The aperiodic exponent of subthalamic field potentials reflects excitation/inhibition balance in Parkinsonism

1Power spectral densities (PSDs) of neural time series, such as electroencephalography (EEG), electrocorticography (ECoG), or local field potentials (LFPs), tend to follow a 1/f power law distribution, where f is frequency, meaning that power is greatest at low frequencies and diminishes rapidly as frequencies increase. In this study, we will refer to the slope of the PSD as the aperiodic exponent. For decades, the aperiodic exponent has been deemed unimportant and was often removed from analyses to emphasise brain oscillations. Only recently did the aperiodic exponent gain more attention and was attributed a physiological meaning. Aperiodic exponents in LFP, EEG, and ECoG recordings vary by age, cortical depth, psychiatric disorders, and Parkinson’s disease (PD). They track sensory stimuli and change with movement. Moreover, the aperiodic exponent was suggested to reflect neuronal spiking, synaptic currents, and excitation-inhibition (E/I) balance, which describes the delicate balance of inhibitory and excitatory synaptic inputs to neurons. The latter is supported by multiple studies showing that aperiodic exponents in non-invasive EEG and invasive LFP measurements were modulated by sleep and anaesthesia, with lower exponents, corresponding to slower decay of power with increasing frequencies, during the conscious state, which is linked with increased excitation. Inversely, higher aperiodic exponents, corresponding to faster decay of power with increasing frequencies, were observed during the unconscious state (NREM sleep, anaesthesia), which is linked with more inhibition. In addition, Gao and colleagues found that theta cycle-modulated E/I changes in the rat hippocampus are reflected in the per-cycle PSD exponent of hippocampal LFPs calculated at different theta phases (peaks or troughs) confirming the E/I hypothesis for LFPs.

2In our study, we seek to test whether the aperiodic exponent of LFPs recorded in the subthalamic nucleus (STN) tracks changes in E/I balance. To this end, we take advantage of the well-characterised rhythmic changes in neuronal firing patterns within the basal ganglia during slow-wave activity (SWA, see Figure 1A) induced in dopamine-depleted rats by general anaesthesia. STN and external globus pallidus (GPe) neurons are rhythmically active in time with cortical SWA in rats rendered Parkinsonian by lesion of midbrain dopamine neurons with 6-hydroxydopamine (6-OHDA) (Figure 1A). STN neurons are predominantly active during the active phase of cortical slow (~1 Hz) oscillations. Inversely, STN neurons reduce their firing around the inactive phase when GPe-Ti (‘type-inactive’) neurons tend to fire most. GPe-Ti neurons largely correspond to prototypic GPe neurons that are GABAergic and project to and inhibit STN; the GPe is considered the primary source of inhibitory inputs to the STN. Based on single-unit activity, we extracted separate periods with high levels of STN excitation or inhibition, and applied the FoooF algorithm to parameterise PSDs of LFPs during both states. Aperiodic exponents of STN-LFPs were consistently modulated with expected differences of the E/I ratio of STN in these states.

3In a second step, we tested whether similar findings can be obtained in human STN-LFP recordings from awake patients with PD. In PD, STN shows exaggerated and synchronised oscillatory activity in the beta range. Dopaminergic medication and deep brain stimulation (DBS) desynchronise STN in the beta range and reduce STN single-unit activity. Here, we compare aperiodic exponents of the STN-LFP ON and OFF dopaminergic medication and ON and OFF DBS. We show that aperiodic exponents of the STN-LFP were increased with both therapies, and these results from PD patients are also consistent with the E/I hypothesis.

4To validate the aperiodic exponent of STN activity as an estimate for E/I changes, we first took advantage of the distinct rhythmic changes in neuronal firing patterns within the basal ganglia during SWA in 6-OHDA-lesioned rats under anaesthesia. During SWA, STN neurons exhibit distinct periodic changes in firing rates, which are tightly linked with the phase of cortical slow (~1 Hz) oscillations that dominate SWA (Figure 1A; ). These changes in STN firing rates have been defined, by us and others, in relation to their major excitatory and inhibitory inputs.

