## Introduction

Psychotic disorders cause significant global burden to affected individuals, families and healthcare systems. In Parkinson’s disease (PD), psychosis is common, and visual hallucinations are associated with cognitive decline1, poorer quality of life2 and increased mortality3. However, despite their impact, the brain changes that give rise to psychotic hallucinations are not fully understood. The transient, unpredictable nature of hallucinations, even in patients who regularly experience them, suggests they relate to changes in dynamic brain processes and shifts in states. Resting-state functional MRI (rsfMRI) measures spontaneous fluctuations in brain activity based on correlated fluctuations in blood oxygenation4 and has shown changes in the relative activity of specific functional brain networks in patients with PD-hallucinations5, with increased activation of the default mode network (DMN) and impaired recruitment of the dorsal attention network6,7,8,9. However, these studies only provide a static image of functional connectivity, calculated over an entire scanning period, rather than examining dynamic changes in brain states.

An extension of this approach is dynamic functional connectivity analysis, which measures spontaneous fluctuations in connectivity over time10,11,12 and may be a more accurate representation of fluctuating cognitive states than previous static approaches13. Changes in temporal dynamics are seen in schizophrenia and other psychiatric conditions14,15,16,17, and recent work showed imbalance of temporal dynamics of integrated and segregated states in anaesthesia and disorders of consciousness18,19 and after administration of the psychedelic LSD, known for its hallucinogenic properties20. Changes in dynamic functional connectivity are described in PD21 and are associated with severity of both motor and cognitive symptoms22,23,24 but are as yet unexplored in relation to neuropsychiatric symptoms.

Functional connectivity is likely to be affected by breakdown in the anatomical connections between regions. Indeed, PD patients with hallucinations show widespread disruption in structural connections between brain regions, measured using diffusion MRI25,26. These changes particularly affect highly connected brain regions or “hubs” important for switching the brain between different states27,28. Network control theory is a mathematical framework developed to study how the activity of a network’s nodes is influenced by the network’s structure. In the context of neuroscience, it offers a mechanistic explanation of how the brain transitions between cognitive states based on its structure, enabling behaviour29. It integrates information from an individual’s structural connectome (white matter connectivity derived from diffusion-weighted imaging) and temporal activation patterns (derived for example from fMRI) to specify how observed temporal activation patterns are constrained by the structural connectome29,30. This framework defines brain states as the magnitude of haemodynamic activity across brain regions at a single time point and assumes that the brain’s activation state at a given time is a linear function of a previous state, the underlying structural connectome and the additional control energy that is added to the system29,31. In this way, the minimal energy cost needed to move the brain from one state to another can be calculated based on its structural network29,31,32. A state that is less energy-demanding to maintain, or requires lower energy for transition, will be preferred. Recent work has shown that certain state transitions are preferable in the resting brain over others but this can be overcome by cognitive demands and is related to brain development and cognition33,34,35,36. This framework has the potential to explain why a particular state is predominantly seen in health and how the balance between states may change in the presence of disease.

Transitions between functional states may be modulated by neurotransmitter systems37. Dopamine transmission, particularly D2 receptor expression guides state transitions during a working memory task34. Excess dopamine release is a core neurobiological theory of schizophrenia38, and excess striatal dopamine has been linked to hallucinatory experiences39. Dopamine has long been considered the key driving neurotransmitter for PD hallucinations40 with higher daily levodopa doses associated with higher risk of hallucinations41,42. However, recent studies have challenged this model and implicated other neurotransmitters in PD-hallucinations: higher density of 5HT2A serotonin receptors43, reduced GABA concentration44 and cholinergic neuronal loss45 have each been described in patients with PD and visual hallucinations. The role of dopamine in cognitive state transitions in health has also been challenged, with regional expression patterns of inhibitory and facilitatory neurotransmitters other than dopamine recently linked to dynamic functional states46 and both noradrenaline12,47 and serotonin37 driving whole-brain functional connectivity changes. A better understanding of the complex changes in neurotransmitter systems causing hallucinations would inform the development of more effective and targeted treatments for this distressing symptom.

Here, we aimed to investigate the nature of temporal dynamics in PD-associated visual hallucinations using rsfMRI; and determine whether the balance between predominantly Integrated and Segregated states of functional connectivity is altered in PD patients with hallucinations compared to patients without hallucinations and controls (overview in Fig. 1). We found that PD patients with hallucinations show impaired temporal dynamics, with a predisposition towards a predominantly Segregated state of functional connectivity. We then applied network control theory to calculate each individual’s required energy cost to transition from the integrated-to-the-segregated state and vice versa, and the cost to maintain each state. We found that Parkinson’s-hallucinators required less energy to transition from the integrated-to-segregated state than those without hallucinations and controls. Finally, we identified the brain regions that contribute most to the transition from integrated-to-segregated state. As dynamic neural systems are modulated by neurotransmitter systems37,47 we related the spatial organisation of this transition to regional neurotransmitter distribution using PET-derived density profiles and regional gene expression for neurotransmitter receptors.

