Motor and higher‐order functions topography of the human dentate nuclei identified with tractography and clustering methods

Abstract Deep gray matter nuclei are the synaptic relays, responsible to route signals between specific brain areas. Dentate nuclei (DNs) represent the main output channel of the cerebellum and yet are often unexplored especially in humans. We developed a multimodal MRI approach to identify DNs topography on the basis of their connectivity as well as their microstructural features. Based on results, we defined DN parcellations deputed to motor and to higher‐order functions in humans in vivo. Whole‐brain probabilistic tractography was performed on 25 healthy subjects from the Human Connectome Project to infer DN parcellations based on their connectivity with either the cerebral or the cerebellar cortex, in turn. A third DN atlas was created inputting microstructural diffusion‐derived metrics in an unsupervised fuzzy c‐means classification algorithm. All analyses were performed in native space, with probability atlas maps generated in standard space. Cerebellar lobule‐specific connectivity identified one motor parcellation, accounting for about 30% of the DN volume, and two non‐motor parcellations, one cognitive and one sensory, which occupied the remaining volume. The other two approaches provided overlapping results in terms of geometrical distribution with those identified with cerebellar lobule‐specific connectivity, although with some differences in volumes. A gender effect was observed with respect to motor areas and higher‐order function representations. This is the first study that indicates that more than half of the DN volumes is involved in non‐motor functions and that connectivity‐based and microstructure‐based atlases provide complementary information. These results represent a step‐ahead for the interpretation of pathological conditions involving cerebro‐cerebellar circuits.


| INTRODUCTION
The brain is the principal organ of the nervous system and is composed of several different neuron types that are structurally and functionally well-organized to create specialized tissues (Voogd & Ruigrok, 2012). Glial cells and neurons are spatially organized in layers which mainly compose the outer part of the brain, the cortex. Axons and dendrites, instead, are organized in coherent bundles belonging to the inner part of the brain, the white matter.
Other gray matter structures, called deep gray matter nuclei, are identifiable within the white matter and are extremely important because they are synaptic relays, meaning that they represent areas where neurons make synapses achieving information transfer and integration. Hence, these regions are responsible to route signals, transported along the axons, to and from specific areas of the brain. Cerebellar nuclei represent important synaptic areas, which are often unexplored in in vivo imaging studies of the human brain.
The biggest cerebellar nuclei are the two dentate nuclei (DN), which are the farthest from the cerebellar midline and one at either hemisphere. Most of the efferent cerebellar connections towards the cerebral cortex synapse in the DN then convey in the superior cerebellar peduncle and pass through the contralateral red nucleus to end in the thalamus (Voogd & Ruigrok, 2012). Commonly, the DNs are known to be involved in sensorimotor processes but recent functional imaging investigations have revealed that they play a role also in non-motor functions (Alahmadi et al., 2017;Bharti et al., 2020;Habas, Guillevin, & Abanou, 2011;Zhang et al., 2015). This finding is in line with the recent understanding that the cerebellum is connected to cognitive and associative cortical areas, as supported by either tract-tracing techniques (Kelly & Strick, 2003;Middleton & Strick, 1994;Schmahmann & Caplan, 2006;Schmahmann & Pandya, 1995;Strick, Dum, & Fiez, 2009a) or diffusion MRI tractography studies of the cerebro-cerebellar loop (Kim, Im, Kim, & Park, 2019;Palesi et al., 2015Palesi et al., , 2016Palesi et al., , 2017. To characterize the DN topography, histochemical and viral tracttracing studies have demonstrated that in animals (e.g., rats, cats, and apes) the DNs present a topographical organization based on their cerebellar cortical connectivity (Matano, 2001;Obadiah, 2015). Two distinct zones can be identified: one rostro-dorsal and one ventrocaudal, associated to motor and non-motor functions, respectively. This result represents a step forward in our understanding of the role of cerebellar nuclei on brain function; nevertheless, given that the cerebellar cortical organization in humans is much more complex than in animals, one has to question what is the DN topography in this case.
To our knowledge, only a study using noninvasive methods has been performed in humans in-vivo to assess DN topography (Steele et al., 2017). Here, sub-millimeter diffusion MR images of the cerebellum of six volunteers were acquired on a 7 T scanner. Probabilistic tractography was used to parcellate DNs in humans on the basis of the cerebellar region that was mostly connected: motor rostrodorsal and non-motor ventro-caudal areas were identified. This was a promising result because supported the fact that the DNs present a topography reflecting different functional properties, but the main limit was that this study focused only on DN connectivity with the cerebellum instead of considering the whole-brain. Furthermore, tractography suffers of some intrinsic limitations and a multimodal approach could provide a mean of validating results. Worth considering that in the last decade machine learning has been widely applied to MRI analysis either to support clinical diagnosis or to improve images accuracy and has been proven to be capable to segment specific brain structures, including recently the DNs, as a whole, with a higher accuracy compared to other automatic methods .
In this study, therefore, we aimed to use a whole-brain MRIbased multimodal approach to reconstruct and investigate the topography of the DNs. Constrained spherical deconvolution tractography (Tournier, Calamante, & Connelly, 2007) was performed to reconstruct connections between DNs and both cerebral and cerebellar cortices, in turns, deriving two independent connectivity-based atlases of the DNs. Furthermore, a clustering approach, based on a fuzzy c-means algorithm, was developed to provide insights about DN topography based on diffusion MRI microstructural properties. The final goal of this study was to compare the atlases obtained with these three approaches and propose a coherent sub-parcellation of the DNs in humans in-vivo, with particular focus on assessing the DNs percentage deputed to motor and to non-motor functions. The resulting DN atlas would be of great interest also for improving structural connectivity investigations in humans; indeed, these cerebellar structures are currently not included in atlases used for anatomically constrained tractography (Smith, Tournier, Calamante, & Connelly, 2012). Given their role in the cerebro-cerebellar connectivity, we believe they should be included in future tractography studies as a synaptic gray matter structure, similarly to what is done with the thalamus. Needless to say that a more correct anatomical connectome of the brain would also impact studies that are investigating brain dynamics (Palesi et al., 2020).

