The rostro-caudal gradient in the prefrontal cortex and its modulation by subthalamic deep brain stimulation in Parkinson’s disease

Deep brain stimulation of the subthalamic nucleus (STN-DBS) alleviates motor symptoms in Parkinson’s disease (PD) but also affects the prefrontal cortex (PFC), potentially leading to cognitive side effects. The present study tested alterations within the rostro-caudal hierarchy of neural processing in the PFC induced by STN-DBS in PD. Granger-causality analyses of fast functional near-infrared spectroscopy (fNIRS) measurements were used to infer directed functional connectivity from intrinsic PFC activity in 24 PD patients treated with STN-DBS. Functional connectivity was assessed ON stimulation, in steady-state OFF stimulation and immediately after the stimulator was switched ON again. Results revealed that STN-DBS significantly enhanced the rostro-caudal hierarchical organization of the PFC in patients who had undergone implantation early in the course of the disease, whereas it attenuated the rostro-caudal hierarchy in late-implanted patients. Most crucially, this systematic network effect of STN-DBS was reproducible in the second ON stimulation measurement. Supplemental analyses demonstrated the significance of prefrontal networks for cognitive functions in patients and matched healthy controls. These findings show that the modulation of prefrontal functional networks by STN-DBS is dependent on the disease duration before DBS implantation and suggest a neurophysiological mechanism underlying the side effects on prefrontally-guided cognitive functions observed under STN-DBS.


Results
The analysis workflow, including the measurement protocol and illustration of fNIRS channel positions, is summarized in Fig. 1. The main analyses were conducted by means of two linear mixed-effects models; the first model investigated whether STN-DBS (compared ON vs. OFF) exerted an influence on the rostro-caudal connectivity in the lateral PFC, while the second model (additionally including data from the second ON measurement, cf. Figure 1A) served as an experimental validation of the main finding of a stimulation-induced alteration of the rostro-caudal connectivity. An overview of the fixed and random effects structures of Models 1 and 2 is summarized in Table 1. The concise report of the results below is complemented by a comprehensive report of the respective statistical indices underlying significant effects, estimates, and contrasts in the Supplementary Table S2. Additionally, control analyses including healthy adults (Supplementary Model S1, Supplementary Fig. S2), assessing the role of the rostro-caudal gradient for cognitive functions (Supplementary Model S2, Supplementary  Fig. S3), and investigating the role of gray matter volume as a proxy of disease-induced cortical atrophy for directed functional connectivity (Supplementary Model S3) are available in the Supplementary Information.

STN-DBS modulates hierarchical processing in the PFC (Model 1)
. In Model 1 we tested the hypothesis that STN-DBS has an impact on rostro-caudally directed interactions in the PFC. Understanding remote effects of STN-DBS is however challenged by the multitude of variables that add to the outcome of the treatment, including e.g. the patient's preoperative clinical status 14 , stimulation parameters 37 , electrode positions 38 , and concomitant drug treatment 39,40 . Moreover, higher age and longer disease duration have been discussed to be disadvantageous for the clinical outcome of STN-DBS 34 . The initial fixed effects structure of model 1 (Table 1) therefore included the following factors of interest: stimulation state (ON vs. OFF), direction of influences (rostro-caudal vs. caudo-rostral), and hemisphere (ipsilateral vs. contralateral with respect to the hemisphere of disease onset) and all possible interactions between this set of within-subject-factors as well as each of the following covariates: (I) age at disease onset (initial diagnosis), (II) disease duration before DBS implantation, (III) time since DBS implantation (I-III summing up to the chronological age), (IV) dopaminergic medication in terms of the levodopa equivalent daily dose (LEDD, calculated according to Tomlinson et al. 41 ), and (V) stimulation intensity in terms of the volume of activated tissue (VAT). This extensive model was successively reduced by non-significant fixed effects terms to yield a parsimonious model 42 . Multicollinearity was controlled using the variance inflation factor (VIF, all VIF < 3.6) 43,44 . Correlation coefficients for the covariates are provided in Supplementary Table S3.
