Spatially coherent and topographically organized pathways of the human globus pallidus

Abstract Internal and external segments of globus pallidus (GP) exert different functions in basal ganglia circuitry, despite their main connectional systems share the same topographical organization, delineating limbic, associative, and sensorimotor territories. The identification of internal GP sensorimotor territory has therapeutic implications in functional neurosurgery settings. This study is aimed at assessing the spatial coherence of striatopallidal, subthalamopallidal, and pallidothalamic pathways by using tractography‐derived connectivity‐based parcellation (CBP) on high quality diffusion MRI data of 100 unrelated healthy subjects from the Human Connectome Project. A two‐stage hypothesis‐driven CBP approach has been carried out on the internal and external GP. Dice coefficient between functionally homologous pairs of pallidal maps has been computed. In addition, reproducibility of parcellation according to different pathways of interest has been investigated, as well as spatial relations between connectivity maps and existing optimal stimulation points for dystonic patients. The spatial organization of connectivity clusters revealed anterior limbic, intermediate associative and posterior sensorimotor maps within both internal and external GP. Dice coefficients showed high degree of coherence between functionally similar maps derived from the different bundles of interest. Sensorimotor maps derived from the subthalamopallidal pathway resulted to be the nearest to known optimal pallidal stimulation sites for dystonic patients. Our findings suggest that functionally homologous afferent and efferent connections may share similar spatial territory within the GP and that subcortical pallidal connectional systems may have distinct implications in the treatment of movement disorders.

In the last decades, this model has extensively influenced stereotactic and functional neurosurgery. The identification of putative functional territories within the designed target, indeed, is of pivotal importance to improve clinical outcomes and avoid collateral effects, which are supposed to be related to stimulation/ablation of inappropriate territories Reich et al., 2019).
GPi implantation for deep brain stimulation (DBS) is a wellestablished therapeutic approach in dystonic patients, as well as in drug-refractory Parkinson's disease (PD) and Gilles De la Tourette syndrome (Deuschl et al., 2006;Weaver et al., 2012). On the other hand, the GPe has been proposed as an effective target for DBS in both primary and secondary dystonia (Houeto et al., 2007;Vitek, Zhang, Hashimoto, Russo, & Baker, 2012), as well as for severe insomnia in PD patients (Castillo et al., 2020).
Recently, DBS has allowed for the electrophysiological characterization of basal ganglia in movement disorders, identifying diseasespecific oscillatory patterns (Silberstein et al., 2003). In particular, studies conducted on implanted dystonic patients showed that: (a) pallidal theta oscillatory activity, a recently proposed dystonia physiomarker, was significantly correlated with severity of symptoms and (b) stimulation delivered in proximity of the theta peak amplitude provided the best outcomes, in terms of motor improvement, both at short and long term. Moreover, electrophysiological mapping revealed that the site of peak of theta activity was close to coordinates of optimal stimulation sites for dystonia, apparently located in the sensorimotor territory of the GPi (Neumann et al., 2017;Scheller et al., 2019).
Diffusion MRI and tractography (Beckmann, Johansen-Berg, & Rushworth, 2009;Saygin et al., 2015;Saygin, Osher, Augustinack, Fischl, & Gabrieli, 2011) have been used to disentangle the topographical organization of the main white matter bundles connecting basal ganglia structures da Silva et al., 2017;Lehéricy et al., 2004;Lenglet et al., 2012;Patriat et al., 2018;Plantinga et al., 2018). In particular, structural connectivity-based parcellation (CBP) (Eickhoff, Thirion, Varoquaux, & Bzdok, 2015) has been employed to reconstruct different spatial maps of GP, each disclosing complementary facets of its topographical organization da Silva et al., 2017;Ewert et al., 2018). Preliminary studies demonstrated the feasibility of such approach to identify the sensorimotor territory of GPi in functional neurosurgery contexts Patriat et al., 2018). However, consistent methodological differences among various works, together with their small sample size, strongly affect the generalization of such results. Therefore, the lack of a comprehensive, unified framework of GP connectivity and functional topography limits the possible translation of such approaches in a clinical context Sweet, Pace, Girgis, & Miller, 2016;Tisch et al., 2007).
In the present study, aimed at characterizing the spatial, topographical arrangement of subcortical connectivity patterns within the GPi and GPe, we combined multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD) (Jeurissen, Tournier, Dhollander, Connelly, & Sijbers, 2014; tractography with a two-stage hypothesis-driven CBP approach on high quality 3T diffusion MRI data of 100 unrelated healthy subjects from the Human Connectome Project (HCP) repository (Behrens et al., 2003). For each GP segment, distinct connectivity maps from striatopallidal, subthalamopallidal, and pallidothalamic pathways were reconstructed and the spatial consistency among functionally homolog maps was assessed by means of Dice coefficient. In addition, we evaluated the reproducibility of the parcellation procedure by calculating intersubject similarity measures (da Silva et al., 2017;Traynor et al., 2010). Finally, we investigated the spatial relationship between putative sensorimotor maps obtained from different bundles of interest and publicly available coordinates of optimal pallidal stimulation sites for dystonic patients in order to evaluate the possible therapeutic implications of connectivity maps obtained from CBP (Neumann et al., 2017;Okromelidze et al., 2020;Reich et al., 2019).