| Subjects
Minimal pre-processed images of 25 healthy subjects (16 females and nine males) were downloaded from those acquired for the Human Connectome Project (HCP; http://db.humanconnectome.org; Van Essen et al., 2013), with age comprised between 26 and 35 years.

| MRI acquisition
The MRI protocol was setup on a Siemens MAGNETOM Skyra 3 T scanner, adapted with high field gradients, using a 32-channel receive head coil. Diffusion weighted images (DWI) were acquired with a multishell spin-echo EPI sequence with these parameters: TR = 5,520 ms, DN masks were extracted from b0 images using a convolutional neural network (CNN) as described by Gaviraghi et al. (2021). This automatic, machine learning based method was proven to be able to extract more accurate DNs masks than other methods using standard atlases and templates. 3DT1-weigthed images were segmented in native space in gray matter (GM), deep GM nuclei, white matter (WM), and cerebrospinal fluid using the 5ttgen algorithm (MRtrix3, https://www.mrtrix.org/; Tournier et al., 2019). To improve the reliability of the segmentation and tractography, DN masks were added to the deep GM mask per each subject. Then, WM-GM interface was also calculated.
The transformation matrix "subject-to-MNI space" was then inverted (MNI-to-subject) to be applied to specific atlases to warp them back to the subject space for the subsequent DN parcellation work (Sections 2.5 and 2.6).

| Whole-brain tractography
The fiber orientation density function was evaluated in native space separately for each tissue using the multi-tissue multi-shell approach (Dhollander, Raffelt, & Connelly, 2016;Jeurissen, Tournier, Dhollander, Connelly, & Sijbers, 2014). Then, a whole-brain probabilistic anatomically constrained tractography  was performed with 30 million streamlines seeded dynamically from the WM-GM interface and cropped to the WM mask. Other parameters were: step of 0.0625 mm (corresponding to half of voxel-size), maximum length of 250 mm, and maximum angle of 45 between two subsequent points of the same streamline, to avoid unrealistic torsions and backpropagations.

| Cerebellar lobule-specific connectivity to the DN
To define masks of different cerebellar lobules, the "Spatially unbiased atlas template of the cerebellum and brainstem" (SUIT; Diedrichsen, Balsters, Flavell, Cussans, & Ramnani, 2009) was warped to the subject space applying the MNI-to-subject transformation. We then merged some of the parcellations based on their known function, creating a final atlas with six parcellations per hemisphere: lobules I-VI (motor area), Crus I-II (cognitive area), lobule VII, lobule VIIIa, lobule VIIIb, and lobules IX-X (visuo-spatial functions; Figure 1). The vermis was discarded because it is directly connected with the fastigial nucleus instead of the DNs (Voogd & Ruigrok, 2012).
From the whole-brain tractography, we selected tracts terminating in each of the identified cerebellar parcellation and connected to their ipsilateral DN. Based on anatomy, no structural internal connection between the two cerebellar hemispheres exists (Pollok et al., 2006), hence an excluding region of interest (NOT-ROI) was placed aligned with the medial plane of the cerebellum to avoid spurious inter-hemispheric streamlines ( Figure 1). This step provided a lobule-specific connectivity map, defining a set of streamlines per cerebellar lobule departing from each of the six parcellations of the cerebellar cortex, which was used to generate the first subject-specific topography map of each DN, on the basis of their structural connectivity with the ipsilateral cerebellar cortex.