Confirming the assumed rostro-caudal hierarchical organization of the PFC, the significant main effect for direction revealed that influences in rostro-caudal direction were generally higher than caudo-rostral influences (F(1,1995.4) = 110.9, p < 0.001, Fig. 2). As STN-DBS is known to have side effects on cognitive functions subserved by the PFC 16,19 , we hypothesized that the prefrontal rostro-caudal gradient could be compromised ON compared to OFF stimulation. While the respective two-way interaction between stimulation state (ON vs. OFF) and the direction of influences (rostro-caudal/caudo-rostral) was not statistically significant on its own (F (1,1995  Scheme of the analysis workflow followed in the present study. Patients watched muted parts of a nature documentary during fNIRS measurements (a). Artifact correction 67 was applied, resulting in perfectly anticorrelated signals of oxygenated and deoxygenated hemoglobin (b). The time-series were standardized before estimation of directed coherence (DC) as a measure of directed interactions between fNIRS channels 69 (c). The maximum DC value in the frequency band between 0.06 and 0.12 Hz was extracted to yield a 2-dimensional, directed connectivity matrix for each measurement (d). According to models postulating a predominant flow of information from rostral to caudal PFC the influences between PFC regions should be significantly stronger in rostral-to-caudal direction than in caudal-to-rostral direction. This prediction was tested by analyzing connections between directly neighboring channels along four rostro-caudal streams comprising four channels each (black and gray arrows in panel e) and covering most of the lateral surface of the PFC in each hemisphere (e). The distinction between rostro-caudal and caudo-rostral connections was represented in the model by the factor direction of influences (f). Influences in both directions were averaged across patients and projected separately on a standard brain surface (g). Table 1. Initial fixed and random effects structure of each model. N.B. Exhaustive models were successively reduced by non-significant higher-order terms to yield a parsimonious model (see Supplementary Table S2 for significant effects). Continuous predictors are underlined. All lower-order terms were included. Random effects were not reduced. dir. direction of influences, LEDD levodopa equivalent daily dose, stim. stimulation state (ON, OFF, and, in model 2, 2nd ON), VAT volume of activated tissue.

Model
Fixed effects terms Random intercepts www.nature.com/scientificreports/ Besides VAT, LEDD was also positively associated with the strength of the rostro-caudal gradient (F(1,1995.4) = 9.6, p = 0.002). However, this two-way interaction between LEDD and the direction of influences was mostly driven by the simple effect of influences in one direction, i.e. LEDD was negatively correlated with caudo-rostrally directed influences, while the relationship between influences in rostro-caudal direction and LEDD failed to reach significance (Fig. 5, Supplementary Table S2).
Albeit weak, a third two-way interaction was present between hemisphere and the direction of influences (F(1,1995.4) = 4.6, p = 0.033). The rostro-caudal gradient appeared to be steeper in the ipsilateral than in the contralateral hemisphere with respect to the hemisphere of disease onset. This within-patient effect hence corroborates the enhancing between-patient effect of the VAT on the rostro-caudal gradient, as VATs were larger in the ipsilateral than in the contralateral hemisphere (mean VAT in ipsilateral hemisphere: 230 mm 3 ; mean VAT in contralateral hemisphere: 174 mm 3 , t(22) = 2.0, p = 0.053). Thus, the hemispheric differences in the gradient may be introduced by the asymmetric stimulation intensities.
