Altered brain metabolic connectivity at multiscale level in early Parkinson’s disease

To explore the effects of PD pathology on brain connectivity, we characterized with an emergent computational approach the brain metabolic connectome using [18F]FDG-PET in early idiopathic PD patients. We applied whole-brain and pathology-based connectivity analyses, using sparse-inverse covariance estimation in thirty-four cognitively normal PD cases and thirty-four age-matched healthy subjects for comparisons. Further, we assessed high-order resting state networks by interregional correlation analysis. Whole-brain analysis revealed altered metabolic connectivity in PD, with local decreases in frontolateral cortex and cerebellum and increases in the basal ganglia. Widespread long-distance decreases were present within the frontolateral cortex as opposed to connectivity increases in posterior cortical regions, all suggestive of a global-scale connectivity reconfiguration. The pathology-based analyses revealed significant connectivity impairment in the nigrostriatal dopaminergic pathway and in the regions early affected by α-synuclein pathology. Notably, significant connectivity changes were present in several resting state networks especially in frontal regions. These findings expand previous imaging evidence of altered connectivity in cognitively stable PD patients by showing pathology-based connectivity changes and disease-specific metabolic architecture reconfiguration at multiple scale levels, from the earliest PD phases. These alterations go well beyond the known striato-cortical connectivity derangement supporting in vivo an extended neural vulnerability in the PD synucleinopathy.

Parkinson's disease (PD) is a neurodegenerative disease predominantly characterized by abnormal intracellular accumulations of insoluble α-synuclein into fibrils 1 . It has been postulated that the synaptic dysfunction caused by the small aggregates of α-synuclein is the initial event leading to neurodegeneration in PD and in other synucleinopathies 2 . Since physiological α-synuclein plays a key role in the regulation of the dopaminergic normal synaptic function, dopaminergic neurons are particularly vulnerable to α-synuclein pathology 2 . Synaptic dysfunction might impair both neurotransmitter release and regulation of synaptic plasticity mechanisms, also producing widespread effects on functional connectivity among distant brain regions which may result in neural networks alterations 3 . All above evidence suggests that PD can be regarded as a "network-opathy" 4 , and that adopting a network perspective is essential to understand its pathophysiology 5 . During the last years, an increasing number of neuroimaging studies reported networks alterations in the PD brain. The most consistently reported connectivity change is the alteration of the striato-cortical loop, both in the form of microstructural damage, as shown by diffusion tensor imaging, or as functional connectivity changes by resting state fMRI (rs-fMRI (see refs 5 and 6). Connectivity changes between striatal and cortical regions have been associated with resting tremor 7 , freezing of gait 8 and overall motor symptoms severity, as measured by UPDRS-III score 9 , thus suggesting that impairment of the cortico-striatal loops is a key phenomenon for the occurrence of motor symptoms in PD 6 . A limited amount of rs-fMRI studies assessed connectivity in non-motor resting state networks, reporting reduced connectivity in (i) default mode network Scientific RepoRts | 7: 4256 | DOI: 10.1038/s41598-017-04102-z were affected. The mesolimbic pathway was instead globally spared, with no difference in the comparison to HC in the total number of metabolic connections (T = −1.529, p > 0.05) (Fig. 2).
All reported differences were statistically significant (p < 0.001).
α-synuclein pathology spreading analysis. We found decreased metabolic connectivity between regions early affected by α-synuclein pathology, namely the lower brainstem, pons and midbrain (Fig. 3). Lower brainstem, pons and midbrain also underwent significant metabolic disconnections with the regions later affected by α-synuclein pathology (i.e. belonging to stages 5 and 6). Among regions later affected by pathology, only stage 5 showed significant local connectivity derangement (t = −18.415, p < 0.001), particularly affecting the orbitofrontal cortex. Orbitofrontal cortex also suffered long-distance disconnections with the frontolateral cortex, a region belonging to the Braak's stage 6. Local connectivity was not affected in Braak's stage 4 nor 6 (t = 0.199, p > 0.05; t = −0.776, p > 0.05).

Resting-state networks analysis.