## Results

Ninety-one patients with PD were included: 16 PD patients with habitual visual hallucinations (PD-VH), 75 PD patients without hallucinations (PD-non-VH) and 32 controls. Demographics and clinical assessments are seen in Table 1. All participants experienced hallucinations in the visual domain, with details on the experienced hallucinatory images in Table 2. PD-VH and PD-non-VH were well matched in demographics, cognitive and motor performance, levodopa equivalent dose, and image quality and motion parameters (Table 1 and Supplementary Table 1). PD-VH participants showed higher depression scores (p = 0.032) than PD-non-VH participants but well below the clinical threshold for depression (≥8). As a result of the presence of hallucinations and higher depression burden (p = 0.014), PD-VH participants showed higher total UPDRS scores, which assessed non-motor symptoms, but they did not differ in terms of motor severity or levodopa equivalent dose. Although disease duration differed between PD-VH and PD-non-VH participants (p = 0.044), there was no correlation between disease duration and temporal functional changes (ρ = −0.110, p = 0.297 between proportion of time spent in an Integrated vs Segregated state and disease duration in PD participants) therefore we did not correct for disease duration in our main comparisons of interest.

### Preserved topology of functional connectivity states

To examine the dynamic changes in functional connectivity underlying PD-hallucinations, we employed an a priori clustering of dynamic functional connectivity into two states of functional connectivity, an Integrated and a Segregated state. After obtaining sliding-windows (44 s duration each) of dynamic functional connectivity for each participant, the joint histogram of participation coefficient and within-module degree Z-score for k-means clustering (k = 2; independently confirmed as optimal number of clusters on data-driven evaluation, Supplementary Fig. 1). The cluster with highest average participation coefficient was identified as the Integrated dynamic state and the cluster with the lowest participation coefficient as the Segregated state, as previously described12,18,20,48,49. This was performed separately for each participant (using the same criteria) leading to individually-defined predominantly Integrated and Segregated states (Fig. 1a). Differences between the two states are seen in Supplementary Fig. 2 and Supplementary Table 3.

These two states did not significantly differ between groups (PD versus controls or PD-VH versus PD-non-VH) when comparing connectivity strength in each state using network-based statistics, or between-group differences in density (Integrated: Kruskal–Wallis H = 2.473, p = 0.290, Segregated: 0.175, p = 0.529), entropy of connectivity values (Integrated: H = 0.723, p = 0.696, predominantly-Segregated: H = 0.905, p = 0.636), structural-functional coupling (Integrated F(111,2) = 1.093, p = 0.339, Segregated: F(111,2) = 1.401, p = 0.251) or small world propensity (Integrated: H = 1.065, p = 0.587, Segregated: H = 4.400, p = 0.111).

### Impaired temporal properties of dynamic functional connectivity in patients with hallucinations

Although the states themselves did not differ between groups, we found significant changes in their temporal properties. PD-VH spent a significantly smaller proportion of time in the Integrated state (therefore more time in the Segregated state) than PD-non-VH (β = −0.113, p = 0.032) and controls (β = −0.128, p = 0.026) (Fig. 2a). Within PD patients, the proportion of time spent in the Integrated state was inversely correlated with hallucination severity (Spearman’s ρ = −0.259, p = 0.013). Mean dwell time (number of consecutive windows spent in each state) in the Segregated state was higher in PD-VH than PD-non-VH (19.1 ± 16.9 in PD-VH vs 9.5 ± 9.1 in PD-non-VH H = 4.058, p = 0.044), but did not differ for the Integrated state (H = 2.166, p = 0.141). No differences were seen in dwell times of either state between PD and controls. Finally, the total number of transitions was lower in PD-VH than PD-non-VH (5.7 ± 5.3 in PD-VH vs 8.5 ± 6.2 in PD-non-VH, H = 3.87, p = 0.049) (Fig. 2b). Results were replicated using a finer parcellation (Supplementary Fig. 4). Overall, this suggests that PD-VH spend more time in the Segregated state than PD-non-VH, with fewer total transitions and longer dwelling time within the Integrated state.

### Reduced energy costs to transition from the integrated to segregated state in patients with visual hallucinations

Having identified significant differences in terms of brain dynamics between PD-VH and PD-non-VH, which are specifically related to the severity of visual hallucinations (the focus of our present investigation), we sought to interrogate further this difference between PD patients. We have previously shown widespread structural connectivity changes in PD-VH28. Given neural dynamics are constrained by the structural connectome, we used the framework of network control theory to integrate information about structural network topology and functional brain dynamics29,31,32. Using this framework, the minimal energetic cost to transition from one specific functional brain state (defined as the magnitude of brain activation at a specific time point) to another can be calculated using the structural brain network topology31,32,50; lower energetic costs required to transition to a specific state may make this transition preferable.

