We used the GRETNA toolbox (Wang et al., 2015) automated software to calculate the NBS of mice and humans based on diffusion-weighted structural connectivity. We chose to evaluate the global network properties of Efficiency, Small Worldliness, Hierarchy, and Assortativity to understand how heterotopic connections influence the whole-brain network. Efficiency is the number of paths connecting two nodes and relates to efficiency and the network’s redundancy. Small Worldliness is how the network approaches a pure small world motif (many short-range connections and few long-range integrative connections), usually associated with high communication efficiency and information transfer reliability. On the other hand, Hierarchy comprises classifying individual nodes (e.g., MRI atlas ROIs) according to each node’s degree (number of connections). Finally, Assortativity defines if these nodes communicate with nodes of a similar class, relating to the network’s pattern and type of connectivity (Sporns et al., 2005).

We calculated the non-heterotopic (NH) network by subtracting the heterotopic connections from the whole-brain connectome full network (FN). This way, we could compare the whole-brain connectome with and without the heterotopic connections. The delta NBS values were obtained by subtracting the NH values from each subject’s FN values, leaving only the heterotopic contribution to the NBS. We evaluated the Network-Based-Statistics with a pairwise parametric t-test and the deltas with an unpaired parametric t-test using GraphPad 7.0 Software (GraphPad Inc.).

In order to understand the anatomical placement of the heterotopic connections within the CC, we mapped the interhemispheric connections in each midline callosal voxel and calculated their heterotopicity indexes for each subject. In C57bl6/J mice, the heterotopic connections are distributed along the anteroposterior axis but concentrated in the center of the CC (Figure 5A), while in the CCD Balb/c mouse model, there is clearly a cluster of high heterotopicity in the genu of the CC (Figures 5C,D,G–I) or CC remnants (Figures 5B,E,F).

Control human subjects displayed heterotopic callosal connections that were distributed along the core of the CC, and surrounded by homotopic connections dispersed along its periphery (Figure 6A), as previously published (Szczupak et al., 2022). However, similar to their heterotopicity of individual cortical maps, hypoplasic CCD subjects showed variable heterotopicity topographies with specific focal clusters of high heterotopicity (Figures 6B–F).

To understand the importance of heterotopic connections to the overall brain function, we used graph theory and network-based statistics to compute the properties of Hierarchy, Efficiency, Small Worldliness, and Assortativity under two conditions. First, the NBS properties were calculated using the full brain network (FN). Then, we removed the heterotopic connections, and assessed the NBS properties for the remaining non-heterotopic network (NH, comprising intrahemispheric and homotopic connections). The data for normal brains and CCD individuals are shown in Figure 7. In the C57bl6/J strain, heterotopic connections contributed significantly to all tested NBS properties (Figures 7A–D). However, removing heterotopic connections in the CCD mouse Balb/c impacted only Efficiency and Assortativity (Figures 7F,H), but not Hierarchy and Assortativity (Figures 7E,G). These results indicate that in the Balb/c mouse brain, the heterotopic streamlines connect different regions and node classes than in the C57bl6/J brain.

Similar results were found in humans. Removal of heterotopic connections severely impacted all NBS properties in healthy subjects (Figures 7I–L), and all but Hierarchy in hypoplasic CCD patients (Figures 7M–P). As Hierarchy presented the highest variance across human subjects, the lack of significance between FN and NH is likely due to the small sample size associated with the heterogeneity of the CCD condition.

To gauge the relevance of heterotopic connections in CCD, we first subtracted the NBS values of NH from FN (Figure 8—see Methods) and compared results between normotypical C57bl6/J control mice and Balb/c CCD mice (Figures 8A–D), and between healthy subjects and hypoplasic CCD patients (Figures 8E–H). There is a clear difference between the mouse strains on ΔEfficiency, ΔSmall Worldliness, and ΔAssortativity (Figures 8B–D), revealing a higher impact of heterotopic connectivity to the CCD phenotype.

In humans, there is a difference between healthy subjects and CCD patients in ΔHierarchy (Figure 8E) and ΔSmall Worldliness (Figure 8G), indicating a higher effect of heterotopic connections to CCD. However, this was not observed for ΔEfficiency (Figure 8F) and ΔAssortativity (Figure 8H), indicating an equal effect of heterotopic connections in both healthy and CCD brains.

Neuroscientists have studied brain development for decades, especially the formation of the corpus callosum (LaMantia and Rakic, 1994; Wahlsten et al., 2003; Donahoo and Richards, 2009). Historically, the corpus callosum was viewed as a primarily homotopic structure (Zhou et al., 2013; Fenlon and Richards, 2015; Suárez et al., 2018; Mancuso et al., 2019) with few heterotopic connections (Houzel et al., 2002; Marconi et al., 2003; Lanz et al., 2017). However, recent comprehensive studies investigating callosal connectivity concluded that most callosal connections are, in fact, heterotopic (Swanson et al., 2017; Szczupak et al., 2022), and that these connections have an essential role in defining the properties of brain networks (Szczupak et al., 2022). These newly discovered predominance of heterotopic connections in the healthy brain called into question their role in developmental disorders of the corpus callosum. It is well described in the literature that due to the CCD, new heterotopic bundles can be formed. The sigmoid bundle, a heterotopic frontal parieto-occipital connection (Tovar-Moll et al., 2006; Paul et al., 2007; Jakab et al., 2015;Edwards et al., 2020; Szczupak et al., 2020a), is the most iconical example. Whole-brain structural connectome studies have also demonstrated that heterotopic connections are prevalent in congenital CCD humans (Owen et al., 2013a,b; Jakab et al., 2015; Szczupak et al., 2021b) and mice (Edwards et al., 2020; Szczupak et al., 2020a).