| Subjects
We employed minimally preprocessed diffusion and structural data of 100 unrelated healthy subjects (males = 46, females = 54, age range 22-36 years) obtained from the HCP repository. Data

| Data acquisition
MRI acquisitions were carried out using a custom-made Siemens 3T "Connectome Skyra" (Siemens, Erlangen, Germany), provided with a Siemens SC72 gradient coil and stronger gradient power supply with maximum gradient amplitude (Gmax) of 100 mT/m (initially 70 and 84 mT/m in the pilot phase), which allows improvement of diffusionweighted imaging (DWI).

| Regions of interest
ROIs of cortical areas and thalamic masks were obtained from the Desikan-Killiany atlas (Desikan et al., 2006) featured in the FreeSurfer software (https://surfer.nmr.mgh.harvard.edu) (Fischl et al., 2002). A modified and improved version of FreeSurfer's recon-all pipeline is part of the minimal preprocessing procedures provided by the HCP repository; further details can be found in Glasser et al. (2013).
All the obtained masks were then visually inspected and, if needed, manually corrected by a trained neuroanatomist (D. M.). Like in previous studies Patriat et al., 2018;Plantinga et al., 2018), cortical gyral ROIs were merged into four function-related groups: a limbic group including lateral orbitofrontal cortex, medial orbitofrontal cortex, frontal pole, and anterior cingulate cortex; an associative group, consisting of superior, middle, and inferior frontal gyri; a sensorimotor group, corresponding to precentral gyrus, postcentral gyrus and paracentral lobule; finally, all the remaining cortical ROIs were included in an "other" group.

| Connectivity-based parcellation
CBP was carried out for GPi and GPe separately, employing a winnertakes-all algorithm (Behrens et al., 2003;da Silva et al., 2017;Steele et al., 2016). We employed a two-stage hypothesis-driven parcellation: i. CBP of the striatum (caudate, putamen and nucleus accumbens), STN and thalamus according to their cortical connectivity using previously mentioned functionally-related groups as targets, obtaining for each group (limbic, associative, sensorimotor, "other") striatal, subthalamic, and thalamic connectivity maps.
ii. CBP of GPi and GPe employing striatal, subthalamic and thalamic connectivity maps obtained in the first stage as targets, thus retrieving distinct parcels for GPi and GPe.
As output, we obtained a total of 12 maps (four maps for three bundles of interest: striatopallidal, subthalamopallidal, pallidothalamic) for GPi and 8 maps for GPe (four maps for two bundles of interest: striatopallidal and subthalamopallidal).
The first parcellation procedure (i) was carried out implementing the following pipeline: 1. Connectivity profiles were obtained by filtering tractograms to obtain tracts of interest.
2. Tracts were mapped to voxels retrieving track density imaging (TDI) maps (Calamante, Tournier, Smith, & Connelly, 2012) which were then multiplied for ROI of GPi and GPe to obtain connectivity density-weighted maps.
3. TDI maps were normalized by calculating for each map the ratio between its voxels' intensity and its mean intensity value. This was done in order to obtain comparable connectivity density values among different maps.

4.
A "winner-takes-all" algorithm (find_the_biggest FSL command) was applied to normalized maps in order to univocally attribute voxel to targets (Behrens et al., 2003).
All the obtained parcels were registered to the ICBM 2009b nonlinear asymmetric template, binarized and summed up to obtain maximum probability maps (MPMs) reflecting the average parcellation at the whole sample level. Finally, a 50% threshold has been applied to these maps to retain only voxels overlapping in at least half of the sample (da Silva et al., 2017;Domin & Lotze, 2019).
The second analysis (ii) was carried out following the same procedure of (i) with exception of the Step 1. Indeed, we employed seed- F I G U R E 1 Connectivity-based parcellation of striatum, subthalamic nucleus (STN), and thalamus. The uppermost row (a) shows 3D lateral and inferior views of the ICBM 2009b nonlinear asymmetric template depicting cortical regions grouped in four functional targets: Limbic (red), associative (green), sensorimotor (blue), other (yellow). In the lower rows, coronal, sagittal, and axial sections of the ICBM 2009b nonlinear asymmetric template showing 3D-volume rendering of striatal (b), subthalamic (c), and thalamic (d) maximum probability maps. Connectivity maps of striatum, thalamus, and STN follow the color-code provided for cortical targets. Images are shown in neurological convention Finally, volumes and center of gravity (COG) of 50%-thresholded pallidal MPM have been extracted.

