Does vestibular motion perception correlate with axonal pathways stimulated by subthalamic deep brain stimulation in Parkinson's disease?

Perception of our linear motion – heading – is critical for postural control, gait, and locomotion, and it is impaired in Parkinson’s Disease (PD). Deep brain stimulation (DBS) has variable effects on vestibular heading perception, depending on the location of the electrodes within the subthalamic nucleus (STN). Here, we aimed to �nd the anatomical correlates of heading perception in PD. Fourteen PD participants with bilateral STN DBS performed a two-alternative forced-choice discrimination task where a motion platform delivered translational forward movements with a heading angle varying between 0 and 30 degrees to the left or to the right with respect to the straight-ahead direction. Using psychometric curves, we derived the heading discrimination threshold angle of each patient from the response data. We created patient-specic DBS models and calculated the percentages of stimulated axonal pathways that are anatomically adjacent to the STN and known to play a major role in vestibular information processing. We performed correlation analyses to investigate the extent of these white matter tracts’ involvement in heading perception. Signi�cant positive correlations were identi�ed between improved heading discrimination for rightward heading and the percentage of activated streamlines of the contralateral hyperdirect, pallido-subthalamic, and subthalamo-pallidal pathways. The hyperdirect pathways are thought to provide top-down control over STN connections to the cerebellum. In addition, STN may also antidromically activate collaterals of hyperdirect pathway that projects to the precerebellar pontine nuclei. In select cases there was strong activation of the cerebello-thalamic projections, but it was not consistently present in all participants. Large volumetric overlap between the volume of tissue activation and the STN in the left hemisphere positively impacted rightward heading perception. Altogether, the results suggest heavy involvement of basal ganglia cerebellar network in STN-induced modulation of vestibular heading perception in PD.


Introduction
Postural instability and navigational de cits are typical in Parkinson's Disease (PD), contributing to fall-related morbidity [1][2][3][4].The ability to perceive self linear motion, also known as heading perception, is instrumental for maintaining gait and postural stability during locomotion.A recent study found a severitydependent impairment in heading perception in PD [5].The impairment was prominent when the participants relied on vestibular sensory information, but there were no signi cant effects on the visually cued heading perception.Abnormal heading perception was correlated with veering, increased falls, and gait impairments in PD [5].Deep brain stimulation (DBS) of the subthalamic nucleus region (STN), which is known to improve motor symptoms [6], also improves deteriorated heading perception [7].The hypothesis describing these ndings is that the effects of STN DBS on vestibular heading perception depend on two factors: 1) the speci c location of the active electrode contact within the STN; and 2) modulation of axonal pathways such as the cerebello-thalamic pathway and the hyperdirect pathway, that are anatomically in close proximity to the STN, which are implicated in vestibular information ow [8][9][10].
The premise of the hypothesis originates from the connectivity patterns of the STN.DBS of the ventral STN is associated with blood ow changes in the premotor cortex, while dorsal STN DBS correlates with changes in the discharge of the anterior cerebellar vermis [11].The dorsal STN also projects to the pedunculopontine nucleus, a collection of brainstem cholinergic neurons [12].The modulation of pedunculopontine nucleus is known to improve gait and postural instability in PD [13].Stimulation of rodent subthalamic region modulates the activity of the cerebellar neurons [14,15].The cerebellar modulation through subthalamic stimulation possibly happens via connections of dorsal subthalamus to the deep cerebellar nuclei by the way of pedunculopontine nucleus [16][17][18][19][20][21] or pontine gray [22] (red arrows, Fig 1).Downstream from the subthalamo-ponto-cerebellar connections is the cerebello-thalamic pathway.This pathway, forming a cerebellar out ow, connects the vestibular nuclei and deep cerebellar nuclei to the thalamus [23][24][25] and then to the parieto-temporal cortex [26], the cortical region that is instrumental for vestibular heading perception [27,28] (blue arrow, Fig 1).The cerebello-thalamic pathway is in the physical vicinity of the STN, initially in medial, posterior, and then dorsal aspect of the nucleus.Another pathway of interest involves the orthodromic activation of the hyperdirect pathway, which also projects to the precerebellar nuclei and then to the cerebellum (green arrows in Fig 1).
In our previous experiments examined effects of STN DBS on vestibular and visual heading perception in a controlled experiments using state-of-art sixdegree-of-freedom motion platform (i.e., hexapod, Moog, Aurora, NY) and immersive virtual reality goggles (Fig. 2A,B) [7,29].We found improvement in vestibular heading response accuracy in PD when STN DBS was turned on.This DBS-related improvement was more prominent in the rightward motion direction (Fig. 2C, see [7] for statistics).In line with this nding, a signi cant reduction in heading direction threshold in the rightward direction was detected in PD with DBS-ON (Fig. 2E).The thresholds of PD, which declined as a result of DBS resulting in better discrimination, were comparable to healthy controls at the group level (Fig. 2E).Also, STN DBS improved the goodness of t of psychometric curves in PD [7].For visual heading perception, the performance of PD in DBS-OFF condition was comparable to that of controls as depicted by the group psychometric curves plotted for visual heading perception in Fig. 2D and Fig. 2E.DBS did not affect the visual heading discrimination thresholds in PD (Fig. 2F, see [7] for statistics).Furthermore, vestibular heading response accuracy and discrimination threshold were signi cantly correlated with the disease duration tremor severity [5].
Utilizing patient-speci c DBS models, we identi ed an association between the change in vestibular heading perception and modulation of the dorsal STN, supporting the rst half of our hypothesis [7].In addition to the effects of the dorsal STN DBS on cerebellum, the stimulating electrical eld may modulate a number of other neural pathways in the vicinity of the STN.These pathways include the hyperdirect and cerebello-thalamic pathways.With the current study, we thoroughly examined the neural correlates of heading perception using patient and hemisphere-speci c DBS models and investigated the axonal pathways that are associated with improved heading perception in PD.We speci cally tested the hypothesis that STN DBS modulates vestibular heading perception via anatomically adjacent white matter tracts such as the cerebello-thalamic and hyperdirect pathways, which have been implicated in the transmission and modi cation of the vestibular information involved in accurate heading perception.These effects could be manifested by orthodromic activation of the cerebello-thalamic bers and antidromic activation of the hyperdirect pathway.As a comparison to the benchmark assessment of PD symptoms, we also examined the correlations between the motor improvements (i.e., UPDRS-III scores) and white matter tract activation of these pathways.
We hypothesized that our methodology combining an objective assessment of heading perception and the use anatomically patient-speci c DBS models may improve the accuracy in monitoring of the stimulation-related effects on complex PD symptoms.

