Architecture of functional lateralisation in the human brain

Architecture of functional lateralisation in the human brain Karolis V , Corbetta M c-g & Thiebaut de Schotten M a,b,h* a Brain Connectivity and Behaviour Group, Sorbonne Universities, Paris France. b Frontlab, Institut du Cerveau et de la Moelle épinière (ICM), UPMC UMRS 1127, Inserm U 1127, CNRS UMR 7225, Paris, France. c Department of Neurology, Washington University Saint Louis, USA d Department of Radiology, Washington University Saint Louis, USA c Department of Neuroscience, Washington University Saint Louis, USA e Department of Biomedical Engineering, Washington University Saint Louis, USA f Department of Neuroscience, University of Padova, Italy g Padova Neuroscience Center, University of Padova, Italy h Groupe d’Imagerie Neurofonctionnelle, Institut des Maladies Neurodégénératives-UMR 5293, CNRS, CEA University of Bordeaux, Bordeaux, France

"Are you left-or right-brain?". The widespread belief that hemispheric dominance influences the human character and habits comes from the misinterpretation of decades-long neuropsychological findings 1 . This research demonstrated functional lateralisation as a fundamental principle of brain's organisation [2][3][4] . Today, informed by neuroimaging measures, theories on functional lateralisation suggest a less radical organisation and assume that the two hemispheres balance each other 5 . Despite the implications of functional lateralisation theories for neurodevelopmental and psychiatric disorders 6,7 , as well as for stroke recovery 8,9 , a comprehensive mapping of lateralised cognitive functions is, to our knowledge, still missing in the literature. Furthermore, the mechanisms sustaining functional lateralisation, such as the communication between the hemispheres remains an open debate 10,11 .
The contribution of the corpus callosum, the most considerable interhemispheric connection, to the emergence of functional lateralisation arise from two different ideas 12 . The first hypothesis suggests that, during evolution, brain size expansion led to functional lateralisation to avoid excessive conduction delays between the hemispheres 13 . Accordingly, functionally lateralised regions will be connected less strongly via corpus callosum connections than nonlateralised regions to function efficiently 14 . The second hypothesis proposes that functional lateralisation arises from the competition between the hemispheres that inhibits each other via the corpus callosum. As functionally lateralised regions would need to inhibit more the opposite hemisphere than non-lateralised regions, they could be more connected by the corpus callosum. Preliminary anatomical 15 and fMRI 16 studies provide support for both theories.
However, the small range of functions investigated and shortcomings in the methods often limit the interpretability of the findings 11 . Overall, the generalisation of these theories and findings to the whole brain functional organisation remains unknown.
Here, we took advantage of the largest fMRI meta-analytic dataset 17 with the highest quality structural connectivity data 18 to produce, for the first time, a comprehensive mapping of functional lateralisation, demonstrate its low dimensional structure, and examine its relationship with corpus callosum connectivity.

Global structure of functional lateralisation
We selected terms related to specific cognitive processes out of the whole Neurosynth database (see Supplementary Table 1).
After correction for anatomical differences between the left and the right hemispheres 19 , a functional lateralisation map was computed for each term to compare voxels between hemispheres. A varimax-rotated principal component analysis indicated that 171 principal components (PCs with eigenvalues higher than the grand average) explained 72.6 % of the variance of the lateralisation maps. General linear modelling was subsequently employed with PCs loads as a set of predictors to fit LI maps data and identify voxels with a significant lateralisation associated with each component. After 5000 permutations 25 PCs showed voxels with a significant lateralisation (>20 voxels; P < 0.05 family-wise error corrected) (see Supplementary Table 2).
Next, a multivariate spectral embedding ordered the lateralisation maps spatially according to their similarity. As a first step, Figure 1a