5To contrast STN activity during opposing conditions of E/I balance, we first distinguished 250 ms epochs of ‘high’ and ‘low’ levels of spiking of STN single units during SWA (Figure 1—figure supplement 1B). Because STN and GPe-Ti neurons fire in a near anti-phase relationship during cortical SWA, high- and low-spiking epochs of STN neurons tend to occur in time with, respectively, low and high levels of GPe-Ti spiking (Figure 1B). We assume that, during low and high levels of GPe-Ti spiking, STN neurons receive low and high levels of inhibitory input from the GPe, respectively. Previous studies have shown that during SWA, excitatory input from cortical projection neurons would be in-phase with the high-spiking epochs of STN neurons, and thus, anti-phase to inhibitory inputs from GPe. First, we computed PSDs of STN-LFPs for the two states (high and low STN spiking epochs, Figure 1C) and extracted both aperiodic exponents and average power between 30 and 100 Hz. Aperiodic exponents were smaller in high compared to low STN spiking epochs, consistent with small exponents being generated in conditions of more excitation/less inhibition and vice versa (LME: estimate = 0.12, t = 3.92, p<0.001; Figure 1D). The total power of activities between 30 and 100 Hz in STN-LFP was smaller during low STN spiking epochs compared to high STN spiking epochs (LME: estimate = –0.02, t = –2.34, p=0.02; Figure 1E). Furthermore, the lack of correlations between power and aperiodic exponents suggests that both power and exponents from the same frequency range are dissociable and might contain different information (Spearman; ρ = –0.07, p=0.56 and ρ = –0.18, p=0.14 for high and low STN spiking epochs, respectively). When pooling aperiodic exponents and power from high and low STN spiking epochs, we still did not observe a significant correlation (ρ = –0.15, p=.07).

6Overall, these results from 6-OHDA-lesioned rats suggest that the aperiodic exponent of STN-LFPs is altered according to different levels of STN spiking. The high- and low-spiking epochs of single STN neurons can in turn be ascribed with confidence to an E/I balance that is tipped in favour of excitation and inhibition, respectively. As such, these results support the notion that STN-LFP aperiodic exponents may become valid markers of overall E/I balance in STN.

7After corroborating the link between aperiodic exponents in STN-LFPs and changes in E/I balance in the STN in an animal model under anaesthesia, we sought to apply the same concept to clinical data from awake PD patients. According to the classical direct/indirect pathways model of basal ganglia functional organisation, the Parkinsonian STN is overactive (reduced inhibition), which is alleviated by dopaminergic stimulation. Therefore, we hypothesised that aperiodic exponents of STN-LFPs are relatively low in the untreated Parkinsonian state and would be increased with dopaminergic medication. To test this hypothesis, we estimated aperiodic exponents in STN-LFPs recorded from 30 hemispheres in 17 patients both ON and OFF levodopa (Figure 2A and B). Aperiodic exponents at 40–90 Hz successfully distinguished dopaminergic medication states (paired samples permutation t-test; t = –3.31, p=0.0015, Cohen’s d: 0.60) and were larger ON medication (in 66% of hemispheres), suggesting a faster drop of power with increasing frequencies and in keeping with more inhibition of STN (Figure 2C). The levodopa effect on aperiodic exponents was robust against different settings for FoooF parameterisation (Figure 2—figure supplement 1). Note that for human data, the frequency range was adjusted to 40–90 Hz (the lower bound due to high-amplitude beta peaks crossing the fitting range and the upper bound due to the harmonic of mains interference; see section ‘Signal processing’ for more details).

8In addition, we quantified periodic beta power identified using the FoooF parameterisation (Figure 2B) and average power of six different frequency bands and compared them between conditions ON and OFF levodopa. Periodic beta power differed between the two medication states (paired samples permutation t-test, t = 2.08, p=0.048), with higher power in the OFF medication state consistent with previous studies (;; Figure 2C). Of the six frequency ranges, only beta power distinguished medication states (Figure 2—figure supplement 2A). However, neither average (Spearman; ρ = –0.08, p=0.67), low (ρ = –0.20, p=0.28), nor high beta power (ρ = 0.004, p=0.99) correlated with aperiodic exponents (Figure 2—figure supplement 2B). In 10 of 20 cases in which the aperiodic exponent was higher ON medication, there was either no clear beta peak in the OFF state or no clear beta reduction with levodopa. This underlines the benefit of multi-biomarker adaptive DBS compared to an algorithm that only relies on beta power as a feedback signal. In 8 of 10 hemispheres in which aperiodic exponents were not higher ON medication, exponents were either very similar and the difference between medication states was <0.1 (four cases) or beta power was not affected by levodopa either ( four cases).

