Network controllability of structural connectomes in the neonatal brain

White matter connectivity supports diverse cognitive demands by efficiently constraining dynamic brain activity. This efficiency can be inferred from network controllability, which represents the ease with which the brain moves between distinct mental states based on white matter connectivity. However, it remains unclear how brain networks support diverse functions at birth, a time of rapid changes in connectivity. Here, we investigate the development of network controllability during the perinatal period and the effect of preterm birth in 521 neonates. We provide evidence that elements of controllability are exhibited in the infant’s brain as early as the third trimester and develop rapidly across the perinatal period. Preterm birth disrupts the development of brain networks and altered the energy required to drive state transitions at different levels. In addition, controllability at birth is associated with cognitive ability at 18 months. Our results suggest network controllability develops rapidly during the perinatal period to support cognitive demands but could be altered by environmental impacts like preterm birth.

Table S2: Structural network properties for each infant group (mean(std)) and their associations with controllability Table S3: Controllability maturation during perinatal period controlling for network strength/network density (r-value between controllability and postmenstrual age) Table S4: Pearson's correlation between regional controllability value and its maturation controlling for network strength/network density Fig. S5: Group differences in controllability between preterm and term infants with network strength as the additional covariance.

Fig. S6: Group differences in controllability between preterm and term infants with network density as the additional covariance.
Table S5: Sex consistency in the whole-brain controllability (Spearman's correlation between whole-brain controllability in female and male groups) Table S6: Sex difference in controllability maturation (Pearson's correlation between controllability and post-menstrual age) Table S7: Control energy consumption for null models and real brain networks of term and preterm infants (t-stats from paired t-test) Fig. S7: Scatterplots of controllability at birth and behavioral performances at 18 months old.Table S8.Neonatal 90 node parcellation's regional names and resting-state networks(RSNs)

Analysis with modal controllability
Average controllability and modal controllability are two distinct but complementary measurements of network controllability based on the network control theory.While average controllability quantifies the ability of each node to drive nearby state transitions with minimal energy input, modal controllability measures the capacity to drive more distant state transitions with higher energy requirements.Although these two measurements are highly correlated, they exhibit differences in several ways.In the main text, we presented the analysis of average controllability, while in this supplementary section, we discussed modal controllability to provide a comprehensive understanding of the controllability of the infant brain network.
Regional average controllability was negatively correlated with regional modal controllability average across all three infant groups (r<-0.99,p<0.001), in alignment with the structural connectomes of older individuals 1 .The strongest regions with modal controllability were mainly concentrated in somatomotor, dorsal attention, frontoparietal and subcortical networks.For modal controllability, the important cognitive networks in the infant brain overlap with the adult brain, mainly including the somatomotor and frontoparietal networks (Fig. S1a).
In contrast to whole-brain average controllability, whole-brain modal controllability changed similarly between 38-44 weeks PMA (r=-0.35,p=0.002) compared to 28-36 weeks PMA ( r=-0.44,p=9.5e-5)for preterm infants.For the term group, postmenstrual age at scan negatively correlated with whole-brain modal controllability r=-0.50, p=2.7e-29;Fig. S1b).No significant difference in the rate of maturation on the regional level between term infants and preterm infants at TEA was detected.
For modal controllability, term and preterm infants showed no significant whole-brain level difference (t=-0.46, p=0.64, df=519).The patterns of group differences in regional controllability were reversed to that of average controllability and the affected regions by preterm birth were more widely distributed than those of average controllability (Fig. S1c).Most significantly changing regions are located in the frontal cortex and limbic lobe, where preterm infants change more rapidly compared to term infants (Fig. S1d).Similar associations were observed for modal controllability (term: r=0.21,p=0.047;preterm at TEA: r=0.37,, but the difference between preterm and term groups was insignificant (z=1.36,p=0.086) (Fig. S1e).

Fig. S1 Analysis with modal controllability
(a) Negative associations between regional (or, the mean controllability across every individual for each brain region) average controllability and regional modal controllability among three subgroups (Pearson's correlation: term r=-0.99,p=1.8e-82; preterm at birth r=-0.99,p=1.0e-78;preterm at TEA r=-0.99,p=6.3e-84; two-sided).Each dot represents the regional average and modal controllability for each brain region.(b)Normalized regional modal controllability was spatially similar across the preterm at birth, preterm at TEA infants, and term groups.(c) Modal controllability matures steadily over the perinatal period (Pearson's correlation: preterm at birth: r=-0.44,p=9.5e-5;preterm at TEA: r=-0.35,p=0.0024;term: r=-0.50, p=2.7e-29; two-sided).The shaded envelope denotes the 95% confidence interval.The gradual change in normalized modal controllability is shown underneath the timeline on the brain maps.(d) Modal controllability distribution differences between preterm and term infants (t stats value from the two-sampled t-test).(e) Modal controllability maturation rate differences between preterm and term infants (z-stats value from correlation comparison).(f) Positive correlations between regional modal controllability and their rate of maturation for both preterm (Pearson's r=0.37, p=3.2e-4; two-sided) and term infants(Pearson's r=0.21, p=0.047; two-sided).The shaded envelopes in the scatterplots denote the 95% confidence interval.Source data are provided as a Source Data file.
Regions and networks with the highest controllability.Regions with significant longitudinal differences for preterm infants (at birth v.s. at TEA) in average controllability maturation (z test for comparison of correlations).Source data are provided as a Source Data file.

