Callosal fiber length scales with brain size according to functional lateralization, evolution, and development

Brain size significantly impacts the organization of white matter fibers. Fiber length scaling – the degree to which fiber length varies according to brain size – was overlooked. We investigated how fiber lengths within the corpus callosum, the most prominent white matter tract, vary according to brain size. The results showed substantial variation in length scaling among callosal fibers, replicated in two large healthy cohorts (∼2000 individuals). The underscaled callosal fibers mainly connected the precentral gyrus and parietal cortices, whereas the overscaled callosal fibers mainly connected the prefrontal cortices. The variation in such length scaling was biologically meaningful: larger scaling corresponded to larger neurite density index but smaller fractional anisotropy values; cortical regions connected by the callosal fibers with larger scaling were more lateralized functionally as well as phylogenetically and ontogenetically more recent than their counterparts. These findings highlight an interaction between interhemispheric communication and organizational and adaptive principles underlying brain development and evolution. Significance Statement Brain size varies across evolution, development, and individuals. Relative to small brains, the neural fiber length in large brains is inevitably increased, but the degree of such increase may differ between fiber tracts. Such a difference, if it exists, is valuable for understanding adaptive neural principles in large versus small brains during evolution and development. The present study showed a substantial difference in the length increase between the callosal fibers that connect the two hemispheres, replicated in two large healthy cohorts. Altogether, our study demonstrates that reorganization of interhemispheric fibers length according to brain size is intrinsically related to fiber composition, functional lateralization, cortical myelin content, evolutionary and developmental expansion.


Introduction
27 Total brain size varies dramatically across evolution, development, and individuals. 28 Large brains' structures are not simple linearly scaled versions of small brains, e.g., cortical 29 expansion of large brains is disproportionately larger for higher cognitive function regions 30 (Hill et al., 2010;Reardon et al., 2018). The scaling patterns of specific brain structures 31 provide essential clues for understanding organizational and adaptive principles underlying 32 brain development and evolution (Zhang and  An increase in brain size also has a significant impact on brain circuits (Kaas, 2000). 35 In larger brains, fiber length is inevitably increased, accompanied by a longer delay in 36 conduction and slower information transfer. It is well known that brain fibers can increase 37 their myelination and diameter to increase conduction velocity and compensate for this 38 delay (Waxman et al., 1995;Wang et al., 2008). These adaptations, however, cannot apply 39 systematically to all fiber tracts due to the limit in brain space and energy consumption 40 (Ringo et al., 1994), leading to alternative biological strategies that might impact fiber 41 length differently. While the fiber length adjustment to brain size has been assumed 42 uniform so far, heterogeneity in fiber length scaling may reveal adaptive principles 43 underlying brain development and evolution. 44 In the present study, we assessed whether length scaling variations exist according to 45 brain size within the corpus callosum (CC), the principal white matter (WM) bundle 46 supporting the communication between the two brain hemispheres. We further investigated 47 Theoretically, if WM fibers' internal geometrical shape is invariant for brain size, the 163 WM fiber length should scale as the 1/3 power of brain size. In this case, the proportional 164 relationship between the two measures, one in 1-dimension and the other in 3-dimension, 165 is preserved during scaling. This is referred to as the isometric scaling or iso-scaling. For 166 empirical scaling coefficients, coefficients > 1/3 indicate that the WM fiber length scales 167 more with greater brain size, i.e., over-scaling; coefficients < 1/3 indicate that WM fiber 168 length scales less with brain size, i.e., under-scaling. Each voxel's scaling coefficient on 169 the mCC template was statistically compared to 1/3 to identify the significant clusters with 170 over-scaling or under-scaling. To correct for multiple comparisons, the false discovery rate 171 (FDR) procedure was performed at q value of 0.05 (Genovese et al., 2002). 172