Resting-state networks obtained from the seed-based inter-correlation analysis are shown in Fig. 4. Alterations in the metabolic connectivity maps were present in all the analysed resting-state networks. As for the attentional network, a disconnection of the dorsolateral prefrontal cortex from the seed (i.e. the inferior parietal lobule) was observed. Regarding the posterior DMN, the anterior regions (i.e. ventromedial, orbital and dorsolateral frontal cortex) were completely disconnected from the seed (i.e. posterior cingulate cortex). The anterior DMN showed also loss of connectivity between the seed (i.e. anterior cingulate/ ventromedial frontal cortex) and the posterior regions of the network. The motor network showed reduced connectivity within the cortical regions (i.e. premotor cortex, superior medial frontal gyrus, dorsolateral prefrontal cortex) and a total disconnection with the subcortical regions (i.e. putamen bilaterally) and from the seed. The executive network was affected to a lesser extent, with a loss of connectivity in orbitofrontal, lateral inferior parietal and cingulate regions.

Discussion
Previous studies investigating metabolic connectivity in PD mainly focused on the identification of specific patterns of metabolic covariance and their association to motor and cognitive symptoms, using principal component analysis [28][29][30] . Our study applied for the first time an alternative approach, namely SICE in combination with seed-based inter-correlation analysis for a multiscale assessment of metabolic connectivity in PD, by exploiting the unique sensitivity of [18F]FDG-PET in capturing the pathological events affecting brain functionality. Metabolic connectivity, as revealed by [18F]FDG-PET, should reflect in particular the neuropathological events The second column shows PD and HC connectomes projected on a 3D brain template. A global connectivity reconfiguration is present, with frontal and cerebellar regions being the most affected in PD patients. Node degree, i.e. the number of connections for each region, is represented by the size of each dot. Connection strength is represented by the colour and thickness of each line connecting two nodes. (B) The T-score matrix shows differences in the number of connections within and between each sub-matrix in PD versus HC. Abbreviations: F: Frontal. (C) Figure shows lost hub regions, i.e. nodes that assume the role of hubs in HC but not in PD. Hub identification was based on participation coefficient. Hubs are represented on a 3D brain template using BrainNet toolbox.
affecting synaptic functions in PD, such as neurodegenerative processes related to aggregation of α-synuclein at the presynapsis 2 , which interferes with synapthophysin 31 and synapsin-III 32 proteins functioning, and neurotransmitters alterations 33 .
We assessed whole-brain metabolic connectivity without a priori constraints, in order to explore possible local and long-distance disconnections and adaptive compensatory changes in the brain organization. We showed that  Metabolic connectivity alterations first appear in the lower brainstem, pons and midbrain (Braak's stages 1, 2, 3) and furthermore spread to the orbitofrontal regions (stage 5). Connectivity between orbitofrontal (stage 5) and frontolateral cortex (stage 6) was also partly affected (right panel). The ROIs were defined according to AAL atlas (see text for details). α-synuclein-spreading connectivity results projected on a 3D brain template for PD and HC groups (right panel). Node degree, i.e. the number of connections for each region, is represented by the size of each dot. Connection strength is represented by the colour and thickness of each line connecting two nodes.
Scientific RepoRts | 7: 4256 | DOI:10.1038/s41598-017-04102-z early PD is associated with a whole-brain architecture reorganization, with connectivity changes largely affecting frontolateral cortex and cerebellum, both locally and at long-distance.
We also assessed pathology-driven alterations in metabolic connectivity by specifically targeting the metabolic architecture of the dopaminergic pathways and the regions involved in α-synuclein pathology spreading. The connectivity within the dorsal dopamine pathway was selectively affected, with concomitant sparing of the mesolimbic pathway. As for the α-synuclein spreading, metabolic connectivity was more impaired in the regions early affected by α-synuclein pathology (Braak's stages 1-3) 27 .
Finally, we evaluated the degree to which high-order resting state networks are affected in PD, revealing a common pattern of connectivity impairment, with a major disconnection to and within the frontal regions across all resting state networks.
Altogether, these results show that alterations in PD metabolic connectome are strongly consistent with those found in other synucleinopathies such as DLB (cfr. ref. 24), thus supporting a backbone of shared neuronal vulnerabilities consistent with the common underlying pathology. Connectivity changes at each scale level are discussed in detail as follows.