Corpus Callosum and functional lateralisation
Given that water more likely diffuse within and along axons in the brain, tractography derived from diffusion-weighted magnetic resonance imaging allows for peering into the structural organisation of brain connectivity (Figure 2a) .
In the following, we analysed the relationship between functional lateralisation maps and corpus callosum connectivity measures. Two measures of connectivity were employed. One, macroscopic, was replicability 21, 22 of a voxel's connection to the corpus callosum across the HCP sample. We will refer to this measure as a "probability of connection" for shortness. The second, microscopic, corresponded to the axonal water fraction 23 estimated in the midsection voxels crossed by corpus callosum streamlines seeded from functionally lateralised regions.
We first contrasted the connectivity profiles of lateralised regions and non-lateralised regions.
As there was a higher (by a factor of 3.6) number of non-lateralised voxels, we sampled 1000 random subsets of non-lateralised voxels, for each hemisphere separately. The number of voxels in each subset was equal to the number of lateralised voxels. We then constructed the connectivity distribution of non-lateralised regions by calculating an average corpus callosum probability of connection for each sample. These values were subtracted from the average connectivity value of lateralised voxels in the corresponding hemispheres. Figure 2a demonstrates that lateralised regions in the right hemisphere have a lower probability of connection with the corpus callosum than non-lateralised regions. However, there was no difference between lateralised and non-lateralised regions in the left hemisphere. These results were contingent on the fact that non-lateralised regions have a higher probability of connection with the corpus callosum in the right than the left hemisphere (Supplementary

Figure 3).
As probability of connections estimates derived from diffusion weighted imaging have well known methodological shortcomings 24 , we replicated the same analysis by sampling axonal water fraction in the mid-section of the corpus callosum respectively for lateralised maps and subsets of non-lateralised voxels. Figure 2c indicates axonal water fraction was consistently lower for corpus callosum voxels projecting onto lateralised regions when compared to nonlateralised voxels. Additionally, the plots suggested a slightly lower axonal water fraction for left hemisphere regions as compared to the right hemisphere. can vary -from a unilateral to a relatively asymmetric pattern of activity. In the latter case, both hemispheres are involved in a function, but one is more active than the other. Therefore, we explored whether a proportional relationship existed between the degree of functional lateralisation and the probability of corpus callosum connectivity. Figure 2d indicates a negative relationship between the probability of and the degree of functional lateralisation, both for the left and the right hemisphere (r = -.81 and r = -.69, respectively, p < .001).
Furthermore, we repeated the same analysis regressing out the average level of activity in functionally lateralised areas. The relationship between the level of functional dominance and the probability of connection to corpus callosum remained unchanged for the left hemisphere (r= -.79) and increased for the right hemisphere (r= -.87).

Discussion
In the present study, we provide for the first time a comprehensive mapping of the brain functional lateralisation. Results indicated a low-dimensional structure of functional lateralisation along four axes. Additionally, lateralised regions were characterised by reduced corpus callosum connectivity compared to areas without a distinct functional lateralisation.
Finally, within the pool of lateralised regions, inter-hemispheric connectivity was proportionally associated to the degree of the hemispheric functional dominance.
Based on the meta-analysis of the task-related functional magnetic resonance literature we The overall functional lateralisation of the brain demonstrated a low-dimensional structure along four axes corresponding to their respective contribution to symbolic communication, perception/action, emotion, and decision making. The triangular organisation represents a certain interest as it may be related to the concept of Pareto optimality. In evolutionary biology 20 , the concept presumes that distribution of traits across species demonstrates a trade-off: a prominence of a particular trait in a species exists at a cost of other traits being relatively silent. This gives a rise to a triangular organisation of traits across species, known as a Pareto front, with the apices of the triangles which encompass the trait distribution ("Pareto front") known as archetypes. Our result therefore indicates that a trade-off between lateralisation brain states exists and there are four archetypical states of brain lateralisation.
This result supports previous findings reporting a low dimensionality of functional networks 32  The distribution of the probability of connection of the corpus callosum onto the brain surface matched the previous atlases derived from interhemispheric homotopic functional connectivity analyses 42 . Time and energy costs are required to integrate information across hemispheres. Therefore, the role of inter-hemispheric connectivity for functional lateralisation has long been debated in the literature 43 . The current study presents a comprehensive demonstration that functional lateralisation is linked to a decrease of callosal function 12 , possibly through the mechanisms of callosal myelination and pruning 44 . Hypothetically, this reduced inter-hemispheric communication would optimise the treatment time in the brain at the expense of a decreased capacity of recovery after a brain injury.
However, it is important to stress that several factors limited the interpretation of the findings.
For instance, while the meta-analytic approach has the power to summarise thousands of taskrelated fMRI findings, it is limited by publication biases which prevent to generalise the current findings to all brain functions 45 . The limitations of the connectivity analyses derived from diffusion-weighted imaging 46 also prevented us from investigating with confidence the distinct contribution of homotopic and heterotopic areas to the functional lateralisation. The advent of new diffusion imaging methods 47 , as well as post-mortem investigation 48 , might circumvent this bias in the future.
In conclusion, the present analysis provides us with a comprehensive view of functional lateralisation in humans, which mostly concerns symbolic communication, perception/action, emotion-related and decision-making functions. It also reveals some of its mechanisms such as the relationship between functional lateralisation and the strength of communication between the hemispheres. The similarity between the current findings and recent work on neurological symptoms bring up new hypotheses on the mechanisms supporting brain recovery after a brain lesion.