| Similarity across different white matter bundles
In order to investigate whether connectivity maps resulting from striatopallidal, subthalamopallidal and pallidothalamic pathways showed similar spatial organization within GP, similarity across homologous parcels (same functional territory) derived from different bundles of interest has been quantified computing the Dice coefficient (Dice, 1945): and GPe (e.g., striatopallidal vs. subthalamopallidal).

| Reproducibility across subjects
In order to quantify the interindividual variability of the connectivity maps across subjects, we computed two different similarity measures.
In particular, reproducibility of pallidal parcellations was evaluated by calculating the overlap-by-label (OBL), which represents a measure of the overlap of each cluster across all datasets, and the total accumulated overlap (TAO) that measures the overall, groupwise overlap for a given parcellation type. Both OBL and TAO are based on the Tanimoto coefficient, which measures the similarity between different sets. Being A and B two images on the same space from different subjects, the Tanimoto coefficient is defined as: where N represents the number of voxels (Crum, Camara, & Hill, 2006).
For a group of m pairs of images, where m represents all the possible pairwise combinations of the same connectivity map i across different subjects, OBL is defined as: In order to avoid overestimation of larger parcels, a weighting coefficient α is employed. We defined α as the inverse of the mean of the absolute value of volumes for A and B: On the other hand, for a number n of clusters from a given parcellation TAO is defined as: (da Silva et al., 2017;Traynor et al., 2010).
For both similarity indices, the result is a number ranging between 0 and 1, where a value closer to 1 indicates higher similarity and a value closer to 0 indicates high dissimilarity.

| Quantitative analysis
A quantitative volume-based measure for each GP parcel at subject level was estimated by calculating the streamline density index (SDI), defined as the percentage ratio between each map volume and the GPi or GPe ROI volume, respectively, as reported in the following formula (Theisen et al., 2017): where v is the volume (in voxels) of parcel obtained after the application of the hard segmentation algorithm and V ROI is the volume (in voxels) of the ROI of either GPi or GPe.
In order to assess statistically significant lateralization for each connectivity map, permutation tests based on a t-statistic were performed using the connectivity profiles as defined by SDI of each hemisphere gathered from each subject. Then, 50,000 permutations were used to estimate the distribution of the null hypothesis, alpha level was set to .05, and the "t-max" method was adopted to correct the p-values of each variable for multiple comparisons (Blair & Karkiski, 1993).
Moreover, a lateralization index (LI) has been computed to identify eventual side dominance at subject level (Parker et al., 2005;Wang et al., 2020). LI was calculated for each connectivity map in the native space according to the following formula: Positive values stand for left-lateralization (LI > 0.1), while negative values suggest right-lateralization (LI < −0.1).

| Spatial relations between COG and optimal stimulation sites in dystonia
In order to quantify the spatial relations between GPi sensorimotor maps and optimal stimulation sites for dystonic patients provided by previously published studies, the Euclidean distances (in mm) between the COG of the GPi sensorimotor maps and the literature-based coordinates of the optimal stimulation sites were computed. Specifically, six optimal stimulation sites were considered: i. the peak of theta activity, defined as the centroid of contact pair locations ranging above the 95th percentile in theta amplitude; ii population threshold is depicted in Figure 1. The spatial organization of connectivity maps described for these subcortical structures is in line with previous investigations Plantinga et al., 2018;Tziortzi et al., 2014). For the striatum, the limbic territory occupies the nucleus accumbens as well as the ventral portion of caudate and putamen.
Connectivity to associative areas segregated in the anterior portion of caudate and putamen, posteriorly to their limbic territory; sensorimotor connectivity involves posterior portion of striatum while "other" regions were localized in the caudal tip of putamen and in the tail of caudate nucleus.
The STN parcellation resulted in an anterior limbic region, a dorsal associative region, a ventral "other" region, both located in the intermediate portion of the nucleus, and a posterior sensorimotor region.
For thalamus, connectivity with limbic cortical areas involves the medial half, extending to the most posterior portion, while associative connections segregate in the anterolateral thalamus, followed posteriorly by the sensorimotor and the "other" parcels which were located in a posterior lateral region.
Spatial organization of MPMs within GPi and GPe is described below. Volumes (in mm 3 ) and COG (x, y, z) are provided in Table 1, while SDI values (mean ± SD) of both GPi and GPe are summarized in Table 2.