Subjects
We studied 13 PD (all male, mean ± SD age 65.54 ± 8.30 years).The patients had Hoehn and Yahr stage 2-4 when off medication and were stable on antiparkinsonian medication at the time of the study with an average 595.62±425.83mg Levodopa Equivalent Dose (LED) of daily dopaminergic medications.
The study excluded the patients with vestibular or visual dysfunciton, dementia, uncontrolled depression or anxiety, and atypical parkinsonism.The baseline UPDRS-III scores of the cohort with dopaminergic medication but without stimulation was 39.38±12.66.Demographic and clinical information of PD subjects is depicted in Table 1.Patients were treated with STN DBS for an average of 3.35±2.64years.Average UPDRS-III score with DBS and dopaminergic medication was 13.08±6.79.All patients except for PD16 had Medtronic Activa PC system implemented with 3389 leads.PD16 had an Abbott In nity system with 6171 leads.All patients had bilateral STN DBS.Clinically optimal DBS settings were used during the study (Table 1).
All patients performed the experiment under DBS-ON and DBS-OFF conditions, in a randomized order.Two sessions were done within 2-hour time frame of their medication, separated by 20 minutes.All participants had normal vestibular function tested clinically using heave (otolith function) and rotational (semicircular canals function) head impulses.Joint position and tuning fork test revealed normal proprioceptive function.PD participants took their routine doses of antiparkinsonian medications during the experiment.All subjects provided written informed consent that was adherent to the Declaration of Helsinki.
The Institutional Review Board approved the research protocol and the consent form of the Louis Stokes Cleveland VA Medical Center and University Hospitals Cleveland Medical Center.