| Subthalamic-specific connectivity to the DN
The second subject-specific DN topography map was defined based on the DN connectivity to the cerebral hemisphere, rather than cerebellar cortex. Most of the cerebellar output connections pass through the DN and synapse into the contralateral thalamus before reaching the cerebral cortex. Because our tractography was anatomically constrained, only monosynaptic streamlines were reconstructed. Thus, we used the contralateral thalamus as target to study the connections between the DNs and the contralateral cerebral cortex. Thalamic parcellation in native space was defined by applying the MNI-to-subject transformation to the atlas defined by ; , whose classification was made on the basis of connectivity between the thalamus and the cerebral cortex. Since primary motor and pre-motor regions were merged for the cerebellar cortex parcellation, we did the same for the thalamus where six ROIs were identified: motor, prefrontal, sensory, posterior parietal, occipital, and temporal ( Figure 1).
Subthalamic-specific tracts were selected from the whole-brain tractography using the DN and the contralateral subthalamic areas as target ROIs.

| Connectivity-based topography atlases of the DN
For each subject, the cerebellar lobule-specific and subthalamicspecific topography atlases of DNs were created following several steps, as described below. The same steps performed to reconstruct the cerebellar lobule-specific atlas were repeated, as reported in square brackets, to reconstruct the subthalamic-specific atlas.
First, a track-density image (TDI), namely an image whose intensity is proportional to the number of streamlines passing through each voxel, was calculated for each of the parcellation-specific tract (Calamante, Tournier, Jackson, & Connelly, 2010). Then, TDI maps were  The resulting dataset was used as input to a fuzzy c-means (FCM) clustering algorithm in MATLAB routine (Fuzzy Logic toolbox-Data Clustering, https://it.mathworks.com/help/fuzzy/ fcm.html; Bezdek, 1981). Differently from the k-means algorithm, which is a hard clustering method, the decision boundary of the fuzzy c-means is softer and the output for each data point is the probability of belonging to each cluster. After several tests, qualitatively optimal results were obtained using three clusters as the number of parcellations, while the fuzziness parameter was set as default (m = 2; Campello & Hruschka, 2006). To create a topography map of the DNs based on the clustering of microstructural features, each DN voxel was assigned to the most probable cluster selected with a maximum likelihood algorithm.
Volumes of each cluster were calculated for each subject.
F I G U R E 1 Atlases and NOT-ROI used to identify cerebellar and thalamic connectivity with the DNs. All maps were in standard MNI152 space (radiological view) and were superimposed on the standard T1 weighted image. Panel A shows the sagittal NOT-ROI (fuchsia), used to avoid false positives in tractography, and the cerebellar parcellations: lobules I-VI (yellow), Crus I-II (green), lobule VIIb (violet), lobule VIIIa (blue), lobule VIIIb (orange), and lobules IX-X (red). Panel B shows the thalami parcellation based on the atlas described by : motor (blue), prefrontal (green), sensory (fucshia), posterior parietal (yellow), occipital (violet), and temporal (orange) 2.9 | Inter-subject topography atlases of the DNs DN topography maps of all subjects were warped to a common space to achieve inter-subject DN topography based on structural connectivity and microstructural features. Since DNs are small structures within the large brain volume, the SUIT ROI-driven normalization algorithm was used (www.diedrichsenlab.org/ imaging/suit_function.htm#norm_dentate), where the DNs masks have been inputted to drive the warping to the common SUIT space for the cerebellum, forcing a good overlap between deep cerebellar nuclei of different subjects in common space. Normalized DN masks of all subjects were visually inspected to confirm alignment across subjects.
For each subject, a numeric label was associated to each parcellation of the cerebellar lobule-specific and subthalamic-specific topography map. Then, their inter-subject topography atlases were created assigning, to each voxel of the DNs, the mode of the numerical label across all subjects, as a standard approach when averaging categorical values.
To create the inter-subject topography map based on microstructural features, we first defined a regulatory function (bottomup hierarchic classifier) that tooks as input the atlas found with the fuzzy c-means algorithm, to provide up to three nonordered clusters for each subject. Given that DNs were separated into three parcellations only in a subset of subjects, a posteriori we reduced the number of clusters to two in order to improve reproducibility.
In this way, a medial and a lateral cluster were identified and labeled in the same order for all subjects. Then, the mode of the values across subjects was calculated to generate the inter-subject microstructure-based atlas.