Taken together, the key finding of Model 1 constituted a significant modulation effect of STN-DBS on the rostro-caudally directed interactions in the PFC that was moderated by the patients' disease duration before DBS implantation. Given that disease duration before DBS implantation was highly correlated with the overall disease duration (Pearson's r = 0.79, p < 0.001), we conducted a control analysis and refitted the model with (I) the variables disease duration before DBS implantation and time since DBS implantation substituted by the overall disease duration and (II) with all three time-related covariates (age at disease onset, disease duration before DBS implantation and time since DBS implantation) substituted by chronological age. Neither overall disease duration nor chronological age exerted any significant moderator effect (all p > 0.05) on the directed interactions in the PFC, demonstrating that the impact of STN-DBS on the rostro-caudal gradient was indeed specifically dependent on the disease duration before DBS implantation.

Remote effects of STN-DBS on PFC are reproducible (Model 2). As an experimental validation, in
Model 2 we addressed the reproducibility of the modulation effect of STN-DBS on the rostro-caudally directed interactions in the PFC and its dependence on the disease duration before DBS implantation. To this end, the examination followed a fixed protocol with the initial ON measurements always being followed by the subsequent OFF measurements. Precluding that the stimulation-dependent results in Model 1 were simply driven by carry-over effects would hence require to demonstrate that the dependence of the STN-DBS effects on the disease duration before DBS implantation was reversible and would reappear after stimulation was switched on again. In consequence, we fitted Model 2 to the data of the ON, OFF, and ON2 measurements and, as a fixed Granger-causality analysis of directed interactions reveals the rostro-caudal hierarchical organization in the PFC. The significant main effect for direction in the mixed effects model showed that influences from rostral to caudal PFC were stronger than from caudal to rostral (top panel). For cortical projections (bottom panel), directed coherence (DC) values were averaged across hemispheres and projected onto the cortical surface to represent the influences from channels (black dots) toward caudally (left brain) and rostrally (right brain) neighboring channels as indicated by arrows. Darker red colors signify stronger influences in terms of higher DC values. Bars in the top panel represent least square means; error bars indicate 95% confidence intervals; n = 24.  Figure 3. The effect of DBS on rostro-caudally directed interactions in the PFC depends on the disease duration before DBS implantation. The relationship between the rostro-caudal gradient and the disease duration before DBS implantation in the ON stimulation state (top row, n = 24) shows that patients who received DBS early in the course of their disease had a strong gradient that was even stronger than in the OFF stimulation state (middle row, n = 22 www.nature.com/scientificreports/ effect, included the respective three-way interaction between stimulation state, direction of influences and disease duration before DBS implantation as well as all corresponding lower-order terms. As depicted in Fig. 3, the negative correlation between the disease duration before DBS implantation and the rostro-caudal gradient was present in the ON state and absent in the OFF state. Most importantly, it reemerged in the ON2 state (Fig. 3, bottom row), within only a few minutes after the stimulation was switched on again. As the three-way interac-     www.nature.com/scientificreports/ tion closely resembled the pattern observed in Model 1, it hence demonstrated its immediate reproducibility (F(2,2949.6) = 3.2, p = 0.041). Post-hoc comparisons further confirmed that for influences in rostro-caudal direction the effect of disease duration before DBS implantation in the ON and ON2 state was significantly different from the OFF state, while there was no significant difference between the ON and the ON2 state (Fig. 3, Supplementary Table S2). Regarding caudo-rostral influences, there was no significant simple effect of disease duration before DBS implantation in any stimulation state.
In summary, the modulation of directed influences between PFC sub-regions by STN-DBS and its moderation by disease duration before DBS implantation was not only replicable, but also specific to the predominant rostro-caudal direction within the PFC and specific for ON states, arguing for a significant stimulation-induced network effect of STN-DBS on PFC integrity.

Supplemental control analyses.