Patient-speci c DBS Models and Metrics:
We used StimVision, an academic DBS research software, to develop a 3D representation of the DBS system implanted in each patient's brain [30,31].
StimVision models the simulated volumes of the STN as well as the subcortical brain regions and the axonal pathways in the vicinity of the STN that are theoretically activated by DBS.The models used the patient's MRI images, active electrode contacts, and stimulation settings listed in Table 1.These models quantify the volume of the activated brain tissue (VTA) and its overlap with anatomically realistic axonal pathway models [7].
DBS models used in this study were based on the clinically optimal stimulation settings used at the time of the study for each patient.These models provided the following metrics: (i) VTA (mm 3 ), (ii) the overlapping VTA and the STN volume (mm 3 ), (iii) Euclidean distance between the centers of the STN and the total volume of activated brain tissue (mm), as well as the distances between the centers of the STN and the VTA along the (iv) x, (v) y, and (vi) z axes (mm).
It is important to note that -x corresponds to lateral direction for the left hemisphere and medial direction for the right hemisphere; +x corresponds to the medial direction for the left hemisphere and lateral direction for the right hemisphere.For both hemispheres +y designates anterior while -y designates posterior direction.Similarly, independent of the hemisphere, +z represents dorsal and -z represents ventral orientations.Therefore, for the left brain, a negative VTA-STN distance along the x-axis means that VTA is lateral to the STN whereas a positive value indicates that VTA is medial to the STN.For the right brain, a negative VTA-STN distance along the x-axis means that VTA is medial to the STN, whereas a positive value means that VTA is lateral to the STN.
A negative VTA-STN distance along the y-axis means that VTA is posterior to the STN and a positive value means that VTA is anterior to the STN.A negative VTA-STN distance along the z-axis means that VTA is ventral to the STN while a positive value means that VTA is dorsal to the STN.
In addition to the VTA-based metrics, StimVision provided the percentage of stimulated streamlines of the following pathways: (vii) the ansa lenticularis and (viii) the lenticular fasciculus (together called the thalamic fasciculus or pallidothalamic pathway); (ix) the cerebello-thalamic pathway; the pallidosubtahalmic and subthalamo-pallidal pathways connecting (x) the globus pallidum (GP) and the STN, (xi) the STN and GP; (xii) the primary motor cortex (M1)-HDP, (xiii) premotor-HDP, and (xiv) the supplementary motor area (SMA)-HDP, which are parts of the hyperdirect pathway that runs from the frontal cortex to the STN, putatively carrying motor commands.An example patient-speci c DBS model is shown in Fig. 3A with orange streamlines representing the cerebello-thalamic pathway, blue streamlines representing the pallido-subtahalmic and subthalamo-pallidal pathways, and magenta streamlines representing the hyperdirect pathway.Table 2 summarizes the VTA-based metrics and the percentages of activated streamlines of the aforementioned pathways for each patient.

Experimental protocol and data analysis:
A two-alternative-forced-choice task was employed to quantitatively measure vestibular heading perception using en bloc body motion platform, hexapod (Moog, North Aurora, NY) (Fig. 2A).Our previous reports provide the detailed information on our experimental protocol and data analysis [7,29].In summary, the task had a total of 99 trials, which were comprised of a step of forward movement in a heading direction randomly chosen from 0°, 5°, 10°, 20°, and 30° degrees to the right (indicated by positive degrees) or to the left (indicated by negative degrees) as can be seen in Fig. 2A.The subjects used a hand-held input response device to report whether the perceived movement was rightward versus leftward in relation to their perceived straight-ahead.To evaluate the overall performance, we calculated the percent correct response of each patient for leftward and rightward translations using the raw choice data.Results are listed in Table 3 in "Accuracy" columns for DBS-OFF and DBS-ON conditions.We then carried out a psychometric analysis to estimate each patient's discrimination threshold angle (in degrees) by tting a Weibull cumulative distribution to the percent correct response data.Low discrimination threshold angles represent high performance in discriminating translation direction.R 2 values of patient-speci c psychometric model ts were also calculated as a measure of noise in the vestibular heading perception.R 2 values vary with a range between zero and one.Low R 2 values represent a perception trend that do not follow the expected S-shaped psychometric curve.In other words, for patients with low R 2 values, incremental increase in heading direction angles does not translate to a gradual improvement in the vestibular perception performance normally observed in an age-matched control group [1,7,29].This results in relatively atter psychometric curve ts with values closer to zero.Vestibular heading parameters were calculated independently for the left and the right direction.Table 3 lists the threshold and R 2 parameters of each patient under DBS-OFF or DBS-ON conditions.
We designated the discrimination threshold parameter as the benchmark for evaluating heading perception under the two DBS conditions and investigating its anatomical correlates in PD because vestibular heading perception impairment in PD has been shown to be best captured by this parameter.This impairment is shown in Fig. 2C by group-level psychometric curves and in Fig. 2E by discrimination threshold distributions of subject groups, demonstrating signi cant vestibular heading perception decline for PD in DBS-OFF.
We also assessed the visual heading perception of the same cohort using the experimental set-up shown in Fig. 2B.In summary, a 3D optical ow pattern was generated via virtual reality (VR) goggles, mimicking the linear translations used in vestibular heading task.The heading angle in the visual heading experiment was equally randomized across trials at 0°, 5°, 10°, 15°, 20°, 25°, and 30° to the right or left (Fig. 2B).The subjects used a joystick to report their responses.Further details can be found in our previous reports [7,29].Heading perception cued visually by optic ow stimuli remained intact in PD with DBS-OFF, and no signi cant effect of DBS was identi ed as seen in the psychometric curves in Fig. 2D and discrimination threshold distributions in Fig. 2E.When compared to the results we obtained from the vestibular heading experiment (compare Fig. 2B to Fig. 2A, and Fig. 2D to Fig. 2C) we observed that visual heading was not able to tease apart the effects of PD or DBS.Hence, vestibular heading parameters were selected for the following correlation analyses.