Specifically, we aimed to investigate whether the Segregated state predominance observed in hallucinators could be explained by differences in ease of transition from the integrated-to-segregated state or vice versa or a difference in ease of maintaining the Segregated state. To do this, we calculated the minimal control energy that needs to be applied to the structural network of each participant to (1) transition from integrated-to-segregated state, (2) transition from segregated-to-integrated state, (3) maintain the Integrated state and (4) maintain the Segregated state (Fig. 1b). Minimal control energies were calculated for each subject based on their structural brain network, which was estimated using diffusion imaging and probabilistic tractography. For the purposes of this calculation, and in contrast to previous publications, we represented the Integrated and Segregated states as a vector of sum functional connectivity for each brain region. We then examined whether transition and persistence energies in each state differed between PD-VH and PD-non-VH.

Similarly to previous work in healthy individuals34, persistence energy for the more connected Integrated state was higher than the Segregated state for all participants (repeated measures ANOVA main effect of Integrated to Segregated state persistence energy F(1,113) = 12.432, p < 0.001). Similarly the minimal energy needed to transition from the Segregated to Integrated state was higher (F(1,113) = 6.722, p = 0.011) (Supplementary Fig. 3). When we examined differences between patients with PD with and without hallucinations, PD-VH needed significantly lower control energy to transition from the Integrated-to-Segregated state than PD-non-VH (effect size Hedge’s g = 0.922, t = 2.376, p = 0.029) (Fig. 3a). There were no statistically significant differences between PD-VH and PD-non-VH in the minimal control energy needed to transition from Segregated-to-Integrated state (t = 1.346, p = 0.195), or to persist within the Integrated (t = 1.041, p = 0.312) or Segregated state (t = 1.079, p = 0.295). Therefore, network control theory reveals that the higher proportion of time that PD-VH patients spend in the Segregated state may be accounted for in terms of this state being easier to transition to from the Integrated state (as opposed to being easier to persist in).

### Transition from integrated to the segregated state is driven by subcortical and more multimodal brain regions

A further benefit of applying control theory to functional brain states is that it provides regional information about the cost of maintaining and transitioning between these states.

We therefore aimed to identify which brain regions contribute more to this transition from the Integrated-to-Segregated state (which nodes require more energy in order to transition, with high contributors defined as the top 20% of regions). These higher contributors are more likely to be responsible for the changes in energy costs seen in PD-VH (significantly less control energy needed to transition from Integrated-to-Segregated state in PD-VH). As expected51, subcortical regions were strongly represented, with 25 subcortical nodes amongst the top 20% of contributors (25/47 or 53.2%) with thalamic regions amongst the highest contributors. Of the cortical nodes, top contributors included predominantly right hemispheric regions (20/22 cortical nodes) including regions of the Default mode network: cingulum, precuneus, inferior and superior temporal regions and medial frontal regions (Table 3 and Fig. 3b). There was a significant correlation between the Integrated-to-Segregated state transition energy required at each node and the node’s position in the cortical hierarchy, with higher energy needed for more transmodal regions (ρ = 0.526, p < 0.001) (Fig. 3c).

### Correlation with neurotransmitter systems

Finally, we examined whether the Integrated-to-Segregated state transition (which was the state transition that specifically differed for PD-VH patients), is associated with specific neurotransmitter systems (Supplementary Table 2) in the healthy brain. To do this, we correlated the mean control per node to transition from the Integrated-to-Segregated state with mean regional neurotransmitter density (derived from open-access PET data) and neurotransmitter receptor gene expression levels (derived from the Allen Brain atlas52) in health; we tested this against spatially-correlated null models through sphere permutations, FDR-corrected for multiple comparisons over 232 nodes (Fig. 1c).

We found a significant correlation between regional log(Energy) and density of 5HT1b (ρ = −0.274, qspin = 0.009), 5-HT2a (ρ = −0.347, qspin < 0.001) and GABAA receptors (ρ = −0.317, qspin = 0.022), from open-access atlases of PET data (Fig. 4). Regional energy and regional expression levels of genes relating to 5-HT2a receptors were also significantly correlated (ρ = −0.1438, qspin = 0.044) as well as two GABAA receptors [GABRA1 (ρ = −0.2437, qspin = 0.020) and GABRA2 (ρ = 0.128, qspin = 0.023)]; gene expression data for 5-HT1b receptors were not available. Although noradrenergic and acetylcholinergic PET data are not publicly available, genetic expression of noradrenergic (ADRA1B and ADRA2A), muscarinic (CHRM1, CHRM2, CHRM3, CHRM4) and nicotinic receptors (CHRNA3, CHRNA4, CHRNA7, CHRNB2) was correlated with regional transition energy. Gene expression of DRD2 was also correlated with regional control energy for the Integrated-to-Segregated state transition (ρ = 0.318, qspin = 0.013) but this was not replicated using density PET-derived data (ρ = 0.056, qspin = 0.800). The detailed correlations between regional control energy and transmitter density and regional gene expression are seen in Table 4.