Validation analysis of callosal tractography 173
The validity of our callosal tractography is critical for measuring callosal fiber length 174 and performing subsequent length scaling analyses. To validate our callosal tractography 175 results, we evaluated a set of characteristics of tractography-based callosal connections as 176 following. 177 First, we selected several cortical regions of interest (ROIs) that showed length under-178 scaling and over-scaling in scaling analyses, and investigated how tightly their callosal 179 streamlines are clustered on the mCC and how the clusters on the mCC correspond with 180 previous anatomical studies. Specifically, we extracted the cortical ROIs using the 181 HCPMMP atlas (Glasser et al., 2016). The selected ROIs included 1) area 4 on the primary 182 motor cortex, 2) area 2 on the somatosensory cortex, 3) area TE1p on the lateral temporal 183 cortex, 4) area 7AL on the lateral parietal cortex, 5) area POS2 on the medial parietal cortex, 184 6) area 9-46d on the lateral prefrontal cortex, and 7) area 9m on the medial prefrontal cortex. 185 For each ROI, a streamline count map was generated by projecting the ROI-connected 186 callosal streamlines onto the mCC for each individual. The resultant maps were further 187 binarized and averaged across individuals, resulting a group pattern map ( Fig. 2A) Specifically, we adopted the HCP minimally preprocessed rs-fMRI data, and the 217 preprocessing procedures included magnetic gradient distortion correction, EPI distortion 218 correction, nonbrain tissue removal, MNI standard space registration, and intensity HCPMMP region, the averaged rs-fMRI time series across all vertices was calculated as 224 the regional rs-fMRI time series. For each HCPMMP homotopic regional pair, the FC 225 strength was measured using the Pearson correlation coefficient (converted to Fisher's Z-226 values) between the two regional time series. The group-averaged FC was then generated 227 for each HCPMMP homotopic regional pair. 228

WM microstructural measures on the mCC 229
To measure callosal fiber composition, two widely used dMRI-derived parameters, 230 i.e., neurite density index (NDI) and fractional anisotropy (FA), were estimated for each representative NDI and FA maps in healthy adults were then generated by averaging all 234 HCP individual maps of the template space. Such representative maps were used to assess 235 the relevance of length scaling to callosal fiber composition. 236

Mapping cortical topography of each mCC voxel 237
For each HCP subject, the minimal preprocessing pipeline outputted FreeSurfer-238 generated pial and white surfaces resampled onto the standard 32k_fs_LR mesh in the 239 native volume space. Each mCC voxel's streamlines were assigned to their closest vertex 240 on the white surface within a sphere with a 2-mm radius centered at its endpoint, therefore 241 yielding a standard 32K surface map of streamline counts for this voxel. For each voxel on 242 the mCC template, such a streamline count map on the standard 32K surface was 243 comparable across individuals. The group streamline count surface map was then obtained 244 by averaging the individual streamline count surface maps across all HCP individuals. We 245 applied a threshold to the group streamline count surface map to extract a binary cortical 246 topography map for each mCC voxel. Specifically, the mean + 0.5*standard deviation 247 (STD) of the group streamline count value across the entire surface was used as the main 248 threshold. To evaluate the influence of such a threshold on the results, we reran relevant 249 analyses by applying the following two thresholds: 1) a less stringent threshold, i.e., the 250 mean of the group streamline count value across the entire surface, and 2) a more stringent 251 threshold, i.e., the mean + 1*STD of the group streamline count value across the entire 252 surface. 253

Cortical measures 254
To assess the relevance of callosal fibers' length scaling to particular functional and 255 structural aspects of their connected cortical regions, we derived several cortical measures; 256 these measures are described below. 257

Statistical analysis 285
To determine whether the length scaling coefficient was related to callosal 286 microstructural measures and cortical measures above, we calculated the Spearman 287 correlations across all mCC voxels. We used the Spearman correlation because the length 288 scaling coefficient showed a nonnormal distribution on the mCC. A permutation test 289 (10,000 permutations) was adopted to estimate the Spearman correlation coefficient's 290 statistical significance (rs). To evaluate the robustness and reproducibility of the observed 291 correlation across the analysis resolution of the mCC, we additionally parcellated the entire 292 mCC into ten segments. The parcellation scheme followed an influential mCC study, which 293 measured histological fiber density for each of the ten segments (Aboitiz et al., 1992). 294 Likewise, we assigned the mean callosal microstructural measures or the mean cortical 295 index value of the connected cortical region to each mCC segment. We then reran the 296 Spearman correlation analysis across all ten mCC segments. 297