| Striatopallidal parcellation
Maps obtained from striatopallidal connectivity are depicted in

| Subthalamopallidal parcellation
After mapping, the subthalamopallidal connections in the GPi, limbic, associative, and sensorimotor maps resulted to be arranged along the anteroposterior axis of the nucleus (Figure 3a, Supplementary Figure S2a). The "other" parcels were located anteriorly on the left, while on the right they were placed between associative and sensorimotor clusters.
In GPe, the limbic territories were located in the most anterior aspect with the associative territories segregating behind, followed by the sensorimotor territories, which extended from

| Pallidothalamic parcellation
Spatial organization of maps derived from pallidothalamic connectivity was similar to those reported for striatopallidal parcellation (Figure 4a).

| Similarity across parcellation schemes
Dice coefficient values referred to functionally homologous connectivity maps on the standard space are summarized in Table 3.

| Reproducibility analysis
We calculated two different measures of similarity (OBL and TAO) to evaluate reproducibility of CBP for each pathway of interest (Table 4).

| Hemispheric asymmetries
Interhemispheric (left vs. right) asymmetries ( and in GPe (p < .05 and p < .05) but not for the pallidothalamic pathway. "Other" clusters were not significantly lateralized in GPi while being right lateralized and left lateralized in striatopallidal (p < .05) and subthalamopallidal (p < .001) pathways respectively in GPe.
In addition, a LI for each subject was calculated on SDI of probabilistic maps obtained from different bundles of interest, in order to investigate the distribution of left-or right-sided dominance on the whole sample ( Figure 6).    (2002), superimposed on the ICBM 2009b nonlinear asymmetric template. In (a), the spatial relation between the site of peak theta activity (red circle) and striatopallidal (yellow), subthalamopallidal (blue), and pallidothalamic (green) maps is shown. In (b), the spatial relation between average optimal deep brain stimulation (DBS) electrode position (violet circle) and subthalamopallidal (blue), pallidothalamic (green) and striatopallidal (yellow) maps is depicted. In (c) and (d), the spatial relationships between the sensorimotor connectivity maps and pallidal optimal stimulation sites for dystonia identified respectively by Schöneker et al.  3.9 | Spatial relations between sensorimotor maps and pallidal optimal stimulation sites in dystonia In addition, we also considered other four optimal stimulation sites as provided in Reich et al., 2019;Schönecker et al., 2015;Starr, 2002). Similar results have been obtained for coordinates derived from (Starr, 2002) and (Schönecker et al., 2015) and derived sensorimotor MPMs (Figure 7) (Alexander et al., 1990;Saga et al., 2017). Although other works investigated the topographical organization of GP, most of them are focused only on a specific pathway and are based on a small number of subjects. In the present work, in order to overcome such limitations and to provide a wider framework, we test the hypothesis that the striatopallidal, subthalamopallidal, and pallidothalamic pathways are spatially coherent and topographically organized within the GP in a large sample of healthy subjects (n = 100).
Our results suggest that the general topographical organization of connectivity parcels is highly consistent across the GPi and GPe, regardless of the bundle of interest, corroborating the hypothesis that different pathways, running parallel and in series to one other, may share the same spatial organization pattern ( Figure 5). Indeed, we found high similarity among functionally homologous connectivity maps derived from the striatopallidal, subthalamopallidal and pallidothalamic tracts (Table 3).
In other words, we show neuroimaging evidences suggesting the existence of partially segregated yet integrated functional territories within the GPi and GPe, derived from connectivity patterns that maintain a consistent topographical arrangement throughout the entire cortico-basal ganglia-thalamo-cortical circuitry (Figures 1 and 5).
Such findings are in line with tract-tracing and virus-tracing studies, which revealed that different cortical areas, projecting to GP via distinct portions of the striatum and STN, delineate a tripartite organization which is similar, albeit not identical between the GPi and GPe (Saga et al., 2017). Indeed, limbic, associative and sensorimotor cortical areas project respectively to anteroventral, anterodorsal and posterior portions of both GPi and GPe (Haber, Groenewegen, Grove, & Nauta, 1985;Hedreen & Delong, 1991;Hoover & Strick, 1993;Joel & Weiner, 1997;Kelly & Strick, 2004;Middleton, 2002;Nauta & Cole, 1978;Shink, Bevan, Bolam, & Smith, 1996;Spooren, Lynd-Balta, Mitchell, & Haber, 1996). However, despite such a consistent spatial organization, Saga et al. demonstrated that patterns of neuronal labeling in GPe were broader and boundaries of functional territories lessdefined than in GPi, thus proposing that the connectivity patterns within the GPe may be less segregated (Saga et al., 2017). This is in line with our results, which show that, although connectivity parcels of GPi and GPe grossly share a very similar spatial organization, a higher degree of overlap among MPMs of different functional territories could be noticed in the GPe (Figures 2-4). However, it should be kept in mind that MPMs represent voxels which are most coherently part of each connectivity parcel within our sample, rather than biologically grounded representations of connectivity territories within GP. On the other hand, Dice coefficients show generally lower values in the GPe if compared to GPi, in particular for limbic and associative territories (Table 3), likely suggesting a less marked pattern of segregation in the GPe.