DBS-related Changes in the Vestibular Heading Perception vs. DBS Metrics
We tested the correlations between the performance changes of the patients in the vestibular heading perception due to DBS and their DBS metrics derived from the anatomically patient-speci c volume conductor models of the stimulation.To measure the change in vestibular heading, psychometric parameters estimated from the behavioral data recorded in DBS-OFF condition were subtracted from the ones estimated from the DBS-ON condition at the patient level (Table 3).Constructed delta values of percent response accuracy, discrimination threshold, and R 2 were then included in the correlation analysis with the DBS metrics listed in the section above (Table 2).
Selected DBS metrics as well as the vestibular heading parameters were speci c to the left and the right hemisphere and heading direction, respectively, enabling us to test the ipsilateral and contralateral effects of DBS on vestibular heading in the left and right direction.Because the data did not meet normality assumptions of Pearson correlation, we used the Spearman's rank-order correlation.A correlation was considered statistically signi cant if the p-value is lower than 0.05 (two-tailed).We also calculated the correlation coe cients (Spearman's r) and p-values corrected for age, disease duration, and asymmetry index for the UPDRS-III, which was derived by dividing UPDRS-III left-sided total score by right-sided total score for each patient.
To verify that signi cant correlations were not driven by outliers, correlation analyses were carried out after excluding the data points following the interquartile range rule.Values were excluded from the analyses if they were larger than the 1.5 times of the interquartile range above the third quartile, or lower than the 1.5 times of the interquartile range below the rst quartile.These data points were the discrimination threshold parameters of the patients, whose heading perception in that particular direction was severely impaired (PD05 and PD14 for left, PD06 and PD11 for rightward heading) to the degree that the response data did not t to the psychometric function that is used to estimate the threshold parameters.Because of the lack of convergence, threshold parameters in those cases took extreme values [7].Hence, these values had to be excluded from the analyses and the related visualizations.Due to the study's limited sample size and exploratory nature, p values were reported as uncorrected for multiple comparisons.

DBS-related Changes in UPDRS-III Scores vs. DBS Metrics
As a secondary analysis, we also investigated the relationship between stimulation metrics and the change in UPDRS-III [34] scores due to DBS.For each patient, UPDRS-III scores evaluated during stimulation were subtracted from the baseline scores evaluated when DBS devices were turned off.We included the following UPDRS-III scores in the analysis: total UPDRS-III score; total UPDRS-III score of the left extremities; total UPDRS score of the right extremities; tremor severity as measured with the sum of items 20 and 21; rigidity severity as measured with the item 22; severity of axial symptoms as measured with the sum of items 18-20, 22, and 27-31; and posture and gait-related score (i.e.sum of items [27][28][29][30].Table 4 lists these scores for patients in DBS-OFF and DBS-ON conditions.DBS metrics explained above and listed in Table 2 were included in the correlation analysis.

Results
Our goal was to test the hypothesis that the effects of STN DBS on vestibular heading perception depend on the speci c location of the active electrode contact within the STN and the modulation of the white-matter pathways in the vicinity of the STN.Our recent study examined the rst part of the hypothesis and the ndings suggested that stimulating the dorsal subthalamic region correlates with vestibular heading perception [7].Visual heading perception was minimally affected in PD; and DBS did not create a signi cant effect on heading motion perception cued by optic ow [7,29].Here, we examine the second part of our hypothesis and test if STN DBS induced activations of white-matter pathways create the change we observed vestibular heading perception of subjects with PD.An example patient-speci c DBS model is displayed in Fig. 3A with orange streamlines depicting the cerebellothalamic tract, magenta streamlines depicting the hyperdirect pathway, and blue streamlines depicting the connections between the STN and the globus pallidus.