## Discussion

We have used dynamic functional connectivity and network control theory to explore the temporal dynamics underlying visual hallucinations in Parkinson’s, and examined how these can be explained through changes in brain structure. We found that PD-hallucinators spent more time in a predominantly Segregated state of functional connectivity than those without hallucinations, with fewer total transitions and longer dwelling time within the Segregated state. The transition from the Integrated-to-Segregated state was less energy-demanding in PD-hallucinators than non-hallucinators. This transition is mediated by transmodal brain regions that are associated with specific neurotransmitter systems, as confirmed through both in vivo PET mapping and post-mortem gene expression microarray data.

Previous studies have shown that PD patients with cognitive impairment similarly spend more time in a Segregated state and show fewer transitions between states than PD with intact cognition and controls23,24. There were no differences in cognitive performance between PD patients with and without hallucinations in our cohort, but visual hallucinations are known to be associated with incipient dementia in PD53. In schizophrenia, where auditory hallucinations are a core feature, similar findings of altered dwell time are seen14,54, correlated with severity of hallucinations55. We similarly saw patients with visual hallucinations spending less time in the Integrated (and more time in the Segregated) state suggesting this finding may be specific to hallucinations as a trait.

We found that only the temporal dynamics of functional connectivity were altered in patients with hallucinations. This indicates that a change in the temporal balance between normal/preserved states rather than a change in the states themselves underlie PD-hallucinations. This contrasts with work using similar methodologies in patients with loss of consciousness and in healthy volunteers after LSD administration where within-state changes particularly within the Integrated state18,20, were also seen. However, as we examined the propensity to hallucinate rather than the hallucinatory state itself (participants were not actively experiencing hallucinations during scanning) it is possible that additional within-state changes could underlie visual hallucinations in PD, in the moment when they actually occur, an avenue for potential future investigations. In addition, although hallucinations in our participants were frequent (at least weekly in most participants) they were not universally complex and severe. Other important differences are that LSD-induced visual hallucinations are associated with changes in other sensory modalities including time/space dysperceptions and ego dissolution56, which are not seen with PD-associated hallucinations; thus it is not unexpected that the underlying changes in temporal dynamics are different between these hallucinatory conditions.

As temporal transition between functional states is constrained by structural connectivity31,33,57, we used network control theory to model the ease and regional contribution to the brain’s activation for each of these two states, represented as the vector of sum connectivity for each region at each time point31. Specifically, we examined the energy cost of transitioning between and maintaining the Integrated and Segregated states. Minimisation of the control energy cost to transition into a state will make this transition more preferable, and evidence in healthy adolescents suggests lower control energy to activate the frontoparietal network during development (secondary to structural connectome reconfiguration) supports improved executive function35. In addition, hallucination-inducing substances such as LSD and psilocybin have been recently shown to reduce overall control energy needed for between brain-state transitions leading to a more temporal labile functional landscape58. We found a significantly lower energy cost to transition from the Integrated-to-Segregated state for PD-hallucinators than non-hallucinators. In this way, network control theory provides mechanistic insights about why patients with PD-VH spend more time in a more Segregated state: as it is more energy efficient to transition from the Integrated-to-Segregated state due to constraints caused by loss of structural integrity. Further, this framework enabled us to identify the particular nodes most critical in mediating these transitions, with subcortical (especially thalamic nodes) and regions within the DMN especially implicated, consistent with previous work highlighting DMN involvement in PD hallucinations6. Thalamic regions were amongst the highest contributors to this transition. Thalamic involvement has been previously described in visual hallucinations50,59 and we recently showed longitudinal changes in grey and white matter within the medial mediodorsal thalamus60. This provides further evidence of the thalamus as a key driver of network imbalance in PD-hallucinations51,61.

Interestingly, the brain regions contributing most to this transition from Integrated-to-Segregated state showed a correlation with specific neurotransmitter systems in health. Although the directionality of the relationship is difficult to interpret as data on regional neurotransmitter density and gene expression were derived from healthy individuals, regional density of 5HT2A receptors was significantly correlated with the regional control energy needed for Integrated-to-Segregated state transition; this was replicated using regional expression data for the 5HT2A receptor gene.