Although several studies suggested such a tripartite organization of the GPi and GPe according to their afferent connections, such pattern of spatial coherence might be no longer maintained in the efferent pallidothalamic tract, likely reaching distinct thalamic nuclei instead of being spatially organized along its anterior-posterior axis (Alexander et al., 1990).
In order to verify the possible spatial, topographical organization of the pallidothalamic tract, similarly to previous studies (Behrens et al., 2003;Patriat et al., 2018), we parcellated the thalamus according to its cortical connectivity retrieving "functional maps" that are likely to oversimplify the anatomical and functional complexity of thalamic nuclei (Morel, Magnin, & Jeanmonod, 1997). Then, we performed the parcellation of the GPi using the abovementioned thalamic parcellations as tractography targets, founding high spatial consistency between MPMs obtained from the pallidothalamic tract and those obtained from the striatopallidal and subthalamopallidal pathways, suggesting that functional territories within the GPi are likely to be shared by afferent and efferent tracts.
It is worth to note that we could not distinguish ansa lenticularis from lenticular fasciculus which is still beyond the possibilities of conventional diffusion MRI (Alho et al., 2020). Moreover, connections between the GPe and thalamus have not been taken into account, as GPe main afferent and efferent connections involve the striatum and STN (Kita, 2007), despite sparse GPe projections to the ventral lateral nucleus, parafascicular complex, and reticular nucleus have been also described (DeVito & Anderson, 1982;Gittis et al., 2014).
To add further information on the topographical organization of pallidal connectivity parcels we evaluated intersubject reproducibility of CBP for each pathway of interest (Table 4).
In particular, in our reproducibility analysis of pallidal parcellations, In the present study, we found also evidences of lateralization between different functional territories within the GP as shown by significantly different SDI values which are coherent with subjectlevel LI values. In particular, limbic clusters showed significant leftlateralization for striatopallidal both in GPi and GPe while being right lateralized in subthalamopallidal and pallidothalamic pathways in GPi.
Associative clusters were left-lateralized for pallidothalamic and subthalamopallidal pathways and right-lateralized for striatopallidal pathway in GPi, no significant lateralization was noticeable in GPe. A significant right-lateralization was observed for sensorimotor clusters both in GPi and in GPe except for pallidothalamic pathway. "Other" clusters were not significantly lateralized in GPi while being right lateralized and left lateralized in striatopallidal and subthalamopallidal pathways respectively in GPe.
While lateralization of functions of the cerebral cortex has been widely studied (Gotts et al., 2013), functional lateralization of basal ganglia both in term of volume and connectivity has been poorly investigated (Greene et al., 2014;Griffanti et al., 2018;Lenglet et al., 2012).
Although the significance of such asymmetries is currently unknown, these findings bear further studies, as these subcortical pathways play a pivotal role in both physiological and pathological conditions.
The results of the present study extend previous findings based on diffusion imaging of the human brain, that are mainly focused on the parcellation of GPi, due to its well-known pathophysiological implications in movement disorders . In particular, a very similar topographical organization was formerly described on territories. In a recent study, CBP of GPi according to its thalamic connections has been performed on 32 subjects employing a winnertakes-all approach, finding a very similar functional topography to that reported in the present study (Ewert et al., 2018). between the poorly and the strongly labeled region (Karachi et al., 2002). This pattern of calbindin expression has been reported also for the striatum (Karachi et al., 2002) and substantia nigra (Damier, Hirsch, Agid, & Graybiel, 2002), suggesting that these areas may correspond to putative limbic, associative, and sensorimotor functional territories described in primates (Haber, 2016).
As a final remark, in line with several anatomical studies reporting the involvement of functionally heterogeneous parietal, temporal, and occipital cortices in the basal ganglia loops (Middleton & Strick, 1996;Yeterian & Pandya, 1993, 1995, Patriat et al. introduced a "other" region including such cortical areas in addition to the classical tripartite model. Following the same parcellation scheme, we found that this additional "other" parcel has a highly variable spatial organization both in the GPi and GPe and across different bundles of interest. This is reflected by highly variable Dice coefficient values, ranging from 0.27 to 0.81, indicating the highest spatial heterogeneity across different parcellations. This finding might be explained by the wide functional diversity of cortical areas included in the "other" target, likely suggesting that connections with parietal, occipital, and temporal areas are not organized in segregated anatomical territories but may be rather involved in different functional basal ganglia loops. Despite heterogeneity among "other" territories derived from different pathways is remarkable, reproducibility as measured by OBL underlines that intersubject variability of "other" clusters among each pathway of interest is comparable to the rest of functional territories. This suggests that the same spatial configuration is likely to be maintained across subjects in the same pathway of interest.