| Atlas comparison
To further investigate the comparison between the different topography atlases of DNs found with different approaches, we computed the DICE similarity coefficient (DSC) between all the parcellations of the three atlases in standard space. The DSC between two parcellations was computed doubling the intersection volume over the sum of the two volumes (Prados et al., 2015)  non-parametric Mann-Whitney test (p < .05) between females and males, in order to assess whether gender-related differences exist. 3.1 | Cerebellar lobule-specific topography atlas of the DN An example of cerebellar lobule-specific topography atlas of the DNs in a random chosen subject is shown in Figure 3a.

Connectivity
Group atlas in SUIT cerebellar space showed an overall good agreement between subjects as shown by Figure 4a. Although we started from six parcellations, only three were characterized by more than 10,000 streamlines connecting them to specific cerebellar lobules and with a parcellation volume >15% of the overall DN volume; these three parcellations were those connecting the DN to lobules I-VI, Crus I-II and lobules IX-X of the cerebellar cortex. Lobule VIIb showed a few consistent overlapping voxels across subjects, while lobules VIIIa and VIIIb did not identify a consistent area as their connectivity produced smaller clusters or even isolated voxels ( Figure 4a). The main results in terms of statistical descriptive features, averaged across all subjects, are summarized in Table 1 (streamlines) and

| Subthalamic-specific topography atlas of the DN
An example of subthalamic-specific topography atlas of the DNs in a random chosen subject is shown in Figure 3b.
Inter-subject subthalamic-specific topography atlas of the DNs showed an overall good agreement between subjects as shown by Figure 4b. Although we started from six parcellations, only two were characterized by more than 300 streamlines connecting them to specific subthalamic areas and with a parcellation volume >40% of the overall DN volume; these two parcellations were those that  associated with projections to the mediodorsal part of the thalamus and, indirectly, with the prefrontal cortex.
The right DN showed significantly higher number of streamlines connected with the contralateral motor area (p < .019) and smaller volume associated with the contralateral prefrontal cortex (p = .030).

| Microstructure-based atlas of the DN
An example of microstructure-based atlas of the DNs in a random chosen subject is shown in Figure 3c.
Inter-subject microstructure-based atlases of the DNs were obtained using as input voxel-wise feature vectors of FA, MD, AD, RD, MK, AK, RK metrics computed from DWI data. Results show that this method divided the DNs in two parcellations, despite asking the algorithm to find up to 3.
The main results, averaged across all subjects, are summarized in Table 2 and shown in Figure 4c.
For each DN, the biggest parcellation accounted for about 55% of the DN volume and was located laterally, whereas the second parcellation counted for about 45% of the DN volume and was located medially.
No statistically significant differences were identified between left and right DN volumes.

| Atlas comparison
Inter-subject DSC between each parcellation of different topography DN atlases are reported in Figure 5.

| Diffusion-derived metrics in cerebellar lobule-specific DN parcellations
Given the outcome of the subthalamic-specific connectivity, we decided to assess microstructural features only for the DN parcellations obtained with cerebellar lobule-specific connectivity.
Across subjects mean values of diffusion-derived metrics (FA, MD, and MK) in cerebellar lobule-specific parcellations are reported in Table 3. We choose those parameters because they were the less

| Gender-related effect on connectivity and microstructure features
Gender-related differences were found mainly in the left DN, as reported in Table 4. Lobule VIIIa. FA and MK were lower in females while MD was higher in females with respect to males.