Healthy participants that were matched to PD patients in terms of age and sex (Supplementary Fig. S1) were assessed in two supplemental analyses. Supplementary Model S1 revealed that the rostro-caudal connectivity gradient was also apparent in healthy controls (Supplementary Fig. S2). Supplementary Model S2 included both PD patients and matched healthy controls and demonstrated that the resting-state connectivity gradient within the rostral PFC was associated with performance in a prefrontally-guided cognitive planning task as well as a more general measure of global cognitive ability (Supplementary Fig. S3). Thus, the present approach consistently detects a rostro-caudal functional network in the PFC that underlies higher cognitive abilities. Another supplemental control analysis testing the predictability of the directed functional connectivity by gray matter volume in the PFC revealed no significant interaction effects, precluding that the variance in the rostro-caudal gradients within the functional networks was significantly driven by differences in cortical atrophy (Supplementary Model S3).

Discussion
The present study revealed that STN-DBS in Parkinson's patients significantly modulates the hierarchical organization of the PFC. Most crucially, this remote network effects of STN-DBS on the PFC depended on disease progression and hence possibly on the level of sustained integrity of nigro-striatal and fronto-striatal circuits: Patients who underwent DBS implantation earlier after disease onset had a stronger rostro-caudal gradient of directed interactions ON versus OFF stimulation. In contrast, patients who received a DBS implantation after longer disease durations showed diminished rostro-caudally directed interactions ON compared to OFF stimulation. Importantly, this effect was clearly reproducible: In the transition when stimulation was switched ON again after steady-state OFF, the dependence of the rostro-caudal gradient in the PFC on the disease duration before DBS implantation re-emerged in the same systematic fashion as before (Fig. 3).
The role of the basal ganglia for the rostro-caudal hierarchy in the PFC. One hypothesis is that the STN-as a major input nucleus of the basal ganglia-plays an important role in integrating sensorimotor information and regulating the activity of two opposing signaling pathways: the direct, movement-facilitating pathway and the indirect, movement-inhibiting pathway 9,45 . Loss of dopaminergic neurons in the substantia nigra pars compacta in Parkinson's disease leads to an excessive activity of the STN and an imbalance in favor of the indirect pathway causing hypokinetic symptoms 9 . DBS is known to elicit action potentials in afferent and efferent axons 37 thus not only exciting downstream neurons in basal ganglia output nuclei but also antidromically modulating cortical neurons projecting (as part of the hyperdirect pathway) to the STN 46 . Although the STN was previously assumed to receive cortical projections only from motor cortices 47 a recent tracer study in macaques revealed topographic projections from various PFC regions (including the dorsolateral PFC) to the dorsomedially located associative functional zone of the STN 48 which could also be reproduced in human imaging studies 2,3,49 . Antidromic activation of the limbic hyperdirect pathway may therefore contribute to the present stimulation-induced changes in the hierarchical organization of the PFC, affecting cognitive functions 4,50 . Alternatively, remote STN-DBS effects on the PFC may be mediated through the downstream nigro-thalamocortical pathway 37 -in particular as the impact of STN-DBS on rostro-caudally directed prefrontal interactions depended on the disease duration before DBS implantation and therefore on the disease progression at the time STN-DBS was initially administered. In Parkinson's disease dopamine depletion often progresses from sensorimotor towards associative/cognitive basal ganglia-thalamocortical circuits and affects cortical afferents in caudal PFC earlier than in rostral PFC 5,39 . The enhancement of directed interactions within lateral PFC by STN-DBS may thus be mediated through the intact associative circuits in early-stage Parkinson's disease, while STN-DBS has debilitating effects on PFC integrity as soon as disease progression has reached associative circuits.