Datasets
In this study we used a meta-analytic approach to functional MRI studies described by Yarkoni  The scanning parameters have previously been described in Vu et al. 49 .

A) Neurosynth data
Two researchers (V.K & M.TdS) acted as judges selecting terms which in their view related to specific cognitive processes. The selection procedure was two-stage. At the first stage, the judges made their selection independently. Brain anatomical (e.g., "salience network"), psychiatric (e.g., "schizophrenia"), or pathological (e.g., "alzheimer") terms were systematically excluded. The two judges agreed on 422 terms as related to cognitive processes and on 2309 terms as unrelated, hence to be discarded (88% reproducibility). For the other terms, the judges made their decision together. In the end, 590 cognitive terms were selected for the study. The estimated transformation between non-symmetrical and symmetrical MNI spaces were then applied to all functional maps.
The following steps were performed to obtain lateralisation indices for each functional map following their co-registration with symmetrical template. Firstly, we split the functional maps into the left-and right-hemisphere parts and smoothed the resulting maps using a 6 mm FWHM Gaussian filter. We then flipped the left-hemisphere maps and subtracted them from unflipped right-hemisphere maps in order to obtain laterality indices (LI) maps (see 19 for a similar approach). Positive and negative values in these maps would signify a higher metaanalytic evidence for, respectively, right and left lateralisation of the function associated with a term.

B) Structural connectome data
The following pre-processing steps have been applied to the HCP dataset. Firstly, the images were corrected for signal drift motion and eddy current artefacts using ExploreDTI toolbox for Matlab (http://www.exploredti.com 51,52 ). ExploreDTI has also been used to extract estimates of axonal water fraction 23 . Whole-brain deterministic tractography was performed in the native DWI space using StarTrack software (http://www.natbrainlab.com). A damped Richardson-Lucy algorithm was applied for spherical deconvolutions 53 . A fixed fibre response corresponding to a shape factor of α = 1.5x10-3 mm2/s was adopted, coupled with the geometric damping parameter of 8. Two hundred algorithm iterations were run. The absolute threshold was defined as 3 times the spherical fibre orientation distribution (FOD) of a grey matter isotropic voxel and the relative threshold as 8% of the maximum amplitude of the FOD 54 . A modified Euler algorithm 55 was used to perform the whole brain streamline tractography, with an angle threshold of 35°, a step size of 0.625mm, and a minimum streamline length of 15mm.
In order to co-register the structural connectome data to the standard MNI 2mm space, the data were converted into streamline density volumes where the intensities were given by the number of streamlines traversing each voxel. The study-specific template of streamline density volumes was generated using the Greedy symmetric diffeomorphic normalisation

A) Determination of lateralisation maps
The construction of brain's functional lateralisation maps was completed in two steps. In the first step, we sought to address the redundancy while preserving the richness of the Neurosynth data. For instance, many selected terms were related as singular and plural forms of the same word (e.g, "visual form" and "visual forms") and therefore their maps are likely to be very similar. To address this issue we grouped the terms on the basis of their similarities In the second step, a general linear modelling was employed to identify voxels with a significant lateralisation associated with a particular component. In this analysis, the PC were used as a set of predictors to fit LI maps data and obtain beta maps. The permutation test was performed to identify significantly lateralised regions. Given that varimax rotation may impose correlations between the columns of the PC matrix, we performed permutation on the rows of the unrotated matrix, subsequently applying component rotation and calculating the beta maps for each permutation. This procedure allowed us to mimic the correlational structure of the unpermuted data and provide a more robust test of significance. In order to account for multiple comparisons, the maximal statistics approach was used whereby the beta values for the real data were compared to the maximal (either positively or negatively) beta values estimated on each permutation across all voxels. 5000 permutations were run. The voxels were considered as showing a significant lateralisation if they simultaneously satisfied two criteria: 1) their beta values were in 97.5% cases higher or lower than, respectively, maximal positive and negative beta values obtained via permutations (i.e., p < .05, two-tailed and FWE-corrected); 2) they formed a cluster of at least 20 voxels. The second criterion was used to exclude small and possibly spurious effects observed in a small number of voxels.