The whole brain analysis revealed long-distance connectivity decreases whose most prominent feature was the widespread disconnections affecting the frontolateral submatrix (see Fig. 1). Previous studies in PD have almost exclusively focused on the fronto-striatal circuit 34,35 , reporting functional disconnections between wide portions of the frontolateral cortex and striatum 34 , with metabolic changes in the dorsolateral and anterior prefrontal regions coupled to caudate dopamine depletion 35 . Cortico-cortical connectivity alterations involving the frontolateral cortex were previously reported in PD, although limited to the connections between frontolateral cortex and premotor/supplementary motor areas 36 . Our results add further evidence for more widespread frontal connectivity changes, showing altered connections with parietal, occipital and temporal cortices, as well as with the basal ganglia, brainstem and cerebellum. The significance of frontal disconnections for specific PD symptoms remains hitherto to be explored. Fronto-striatal system abnormalities, however, are known to be at the basis of PD executive dysfunction, such as planning, spatial working memory and attentional set-shifting 37 . This extensive pattern of connectivity derangement supports the major frontal pathophysiology in early PD 38 .
Cerebellum submatrix showed also widespread long-distance disconnections, particularly with frontolateral and premotor areas. This evidence indicates that also specific cerebellar-cortical networks are involved in PD, together with an abnormal cerebello-thalamic connectivity, which we also found altered 39 .
The basal ganglia submatrix revealed selective connectivity decreases with the frontolateral, premotor, somatosensory, insular and brainstem submatrices, consistent with previous studies using fMRI, that showed a reduced functional connectivity among striatum and dorsolateral prefontal cortex 40 , sensorimotor cortex 41 and Resting-state networks were obtained using seed-based intercorrelation analysis. Clusters with a minimum spatial extent of 50 voxels are shown, with a voxel-wise significant threshold of p < 0.01 FDR-corrected. brainstem 9 . The disconnection between basal ganglia and brainstem is particularly relevant, since it is the very early locus of PD neuropathology 27 .
As for the long-distance connectivity increases, these were observed in posterior brain regions, namely between the parietal, temporal and occipital cortices. Parietal, occipital and temporal cortices were also the core of a widespread number of connectivity increases involving other cortical and subcortical regions (see Fig. 1). The cerebellum showed also selective connectivity increases, that were previously reported using rs-fMRI and ascribed to a compensatory role of cerebellum during the early PD stages 42 . However, the interpretation of connectivity increases as due to compensatory mechanisms needs a note of caution, since evidence suggesting maladaptive mechanisms also exists (cfr. ref. 25). This change in connectivity may indeed reflect ineffective "compensatory" mechanism present in the early PD phase. As all PD patients included in the study were cognitively stable, we might also argue that the presence of compensatory mechanisms acting particularly in the posterior brain regions might contribute to the preservation of cognitive functioning in early PD. A progressive posterior cortical impairment is thought to be related to cognitive decline and development of dementia in PD 43 .
As for local connectivity decreases, frontolateral, orbitofrontal and cerebellar submatrices suffered the major loss of local connectivity (see Fig. 1). The frontal lobe dysfunction is an established feature of PD 38 , and considered a major consequence of the striatal dopaminergic deficits, running through the strong interconnections between frontal cortex and striatal regions 38 . Consistently, reductions in glucose metabolism in both prefrontal and orbitofrontal regions have been reported in PD and associated with dopaminergic striatal depletion 35,44 . Intra-cortical dopamine deficits have been suggested to play a role in the regulation of prefrontal activity in PD, with dopamine depletion leading to defective activation of the dorsolateral prefrontal cortex during motor tasks 45 .
As for the cerebellum local loss of connectivity, we might argue that a crucial role might be played by pathological changes such as α-synuclein pathology 46 , dopaminergic degeneration 42 , loss of dopaminergic D 1 -D 3 receptors 47 , atrophy 48 , and white matter damage 49 . Cerebellum is involved in the planning and execution of motor movements, postural control and tremor as well as in a wide range of cognitive functions 39 and its derangement, as clearly shown in the present paper, crucially highlights its role in PD.
We found local connectivity increases in cortical temporal, parietal and occipital regions that were previously interpreted as compensatory mechanisms, occurring in the extra-striatal regions 50, 51 (see Fig. 1). In addition, we found local striatal connectivity increases, as also previously reported 40,41 . Compensatory mechanisms within the striatum have been suggested to play a role in particular during the very early disease phases, with extra-striatal compensatory mechanisms acquiring importance with disease progression 50 . A recent study has shown that striatal compensatory mechanisms are pivotal to compensate for striatal dopaminergic depletion and maintaining a normal cognitive functioning 52 .