16
To examine an independent relationship between callosal fiber length scaling and the 298 aforementioned cortical measures, we reran the Spearman correlations across the mCC 299 voxels or segments described above while controlling for the NDI and FA. 300 301

Validation of callosal tractography 303
As shown in Fig. 2, the streamlines from the primary motor cortex mainly traversed 304 the posterior body; the streamlines from the somatosensory cortex mainly traversed the 305 posterior body and anterior splenium; the streamlines from the lateral temporal cortex and 306 medial parietal cortex were tightly distributed on the posterior splenium; the streamlines 307 from the lateral parietal cortex were distributed on the anterior splenium. In contrast, the 308 streamlines from the lateral and medial prefrontal cortex were mostly clustered on the genu. 309 The observed spatial pattern on the mCC was strikingly similar for homotopic ROI pairs For all mCC voxels, their passing streamlines termination pattern on the hemisphere 329 was quite similar between the two hemispheres (Fig. S5). This corresponds well with the 330 largely mirrored nature of callosal connectional termination on the two hemispheres, 331 therefore favoring the validity of our CC tractography. 332 However, we did not observe significant SC-FC correlation across the homotopic 333 HCPMMP regional pairs (Fig. S6), which is consistent with a recent study (Rosen and 334 Halgren, 2021). This negative result might reflect biases of our callosal tractography or 335 biologically meaningful divergence between these two types of interhemispheric 336 connectivity. 337 Callosal fiber variation in length scaling with brain size 338 As shown in Fig. 1 into Aboitiz's ten segments, which measured histological fiber density for each of the ten 360 segments (Aboitiz et al., 1992). Across the ten mCC segments, significant correlation was 361 found between the histological fiber density of callosal fiber > 0.4µm and NDI (rs = 0.74, 362 p = 0.008) but not with FA (rs = 0.12, p = 0.36). There was no significant correlation 363 between the length scaling coefficient and NDI or FA (Fig. 4), possibly due to the limited 364 statistical power. 365

Relevance to cortical functional lateralization 366
The length scaling variation between callosal fibers putatively reflected cortical 367 differences in evolutionary or developmental demands for rapid interhemispheric 368 communication, which may have accounted for cortical differences in functional 369 lateralization of the human brain. To assess this hypothesis, we estimated an overall 370 20 functional lateralization index (LI) across cognitive domains (all 575 cognitive terms in the 371 current Neurosynth database) on the cortical surface (Fig. 5A) (Table 1). 384

Relevance to cortical expansion 392
To directly assess its evolutionary and developmental relevance, we investigated 393 whether the length scaling of callosal fibers was related to the evolutionary and 394 developmental expansion of their connected cortical regions, i.e., i) cortical expansion in 395 humans relative to macaques and ii) cortical expansion in human adults relative to human 396 infants. As described above, we assigned the mean cortical expansion index from the 397 connected cortical region to each mCC voxel/segment. As shown in Fig. 5C (Table 1). 405