B) Determination of non-lateralised regions
To enable a comparison between lateralised regions and regions without a significant lateralisation, the latter were identified by repeating the analyses outlined in the previous section for the left and right hemispheres separately. The clusters which passed the significance threshold at least for one component and one hemisphere, and non-overlapping with lateralised regions, were taken to denominate the regions without significant lateralisation ("non-latereralised regions").

C) Multivariate embedding
In order to characterise the low dimensionality of functional brain lateralisation, a spectral embedding of the LI maps was performed using eigen decomposition of graph normalised Laplacian of similarity matrix 58 . This similarity matrix was obtained as follows. left-right random pairs. For each set, random LI maps were calculated for each pair and then submitted to varimax analysis with the number of PCs = 171. The embedding procedure was identical to the procedure applied to non-random LI maps. The dimensional span of triangular organisation was evaluated by testing if t-ratio for non-random LI maps was greater than t-ratios of random LI maps in each 2-dimensional subspace of embedding (p < .05, Bonferronicorrected).

Analyses of function-structure relationship (see Supplementary Figure 5)
A)

Measures of the connectivity strength
We combined lateralisation maps and structural connectivity by first projecting lateralised maps, irrespective of the left and right polarity of lateralisation, onto white matter boundary of non-symmetrical MNI template, determining the overlapping voxels and subsequently by seeding tractography from these voxels to the corpus callosum.
Two measures for the strength of structural inter-hemispheric connectivity were analysed.
Macrostructurally, the strength of connectivity was measured in terms of replicability 22 of a connection between a seeded voxel and corpus callosum across the HCP sample. In other words, this measure represents a ratio of the number of participants in which a connection exists between a seeded voxel and the corpus callosum to the overall HCP sample size. A connection was classified as existing if tractography seeded from a voxel in a participant's brain generated at least one streamline passing through any voxel situated in the corpus callosum. We will refer to this measure as a "probability of connection".
The second, microstructural, measure referred to the axonal water fraction in the voxels of corpus callosum which were hit by streamlines from the seeded lateralised (or non-lateralised) regions. This measure was calculated as a weighted average of the axonal water fraction of the voxels in the corpus callosum, whereby the weights were calculated as a probability that a voxel in the corpus callosum is connected by at least one streamline to any lateralised voxel in the brain.
The same procedure applied to the calculation of the connectivity measures for non-lateralised regions. The number of non-lateralised voxels was 3.6 times greater than the number of lateralised voxels.

B) Comparison of the connectivity between lateralised and non-lateralised regions
The comparison of connectivity between lateralised and non-lateralised regions was performed by randomly sampling (without replacement) a subset of lateralised voxels and comparing the average connectivity measures of lateralised voxels to the connectivity measures of the sampled non-lateralised regions. 1000 samples were drawn for each hemisphere separately. The number of voxels in each sample of non-lateralised voxels was equal to the number of lateralised voxels.

C) Hemispheric dominance
The degree of functional hemispheric dominance was evaluated in radians as an arctangent of the ratio between the strengths of activation in two hemispheres. Pi/4 was subtracted from this value to ensure that the absolute magnitude of this value increases if the task activation is unilateral and decreases if both hemispheres demonstrate comparable levels of task activity.
Given that a partial spatial overlap between lateralised regions associated with different components is possible, in the analyses we picked the dominance values associated with components which rendered a largest z-score in a particular voxel. In order to obtain robust estimate for the relationship between hemispheric dominance and the strength of interhemispheric connectivity, the voxels were binned by the probabilities of connection such that the smallest bin width (given by logspace function in Matlab) was of the size equal to 1/163 and increased with the probability of connection. This procedure was used to partially compensate for the fact that only a very limited number of voxels had a high probability of connection to corpus callosum, whereas the majority were characterised by small values.