Activation of 5HT2A receptors is a key mechanism for drug-induced hallucinations occurring with the psychedelic drugs, LSD, psilocybin and ayahuasca62 and modelling studies have shown that this receptor plays a key role in engendering the characteristic brain dynamics of LSD63. Recent work highlighted the crucial role of 5HT2A in neuronal-neurotransmission dynamic coupling across the brain37. 5HT2A has also been implicated in PD-hallucinations; evidenced by the higher density of 5HT2A receptors within frontal, temporal and occipital regions in patients with PD hallucinations in post mortem and in vivo studies43,64 and the efficacy of the novel 5HT2A inverse agonist Pimavanserin in the treatment of PD-hallucinations65. Visual hallucinations are a common phenomenological endpoint of both LSD and PD; our findings provide further evidence for the role of 5HT2A involved in PD-hallucinations, suggesting a convergent biological substrate across hallucinations irrespective of cause.

Other serotonergic receptors were also important for the Integrated-to-Segregated state transition including: 5HT1B (receptor density, but no genetic expression data), 5HT1E, 5HT1F and 5HT5A (gene expression data only). The correlation with multiple serotonin receptors, indicates that serotonergic modulators targeting multiple receptors could be potential therapeutic targets for PD-hallucinations. Of note, no receptor density or gene expression data were available for 5HT3 receptors, a target of interest for Ondansetron, a 5HT3-antagonist currently under evaluation as a treatment of hallucinations66.

Regional receptor density and gene expression for GABAergic receptors were also correlated with regional transition energy in line with previous studies showing reduced GABA concentration in the visual cortex of PD-hallucinators44,67. Visual processing involves a complex interplay between monoaminergic, cholinergic and GABA/glutamatergic neurotransmission61. The observed correlation between the Integrated-to-Segregated state transition and regional gene expression of noradrenergic (ADRA1B, ADRA2A) and cholinergic (muscarinic and nicotinic) receptors is consistent with this, but there were no available PET-derived density data to replicate this.

Convergent evidence has recently highlighted the importance of the noradrenergic system in some non-motor PD symptoms68,69,70. Noradrenaline plays a key role in modulating selective attention71 and with serotonin, modulates behavioural responses to incoming visual information61. The noradrenergic system is also likely to play a key role in mediating functional state transitions: noradrenaline-mediated apical amplification of pyramidal cells differentiates waking and anaesthesia72, extracellular noradrenaline is associated with sleep-state transitions73 and locus coeruleus activity flexibly mediates the recruitment of other neural circuits particularly the prefrontal cortex74, leading to dynamic changes in functional networks, specifically transitioning between motor and task-negative networks75. Changes within the noradrenergic system may be involved in altered state transitions in PD-hallucinations by modulating the activity of sensory cortices and thalamocortical neurocircuitry76.

In contrast to these other neurotransmitters, we found no consistent correlation with dopaminergic receptors. It is important to note that although DRD1 is one of the major dopamine receptors in the cortex no DRD1 density data was publicly available at the time of the study; however, no correlation was seen between genetic expression of DRD1 and regional contribution to the Integrated-to-Segregated state transition. Although a lack of correlation between regional dopamine expression and regional energy does not exclude an indirect dopamine effect in visual hallucinations, our findings highlight the role of transmitters other than dopamine in the development of PD-hallucinations. Rather than a simple hyperdopaminergic state leading to PD-hallucinations, our findings suggest a complex imbalance in multiple neurotransmitter systems, with changes in 5HT2A, GABA and noradrenergic receptors all contributing. Treatment options targeting more than one neurotransmitter system may therefore be needed to manage visual hallucinations in PD and other psychotic illnesses.

Our findings describe that temporal functional dynamics are altered in PD-hallucinations, with a predisposition towards a Segregated state of functional connectivity. This segregated state predominance can be explained by a reduced energy cost to transition from the integrated-to-segregated state in PD patients with hallucinations compared to those without hallucinations. We have also clarified the neuromodulatory correlates of the integrated-to-segregated state transition in the healthy brain. These results provide mechanistic insights into visual hallucinations in PD with implications for other psychotic disorders. By linking these changes to neurotransmitter systems, our findings highlight possible therapeutic targets for hallucinations, a core symptom of psychosis.

## Methods

### Participants

123 participants were included: 91 PD patients and 32 unaffected controls. The study was approved by the Queen’s Square Ethics Committee and participants provided written informed consent. Patients with PD were classified as PD with visual hallucinations (PD-VH, n = 16) if they scored ≥1 in Question 2.1 of the Unified Parkinson’s Disease Rating Scale (UPDRS); the rest were classified as PD-non-VH (n = 75). We collected additional information on severity, frequency and phenomenology of experienced hallucinations with the University of Miami Parkinson’s Disease Hallucinations Questionnaire (UM-PDHQ)85. General cognition was assessed using the Mini-Mental State Examination (MMSE) and Montreal Cognitive Assessment (MoCA)86,87. In addition, domain-specific cognitive assessments with two tests per domain included: Attention: Digit span backwards88, Stroop, Naming89; Executive functions: Stroop Interference89, Category fluency90; Memory: Word Recognition Task91, Logical Memory88; Language: Graded Naming Task92, Letter fluency90; and Visuospatial: Benton’s Judgement of Line93, Hooper Visual Organization Test93. Mood was assessed using the Hospital Anxiety and Depression Scale (HADS)94. Disease-specific measures for PD included: motor assessment using the Movement Disorder Society UPDRS95, smell: Sniffin’ Sticks96, and sleep: REM Sleep Behaviour Disorder Questionnaire (RBDSQ)97. Levodopa equivalent daily doses (LEDD) were calculated for PD participants98.