9Medication-induced changes of aperiodic exponents and periodic beta power displayed a trend for a negative correlation (Spearman; ρ = –0.33, p=0.07, n = 30; Figure 2D), indicating that they may contain similar information on levodopa-induced changes in the STN. This may also hint at a physiological meaning of aperiodic exponents. Furthermore, neither levodopa-induced changes of periodic beta power (Spearman; ρ = –0.04, p=0.85, n = 28; Figure 2E) nor aperiodic exponents (Spearman; ρ = –0.014, p=0.94, n = 28; Figure 2F) were correlated with contralateral appendicular bradykinesia and rigidity UPDRS part III sub-scores OFF-ON levodopa in this cohort.

10These results suggest that aperiodic exponents of STN-LFPs may be a useful measure to distinguish and track medication states.

11High-frequency DBS was thought to induce functional inactivation of the neurons in the stimulated area. Furthermore, the inactivation hypothesis was corroborated when suppression of neuronal activity was recorded surrounding STN-DBS leads in patients, non-human primates, and rodents in line with the classical rate model of movement disorders. Here, we compared aperiodic exponents at 10–50 Hz of STN-LFPs ON and OFF high-frequency DBS in 26 hemispheres from 17 PD patients. Compared to previous analyses, we lowered the frequency range for parameterisation to avoid a spectral plateau starting >50 Hz when stimulation was on (Figure 3A). We found increased aperiodic exponents ON DBS (paired samples permutation t-test; t = –6.27, p<0.001, Cohen’s d: 1.23, Figure 3B), a similar effect as levodopa, in keeping with the E/I hypothesis and of the notion that DBS supresses STN firing to some degree.

12When the average power of six different frequency ranges and periodic beta power was compared immediately before and during 130 Hz STN-DBS, beta power (primarily high beta) and low gamma power were suppressed with DBS (Figure 3C, Figure 2—figure supplement 2C) in accordance with our previous work. The power increase of the high gamma band (51–90 Hz) was driven by artefacts of stimulation in that range (Figure 3A). Aperiodic exponent changes with DBS were not correlated with spectral changes of any frequency (Figure 2—figure supplement 2D). Again, this implies that the aperiodic exponent is independent of spectral changes averaged over pre-defined frequency ranges or periodic beta power and might provide additional information.

13In this study, we validated the aperiodic exponent of STN-LFPs as a marker of E/I balance using single-unit activity from the basal ganglia in 6-OHDA-lesioned animals, under conditions of where the activity levels of neurons providing major excitatory and inhibitory inputs to STN neurons are well defined. Having validated the approach with single-unit activities under these controlled conditions in rodents, we found that the aperiodic exponent of STN-LFPs recorded from awake PD patients distinguishes medication and stimulation states. Its sensitivity to levodopa and DBS underlines the notion that the aperiodic exponent of the STN-LFP may indicate pathological states of PD and can potentially serve as a feedback signal for adaptive DBS.

14Our results support that the aperiodic exponent of STN-LFPs changes with excitatory and inhibitory inputs to STN in both a rodent PD model and patients with PD. STN dendrites are innervated by glutamatergic inputs from ipsilateral somatomotor and frontal cortical areas, glutamatergic intralaminar thalamic nuclei, and GABAergic inputs from prototypic GPe neurons. In lesioned animals, on the active phase of the cortical slow oscillation (here referred to as high STN spiking epochs), STN neurons are expected to receive intense excitatory input from cortical and thalamic afferents and decreased inhibitory input from prototypic GPe neurons, conditions that lead to vigorous STN spiking. In contrast, during the inactive phase of the cortical slow oscillation, inhibition from prototypic GPe neurons should be high and excitation from cortex and thalamus is relatively low, conditions that can completely prevent STN spiking. We found clear differences in the aperiodic exponents of STN-LFPs between these extreme states of local excitation and inhibition (Figure 1).