As for the dopaminergic systems analysis, the results notably showed a different vulnerability of the two dopaminergic systems, with a significant loss of connectivity in the dorsal dopamine pathway, and a preserved connectivity in the mesolimbic pathway (see Fig. 2). Dopamine depletion impairs the frontostriatal functional connectivity contributing to the pattern of altered metabolic connectivity here observed 53 . In addition, α-synuclein plays a key role in both dopaminergic neurotransmission pathways, i.e. regulating the filling and fusion of vesicles via vesicular monoamine transporter 2 and the dopamine reuptake via dopamine transporter 2 . It has been shown that substantia nigra neurons are more vulnerable to α-synuclein pathology than ventral tegmental area neurons, possibly due to the higher energy demand of the former 54 . The present findings confirm for the first time at the "metabolic level" the specific dorsal dopamine pathway involvement in early PD patients. Comparable findings were also reported in our previous work on metabolic connectivity in DLB, thus showing that a major vulnerability of the dorsal dopamine pathway is not a disease-specific feature of PD, but extends to other diseases in the synucleinopathies spectrum 24 .
The pattern analysis of α-synuclein pathology spreading revealed altered metabolic connectivity in the regions early affected by α-synuclein pathology (see Fig. 3). The specific connectivity impairment involving the regions of interest (ROIs) part of the first three Braak's stages (i.e. midbrain, pons and lower brainstem) is consistent with the pathology model postulating that the clinical signs of parkinsonism appear when α-synuclein pathology reaches the third stage, and degeneration of substantia nigra occurs 27 . Notably, these regions were also disconnected at long-distance from regions later affected by α-synuclein pathology, i.e. the regions belonging to stage 5 and 6.
We also found a partial local connectivity impairment in stage 5 (i.e. the orbitofrontal cortex) and in stage 6 (i.e. the frontolateral cortex). The orbitofrontal and frontal lateral cortex have consistently been reported as loci of damage in PD 49,55 , due to the dopamine-mediated striato-frontal disconnection 35,38,44 . Stage 4 did not show significant local connectivity changes. From the methodological standpoint, it must be acknowledged that the anatomically-restricted analyses for the α-synuclein spreading were performed using the automated anatomical labelling atlas (AAL) functional-anatomical regions, not specifically constructed for pathology-driven analysis. Stage 4, that includes temporal mesocortex and allocortex, might have suffered for the ROIs subdivision derived from the AAL. In the future, atlases based on histopathology may become available, allowing this limitation to be overcome. Alternatively, it is possible that the "hippocampus, parahippocampus and amygdala" ROIs we chose for Stage 4, could be less affected by α-synucleopathy in PD, given the complete absence of memory related deficits in our series. Taken together, these results support the link between α-synuclein accumulation and synaptic dysfunction as measured by [18F]FDG-PET and notably give an in vivo support to Braak's staging model 27 . Also, this result is consistent with our previous α-synuclein-spreading-based connectomics analysis in DLB 24 , thus in vivo supporting a common pattern of α-synuclein-spreading across the two diseases belonging to the same pathology spectrum.
As for resting-state networks analysis, we found a loss of connectivity in the dorsolateral prefrontal cortex and the parietal regions, affecting the attentional network (see Fig. 4B), consistently with a previous rs-fMRI study in PD 11 , which reported also an association between the impairment of attention network hubs and poor performance in perceptual tasks.
Scientific RepoRts | 7: 4256 | DOI:10.1038/s41598-017-04102-z As for DMN, there was a loss of connectivity in both the anterior and posterior components (see Fig. 4A). This pattern of disconnection has been previously described in normal aging and, at an accelerated rate, in Alzheimer's disease 56 . The author speculated that this pattern of disconnections could be due to age-related increasing synaptic inefficiency, to which subject vulnerable to develop Alzheimer's disease would be more susceptible 56 . Our results suggest that not only Alzheimer's disease but also PD would produce a similar pattern of connectivity impairment in the DMNs that might be prodromal to further development of cognitive symptoms. Notably, recent studies have shown that DMN is disrupted even in cognitively unimpaired PD patients 10,57 . It has been suggested that DMN disruption mainly arises as a direct consequence of PD pathology 57 and maximally as the result of PD dopaminergic impairment 58 . Consistently, it was shown that administration of drugs enhancing dopaminergic activity is able to restore normal DMN functioning in PD 58 .