Callosal fibers of length over-scaling or under-scaling with brain size 406
Theoretically, a callosal fiber length coefficient of 1/3 indicates iso-scaling with brain 407 size. In contrast, coefficients > 1/3 indicate that callosal fiber length scales more with 408 greater brain size (i.e., over-scaling), and coefficients < 1/3 indicate that callosal fiber 409 length scales less with brain size (i.e., under-scaling). As illustrated in Fig. 6A, significant 410 mCC clusters (false discovery rate, FDR corrected p < 0.05) existed for both over-scaling 411 and under-scaling. The overlapping regions between the clusters from the two datasets 412 were designated as the final clusters; one large cluster exhibited over-scaling, and two small 413 clusters demonstrated under-scaling (Fig. 6B). The over-scaling cluster covered most of 414 the anterior half of the mCC, which mainly connects the prefrontal cortices between the 415 two hemispheres. In contrast, the first under-scaling cluster was located on the splenium, 416 mainly connecting the precuneus and superior parietal lobule; the other under-scaling 417 cluster was on the posterior body, mainly connecting the paracentral lobule and precentral 418 gyrus (Fig. 6C). 419 As shown in Fig. 6E, the callosal fibers of over-scaling showed greater NDI value 420 diameter/myelination and length, to reach an optimal fiber composition of the entire brain 474 to achieve structural and functional efficacy best. Such a strategy is theoretically 475 advantageous compared to solely adjusting either fiber diameter/myelination or length. The 476 joint adjustment strategy offers a larger search space for the optimal fiber reorganization 477 25 solution by providing two-parameter dimensions. Notably, the median or mean diameter 478 of callosal fibers did not significantly differ between species or human individuals, 479 although the largest diameter of callosal fibers did increase in species with larger brains 480 (Olivares et al., 2001;Wang et al., 2008). Therefore, larger brains seem to adjust the 481 relative length across the CC more than they adjust the fiber diameter/myelination. This 482 particular adjustment model might be specific to the CC, and its underlying mechanisms 483 deserve further investigation. The present study used two dMRI parameters to estimate the spatial pattern of mCC 503 fiber composition in-vivo. Notably, in contrast to the FA, the NDI showed a strong 504 correlation with the influential Aboitiz's histological fiber density, so far the golden 505 standard for such a measure (Aboitiz et al., 1992). This strongly verifies that the NDI can 506 sensitively reflect axonal density in uncrossing areas (e.g., mCC), supporting relevant 507 applications for this particular imaging parameter. Putatively, lower fiber density comes 508 with a larger local fiber diameter on the mCC. The mCC FA did not correlate with 509 histological fiber density and may reflect the myelination degree (Chang et al., 2017). The 510 observed length scaling's positive correlation with NDI and negative correlation with FA 511 suggested that callosal fibers of less length scaling (i.e., smaller increase in fiber length) 512 had lower density, larger diameter, and were myelinated. These empirical pieces of 513 evidence support that smaller increase in fiber length, larger fiber diameter, and increased 514 myelination are simultaneously implemented to jointly facilitate rapid interhemispheric 515 communications of particular cortical regions in larger brains. On the other hand, the 516 association between these callosal fiber characteristics may relate to cost control of fiber 517 reorganization in larger brains: to save physical space and energy consumption, highly 518 myelinated callosal fibers of large diameter tend to minimize their length increase as 519 possible. Future studies are encouraged to relate the length scaling with other nontrivial 520 callosal measures, e.g., midsagittal callosal thickness (Park et al., 2011). 521 Interhemispheric communication efficacy has long been considered a contributing 522 factor to the emergence of functional lateralization. According to Ringo's influential 523 hypothesis, the excessive callosal conduction delay of larger brains leads to functional 524 lateralization (Ringo et al., 1994). In contrast, functional lateralization may arise due to 525 inter-hemispheric inhibition through callosal fibers (Cook, 1984). Ringo's original hypothesis did specify that an excessive interhemispheric conduction 535 delay, which leads to functional lateralization, is mainly caused by increased callosal fiber 536 length due to brain size expansion. Our observed positive correlation of callosal length 537 scaling with functional lateralization provides more direct support for this influential 538 hypothesis. 539 The association of the callosal fiber length scaling with cortical expansion during 540 evolution and postnatal development provides direct support for evolutionary and 541 developmental contributions to scaling variation. For a cortical region, less demand for 542 rapid interhemispheric communication (as reflected by greater length scaling) and greater 543 expansion of the cortical area are likely rooted in the same motivations for the entire brain's 544 28 optimal functional efficiency. As revealed previously, expansion of the cortical area across 545 human individuals also showed under-scaling, iso-scaling, over-scaling with greater brain 546 size (Reardon et al., 2018). The under-and over-expansion of cortical regions with greater 547 brain size were attributed mainly to under-or over-increased cortical folding (Zilles et al., 548 2013). Notably, cortical expansion can be achieved by modifying the degree of cortical 549 folding, surface outward degree, or both. Given the U shape of callosal fibers, their length 550 scaling can partly represent their connected cortical regions' outward surface degree. (rs) are highlighted in gray. For the partial correlation, the neurite density index (NDI) and