15The majority of previous studies into the relationship between the aperiodic exponent and neuronal activity have been investigated in cortex. However, the anatomy and physiology of STN differs significantly from cortex in that it is made up of relatively homogenous, glutamatergic projection neurons that fire action potentials autonomously and receive tonic inhibition from prototypic GPe neurons. Cortical circuits, in contrast, comprise a vast array of neuron types and activity of cortical projection neurons is predominantly input driven. Thus, our findings provide important validation that aperiodic exponents reflect changes in E/I balance at the synaptic (LFP) levels, specifically in STN. In addition, in contrast to these previous efforts examining the E/I hypothesis, we directly link aperiodic exponents to single-neuron spiking and predefined parameters of the dynamic E/I balance that specifically relate to the majority of neurons in the recorded structure (Figure 1). This approach provided a platform for understanding changes in the aperiodic exponent in STN-LFP recordings from humans.

16Building on these findings, our clinical results hold up against the E/I hypothesis as well (Figures 2 and 3). Aperiodic exponents of STN-LFPs recorded from awake PD patients are increased ON medication and ON DBS when STN local activity is believed to be decreased according to the classical direct/indirect pathways model. The increased exponents ON dopaminergic medication in PD are consistent with a recent study that reported higher aperiodic exponents in dopamine-intact compared to lesioned animals. Furthermore, our results indicate that periodic beta power differs between the two dopaminergic medication states (Figure 2C), consistent with previous findings. Finally, the missing correlation between medication-induced changes of aperiodic exponents and average beta power suggests that aperiodic exponents capture changes with medication that are not reflected by beta power alone and might be complimentary in an adaptive DBS algorithm ( Figure 2—figure supplement 2).

17Beta-band oscillations were identified as the most promising feedback signal for adaptive DBS considering their strong relationship with motor impairment in PD (Kühn et al., 2006; ). However, the correlation between beta and contralateral appendicular bradykinesia and rigidity UPDRS scores was not significant in our cohort, and abnormal beta activity is not observed in all patients nor is it correlated with tremor, freezing of gait, or dyskinesia. It is therefore unlikely that a beta-only feedback model will address all PD symptoms. Several factors point towards the aperiodic exponent as a candidate feedback signal. First, it changes with medication and DBS (Figures 2 and 3), similar characteristics which brought beta oscillations into the spotlight and which may suggest a link to clinical improvement (Kühn et al., 2006; ). Second, we observed medication-related changes of the aperiodic exponent in hemispheres without clear beta peaks or medication-related beta changes. Third, we estimate the aperiodic exponent between 40 and 90 Hz, when studying the effect of levodopa, avoiding lower frequencies, which are particularly susceptible to movement-related artefacts.

18However, there are some obstacles to its use as a feedback marker. First, we could not show a direct link between the aperiodic exponent and clinical symptoms, but a trend for a negative correlation with periodic beta power (Figure 2D) and in our data set UPDRS part III scores were not correlated with periodic beta power either (Figure 2E and F). To unequivocally assess clinical relevance of aperiodic exponents, motor tests with higher discriminatory power than UPDRS motor sub-scores such as the BRAIN TEST may be useful. Second, the aperiodic exponent would present a feedback signal with low temporal resolution. We averaged PSDs over 60 s to isolate exponents of STN-LFPs. Shortening this time window will introduce noise into the PSD and increase the error of aperiodic estimates. While these temporal dynamics prevent aperiodic exponents from targeting beta bursts, they may provide additional information about the E/I balance with slower temporal dynamics. Third, the frequency range is critical for isolating the aperiodic exponent and results may vary considerably depending on this. Moreover, for some PSDs with large oscillatory components and a spectral plateau at low frequencies, it may even be impossible to obtain an unequivocal linear fit. Fourth, it is unclear if a miniaturised implantable device will have the computational power to parameterise PSDs in real time and what effects this may have on battery longevity. Whether aperiodic exponents can be combined with other LFP parameters to improve optimal DBS settings will depend on whether they can add additional clinical information than beta power alone, which our results imply (see section ‘Aperiodic exponents from 40 to 90 Hz separate levodopa medication states in PD patients’). In this cohort, we did not find correlations between levodopa-induced changes of aperiodic exponents and average beta power of three different frequency ranges (Figure 2—figure supplement 2B), but a trend for a negative correlation with periodic beta power, which comprises a measure similar to beta peaks that were used before. It is therefore possible that aperiodic exponents extract similar information than beta power, but may aid in subjects where no beta peaks are present or beta peaks are not affected by levodopa.