### MRI data acquisition and preprocessing

Imaging data were acquired on the same 3T Siemens Prisma-fit scanner: rsfMRI: gradient-echo EPI, TR = 70 ms, TE = 30 ms, 105 volumes; diffusion-weighted (DWI): 64 directions (b-values: 50, 300, 1000, 2000). Scanning took place at the same time of day, with PD patients receiving their normal anti-Parkinsonian medication.

Both imaging modalities underwent rigorous quality assurance: The MRI quality control tool (MRIQC) was used to assess rsfMRI data99. Participants were excluded if any of the following was met: (1) mean frame-wise displacement >0.3 mm, (2) any frame-wise displacement >5 mm, or (3) outliers >30% of the whole sample. This led to 12 participants being excluded (11 PD). Therefore, 91 patients with PD (16 PD-VH and 75 PD-non-VH) and 32 controls are included. Note that our sample includes patients that overlap with other reports from our centre. Slight differences in included patients are caused by exclusions such as head movement and quality control that differ between studies.

All volumes of raw DWI datasets were visually inspected and evaluated for artefact; only scans with <15 volumes containing artefacts100 were included in subsequent structural analyses, resulting in further 5 PD and 2 control participants being excluded.

Preprocessing of rsfMRI data was performed as described previously101. In brief, we used fMRIPrep 1.5.0102 and discarded the first 4 volumes to allow steady-state equilibrium. Functional data were slice-time corrected using 3dTshift from AFNI103 and motion corrected using mcflirt104. Distortion correction was performed using TOPUP105. This was followed by co-registration to the corresponding T1-weighted image using boundary-based registration with six degrees of freedom106. Motion correcting transformations, field distortion correcting warp, BOLD-to-T1w transformation and T1w-to-template (MNI) warp were concatenated and applied in a single step using antsApplyTransforms (ANTs v2.1.0) using Lanczos interpolation. Physiological noise regressors were extracted applying CompCor107. Spurious sources of signal were removed through linear regression: six motion parameters, mean signal from white matter and cerebrospinal fluid. We did not regress global signal given the lack of consensus and potential to distort group differences78.

Preprocessing of diffusion-weighted images was performed in MRtrix3.0108 using dwipreproc, with denoising109, removal of Gibbs ringing artefacts110, eddy-current and motion correction111 and bias field correction112.

### Parcellation

To construct functional and structural connectivity matrices, each participant’s T1-weighted image was parcellated into 200 cortical and 32 subcortical regions of interest (ROIs) using the Schaefer113 and Tian parcellations114, respectively. Parcellations in the order of 200 regions result in connectomes with the highest representativeness115,116 and the combined Schaefer-232 parcellation used here, is considered optimal across structural and functional connectomes115. We used the same parcellation to construct functional and structural connectivity matrices for each participant. To ensure robustness of results, analyses were replicated using the finer-grained Schaefer/Tian parcellations with 400 cortical and 54 subcortical ROIs, respectively.

### Dynamic functional connectivity analysis

Dynamic connectivity matrices were derived using an overlapping sliding-window approach10 with windows of 44 s duration (63*TR, within the recommended range10) in steps of 1 repetition size (63 windows 44 s each) (Fig. 1a). A 232*232 weighted adjacency matrix representing the functional connectome for that time point was calculated for each window.

We then identified states of higher integration or segregation using a “cartographic profile”12,18,20,117. At each time point, the asymmetric algorithm of Rubinov and Sporns118 was used to identify network modules by applying the community Louvain algorithm, which iteratively evaluates different ways of assigning nodes to modules, in order to maximise the resulting modularity function Q:

$$Q=\frac{1}{{\upsilon }^{+}}\mathop{\sum}\limits_{{ij}}\left({{w}_{{ij}}}^{+}-{{e}_{{ij}}}^{+}\right){\delta }_{{M}_{i}{M}_{j}}-\frac{1}{{\upsilon }^{+}+{\upsilon }^{-}}\left({{w}_{{ij}}}^{-}-{{e}_{{ij}}}^{-}\right){\delta }_{{M}_{i}{M}_{j}}$$
(1)

where υ is the total weight of the graph (sum of all the graph’s edges), wij is the signed weight of the edge between nodes i and j, eij is the weight of an edge divided by the total weight of the graph (superscripts denote + positive and − negative edges), and δMiMj is set to 1 when nodes i and j are in the same module and 0 otherwise. We performed 100 iterations for each time-resolved network with module size resolution parameter γ set at the default γ = 1.