DBS-related changes in vestibular heading perception vs. left hemisphere DBS metrics
A correlation analysis was carried out to investigate the association between DBS metrics and the change in vestibular heading parameters induced by stimulation after removing the two extreme data points, i.e., discrimination thresholds of PD05 and PD14 for left, PD06 and PD11 for rightward heading who had extremely poor performance on heading perception task that psychometric function had a very weak t.Pairwise correlation coe cients are listed in Table 5 with statistically signi cant ones marked in bold.Considering the DBS metrics from left hemisphere, we identi ed a positive association between the improvement in discrimination thresholds in the right-sided heading and the percentages of activated streamlines of the contralateral pallido-subtahalmic and subthalamo-pallidal pathways, GP-STN and STN-GP (r = 0.78 and 0.77, p<0.02) (Scatter plots in Fig. 3B with blue).Both correlations stayed statistically signi cant after controlling for age, disease duration, and UPDRS-III asymmetry index (GP-STN vs. right-sided threshold with age as covariate: r = 0.77, p<0.009; disease duration as covariate: r = 0.79, p<0.007; asymmetry index as covariate: r = 0.75, p<0.013) (STN-GP vs. right-sided threshold with age as covariate: r = 0.74, p<0.015; disease duration as covariate: r = 0.80, p<0.006; asymmetry index as covariate: r = 0.75, p<0.013).Activation of the hyperdirect pathways, M1-HDP, premotor-HDP, and SMA-HDP (r = 0.89, 0.81, and 0.69 in the same order, p<0.02), as shown in scatter plots in Fig. 3B with magenta markers, also exhibited a positive correlation.These correlations also stayed statistically signi cant after controlling for age, disease duration, and UPDRS-III asymmetry index (M1-HDP vs. right-sided threshold with age as covariate: r = 0.89, p<0.001; disease duration as covariate: r = 0.89, p<0.001; asymmetry index as covariate: r = 0.88, p<0.001) (premotor-HDP vs. right-sided threshold with age as covariate: r = 0.82, p<0.005; disease duration as covariate: r = 0.81, p<0.005; asymmetry index as covariate: r = 0.79, p<0.007) (SMA-HDP vs. right-sided threshold with age as covariate: r = 0.70, p<0.023; disease duration as covariate: r = 0.70, p<0.026; asymmetry index as covariate: r = 0.66, p<0.038).No signi cant correlation was detected between the percentages of activated cerebello-thalamic pathway and the DBS-related changes in discrimination thresholds (r = -0.43,p > 0.05, see the scatter plot in Fig. 3B with orange markers).
We also found a signi cant and positive correlation between the VTA-STN overlapping volume and the change in R 2 of psychometric curves that were tted to the left-sided vestibular heading (r = 0.70, p < 0.02; r = 0.69, p<0.03 after controlling for age; r = 0.70, p<0.02 after controlling for disease duration; r = 0.69, p<0.03 after controlling for UPDRS-III asymmetry index).This nding suggests that larger left STN volume stimulated by DBS is associated with increased noise in ipsilateral heading perception (R 2 DBS-OFF > R 2 DBS-ON ).On the other hand, larger left STN volume stimulated by DBS is associated with improved discrimination threshold in the contralateral heading perception (r = 0.65, p = 0.03; r = 0.64, p <0.05 after controlling for age; r = 0.64, p <0.047 after controlling for disease duration; r = 0.63, p <0.05 after controlling for UPDRS-III asymmetry index).Hence, patients with large overlaps between the VTA and the STN in their left hemisphere had a positive impact on contralateral but a negative one on ipsilateral heading perception.Additionally, DBS-induced improvement in right discrimination threshold was correlated with the distance between the centers of VTA and the STN positively along the x-axis (r = 0.70, p = 0.02; r = 0.72, p <0.02 after controlling for age; r = 0.72, p <0.02 after controlling for disease duration; r = 0.70, p <0.03 after controlling for UPDRS-III asymmetry index) and negatively along the y-axis (r = -0.63,p = 0.04; r = -0.63,p <0.05 after controlling for age; r = -0.62,p <0.057 after controlling for disease duration; r = -0.58,p <0.078 after controlling for UPDRS-III asymmetry index).That is to say, discrimination threshold for the right-sided heading improved as the center of VTA was located more medially and posteriorly to the STN in the left hemisphere.

DBS-related changes in vestibular heading perception vs. right hemisphere DBS metrics
Considering the DBS metrics derived from right hemisphere, we found that DBS-induced improvement in left-sided heading discrimination threshold was correlated positively with the distance between the centers of VTA and the STN along the y-axis (r = 0.68, p <0.03; r = 0.79, p <0.07 after controlling for age; r = 0.71, p <0.03 after controlling for disease duration; r = 0.66, p <0.04 after controlling for UPDRS-III asymmetry index; Table 5) and the z-axis (r = 0.81, p <0.004; r = 0.94, p <0.001 after controlling for age; r = 0.81, p <0.005 after controlling for disease duration; r = 0.82, p <0.004 after controlling for UPDRS-III asymmetry index; Table 5).These ndings suggest that left-sided heading discrimination threshold decreased when VTA center was more anterior and dorsal to the STN.
On the other hand, the same DBS metrics had a negative correlation with the R 2 of psychometric curves that were tted to the right-sided vestibular heading (yaxis: r = -0.81,p = 0.004; r = -0.83,p <0.003 after controlling for age; r = -0.83,p <0.003 after controlling for disease duration; r = -0.77,p <0.01 after controlling for UPDRS-III asymmetry index) (z-axis: r = -0.62,p = 0.05; r = -0.66,p <0.04 after controlling for age; r = -0.62,p <0.055 after controlling for disease duration; r = -0.62,p <0.055 after controlling for UPDRS-III asymmetry index Table 5).These negative associations mean that a higher level of noise was observed in the right-sided heading discrimination compared to DBS off when the VTA was located more ventrally and posteriorly to the ipsilateral STN.No association was detected between DBS-related changes in vestibular heading perception and the percentages of activated axonal pathways in the right hemisphere (Table 5).