19The chosen frequency band for linear fitting can affect FoooF parameterisation. In the past, many different fitting ranges were applied to extract the aperiodic exponent (reviewed in ). Most of these frequency ranges comprise low-frequency oscillations and start in the delta, theta, alpha, or beta range. If prominent low-frequency oscillations are present, this may lead to steepening of the spectrum and error-prone aperiodic fits. In this study, when parameterising PSDs from rodent data recorded using high-impedance microelectrodes, we chose the frequency band from 30 to 100 Hz to avoid false-high exponents due to high power in the lower frequency bands. The lower fitting bound of 30 Hz was chosen to exclude overlap of the lower fitting bound with the rising or falling arm of alpha or beta oscillations. A similar frequency range has been recommended to estimate the E/I ratio before (from 30 to 70 Hz, if this range is uncorrupted by oscillatory peaks). To asses differences with medication in clinical data recorded using macro-electrodes, we narrowed the fitting range to 40–90 Hz to avoid overlap and false-high estimates due to peaks in the high beta range (Figure 2B), and to avoid the harmonic of mains interference. These results are robust as long as the selected frequency range covers 40–70 Hz (Figure 2—figure supplement 1). For DBS data analysis, we adapted the fitting range to avoid a spectral plateau (Figure 3A) which would have resulted in false-low exponents had we used the same fitting range as for the previous analysis. We observed this prominent plateau at frequencies larger than 50 Hz when DBS was switched ON in addition to prominent peaks at half stimulation frequency and other harmonics (Figure 3A). However, we did observe reduced power in the high beta and low gamma frequency bands (21–50 Hz) with stimulation, suggesting that the signal-to-noise ratio is sufficient to detect physiological signals in this frequency band. Therefore, we have focused on the lower frequency bands (10–50 Hz) for quantifying aperiodic exponents ON and OFF stimulation. In addition, in our dataset we did not see a link between medication-induced changes of either the aperiodic exponent or periodic beta power and contralateral bradykinesia and rigidity scores OFF-ON levodopa (Figure 2E and F) and further studies will be required to investigate if and to what extent aperiodic exponents of STN-LFPs correlate with Parkinsonian symptoms.

20We showed that aperiodic exponents of STN-LFPs reflect STN excitation and inhibition as evinced by single-neuron activity in states of extreme spiking differences in rodents. We further showed that aperiodic exponents of STN-LFP in PD patients are larger ON dopaminergic medication and ON DBS reflecting more inhibition of STN compared to the dopamine-depleted and OFF DBS states. Our results corroborate that the aperiodic exponent contains information with respect to E/I balance and our clinical results give reason to believe the aperiodic component may be useful in a closed-loop feedback algorithm for PD.

21Experiments were performed on adult male Sprague–Dawley rats (Charles River) and were conducted in accordance with the Animals (Scientific Procedures) Act, 1986 (UK). Animal data that was analysed in this paper has been generated under the project licence numbers 30/2131 and 30/2629. All details on the 6-OHDA lesion and electrophysiological recordings were published before.

22Unilateral 6-OHDA lesion was performed as described in;. Then, 25 min before injection, animals received desipramine i.p. to minimise uptake of 6-OHDA by noradrenergic neurons. 6-OHDA was dissolved in NaCl to a concentration of 4 mg/ml of which 3 μl were injected medial to the substantia nigra pars compacta to target the medial forebrain bundle, which results in widespread loss of midbrain dopaminergic neurons. The extent of the dopamine lesion was assessed 14–15 days after injection by apomorphine challenge. Lesions were considered successful if animals made >80 contraversive rotations in 20 min. Electrophysiological recordings were performed ipsilateral to 6-OHDA lesion 21–45 days after surgery when pathophysiological changes in the basal ganglia have likely reached their maxima.