As for the executive network, our results strengthen the link between the dysfunction of the executive network and the alteration of frontal-striatal connectivity (see Fig. 4C). Previous rs-fMRI studies in PD also reported abnormal connectivity within this network 59 , as well as abnormal interactions between the executive network and DMN 60 . The impairment in prefrontal and orbitofrontal regions, considered to be at the basis of the executive dysfunctions in PD, might follow frontal-striatal dopaminergic imbalance 61 . Notwithstanding the role of frontal impairment in the executive dysfunction is well-recognized in PD, it is not clear whether it contributes to cognitive decline and dementia development 62 . An early predictor of dementia in PD is instead the posterior cortical damage 62 . The dual syndrome hypothesis considers the fronto-striatal dysfunction as a characteristic of non-demented PD patients, and the posterior cortical and temporal lobe dysfunction as a signature of rapid cognitive decline 63 .
This study, together with our previous work in DLB 24 , allows for a comparative picture of the metabolic connectome in the two most diffuse α-synucleinopathies. Notably, the whole-brain analyses in PD and DLB groups revealed consistencies and substantial differences. As for the differences, PD showed an extensive decrease of connectivity in frontal regions, with compensatory connectivity increases involving occipital and posterior cortical regions, whereas an occipital connectivity impairment was present in DLB, together with frontal compensatory connectivity increases. This opposite pattern of anterior-posterior connectivity changes in early cognitive stable PD and in DLB patients might be of crucial clinical relevance. It is consistent with the prevalent frontal functional changes previously reported in non-demented PD patients, as opposed to the posterior impairment associated with dementia in PD and DLB. The different impairment of anterior-posterior connectivity might reflect the different vulnerability of the cholinergic system in PD and DLB 61 , leading to disease-specific patterns of neuronal dysfunction 43,[64][65][66] , and metabolic connectivity changes, here reported for the first time.
As for the consistencies, cerebellum, mesencephalic-pontine and striatal regions showed comparable patterns of altered connectivity in both PD and DLB, locally and at long-distance. Pathology-driven analyses provided similar results in the two parkinsonian conditions, with the greatest connectivity impairment in the dorsal dopamine pathway and in the regions early affected by α-synuclein pathology. Further studies within this spectrum, involving populations of PD patients with mild cognitive impairment or dementia, DLB patients at different disease phase and MSA cases, will provide the evidence for common and disease-specific connectivity alterations also linked to the specific clinical phenotypes.
In conclusion, our results show that metabolic connectivity is affected in early PD at multiple scale levels, with (i) a thorough reconfiguration of the global whole-brain architecture, mainly affecting frontal connectivity, (ii) a metabolic connectivity disruption underlying a major impairment in the dorsal dopamine neurotransmission system and in the early spreading of α-synuclein pathology, and (iii) reconfigurations in high-order resting state networks affecting in particular the frontal regions. The reported results point at a disease-specific pattern of frontal disconnection and posterior connectivity compensation, consistent with the "dual syndrome hypothesis" 63 . The present results support the emerging hypothesis that PD is a widespread neurodegenerative disease at multiple scale levels (cfr. ref. 6) and that the era of the axiom "PD equals dopaminergic dysregulation" needs to be rewritten.