Controlling for network measurements
Considering that regional connectivity was correlated with controllability, one may ask if these network properties such as network strength and network density influence our results.
First, we incorporated network strength as an additional covariate in our analysis of whole-brain and regional controllability development.Our findings indicate that the correlations between controllability values and postmenstrual age for term and preterm infants are consistent with the developmental trends we showed in the main text.Second, we also verify that network density can not explain our results by including network density as covariance in our calculations.Average controllability remains positively correlated with postmenstrual age and modal controllability continues to be negatively correlated with postmenstrual age (Table S3).Furthermore, the results that regions with higher controllability value increase more with age are still present for term and preterm infants after controlling network strength or network density (Table S4).
Furthermore, we repeated the analysis of the effects of preterm birth on controllability distribution and controllability maturation with network strength (Fig. S5) and network density (Fig. S6) as additional covariances separately.Overall, the preterm-birth influence patterns were similar to the results shown in the main text (Fig. 4).
Additionally, to test if NCT reflects a unique topology of the infant brain, we constructed null models that preserved the degree distribution on the real brain data and then repeated the controllability analysis.
After permuting connection, brain networks for over 97% infants showed higher average and modal controllability compared to permuted brain networks.
In all, these results suggest that network strength and density do not provide a convincing explanation for our findings about controllability and its development in the structural brain networks during the early stage of infants' life.Source data are provided as a Source Data file.

Sex difference in the controllability of the infant brain structural network
Another regular concern about research on infants is whether sex plays a deterministic role, or more specifically, whether the results align in female/male groups.Here, we repeated the analysis in the main text for females and males separately.The whole-brain controllability distribution shows high consistency between the female and male infants for preterm and term groups (Spearman's correlation: r>0.96, p<0.001) (Table S5).In general, females and males follow similar maturation patterns compared to that of the whole group: average controllability increases with the speed slowing down and modal controllability decreases at a constant pace (Table S5).For the association between regional controllability value and its maturation, similar results are observed for females and males, except the association between regional average controllability and its maturation for males in the term subgroup is not significant (Table S6).

Null models for control energy cost
To determine whether the topology of the infant brain structure facilitated transitions to target state of various functional cognitive networks, we built 100 null models for each subject and compared the control energy consumption of real brain structural networks to that of null models using a paired t-test.We found that for both term and preterm infants, the real brain structural networks required less energy to drive the state transitions to every functional network, with t-test results shown in Table S7.Association with cognitive, language, and motor domains of BSID-III scores Fig. S7: Scatterplots of controllability at birth and behavioral performances at 18 months old.

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Fig. S2: Control roles of cognitive networks.Fig.S3: Regions with the longitudinal difference in average controllability maturation during perinatal period.Fig. S4: Regional controllability development rate for preterm and term infants.
Fig. S2: Control roles of cognitive networks.We calculated the role of each cognitive network in controllability as the percentage of regions with the highest controllability located in each network.(a) For preterm infants at birth, the visual network plays the dominant role in average controllability, and the somatomotor and dorsal attention networks are dominant in modal controllability.(b) For preterm infants at TEA, most regions with high average controllability are located in visual and dorsal attention networks and those with high modal controllability are located in the somatomotor system.(c) For term infants, regions with high average controllability are concentrated in visual, dorsal attention and somatomotor networks; regions with high modal controllability are concentrated in somatomotor, dorsal attention and subcortical networks.The network affiliation was based on the Yeo networks: 1. Visual, 2. Somatomotor (SM), 3. Dorsal Attention (DA), 4. Ventral Attention (VA), 5. Limbic, 6. Frontoparietal (FP), 7. Default (DM), 8. Subcortical (Sub).

Fig. S4 :
Fig. S4: Regional controllability development rate for preterm and term infants.The r-values from Pearson's correlation between regional controllability and post menstrual age are shown for (a) preterm and (b) term infants on the brain maps.Source data are provided as a Source Data file.

Fig. S5 :
Fig. S5: Group differences in controllability between preterm and term infants with network strength as the additional covariance.(a) Average and modal controllability distribution (controlling for network strength) differences between preterm and term infants (t stats value from the two-sampled two-sided t-test).(b) Average and modal controllability development rate differences (controlling for network strength) between preterm and term infants (z stats value from correlation comparison).Source data are provided as a Source Data file.

Fig. S6 :
Fig. S6: Group differences in controllability between preterm and term infants with network density as the additional covariance.(a) Average and modal controllability distribution (controlling for network density) differences between preterm and term infants (t stats value from the two-sampled two-sided t-test).(b) Average and modal controllability development rate differences (controlling for network density) between preterm and term infants (z stats value from correlation comparison).