Disease progression impacts on prefrontal effects of STN-DBS. The present results provide new,
complementary evidence suggesting that implantation at an earlier stage of Parkinson's disease may reduce the risk of DBS-induced detrimental cognitive and psychiatric side effects on prefrontal functioning. As the STN-DBS effect on directed prefrontal interactions depended neither on the duration of stimulation, nor on the overall disease duration, nor on the chronological age but only on the disease duration before DBS implantation, this raises the question whether STN-DBS itself or the reduction of dopaminergic medication following STN-DBS may exert preserving effects on the associative basal ganglia-thalamocortical loops 51 . The stimulation-induced decrease of the rostro-caudal gradient with increasing disease duration before DBS implantation suggests that STN-DBS intervention at early-stage Parkinson's disease may contribute to sustained PFC integrity and that the timing of implantation is of essence for the overall outcome of DBS 52 . When patients notice first symptoms of Parkinson's disease, at least 50% of neurons in the substantia nigra are already lost 53 . Animal models of Parkinson's disease further show that STN-DBS can have neuroprotective effects in the substantia nigra 51  www.nature.com/scientificreports/ not confirmed in humans so far 52 , it has been discussed that DBS implantation may have a slowing effect on the progression of neurodegeneration 51 . Finally, a brain in a healthier state may simply cope with and adapt to an extensive intervention like DBS better than a more depleted one as, for instance, the motor, cognitive, and psychiatric symptoms of Parkinson's disease are alleviated by STN-DBS when applied early in the course of the disease 13,15,52 . In line with this, younger patients are known to recover better and have less cognitive decline after surgery than the elderly 54 .
As STN-DBS electrodes were implanted through prefrontal entry points the penetration of the PFC during STN-DBS surgery may also impact on PFC network integrity. However, the present moderation of the rostrocaudal gradient by disease duration before DBS implantation was reversible and only present under active stimulation. It is hence unlikely to be introduced by the surgery itself. Nevertheless, the lesion of the STN caused by electrode implantation is known to have a temporary effect that clinically mimics the effect of stimulation 55 . This so-called stun effect is a transient phenomenon which is apparent within the first postoperative weeks but usually regresses before initial activation of the stimulator. Preliminary results from a follow-up study indicate that the stun effect caused by STN-DBS surgery indeed attenuates the rostro-caudal gradient post-compared to pre-DBS surgery only in patients with long disease durations but not in patients with short disease durations (F. K. Schumacher, V. A. Coenen, C. P. Kaller, unpublished data) reproducing the moderating effect of disease duration before DBS implantation on the rostro-caudal gradient ON stimulation in the current study.

Effects of stimulation intensities and dopamine level. VAT and LEDD both had a general amplify-
ing effect on the strength of the prefrontal gradient. However, the effect of VAT was driven by both increasing rostro-caudal influences and decreasing caudo-rostral influences, while the effect of LEDD solely relied on decreasing influences in caudo-rostral direction (Figs. 4, 5). The mechanisms behind both effects are hence likely to be distinct 40 . Moreover, shifts in network states induced by the systemic application of dopamine are mainly dosage dependent, whereas the VAT effect on cortical networks is probably transduced through parts of the basal ganglia-cortical loops and may also rely on resonance mediated by the direct, indirect, and limbic hyperdirect pathway 2,45 .
Interpreting the effects of VAT and LEDD is limited by the lack of data from patients OFF medication or before DBS implantation. A stronger gradient may in fact be the cause for rather than the result of stronger stimulation amplitudes (i.e. patients having a stronger gradient might need a stronger stimulation to alleviate motor symptoms). The persistent VAT effect OFF stimulation may support this argument but it may likewise reflect plastic changes in network organization or sustained shifts in neurochemical homeostasis 56 .
Finally, the magnitude of the VAT estimates (Supplementary Table S1) indicates that the stimulation directly affected subcortical structures other than the STN in some patients. Besides stimulation intensities, taking locations of active electrode contacts into account in future studies is therefore vital to understand the role of this excessive stimulation.

Limitations.
A possible limitation of the present approach constitutes its reliance on hemodynamic low-frequency oscillations as systemic physiological oscillations (e.g. Mayer-waves 57 ) may partly contribute to the signal variance in the frequency band used here. However, there is increasing evidence that this signal component reflects neuronal activity 58 and conveys information about functional connectivity 59,60 . In addition, we recently demonstrated the robustness of the present approach against physiological noise 35 . The network connections reconstructed here are hence unlikely to reflect mere physiological artifacts but instead represent (direct or indirect) signaling pathways between neuronal populations.