Materials and Methods
Subjects. Thirty-four idiopathic PD patients without any cognitive impairment at baseline and stable during 4-years follow-up were retrospectively collected from the clinical and imaging database of the Neurology Unit, Department of Clinical and Experimental Sciences, at the University of Brescia, Brescia, Italy. The clinical diagnosis was made according to the UK Brain Bank Criteria 67 by movement disorders specialist (A.P. and A.A.), considering full medical history, neurological examination (including UPDRS-III in ON condition) and a standard neuropsychological assessment. All patients included underwent structural imaging (magnetic resonance imaging or computed tomography (CT)) in order to exclude prominent cortical or subcortical infarcts or brain/ iron accumulation or atypical parkinsonian disorders. Stringent exclusion criteria were applied: presence of deep brain stimulation, verified genetic mutation known to cause PD, concomitant psychiatric or other neurological disorder, hallucination, psychosis or antipsychotic drug use, history of drug or alcohol abuse, mild cognitive impairment. The study crucially excluded PD patients with a mild cognitive impairment or dementia diagnosis defined according to the level II MDS criteria using the neuropsychological assessment and cut-offs recently published 68 . The PD patients included underwent [18F]FDG-PET scans for research purposes. The group comprised 18 males and 16 females with a mean age of 63.71 ± 11.70 years and mean disease duration of 4.5 ± 2.65 years. No patients included in the study developed dementia at 4-year clinical and neuropsychological follow-up, thus presenting a stable cognitive functioning at least until 8.5 ± 2.65 years of disease duration. All patients were taking antiparkinsonian medications and had a mean Levodopa equivalent daily dose of 422 ± 316 mg. Demographic, clinical and cognitive features in PD and healthy controls (HC) groups are reported in Table 1.
[18]FDG-PET scans of 34 age-matched cognitively normal HC were included for comparison. The group comprised 17 males and 17 females with a mean age of 65.55 ± 8.85 years. Age and gender did not differ significantly between PD and HC groups (Age: T = 0.433, p = 0.667; Gender: Χ 2 = 0.059, p = 0.808). Uniform reconstruction protocols were applied in order to factor out possible sources of variability. All images were reconstructed using an ordered subset-expectation maximization algorithm (OSEM). Attenuation correction was based on CT scans. Each reconstructed image was visually inspected in order to check for major artefacts, i.e. defective image uniformity/orientation or attenuation correction due to mismatch between CT and PET images.
Images underwent general pre-processing procedures, using the MATLAB (Mathworks Inc., Sherborn, Mass., USA) based software SPM5 (http://www.fil.ion.ucl.ac.uk/spm/software/SPM5/). Each image was first normalized to a [18F]FDG-PET specific template registered to the MNI standard space 70 and spatially smoothed with an 8 mm isotropic 3D Gaussian FWHM kernel. Images were then proportionally scaled to the global mean.
Whole-brain and pathology-driven metabolic connectivity analyses. We used SICE, a method previously validated by Huang et al. 19 . SICE-based analyses involve the definition of the basic units of each network, i.e. the ROIs/nodes. The [18F]FDG-PET signal is extracted from each ROI and from each subject, thus obtaining SubjectsxROIs matrices. SICE algorithm is then applied on the SubjectsxROIs matrices in order to estimate the metabolic connectivity matrices. Graph theory measures are computed from the metabolic connectivity matrices and a bootstrapping procedure is performed in order to test differences between HC and PD groups.
In the pathology-driven connectivity analyses, we focused on the neural networks related to PD pathology, namely the dopaminergic neurotransmission pathways 26 and the brain regions affected by the spreading of α-synuclein according to Braak's staging 27 .
For the dopaminergic system analysis, we considered ROIs pertaining to the dorsal and the mesolimbic dopamine pathways, as detailed elsewhere 24 . The small dopaminergic nuclei, i.e. substantia nigra and ventrotegmental area, were not included in the analysis, due to the limited spatial resolution of PET method and the lack of reference atlases for these regions.
As for the α-synuclein spreading analysis, we considered the staging system proposed by Braak and colleagues (2003) 27 . Within the α-synuclein network, we considered the lower brainstem and pons for stages 1 and 2 respectively, since these regions contain the grey matter nuclei early affected by α-synuclein pathology in PD, i.e. the dorsal IX-X motor nuclei, intermediate reticular zone, caudal raphe nuclei, gigantocellular reticular nucleus and coeruleus/subcoeruleus complex; the midbrain, which includes the pathological hallmark of the disease, namely the substantia nigra pars compacta for stage 3; hippocampus, parahippocampal gyrus, and amygdala for stage 4; the temporal lobe, anterior cingulate, insular and orbitofrontal cortices for stage 5; the remaining neocortical areas, with the exception of the primary sensory areas and the primary motor fields, for stage 6 27 (Fig. 3).