Here, we focused our work on the Balb/c mouse, a spontaneous CCD model which produces a wide range of callosal phenotypes (Wahlsten et al., 1992; Ozaki and Wahlsten, 1993; Livy and Wahlsten, 1997; Szczupak et al., 2020a) and in a small cohort of hypoplasic human subjects. We restricted our work to subjects presenting at least a callosal remnant in order to map callosal heterotopicity, excluding agenesis patients without callosal connections, which have altered brain connections patterns (Tovar-Moll et al., 2014; Siffredi et al., 2019; Szczupak et al., 2021a) but the relevance of heterotopicity cannot be established. Our data shows that CCD globally increases heterotopicity in both species similarly. However, differently from healthy controls that show a cohesive heterotopicity index (Supplementary Table 1), the spatial pattern of heterotopicity varied greatly across subjects, with several regions almost entirely heterotopic and many regions that could not project across the midline, even in the presence of a hypoplasic CC. Such variability was expected, as CCD is one of the most variable conditions in its genetic makeup (Paul, 2011), midline anatomy (Schell-Apacik et al., 2008), and brain connectivity patterns (Owen et al., 2013b; Jakab et al., 2015; Szczupak et al., 2020b).

In our previous study, we showed in three different mammalian species that the heterotopic connections form the core of the CC, with the homotopic connections located along its periphery (Szczupak et al., 2022). Here, we show that CCD significantly alters the relative spatial arrangement of homotopic and heterotopic connections. In CCD human subjects, we found that the CC of each individual had heterotopicity cluster(s) located in different portions of the CC. On the other hand, the heterotopic connections in Balb/c mice were clearly displaced toward the anterior CC near the genus. This finding agrees with our previous report showing high variability in the anterior cortical connectivity patterns in this mouse strain (Szczupak et al., 2020a). A possible reason for a high cohesivity in Balb/c phenotype is that this is an inbred mouse strain (Wahlsten et al., 2003; Burket et al., 2009) with a relatively stable genetic makeup. The Balb/c mouse strain has been reported to develop a late fusion of the anterior hemisphere (Livy and Wahlsten, 1997) and altered fiber development in the anterior pole (Rayêe et al., 2021) relative to other normotypic strains. Our results reinforce the early CC development time-window importance to the heterotopic connection development in the Balb/c strain. Here, we speculate that the Balb/c anterior CC has a developmental disorder that leads to misregulated interhemispheric crossings. Future studies shall investigate the molecular mechanisms that lead to the anterior CC malformation in the Balb/c strain.

To evaluate the importance of these connections to brain function, we used a standard graph network approach that has been previously applied to CCD (Owen et al., 2013b; Jakab et al., 2015; Edwards et al., 2020; Siffredi et al., 2020; Szczupak et al., 2020a, 2021b) and analyzed specific structural network properties (Assortativity, Hierarchy, Small-Worldliness, and Efficiency—see Methods). Heterotopic connections are fundamental to these network properties in typical brains (Szczupak et al., 2022). Interestingly, Balb/c mice did not show any differences in the Hierarchy and Small Worldliness. These results indicate that the heterotopic connections in Balb/c are equally connecting nodes of different hierarchical orders and not altering the network balance. Also, these connections have a different organization since the small world patterns are preserved despite removing heterotopic connections.

In hypoplasic human subjects, there is a clear pattern of the contribution of heterotopic connections to the NBS despite the high variance of the cohort. Nevertheless, similar to mice, there were no changes in the Hierarchy. It is worth noticing that Hierarchy is the most variable metric in all species and phenotypes. Therefore, the lack of significance in hypoplasic subjects could be due to the small sample size. Future studies shall observe larger cohorts to describe this interaction better.

It is well known that CCD can cause new abnormal heterotopic bundles such as the sigmoid bundle (Tovar-Moll et al., 2006; Paul et al., 2007; Kasprian et al., 2013; Edwards et al., 2020; Szczupak et al., 2020a), although there are reports of normal mice also presenting weaker connections with a similar trajectory (Szczupak et al., 2020a). Other whole-brain CCD connectome studies have also shown heterotopic connections spread around the cortex (Szczupak et al., 2020a, 2021b). Our analysis showed that CCD alters Efficiency, Small Worldliness, and Assortativity but not Hierarchy in mice. This interesting combination indicates a whole-brain reorganization in CCD mice that does not alter the Hierarchy between nodes. Instead, these streamlines connect nodes redundantly in a non-small-world motif, segregating nodes with a similar degree (Assortativity), essentially changing the brain architecture.

In hypoplasic subjects, the presence of CCD caused changes in Hierarchy and Small Worldliness, but not Efficiency and Assortativity. These results differ from CCD mice, indicating that heterotopic connections have different connectivity patterns that suggest distinct developmental trajectories in Balb/c mice and Humans. The long-range heterotopic connections in humans have a clear small world pattern decreasing the global Hierarchy. However, discussing whether these connections are adaptative, maladaptative, or mixed is still premature. Future studies targeting these connections might clarify the role of heterotopic connections to brain function in healthy and CCD brains.