| Spatial relationship between sensorimotor pallidal maps and DBS in dystonia
The results of the present study may have possible therapeutic implications in movement disorders. Approaches similar to that described herein have been employed on patients cohorts for the evaluation of electrodes position and volume of tissue activated (VTA) modeling in respect to putative sensorimotor territory of GPi Patriat et al., 2018). Indeed, Middlebrooks et al.
conducted a pilot study on 11 PD patients, proposing tractographybased identification of the sensorimotor territory of the GPi as an independent predictor of DBS outcomes .
Recent studies have also evaluated the clinical or pathophysiological correlation between DBS electrode location, the associated VTA and related clinical outcomes in dystonia identifying optimal stimulations sites (Neumann et al., 2017;Okromelidze et al., 2020;Reich et al., 2019;Schönecker et al., 2015). Gathering together the findings of these studies, the optimal stimulation site is located within the posteroventral third of the GPi, likely corresponding to its sensorimotor functional territory (Neumann et al., 2017;Okromelidze et al., 2020;Reich et al., 2019). In order to investigate the possible clinical or pathophysiological relevance of our results, we evaluated the spatial relationship between sensorimotor connectivity maps derived respectively from the striatopallidal, subthalamopallidal, and pallidothalamic pathways and optimal stimulation sites in the GPi as previously identified in dystonic patients, obtaining similar, spatially coherent results as shown in Figure 7 (Neumann et al., 2017;Okromelidze et al., 2020;Reich et al., 2019;Schönecker et al., 2015;Starr et al., 2006).
Studies focusing on the analysis of electrode location and its correlation with good clinical outcomes suggested that an optimal stimulation point would be located in the lateral portion of the sensorimotor territory of GPi in proximity of lamina interna (Schönecker et al., 2015;Starr et al., 2006). Our results are in line with these findings showing that coordinates of such optimal stimulation sites are located within sensorimotor striatopallidal, subthalamopallidal, and pallidothalamic MPMs. It is worthy to note that, as expected, coordinates provided by both studies were located along the lateral border of striatopallidal and pallidothalamic MPMs while covered a more central position within subthalamopallidal MPM (see below).
Neumann et al. found that theta activity in the GPi is correlated to severity of dystonic symptoms and DBS in proximity of the peak of theta activity resulted in improved clinical outcomes. Interestingly, electrophysiological mapping of abnormal theta activity revealed that this peak is located in the posterior third of the nucleus (Neumann et al., 2017), which is likely to correspond to the sensorimotor area of the GPi. Indeed, our results showed that coordinates of both peaktheta activity and average active lead location reported in (Neumann et al., 2017), resides within GPi sensorimotor territories reconstructed from striatopallidal, pallidothalamic, and subthalamopallidal pathways in the present study (Figure 7). In a multicenter study conducted on 105 implanted dystonic patients, group-level aggregation of electrode locations and VTA were used to identify an anti-dystonic sweet spot defined as the volume characterized by the highest probability of stimulation-induced motor benefit. Such optimal stimulation site was located along the medial border of posteroventral GPi and in the adjacent subpallidal white matter (Reich et al., 2019) (Starr et al., 2006).
Finally, we also analyzed the Euclidean distances from each COG of sensorimotor maps obtained from different bundles of interest to each optimal stimulation site above described, in order to obtain a quantitative estimation of the spatial relations between connectivity parcels and such stimulation points.
The COG of subthalamopallidal-derived sensorimotor parcellation was closest to coordinates of most of the optimal stimulation sites considered when compared to striatopallidal and pallidothalamic ones.
If, on the one hand, these findings could suggest that an indirect, twostage, subthalamopallidal parcellation approach could be appropriate for targeting GPi in functional neurosurgery settings, more studies are needed to further reinforce this hypothesis. In addition, the STN is a very small structure and its connectivity patterns could be hard to study in common available clinical datasets that have usually lower spatial resolution, b-values, and gradient directions compared to HCP data. The proximity of COG of subthalamopallidal sensorimotor maps to most of the optimal stimulation sites reported in literature may be interpreted considering the presence of theta activity not only in the GPi but also in the STN in dystonia patients. In this regard, Marsden and Obeso proposed that this abnormal subcortical theta synchronization may represent a "noisy signal" in the cortico-basal gangliathalamus circuit which is likely to affect the physiological motor network (Marsden & Obeso, 1994). However, the neuroimaging findings of the present work come from a sample of healthy subjects; therefore, they should be taken as a grain of salt and validated in future studies involving dystonia patients.
Finally, it should be kept in mind that COGs of tractographybased connectivity maps do not necessarily correspond to optimal stimulation sites resulting in good clinical outcomes. In the present study, the COGs of each connectivity parcel have been chosen as a representative set of coordinates in order to provide a quantitative description of the spatial relations between established stimulation points and the connectivity parcels of the present study. Hence, an exact match is not necessarily to be expected.
Spatial relations between sensorimotor connectivity maps here proposed and available optimal stimulation sites could be also interpreted in light of models of dystonia as a network-level disorder which ideally involves both the cortico-basal ganglia-thalamo-cortical and cerebello-thalamo-cortical loops (Corp et al., 2019;Okromelidze et al., 2020). In a lesion network mapping study investigating functional connectivity of lesions leading to secondary dystonia, a negative connectivity to somatosensory cortex and a positive connectivity to cerebellum (vermis, cerebellar cortex, and dentate nucleus) resulted to be specific for cervical dystonia (Corp et al., 2019). In particular, the negative functional connectivity of somatosensory cortex was interpreted as a possible expression of a "missing inhibition" of such area in patients with dystonia and it may be hypothesized that DBS within sensorimotor region of GPi could restore such altered equilibrium . In line with the model proposed by Corp and colleagues, a recent study showed that functional connectivity between VTA and primary sensorimotor regions, motor thalamus and cerebellum was positively correlated to clinical improvements. Hence, stimulation of thesensorimotor territory of GPi could exert an influence at a connectomic level inducing a "rewiring" which may result in the optimal connectivity profiles proposed by Okromelidze and colleagues. Moreover, both structural and functional connectivity profiles associated with UDRS improvement occurred with inferior parietal and lateral occipito-temporal areas, corroborating the hypothesis according to which DBS may have modulatory effects on distributed brain networks (Horn, 2019). It can be hypothesized that the volume of GPi which is actually stimulated during DBS may exert an effect on surrounding and partially overlapping functional territories. In particular, our results show a valuable proximity between sensorimotor and "other" clusters, which include voxels that are supposed to be connected to the aforementioned parieto-temporal-occipital areas. However, further studies on dystonic patients are needed to support such hypothesis.