All the above mentioned ROIs were derived from the same atlas, i.e. AAL 71 , with the exception of ROIs not included in the AAL, namely (i) the brainstem ROIs, (midbrain, pons, lower brainstem) derived from the  19 . Construction of Brain Connectivity Matrices was performed using GraphVar toolbox 74 . SICE allows to estimate the structure of the metabolic connectivity matrix by imposing a sparsity constraint on the maximum likelihood estimate of the inverse covariance matrix 19 . SICE provides a robust estimation of the binary structure of the inverse covariance matrix, but it does not allow to estimate the strength of non-zero entries due to shrinkage 23 . As a consequence, only information on the presence or absence of metabolic connections can be used to build the brain connectivity model 19 . Though information on the strength of the metabolic connections are not provided by SICE, a quasi-measure of strength can be obtained by summing up unweighted binary matrices estimated at different density levels 19 . Only for visualization purposes, we used Stability Approach to Regularization Selection (StARS) (see below) applied to matrices at a predefined range of densities (i.e. 3-18% with an incremental interval of 3%), in order to obtain unweighted binary matrices at different densities. By summing up the six unweighted binary matrices for each group and analysis, summary quasi-weighted matrices were obtained and represented in a 3D brain template using BrainNet toolbox 75 .
Given that robustness of the sparse estimation depends on matrix density 76 , density level must be carefully chosen to ensure that the covariance matrix is sparse 19 . In SICE, density level is controlled for by a regularization parameter λ 19 . Different strategies have been proposed for density selection 77 but no gold standard was established for selection of λ using SICE. A new criterion for λ selection, called StARS, has been recently proposed 78 . StARS allows to select the minimum value of λ necessary to ensure matrix sparsity and replicability under random sampling, avoiding the risk of massive false positives without failing to capture the true structure of the connectivity matrix 78 . In order to select the optimal sparsity level for each group, StARS 78 was applied to both PD and HC matrices. The resulting matrices were used for statistical testing.
Graph theory and statistical analyses. For the whole-brain analysis, we computed the degree and the participation coefficient of each node using Brain Connectivity Toolbox 76 . Participation coefficient (Pi) was defined as: where N m is the number of modules, k i (m) is the number of links of node i to nodes in module m, and k i is the total degree of node i 79 Partecipation coefficient was adopted in order to identify the most important regions/nodes of the network, i.e. the hubs 80 by setting a threshold at 1.25 standard deviation over the average participation coefficient.
Considering the whole-brain sub-matrix-based analysis, we calculated the total number of within or local connections (i.e. connections linking two nodes in the same sub-matrix) and the total number of between or long-distance connections (i.e. connections linking two nodes belonging to different sub-matrices). For the pathology-driven networks, we computed the total number of connections and nodal degree within each network.
A bootstrapping procedure was adopted in order to rigorously test differences between groups 19 . For each connectivity matrix, we extracted 1000 bootstrap samples of 34 subjects, with replacement, for both PD and HC groups. Based on PD and HC respective bootstrap samples, we performed hypothesis testing for each SICE analysis. For the whole-brain analysis, we tested significant differences between PD and HC groups in the total number of connections within each submatrix and between each pair of submatrices. For the pathology-driven analysis, we tested the null hypothesis that the total number of connections in each dopaminergic pathway and in each Braak's stage was equal across groups. Multiple independent t-tests with Bonferroni correction were performed for each analysis. For a thorough explanation of the statistical testing procedure see ref. 19. Resting-state networks metabolic connectivity. We used seed-based inter-correlation analysis, a method previously validate by Lee and colleagues (2008) for [18F]FDG-PET data 20 . We focused our analyses on the attentional, DMN (anterior and posterior), executive and motor networks. For each network, a seed region was selected on the basis of previous literature, namely the inferior parietal lobule for the attentional network 81 , the anterior cingulate cortex/ventromedial prefrontal cortex for the anterior DMN 56 , the posterior cingulate cortex for the posterior DMN 82 , the dorsolateral prefrontal cortex for the executive network 83 , and the precentral gyrus for the motor network 84 . For each group and network, [18F]FDG-PET signal extracted from the designated seed was entered as covariate in a Multiple Regression Model in SPM5 and used to predict [18F]FDG-PET signal elsewhere in the brain, thus allowing the estimation of the corresponding resting state network. Voxel-wise False Discovery Rate (FDR)-corrected p < 0.01 was considered statistically significant.
Data Availability. All relevant data are included in this published article.