DBS-related changes in UPDRS-III scores vs. DBS metrics
The improvement in PD motor symptoms due to DBS was calculated by subtracting the UPDRS-III scores obtained from the patients in DBS-on condition from the ones obtained in DBS-OFF condition.Resulting differences with corresponding DBS metrics (Table 3) were included in a correlation analysis.Table 6 shows the pairwise correlation coe cients with statistically signi cant ones written in bold.Considering the left-brain DBS metrics, we rstly identi ed signi cant and positive correlations between gait improvement and the percentages of stimulated GP-STN, STN-GP, M1-HDP, premotor-HDP, and SMA-HDP pathways in the left hemisphere (r = 0.65, 0.64, 0.66, 0.67, and 0.69 in the same order, p <0.01, Table 6).The percentage of stimulated M1-HDP, premotor-HDP, and SMA-HDP pathways in the left hemisphere were also associated with improved axial symptoms (r = 0.56, 0.56 and 0.57 in the same order, p <0.04, Table 6).Secondly, there was a signi cant positive relationship between total left VTA and improvement in gait (r = 0.67, p <0.009, Table 6), as well as axial scores (r = 0.62, p <0.02, Table 6).Gait improvement was also correlated with the VTA-STN overlapping volume in left hemisphere (r = 0.55, p <0.04, Table 6).
Another signi cant correlation was identi ed between the rigidity improvement in the right body and the contralateral VTA-STN difference along the z-axis (r = 0.67, p <0.009, Table 6).This relationship suggests a link between decreased severity of rigidity in the right body and dorsal location of VTA with respect to the contralateral STN.
Considering the right-brain DBS metrics, we detected that left-sided tremor improvement was positively correlated with VTA-STN differences along the y-axis (r = 0.67, p <0.009, Table 6) and z-axis (r = 0.55, p <0.04, Table 6).These correlations suggest that decline in severity of left-sided tremor was associated with more anterior and dorsal placement of VTA with respect to the contralateral STN.Improved right-sided rigidity was also related to the dorsal location of VTA in the ipsilateral hemisphere (r = .58,p <0.03, Table 6).Lastly, decrease in total left-sided UPDRS-III scores were positively correlated with percent activated right premotor-HDP pathway (r = 0.58, p <0.03, Table 6) and the VTA-STN overlapping volume (r = 0.56, p <0.04, Table 6).

