterative algorithm for calculating eigenvector centrality

• Eigenvector centrality is iteratively updated using the adjacency matrix, and after normalization the limiting vector is the eigenvector associated with its largest eigenvalue.The update uses adjacency entries and the preceding centralities of neighboring nodes.Source: §1.1 · p. 18

1.2 ABIDE data

• The independent ABIDE I dataset comprised 28 healthy controls pooled from Caltech and CMU, and the analyses used the same preprocessing pipeline as the in-house dataset.ABIDE included 92 anatomical ROIs because four temporal ROIs did not overlap across all subjects; the two sites had different acquisition parameters.Source: §1.2 · p. 18, Subjects · p. 18, Preprocessing and analysis · p. 19
• Networks were extracted separately for each subject, with averaging across subjects performed only after network extraction.Source: Preprocessing and analysis · p. 19

2.1 Changes in centrality distributions

• In the in-house data, smoothing increased degree-distribution skewness as the median and standard deviation fell while minimum and maximum degree rose.The analysis considered node degree, degree rank, and eigenvector centrality as centrality measures.Source: §2.1 · p. 19, §2.2 · p. 20
• In the in-house data, median eigenvector centrality decreased and its standard deviation increased with smoothing.The mean also decreased, while minimum and maximum values increased.Source: §2.1 · pp. 19–20

2.2 ABIDE data

• In ABIDE, smoothing strengthened short links more than long links, altering the physical link-length distribution in networks thresholded at 10% density.The strongest links were between physically close ROIs.Source: §2.2 · p. 20, Figure S1 · p. 20
• At 10% density, degree increased for small ROIs and decreased for larger ROIs, with ROI size strongly negatively correlated with degree change.The correlation was r = −0.63, −0.64, and −0.65 for FWHM5, FWHM8, and FWHM12, respectively.Source: §2.2 · p. 20, Figure S2 · p. 21
• In ABIDE, median degree increased while maximum degree decreased with smoothing, unlike the in-house dataset’s decreasing median degree.The authors note that smoothing effects may also depend on dataset properties.Source: §2.1 · p. 19, §2.2 · p. 21
• In ABIDE, mean and median eigenvector centrality decreased with smoothing, while its standard deviation and extremes showed no clear systematic changes.Single-node eigenvector-centrality changes were smaller than in the in-house data.Source: §2.2 · p. 21, Figure S5 · p. 24
• Degree rank rose most in temporal regions and fell most in several frontal, occipital, and cingulate regions.Temporal increases included superior temporal gyrus, central operculum, planum temporale, and Heschl’s gyrus.Source: §2.2 · p. 21, Figure S3 · p. 22, Figure S4 · p. 23
• Smoothing reduced the probability that occipital and frontal areas belonged to the largest connected component, with this pattern less visible in ABIDE than in the in-house data.The authors suggest that ABIDE’s larger sample may leave more inter-subject variance after smoothing.Source: §2.2 · pp. 21, 25, Figure S6 · p. 25

3 Supplementary Table

• The supplementary table lists ROI names and sizes, degree, degree rank, eigenvector centrality, and largest-connected-component membership probabilities across smoothing levels for both datasets.It covers 96 HO ROIs in the in-house dataset and 92 in ABIDE.Source: §3 · p. 25