| Methodological considerations
This work suffers from typical tractography limitations: this technique cannot distinguish polysynaptic from monosynaptic pathways and it does not allow inferences on polarity of connections preventing to differentiate afferent from efferent pathways (Jbabdi & Johansen-Berg, 2011). Moreover, probabilistic tractography may often lead to "false positive" streamlines which do not correspond to ground truth (Maier-Hein et al., 2017). Hence, in order to obtain more robust-tonoise and reliable results, we employed MSMT-CSD, which reduces partial volume effects employing tissue-type specific RFs (Jeurissen et al., 2014).
Connectivity clusters retrieved from CBP do not biologically imply that an effective parcellation exists within the structures considered.
In other words, even if maps obtained from diffusion tractography may be defined as "connectivity modules" within parcellated structures, clear-cut boundaries provided by parcellation techniques may not correspond to anatomical ground truth (Eickhoff et al., 2015).
Moreover, CBP can be performed using different approaches, each one characterized by peculiar advantages and limitations. In the present work, we aimed at testing a specific hypothesis about spatial, topographical coherence in the basal ganglia that is derived from anatomical ground truth both in human and nonhuman primates and, therefore, we decided to employ a hypothesis-driven approach for this aim (Karachi et al., 2002(Karachi et al., , 2005Saga et al., 2017). Moreover, a previous study investigating the effects of different CBP approaches on GP segmentation revealed a good correspondence between hypothesis-driven and data-driven CBP methods (da Silva et al., 2017). Finally, the choice of a hard-segmentation approach could represent an inherent limitation since it attributes voxels to the clusters exhibiting higher connectivity density (Behrens et al., 2003).
Although widely used in literature , the use of such approach may introduce a bias selecting only the most connected voxels as part of each connectivity map therefore imposing a stricter parcellation in respect to the anatomical reality. This is particularly true when brain structures are thought to be composed of partially overlapping functional territories rather than well-delineated subdivisions (Alkemade, Schnitzler, & Forstmann, 2015;Lambert et al., 2015;Plantinga et al., 2018).
However, the most common alternative to hard segmentation approach involves the selection of a connectivity threshold to filter out the voxels with lower connectivity values introducing an additional element of arbitrariness in the parcellation pipeline (Domin & Lotze, 2019;Johansen-Berg et al., 2005;Tziortzi et al., 2014). Moreover, winner-takes-all parcellation appears to be better suited for clinical contexts where identifying the core locus of connectivity to a particular target region is likely to be more important than the connectivity territory as a whole (Clayden, Thomas, & Kraskov, 2019).
The choice of coordinates of electrode locations as optimal stimulation sites could also be considered as an inherent limitation. Indeed, it has been recently demonstrated that the mere contact location is a poor predictor of clinical outcome, with little to absent topographical difference between locations related with excellent outcomes and locations associated with poor outcomes (Reich et al., 2019). Even if VTA modeling has shown to be more consistent to identify sweet spots, such volumes are not easily available; thus, we opted to evaluate the possible translation of our results in clinical settings using available coordinates of optimal stimulation sites provided by different studies. Moreover, COG of MPMs are not expected to match optimal stimulation point within the connectivity map; indeed, the available coordinates related with good stimulation-induced clinical outcomes showed various degree of distance with MPMs COG. However, this choice was guided by the need to provide a quantitative metric of the spatial relations between known stimulation points and the maps herein reconstructed by CBP. Indeed, despite heterogeneity in Euclidean distances, all stimulation points exhibited a plausible spatial relation in respect of striatopallidal, subthalamopallidal, and pallidothalamic maps.
Finally, the optimal stimulation points used in our paper derived from an average of patients coming from different studies. The process of transferring individual stimulation points to template coordinates and vice versa requires the use of nonlinear transformations which may further alter the precise localization of optimal stimulation points which is crucial in functional neurosurgery settings. We acknowledge that, when available, subject-level information could lead to more clinically relevant results.
It is worth to mention that our connectivity maps derive from a sample of young (22-36 years) and healthy subjects; hence, our findings may not be generalizable to populations with different age. Thus, studies using larger and more representative samples are needed to confirm our results. In addition, our study is based on a healthy population and then we cannot rule out eventual alterations in individual connectivity profiles that may be related to the disease itself.