Discussion
In this study, we investigated the neural correlates of heading perception in PD by analyzing the associations between DBS-induced changes in heading perception and simulations of axonal pathways activated by DBS.We objectively assessed perception via a two-alternative-forced-choice task and used psychophysics to infer metrics including response accuracy, discrimination threshold, and the noise in discrimination quanti ed by R 2 of the psychometric curve t.Quantitative measures of pathway activations were calculated by creating DBS models speci c to the brain anatomy and DBS settings of 14 PD participants treated with STN DBS.Previous reports with the same cohort revealed a signi cant deterioration in heading perception for both left-and rightsided heading perception [29] and a DBS-related improvement in the right-sided heading perception [7].
We found neural correlates of heading perception in both ipsilateral and contralateral hemispheres which can be further classi ed based on whether the stimulation creates a positive (improving) or negative (deteriorating) effect and whether the motion is leftward or rightward.Contralateral stimulation was found to be associated with improved vestibular heading perception, particularly for the right-sided heading direction, which showed a de cit in PD [29] and a signi cant improvement with STN DBS in the same cohort [7].Discrimination threshold for right-sided motion was ameliorated by larger left STN volume stimulated by DBS and increased percentages of activated streamlines of the left GP-STN, STN-GP, M1-HDP, premotor-HDP, and SMA-HDP pathways.Such contralateral relationship could not be detected for the right hemisphere activations and left-sided heading.While these results might be due to the limited sample size and lack of correction for multiple comparisons, the large difference in magnitude of left-and right-sided correlation coe cients supports the possibility for an intrinsic lateralization of the cortical and subcortical vestibular network for the putative modulatory effect of STN DBS on heading perception, which needs to be tested by future studies.
Ipsilateral stimulation was associated with deteriorated heading perception.We found increased noise in left-sided heading with large overlaps between the left VTA and the STN.Increased noise indicates higher uncertainty in heading perception, which may preclude accurate predictions of motion perception.Our previous report revealed that left-sided heading is less responsive to STN DBS treatment, creating a signi cant left and right asymmetry in heading perception in these patients with STN DBS [7].Therefore, we can predict that DBS VTAs extending to the majority of subthalamic volume might create side effects for leftsided heading perception despite possible positive motor outcomes such as tremor reduction.This may be one of the underlying factors that can explain why clinical DBS settings optimized mainly for motor symptoms may not be always optimal for accurate navigation during locomotion [35][36][37].
The location of active electrode contact seems to be another important factor determining the effect of DBS on heading perception.Our results suggested that the optimal locations of ipsilateral and contralateral stimulation vary for left-and right-sided heading motion perception.For left-sided heading, the observed improvement occurred when VTA center was located more anterior and dorsal to the STN in the contralateral hemisphere.This is an important insight because left is the direction that is impaired most in PD in a severity-dependent matter [29].Left is also the motion direction that current stimulation settings appear to create minimal improvement [7].For right-sided heading, improved discrimination was observed as the center of VTA was located more medially and posteriorly to the STN in the contralateral hemisphere.However, right-sided heading discrimination became noisier when ipsilateral VTA was located more ventrally and posteriorly to the STN.It has been shown by multiple studies that location of STN stimulation determines the clinical outcomes of the therapy [35,[38][39][40].Our ndings provide additional evidence that optimal stimulation location and settings, even in a relatively constrained perception task like ours, depend on a multitude of factors including but not limited to the stimulated hemisphere, as well as the nature and the variation of the behavioral response targeted for improvement.It is also important to remind that DBS settings (frequency and voltage of the stimulation) do not introduce any bias into our results because the values are transformed to standardized DBS metrics by patient-speci c volume conductor models like the one used in this study.Frequency and voltage values are not comparable without considering the location of the electrodes and the entirety of the DBS settings.They become comparable only when they are inserted in complex nonlinear biophysical volume conductor models, that are tted to each patient's anatomy to approximate the anatomical extent of the stimulation [32,33].
The effects of STN DBS on balance, postural stability and falls are unpredictable with con icting results possibly due to stimulation's effect on multiple distinct pathways [41,42].One such major pathway transmitting vestibular information from deep cerebellar nuclei to the thalamus is the cerebello-thalamic pathway.Another important pathway is the subthalamo-ponto-cerebellar pathway that can alter cerebellar output via the precerebellar nuclei which play a major role in transmitting the external and internal information to cerebellar cortex [43].Our results implied that modulatory effect of DBS on vestibular heading perception is likely to occur via the subthalamo-ponto-cerebellar pathway.The modulation of neural activity in deep cerebellar nuclei by STN DBS may happen through the connections of dorsal aspect of the STN to the deep cerebellar nuclei by the way of pedunculopontine nucleus and pontine gray [16][17][18][19][20]22].However, it is important to note that, our results do not entirely exclude the involvement of the cerebello-thalamic pathway.An fMRI study found thalamic BOLD signal changes in a cohort of STN DBS, however could not clarify whether these changes occur as an indirect result of afferent/efferent thalamic activation or contiguous spread from the STN stimulation target, which might be especially the case when the most dorsal contact is used [35].The same study also found a cerebellar BOLD activity as a result of STN DBS possibly due to a transynaptic circuit effect secondary to the changes in motor cortex activity with STN DBS [35].Another alternative supported by the signi cant correlations we observed between heading perception improvement and GP-STN and STN-GP pathway activations is that STN activity can modulate pallidal out ow and its projections to the thalamus [44].Therefore, the thalamus and the cerebellum are likely implicated in heading perception improvement although our data failed to provide a direct correlation with the cerebello-thalamic white matter activation.
Our study also found a signi cant neural correlates in the corticosubthalamic hyperdirect pathway for the right-sided heading perception.The hyperdirect pathway is thought to provide a top-down control over the subthalamic projections to the precerebellar nuclei that receive bottom-up sensory information from the vestibular nuclei in the lower pons and upper medulla.The hyperdirect pathway is also considered to play a major role in the mediation of STN DBS therapeutic effects in PD patients via the antidromic activation of the motor cortex [45][46][47][48][49][50].A recent single-axon tracing study of the corticosubthalamic hyperdirect pathway in cynomolgus monkeys revealed that the hyperdirect pathway is formed by the collaterals of long-ranged corticofugal axons projecting to lower brainstem regions [51].Hence, our ndings provide the evidence that the modulation of vestibular information by STN DBS might follow the same route.Although UPDRS-III is a crude measure for a complete assessment of gait, our signi cant neural correlates in the hyperdirect pathway for both heading perception and gait improvement encourage further studies with detailed analysis of gait and other axial symptoms contributing to locomotion.DBS-related improvements in UPDRS-III scores for tremor and rigidity were not as strongly correlated with the percentage of activated pathways as the heading perception metrics.We think that this may be due to the subjectivity of the UPDRS.Besides, UPDRS evaluation of PD provides a temporally limited snapshot of the severity of the symptoms [52,53] and may therefore fail to re ect the patient's true response to DBS treatment.We need further investigations of the axonal pathways of parkinsonian motor symptoms with instrumented measurements that more accurately and precisely monitor changes in PD symptoms due to STN DBS [53].
In summary, our study revealed that in addition to dorsal STN, and in select cases cerebello-thalamic projects, the hyperdirect pathway has an important role in modulation of the vestibular heading perception in PD.These pathways modulated by STN DBS involve connection of the basal ganglia to the cerebellum via pontine nuclei or direct cerebello-thalamic projections.The study offers further insights into the involvement of the cerebellum in vestibular heading perception in PD.