A pivotal question that remains is whether the disruption of the prefrontal hierarchy by STN-DBS is indeed causal for cognitive decline. The present findings suggest that receiving STN-DBS in a more advanced stage of Parkinson's disease may increase the risk of cognitive side-effects because the stimulation disturbs the hierarchical organization in the PFC. Furthermore, the relevance of this hierarchical organization in the PFC for cognitive functioning is demonstrated in the Supplementary Model S2. Yet, the present data do not allow to conclude that effects of STN-DBS on cognitive performance are mediated by its remote effects on the PFC. Resolving this issue would require to simultaneously conduct cognitive assessments and fNIRS measurements repeatedly ON and OFF STN-DBS, which would however likely be confounded by the patients' motor symptoms and challenged by psychometric issues 61 .
Although PD patients were assessed on medication adhering to their usual medication to ensure dopamine levels being as stable and as physiological as possible, it cannot be fully excluded that changes in dopamine over time may have at least partly contributed to the differences ON vs. OFF STN-DBS observed in Model 1. However, these STN-DBS effects on the functional network structure in the PFC were replicated in the second (later) ON stimulation measurement (Model 2; cf. Fig. 3 top and bottom row), thus strongly suggesting that the modulation of the rostro-caudal gradient in the PFC was driven by the experimental variation of the STN stimulation and not by changes in dopamine levels over time.

Conclusion
The present study not only provides novel insights into the remote network effects of STN-DBS but also offers a completely new perspective on the potential neurophysiological mechanisms underlying cognitive and psychiatric side effects of STN-DBS in Parkinson's disease. Specifically, we demonstrated that the rostro-caudal hierarchy in the PFC is compromised by STN stimulation in patients who underwent electrode implantation after longer disease duration. In contrast, stimulation enhanced the prefrontal hierarchy in patients who received DBS early in the course of their disease. In addition, stimulation intensities and dopaminergic drug dosages predicted the strength of the prefrontal hierarchy. Taken together, by allowing to directly monitor the remote network effects www.nature.com/scientificreports/ of STN-DBS the novel approach applied here might provide a promising opportunity for future refinements of DBS in the STN and beyond in terms of a methodological foundation for individually tailored optimization and adjustment of stimulation parameters.

Methods and materials
The study protocol was approved by the ethics committee of the University of Freiburg (vote 410/11) and registered at German Clinical Trials Register (DRKS, www.drks.de, identifier DRKS00003530, date of registration: 10/02/2012). The study was carried out in accordance with the Declaration of Helsinki and the guidelines of the local ethics committee on research involving human participants. All participants gave written informed consent prior to participation.