We calculated participation coefficient and within-degree Z-score for each node using the Brain Connectivity Toolbox. Participation coefficient was calculated as:

$${P}_{i}=1-\mathop{\sum }\limits_{s=1}^{M}{\left(\frac{{\kappa }_{{is}}}{{k}_{i}}\right)}^{2}$$
(2)

where κis is the strength of positive connections between node i and other nodes in module s; ki is the strength of all its positive connections; and M is the number of modules in the network, as identified by the modularity detection algorithm. The participation coefficient ranges between zero (no connections with other modules) and one (equal connections to all other modules). High mean participation coefficient within a network implies higher levels of integration between-modules.

The within-module degree Z-score Zi was calculated as:

$${z}_{i}=\frac{{\kappa }_{{is}}-{\bar{\kappa }}_{{is}}}{{\sigma }_{{\kappa }_{{is}}}}$$
(3)

where κis is the strength of connections between node i and other nodes in module s, and $$\bar{\kappa }$$is and σκis are, respectively, the average and the standard deviation of κis over all nodes belonging to module s.

Joint histograms of participation coefficient and within-module Z-score were then derived for each time point12 and for each participant. The cluster with the higher average participation coefficient was defined as the “Integrated” state and the cluster with the lower average participation coefficient as the “Segregated” state, as previously described12,18,20. K-means clustering was then performed and assigned each dynamic functional connectivity matrix to one of two clusters (Integrated vs Segregated)12,18,20 (Fig. 1a). K = 2 clusters was also best performing in data-driven evaluation (Supplementary Fig. 1).

We calculated: (1) proportion of time spent in each state as the number of timepoints within each state divided by number of total timepoints(63), (2) average dwell time as the number of consecutive windows/timepoints belonging to each state and (3) number of transitions as the number of transitions from one state to the other; transitions were further divided into transitions from integrated-to-segregated and from segregated-to-integrated states.

### Structural network construction

After DWI-image preprocessing, diffusion tensor metrics were calculated for each participant and constrained spherical de-convolution performed119 followed by anatomically constrained tractography (10 million streamlines)120 and spherical de-convolution-informed filtering of tractograms (SIFT2)121. The resulting set of streamlines, weighted by a cross-sectional multiplier, was used to construct the structural brain network as a 232*232 undirected weighted connectivity matrix.

### Network control analysis

We examined how the structural brain network of each participant, composed of white matter tracts, constrains the brain in transitioning from one state of functional connectivity (Integrated or Segregated) to the other. To do this, we used a linear time-invariance network model, as previously detailed29,31,50. This can describe neural states as simulated states (x) of a network with n nodes over time steps t using:

$$x\left(t+1\right)={{{{{{\rm{A}}}}}}x}\left(t\right)+{{{{{{\rm{B}}}}}}u}\left(t\right)$$
(4)

where x(t) is a vector (1*n nodes) that represents the brain state at given time t, n is the number of nodes (232 ROIs), matrix A represents the structural connectome n*n (normalised to ensure stability31,32), matrix B is the matrix of control nodes for the network with n*n dimensions and u(t) is the control energy applied for each node at a given time t. In all analyses, we did not constrain the number of nodes that could be controlled, therefore B is an identity matrix.

This model can be used to derive the structural control energy necessary to transition from an initial state x(0) to a target state x(T) where T = 1 is the control horizon31,122 as:

$${{\min }}_{u}{\int }_{0}^{T}{\left({x}_{{{{{{\rm{T}}}}}}}-x\left(t\right)\right)}^{{\prime} }S\left({x}_{{{{{{\rm{T}}}}}}}-x\left(t\right)\right)+\rho u{\left(t\right)}^{{\prime} }t\left(t\right){dt}$$
(5)

where xT is the target state (1*n vector where n is the number of nodes), S is the diagonal n*n matrix that selects a subset of states to constrain (here the identity matrix), ρ is the importance of the input penalty to the state penalty (here ρ = 1) and T is the control horizon.

Importantly, this formalism does not prescribe how the initial “brain state” x(0) and target state x(T) are identified: both data-driven and pre-specified states have been used33,35. Here, our goal is to provide a mechanistic understanding of dynamic transitions between the Integrated and Segregated states of dynamic functional connectivity. Since the network control theory model requires each state to be represented as a 1*232 vector, we represented the Integrated and Segregated states by their sum connectivity profiles (or “connectivity density”), comprised of the sum of the connection weights (Pearson correlation coefficient) from each node to all other nodes; this was calculated separately for each state.