23Data was recorded as described in from eight 6-OHDA-lesioned rats. Here, we summarise key steps of the experimental procedure and data acquisition. Anaesthesia was induced with isoflurane and maintained with urethane, ketamine, and xylazine throughout the recording. Animals were placed in a stereotaxic frame where their body temperature was maintained at 37°C. ECoG, electrocardiograms (ECG), and respiration rate were monitored to ensure animal well-being. ECoG was recorded via a 1 mm steel screw juxtaposed to the dura mater above the frontal cortex and referenced against another screw in the skull above the ipsilateral cerebellum (Figure 1—figure supplement 1A). Raw ECoG traces were bandpass filtered (0.3–1500 Hz) and amplified (2000×) before acquisition. Extracellular recordings of unit activity and LFPs in the external globus pallidus (GPe) and STN were simultaneously made using silicon probes with high-impedance microelectrodes (Figure 1—figure supplement 1A). Each probe had one or two vertical arrays (500 μm apart) with 16 recording contacts along the arrays with 100 μm spacing. Monopolar probe signals were referenced against a screw above the contralateral cerebellum. Probes were advanced into the brain under stereotaxic control and extracellular signals were lowpass filtered (6000 Hz). ECoG and probe signals were each sampled at 17.9 kHz using a Power 1401 Analog-Digital converter. Recording locations were verified after experiments using histological procedures. STN was identified by comparison of recorded unit activity with the known characteristics of STN neurons in urethane anaesthesia.

24The ECoG measurements were used to assess whether the rodent was in SWA state, which accompanies deep anaesthesia and is similar to activity observed during natural sleep. We analysed a total of 28 extracellular LFP channels within STN during SWA (3.5 ± 0.18 channels per animal [mean ± SEM]). STN single-unit activity was isolated from 20 of these channels (2.5 ± 0.07 per animal).

25Data analysis was performed using custom-written scripts in MATLAB (R2020b). Periods of robust SWA were selected according to previously described characteristics of these brain states. Analyses were performed on 97.61 ± 2.17 s of data during SWA in 6-OHDA-lesioned animals. After offline bandpass filtering (500–6000 Hz) of the probe signals, single-unit activity was isolated with standard spike sorting procedures including template matching, principal component analysis, and supervised clustering (Spike2) as described in. Isolation of single units was verified by the presence of a distinct refractory period. Only neurons in which <1% of interspike intervals were <2 ms were analysed in this study. For further analysis, single-unit activity was converted such that each spike was represented by a single digital event. To analyse aperiodic exponents of STN-LFPs, raw signals were lowpass filtered at 300 Hz (third-order Butterworth filter; ). A similar procedure to analyse LFPs from silicon probe electrodes was described before.

26LFPs were downsampled to 2048 Hz. Target channels within STN were re-referenced by subtracting the mean signal across the six neighbouring channels to reduce volume conduction (Figure 1—figure supplement 1C). We computed wavelet magnitude squared coherence between the target LFP channel in STN and ECoG to control for volume conduction and opted for the above re-referencing approach with coherence <0.1 for all frequencies >10 Hz (Figure 1—figure supplement 1C).

27Spectral parameters were evaluated using continuous complex Morlet wavelet convolution. The entire 100 s time series was decomposed from 1 to 100 Hz with a frequency resolution of 1 Hz (frequencies increased linearly) before epoching to reduce the edge effect on each epoch. Morlet wavelets of 50 cycles were used which did not change as a function of frequency. We counted the spike events per consecutive non-overlapping 250 ms epoch for all unit activity channels (Figure 1—figure supplement 1B). The epoch duration was chosen such that it captures the rhythmic dynamics during SWA. For every unit channel, we defined epochs with a spike rate >75th percentile as ‘high spiking’ and all epochs with a spike rate <25th percentile as ‘low spiking’ (Figure 1—figure supplement 1B). We computed the mean PSD for every 250 ms epoch and normalised it by dividing through the mean power from 1 to 100 Hz (Figure 1—figure supplement 1D).