Participants and procedures. Twenty-six patients with idiopathic Parkinson's disease and implanted STN-DBS participated in the present study. To control for hemispheric differences in disease severity, two patients that had no record of the side of disease onset were excluded from the present analyses. Following a neuropsychological assessment (including the Tower of London task, see below), patients were rated by the UPDRS-III and underwent the fNIRS measurements. After the first fNIRS measurement (12 min, ON stimulation), the stimulator was switched off for approximately 2 h. Of the 24 included patients (6 females, mean age ± SD 61.5 ± 9.9 years), 2 dropped out during this period. The second fNIRS measurement was conducted OFF stimulation for 12 min and was preceded by another UPDRS-III assessment. Four further patients dropped out after the measurement OFF stimulation. In order to capture the transition from OFF to ON stimulation, we conducted a third measurement immediately after the stimulator was switched on again. Taken together, three 12-min fNIRS measurements were acquired (Fig. 1a): first ON stimulation (n = 24), thereafter in steady-state OFF stimulation (after 2 h of rest without stimulation; n = 22) and finally in the transition state immediately after the stimulator was switched back on (ON2, n = 18). During all measurements, patients were watching muted movie parts from the nature documentary 'Earth' 62 ; the order of the movie parts was balanced across patients. To ensure dopamine levels to be as stable and as physiological as possible, patients were told to adhere to their usual medication on the day of study participation and were examined during medical ON periods (see Supplemental  Table S1 for patient characteristics; cf. Fig. 1a for experimental workflow). As a control group, 24 healthy adults were matched to the patients in terms of age and sex ( Supplementary Fig. S1)  Acquisition of fNIRS data. Multi-channel fNIRS was used to record brain activity in the PFC (Fig. 1a) and to explicitly test the hypothesis of rostro-caudally directed interactions as it sampled activation in the PFC at a sufficient temporal resolution of 10 Hz 65 and at a spatial resolution that ensured separation of rostral, middle, and caudal PFC (Fig. 1e). FNIRS data was acquired using an ETG-4000 optical topography system (Hitachi Medical Systems, Japan). Spatial optode arrangement was derived from the system's 3 × 11 grid configuration consisting of 17 emitters and 16 detectors. We modified this probe set by placing 12 emitters and 13 detectors on the forehead (interoptode distance of 3 cm resulting in a diagonal channel distance of 2.1 cm), resulting in 38 channels evenly distributed over the PFC (Fig. 1e). Unused emitter optodes were covered by black caps to avoid crosstalk; recordings were performed in a room without windows and the room lights were switched off during measurements. Grid placement over PFC was standardized across patients (I) by aligning the grid center to the sagittal midline and (II) by positioning the lower center optode at a distance of about 1.5 cm above the nasion. Presentation of the nature video and on-/offset of simultaneous fNIRS recordings were controlled by NBS Presentation software (version 12.2; Neurobehavioral Systems Inc., CA). To prevent artifacts during fNIRS measurement due to head movements, participants' heads were stabilized using a chin rest. Raw data of light intensity changes were converted into hemoglobin concentration changes by in-house Matlab software (version 2012b, The MathWorks, Natick, MA, USA, unpublished tool box) using the modified Beer-Lambert law 66 . Due to the absorption of interfering hairs or saturation of detectors some channels did not contain any signal. The respective time series were interpolated from the surrounding channels using the Matlab 4 griddata method. This affected a total of 15 channels in 9 datasets (out of 2432 channels in 64 datasets; 0.6% of channels). In order to remove motion-induced artifacts, we applied the correlation-based correction method developed by Cui et al. 67 . This method not only effectively removes motion artifacts, but also increases the contrast-to-noise ratio. The resulting data for oxygenated and deoxygenated hemoglobin are perfectly anticorrelated and therefore have identical spectral properties. The time series were standardized for Granger-causality analysis. We refrained from applying further artifact correction methods like filtering or resampling, because such data preprocessing has been shown to produce false positives in Granger-causality analysis 68 . Furthermore, we used a frequencydomain measure of Granger-causality (see below) that allowed avoiding frequency bands prone to physiological noise introduced by respiration and heart-beat (see also Refs. 31,35 ). Further information on the validity of the here applied fNIRS approach on directed functional connectivity can be found in Refs. 31 www.nature.com/scientificreports/ with a model order of 20, corresponding to the past 2 s of the time-series and providing a frequency resolution of the DC estimate of 0.5 Hz. Note, however, that for the Fourier transformation the autoregression coefficients were zero-padded to the length of the time series in order to smooth the spectral estimate. As functional connectivity between different brain areas is apparent in low frequency oscillations 59 , we chose the frequency band between 0.06 and 0.12 Hz and used the maximum DC value in this band for further analysis (see also Refs. 31,35 ).

DBS electrode localizations.