We then used this equation to calculate the control energy to be applied to each node of the network to: (1) transition from the integrated-to-segregated state (using x0 (baseline state), the sum connectivity vector of the Integrated state; and xT (target state), the sum connectivity vector of the Segregated state), (2) transition from the segregated-to-integrated state, using as x0 the sum connectivity vector of the Segregated and state xT, the sum connectivity vector of the Integrated state, and (3) persist within the Integrated or within the Segregated state (i.e. transition from one state to itself), using the sum connectivity vector for that state for both x0 and xT (Fig. 1b). A sum of the control energies to be applied across all nodes of the network represents the minimal energy for the specific transition. Thereby, minimal transition and persistence energies were calculated for each individual’s own Integrated and Segregated functional state by capitalising on the availability of both functional and structural data for each individual.

We also identified which brain regions contribute more to the transition from the Integrated-to-Segregated state (which differed between PD-VH and PD-non-VH), or which nodes require more energy to be applied to them in order to transition: high contributors to the state transition were defined as the top 20% of regions.

### Statistics and reproducibility

Between-group differences in clinical characteristics and temporal properties of dynamic states were assessed using ANOVA (post hoc Tukey) or t-tests for normally distributed and Kruskal–Wallis (post hoc Dunn) or Mann–Whitney for non-normally distributed variables (normality assessed using Shapiro-Wilk test and visual inspection). Statistical significance threshold p < 0.05. Differences in transition and persistence energy between PD-VH vs PD-non-VH were performed using repeated measures ANOVA (p < 0.05).

In addition, we investigated whether each of the two states significantly differed across groups using network-based statistics (NBS)123. A general linear model was used with PD-VH versus PD-non-VH and PD versus controls as contrasts of interest and age and total intracranial volume as covariates. Permutation testing with unpaired t-tests was performed (5000 permutations), calculating a test statistic for each connection. An a priori threshold of t = 2.7 was applied based on our sample size and family-wise error rate (FWE) of p < 0.05.

#### Correlation with Neurotransmitter systems

We investigated whether temporal changes in functional connectivity were associated with specific neurotransmitter systems (Fig. 1c). First, we calculated the regional control energy needed to transition towards and persist within a state that was more predominant in PD-VH. This was expressed as a vector 1*232 with one control energy value per node. Neurotransmitter profiles were extracted for each of the 232 ROIs from publically-available maps using JuSpace124:

• Serotonin receptors 5-HT1A, 5-HT1B, 5-HT2A based on carbonyl-(11)C]WAY-100635, [(11)C]P943, [(18)F]altanseri templates125.

• D1 receptors based on the D1R-selective [11C]SCH23390 template126.

• D2/3 receptors based on the [(11)C]raclopride template127.

• and GABAa receptors based on the (11C)flumazenil template128.

Each of the templates was registered to MNl space and parcellated with the Schaefer-232 atlas and mean values of binding potential were extracted from each ROI using the built-in JuSpace function124.

Expression profiles for genes of noradrenergic, cholinergic (nicotinic and muscarinic), dopaminergic and serotoninergic receptors were obtained using data from the Allen Human Brain Atlas (AHBA)52, with preprocessing as recently described129. We extracted and mapped gene expression data to the 232 ROIs of our parcellation using abagen130. Data was pooled between homologous cortical regions to ensure adequate coverage of both left (data from six donors) and right hemisphere (data from two donors). Distances between samples were evaluated on the cortical surface with a 2 mm distance threshold. Probe-to-gene annotations were updated in Re-Annotator131. Only probes where expression measures were above a background threshold in more than 50% of samples were selected. A representative probe for a gene was selected based on highest intensity. Gene expression data were normalised across the cortex using scaled, outlier-robust sigmoid normalisation. 15,745 genes survived these preprocessing and quality assurance steps. Expression profiles for 31 pre-selected genes (Supplementary Table 2) encoding receptors for noradrenaline, acetylcholine, dopamine and serotonin were extracted for each of the 232 ROIs.

We correlated regional control energy with (1) regional receptor density profiles for serotonin (5HT1a, 5HT2a and 5HT1b), dopamine (D1 and D2) and GABA receptors, and (2) regional gene expression for 31 pre-selected genes. The significance of correspondence between regional control energy and regional neurotransmitter density/gene expression was estimated using a spatial permutation test which generates randomly rotated brain maps whilst preserving spatial covariance132. We performed 1000 random spatial permutations133 and calculated the Spearman correlation coefficient between extracted regional control energy values and neurotransmitter maps to build a null distribution. The permutation-based p-value (pspin) was calculated as the proportion of times that the null correlation coefficients were greater than the empirical coefficients132,133. Derived pspin values were then corrected for multiple comparisons (Benjamini Hochberg; FDR-corrected values denoted as qspin).

Statistical analyses were performed in Python 3 (Jupyter Lab v1.2.6).

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.