| DISCUSSION
The present study represents one of the few investigations focused on the topography of the DN based on its structural connectivity to cerebellar lobules or subthalamic nuclei as well as on its microstructural properties, and assessing whether such DNs parcellations compartmentalize motor and non-motor functions. The main observation is that using three different parcellation approaches it was possible to identify two or more DN parcellations, in humans in-vivo, on the basis of structural connectivity and microstructural features. Our findings also suggest that, globally, in both left and right DNs, the non-motor representation is predominant on the motor one. It is to note that, although the predominance of the higher-order functions representation is maintained, the motor component is predominant in females than males.
Previous studies on animals (Matano, 2001;Obadiah, 2015) have demonstrated a dichotomy in the DN role by identifying one rostrodorsal and one ventro-caudal zone related to motor and non-motor functions, respectively. A similar parcellation was also identified in humans by Steele et al. (2017). Here, we reconstructed two different structural atlases of human DNs based on their connectivity either with cerebellar or cerebral cortex, by performing a state-of-the-art probabilistic tractography. A third atlas, which identified two different clusters, was obtained by inputting diffusion-derived metrics in a unsupervised clustering algorithm reflecting underlying microstructural properties.
Cerebellar lobule-specific connectivity provided a DNs topography atlas with three main clusters whose location was reproducible between subjects. The biggest parcellation was located laterally and dorso-caudally in both DNs and was the one connected with the Crus I-II, which represent the most important (Strick, Dum, & Fiez, 2009b;Voogd & Ruigrok, 2012) cognitive areas of the cerebellum. This parcellation involved more than 40,000 streamlines and occupied about 40% of the total volume of each DN. It is worth noting that this finding might support the one reported by Palesi et al. (2015), which asserted that almost 50% of the Crus I-II cortex was involved in the cerebello-thalamo-cortical tract. Furthermore, our results suggest that this parcellation may be affected by gender, as males showed a higher number of streamlines connecting the cerebellar cortex to the left DN compared to females. This may suggest that, although the higherorder functions parcellation is the largest in all subjects, the relative percentage between motor and higher-order functions areas depends and the motor/premotor area (the last nucleus). Again, this atlas identified two separate components related to non-motor and motor functions but the location of these clusters was not well defined across different subjects. There were streamlines starting from adjacent voxels that end in different areas of thalamus, making the generation of the subthalamic-specific parcellation very sensible to this effect. As shown in Figures 3b and 4b (Palombo et al., 2020), might be useful to characterize neurite specific proprieties both in white and gray matter structures.
It is worth noting that present parcellations coming from diffusion MRI analyses might grow their significance by integrating them with other techniques able to quantify specific biological features, such as myelin or iron content. This procedure would allow to merge structural and molecular proprieties information providing a step ahead in the interpretation of specific mechanisms underlying pathologies that are known to affect DNs and cerebellar circuitry, such as cerebellar ataxia and autistic spectrum disorders. Moreover, it is becoming apparent that the cerebellum plays a key role in neurodegenerative pathologies and other neurological diseases, for example, Alzheimer's disease (Castellazzi et al., 2014;Palesi et al., 2018) and epilepsy Streng & Krook-Magnuson, 2020). For example, it is known that the cerebellum and basal ganglia are connected through a polysynaptic connection and that the cerebellum plays a compensative role on the basal ganglia in Parkinson's disease (Simioni, Dagher, & Fellows, 2016;Yu, Sternad, Corcos, & Vaillancourt, 2007).
A full characterization of the DNs in healthy and pathological conditions will contribute to the investigation of mechanisms of damage and repair in a number of different pathologies.
It is clear that all these findings will further improve our anatomical and physiological understanding of the cerebro-cerebellar loops, also providing a more comprehensive structural characterization of brain circuitry. Indeed, the DN atlas provided by this work could be embedded into one of the tissue classes (e.g., the deep gray matter class) used in anatomically constraint tractography framework or in other tractography algorithms using anatomical priors (Schiavi et al., 2020), if data is acquired with a voxel resolution comparable to that of the HCP data. Moreover, using the DN atlas to define multiple nodes within each DN might be useful to identify specific DN connections with cerebellar lobules deputed to specific functions. This knowledge will also support the development of new tools and brain signal models for understanding and predicting brain functioning (Friston et al., 2019;Sanz Leon et al., 2013). In the last years, indeed, growing investigations have developed complex and multiscale approaches with the common goal of employing brain structural proprieties, such as diffusion MRI, to predict brain functional dynamics at single subject's level in both normal and pathological conditions (Palesi et al., 2020;Schirner, Mcintosh, Jirsa, & Deco, 2018;Zimmermann et al., 2018).

| CONCLUSION
For the first time, the topography of the human DNs was defined on the basis of their own connectivity both with the cerebellar cortex and the thalamus, which is the main relay towards the cerebral cortex, as well as by exploiting their microstructural features. Our findings demonstrated that more than half of the DNs volume is involved in non-motor functions, and two distinct regions were consistently identified: one deputed to high-level cognitive processes and one identified with sensory functions. It is to note that these components were affected, although only in the left DN, by gender: females demonstrated a more developed motor component while males showed a larger area supporting higher-order functions. Although connectivitybased and microstructural-based parcellations were in agreement, it is to note that the resulting atlases contained different and complementary information. We speculate that these results should be incorporated into current knowledge on the structural and functional significance of the cerebro-cerebellar loops in humans, also providing novel insights that could be applied for interpretating pathological conditions affecting these circuits.