| CONCLUSIONS
Taken together our results indicate that the topographical pattern of the functional territories of the GP is in line with the organizational pattern found in the striatum, STN and thalamus, thus further reinforcing the idea that the cortico-basal ganglia-thalamo-cortical system is organized in parallel, spatially coherent and topographically organized pathways, that connect similar functional territories.
Moreover, a two-stage CBP of GPi according to its connectivity patterns may be employed for a precise DBS targeting in functional neurosurgery for dystonia. Tractography-derived sensorimotor maps may also represent a good candidate for therapeutic targeting, considering that DBS of sensorimotor GPi is likely to exert part of its therapeutic effect by modulating both local and distributed brain networks, likely inducing a "rewiring" of sensorimotor-related connectivity.
In conclusion, the pallidal connectivity maps obtained in the present study may be employed during preoperative targeting in order to ameliorate clinical outcomes as well as to improve our current knowledge of side effects during postoperative evaluation. We hope that our results may shed new light on the macroscale, anatomicalfunctional organization of the basal ganglia circuitry. sity. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

CONFLICT OF INTEREST
The authors declare no conflict of interest.

ETHICS STATEMENT
Data were acquired by the Washington University, University of Minnesota, and Oxford University (WU-Minn) HCP Consortium. The study was approved by the Washington University Institutional Review Board.

PATIENTS CONSENT
Informed consent was obtained from all subjects.

DATA AVAILABILITY STATEMENT
One dataset of 100 unrelated healthy subjects was used to support the findings of this study. Data were provided by the Human Connectome Pro-