Preoperative T2-weighted MRI and CT scans as well as postoperative axial slabs of CT scans focusing on the subcortical volume around the electrode tips were acquired. Details on imaging parameters varied across patients and can be requested from the authors. Using BRAINSfit software 71 as implemented in 3D slicer (version 4.6.0; www.slice r.org), postoperative CTs were linearly co-registered and fused to preoperative CTs. The fused images were then again linearly co-registered to preoperative MRIs. Preoperative MRIs were nonlinearly warped into International Consortium for Brain Mapping (ICBM) 152 2009b nonlinear asymmetric space using the SyN approach as implemented in Advanced Normalization Tools 72 . Using the Lead-DBS software 73 (version 1.5.1; www.leads uite.io), electrode positions were reconstructed hybridly in native and standard stereotactic space. Renderings of electrode positions in relation to the STN are provided in Supplementary Fig. S4, showing that implanted electrodes mainly resided within the posterior, i.e. the motor subdivision of the STN.

Estimation of the volume of activated tissue (VAT).
To construct a conductor model of the DBS electrode and surrounding tissue, the Medtronic DBS electrode 3391 model was discretized into voxels of 0.22 mm isotropic size. The electrode defined the mid-axis of a volume 101 × 101 × 90 voxels in size. The rest of the space was filled with gray and white matter. Gray matter was defined by the structures STN, red nucleus and internal/ external pallidum as specified by the DISTAL atlas 3 which exactly corresponds to the ICBM 2009b nonlinear template used for normalization. The remaining space was declared as white matter. The volume was converted into a hexaedral mesh using FieldTrip software 74 ; www.field tript oolbo x.org). Conductivities of 0.33 and 0.14 S/m were assigned to gray and white matter respectively. These values are commonly used in neuroscientific modeling studies 75 . For the platinum/iridium contacts and insulated parts of the electrodes, values of 10 8 S/m and 10 -16 S/m were used, respectively. A forward model to obtain the voltage distribution was solved using the SimBio toolbox (Ref. 76 ; https ://www.mrt.uni-jena.de/simbi o/index .php/Main_Page). In case of monopolar stimulation, the surface of the cubic model was used as the cathode. This generated a gradient denoting the voltage distribution for each hexaedral element of the model. The gradient was thresholded for magnitudes > 0.2 V/ mm 2 to define the VAT. The VATs in both hemispheres were substantially correlated (Pearson's r = 0.55, p = 0.007) and were therefore averaged and used as a single predictor in the statistical analysis.
Statistical analyses. DC and between-subject covariates were analyzed in linear mixed effects models using the lme4 package 77 (version 1.1-14) for R statistics (version 3.4.2; http://cran.r-proje ct.org). According to extant models of prefrontal organization 22,23 , we expected influences predominantly in rostro-caudal direction and therefore selected the connections between 4 rostro-caudally adjacent fNIRS channels in 4 parallel rows within each hemisphere for statistical analyses (i.e., resulting in 12 connections per hemisphere; Fig. 1e). Hemispheres were classified into 'ipsilateral' and 'contralateral' with respect to the hemisphere of disease onset. Two linear mixed effects models were computed as summarized in Table 1. Models were analyzed following a top-down procedure 42 : Higher-order fixed-effects interaction terms that did not reach significance (i.e. p > 0.05) were identified using the anova method (Type III F-statistics with Satterthwaite's approximation of degrees of freedom) implemented in the lmerTest package 78 (version 2.0-33) and successively removed to yield a parsimonious model 42 (see Table 1 for the highest-order terms of the initial models and Supplementary Table S2 for the significant highest-order terms of the parsimonious models). Models were fitted with random intercepts for (I) the interaction between participant and stream (identifying channel rows in rostro-caudal direction) and (II) the interaction between participant and level (identifying adjacent channel pairs-i.e. connections-along the rostro-caudal axis) using maximum likelihood estimation. Post-hoc comparisons and calculation of confidence bands were performed using the lsmeans package 79 (version 2.27-2). Multiplicity adjustment was applied using Tukey's method.