ID
Putative pathways and mechanisms for the subthalamic nucleus activity to in uence vestibular perception.One mechanism is via the direct orthodromic stimulation of the cerebello-thalamic pathway (blue arrow).This pathway projects to the thalamus and then to the vestibular cerebral cortex.The second mechanism is via the subthalamic nucleus to the precerebellar nuclei, and then to the cerebellum (red arrows).Final pathway involves the orthodromic activation of the hyperdirect pathway, which also projects to the precerebellar nuclei and then to the cerebellum (green arrows).
of the patients derived from the patient-speci c DBS models based on the patients' clinically optimal stimulation settings used at the time of the study.The following metrics were listed for their left and right hemispheres: (i) Euclidean distance between the centers of the STN and the total volume of activated brain tissue (VTA, mm), the distances between the centers of the STN and the VTA along the (ii) x, (iii) y, and (iv) z axes (mm), (v) the volume of VTA (mm 3 ), (vi) the overlapping VTA and the STN volume (mm 3 ), the percentage of stimulated streamlines of the following pathways: (vii) the ansa lenticularis, (viii) the lenticular fasciculus, (ix) the cerebello-thalamic, (x) GP and STN, (xi) STN and GP, (xii) M1-HDP, (xiii) premotor-HDP, (xiv) SMA-HDP pathways.GP: Globus pallidus, M1: Primary motor cortex, SMA: Supplementary motor area.

Figure 3 (
Figure 3 (A) An example patient-speci c DBS model created using StimVision is shown for the left hemisphere.Yellow volume: the thalamus, Green volume: the subthalamic nucleus, Blue volume: the globus pallidus.Magenta streamlines: the hyperdirect pathway, Blue streamlines: pallido-subthalamo and subthalamopallidal pathways, Orange streamlines: the cerebello-thalamic pathway.(B) Statistically signi cant positive associations between theDBS-related improvement in discrimination thresholds in the right-sided heading (positive values on x-axes: better thresholds with DBS-ON) and the percentages of activated streamlines of the contralateral hyperdirect pathways, M1-HDP, premotor-HDP, and SMA-HDP (r = 0.89, 0.81, and 0.69 in the same order, p<0.02) are shown by scatter plots with magenta markers.Statistically signi cant positive correlations between the DBS-related threshold improvement and the percentage of activated streamlines of the pallido-subtahalmic and subthalamo-pallidal pathways, GP-STN and STN-GP, in the left hemisphere (r = 0.78 and 0.77, p<0.02) are shown by scatter plots with blue markers.No signi cant correlation was detected between the percentages of activated cerebello-thalamic pathway and the DBSrelated changes in discrimination thresholds (r = -0.43,p > 0.05) as shown by a scatter plot with orange markers.Spearman's correlation coe cients are displayed with asterisks denoting statistical signi cance of the correlation at p=0.05.

Table 3
Vestibular heading perception parameters of the patients.Response accuracy (percent correct responses), discrimination threshold, and R 2 goodnessof-t of psychometric curves were selected to represent the performance in heading discrimination.These parameters were individually estimated for each subject for left-and right-sided heading.Poor psychometric curve ts with low R 2 values yield discrimination threshold values that lie out of boundary.These values are indicated by >90 in the table and were not included in the correlation analyses.

Table 4
UPDRS-III scores of the patients.Total score: total score of all items; Left total: total score of the left extremities; Right total: total score of the right extremities; Total tremor: tremor severity as measured with the sum of items 20 and 21; Left and Right tremor: total tremor score of left and right extremities; Total rigidity: rigidity severity as measured with the item 22; Left and Right rigidity: total rigidity score of left and right extremities; Total axial: severity of axial symptoms as measured with the sum of items 18-20, 22, and 27-31; Gait: Posture and gait-related score (i.e.sum of items 27-30).

Table 5
Heading perception vs. DBS metrics correlation matrix for the left (top) and the right (bottom) hemisphere.For each hemisphere, correlation analysis was performed with DBS-related parameter differences, which were calculated by subtracting DBS-ON parameters from DBS-OFF parameters (as designated on the leftmost column).Signi cant correlations are printed in bold.P values are larger than .05indicating no statistical signi cance for all other elements of the matrix.The correlation coe cients with asterisks stayed signi cant after controlling for age, disease duration, and UPDRS-III asymmetry index, which is calculated by dividing right-sided UPDRS-III score by left-sided UPDRS-III score.

Table 6 UPDRS
-III scores vs. DBS metrics correlation matrix for the left (top) and the right (bottom) hemisphere.For each hemisphere, correlation analysis was performed with DBS-related differences in the UPDRS-III scores, which were calculated by subtracting DBS-ON scores from DBS-OFF scores (as designated on the leftmost column).Signi cant correlations are printed in bold.P values are larger than .05indicating no statistical signi cance for all other elements of the matrix.