28For every LFP channel within STN, we computed the mean PSD of all high- and all low-spiking epochs separately. To isolate the aperiodic component from these spectra, we used the open-source FoooF algorithm (version 1.0.0). Settings for the algorithm were set as peak width limits: 2–12; max number of peaks: infinite; minimum peak height: 0; peak threshold: 2; and aperiodic mode: fixed. Power spectra were parameterised across the frequency range 30–100 Hz. The lower bound was selected to avoid the impact of low-frequency oscillations, the upper bound was selected to avoid the impact of spectral plateaus. Moreover, PSDs were linear across this frequency range in log-log space assuming a single 1/f like characteristic and did not contain overlapping periodic components (Figure 1—figure supplement 1E and F). Hence, higher aperiodic exponents indicate steeper power reduction with increasing frequencies in the PSD and vice versa as shown in Figure 1—figure supplement 1F. We evaluated the goodness of fit (R2) for all data used in this study (Figure 3—figure supplement 1). In addition, we evaluated and compared the goodness of fit using either ‘fixed’ mode or ‘knee’ mode in the FoooF fitting. Results show that using the ‘knee’ mode for parameterisation did not improve aperiodic fitting (Figure 1—figure supplement 2). Therefore, we opted to use the ‘fixed’ mode for parameterisation within the selected frequency range. To compare power across different spiking states, we computed the mean power between 30 and 100 Hz of the average PSD of all high or low-spiking epochs.

29This protocol was approved by the Health Research Authority UK, the National Research Ethics Service local Research Ethics Committee (IRAS: 46576), and the local ethics committee at the University of Mainz (837.208.17 [11042]). Patients were recruited at St. George’s University Hospital NHS Foundation Trust, London, King’s College Hospital NHS Foundation Trust, London, and the University Medical Center Mainz. Written informed consent, and consent to publish, was obtained before surgery in line with the Declaration of the Principles of Helsinki. We analysed data from 24 patients from these three centres. Data from 17 patients were previously published.

30Study participants were evaluated by an interdisciplinary team of movement disorder neurologists and functional neurosurgeons and met the UK Parkinson’s Disorder Society Brain Bank Diagnostic Criteria for diagnosis of PD. Baseline motor function in the ON and OFF medication state was assessed pre-operatively using the part III of the Unified Parkinson’s disease rating scale motor subscale (UPDRS-III). When UPDRS part III scores were reported in Figure 2, we used the contralateral appendicular categories (bradykinesia and rigidity scores only). The surgical target was STN. Five models of DBS leads were used: quadripolar (model 3389) or directional (SenSight) leads from Medtronic Inc, Neurological Division, USA, directional (Vercise model DB-2202) or non-directional (model DB-2201) leads from Boston Scientific, USA, and directional leads (Infinity model 6172ANS) from Abbott Inc, USA. DBS implantation was guided either by magnetic resonance imaging alone (St. George’s University Hospital) or with additional intra-operative microelectrode recordings and stimulation (King’s College Hospital and University Medical Center Mainz). The subthalamic leads were connected to temporary extension leads and these were externalised. Assessment of contact localisation was made through co-registration of immediate post-operative CT with pre-operative MRI by an experienced neurosurgeon or neurologist specialising in deep brain stimulation. Assessment was blinded to the electrophysiological data and made using Lead-DBS.

31Recordings were made between 3 and 6 days post-operatively, while lead extensions were still externalised and before implantation of the subcutaneous pulse generator. In total, 24 patients (37 hemispheres) were recorded for this study; 17 patients (30 hemispheres) were recorded ON and OFF dopaminergic medication and 17 patients (26 hemispheres) ON and OFF stimulation. In patients with directional leads, the three directional contacts were joined to form a ring contact (Figure 2Ai). All LFPs were amplified and sampled at either 2048 Hz using a TMSi Porti (TMS International, Netherlands) or at 4096 Hz using a TMSi Saga32 (TMS International, Netherlands). The ground electrode was placed on the non-dominant forearm. High-frequency stimulation at 130 Hz was only tested at the middle contacts to allow bipolar LFP recordings from the two surrounding contacts (Figure 2Aii). A self-adhesive electrode attached to the patient’s back served as a reference for stimulation, which was delivered using a custom-built highly configurable in-house neurostimulator. Stimuli comprised symmetric constant-current biphasic pulses (60 μs pulse width, negative phase first). The stimulation current was started at 0.5 mA and increased in increments of 0.5 mA until first a benefit in Parkinsonian motor symptoms was observed and second side-effect threshold was reached. The contact and current associated with the best clinical improvement were selected. If no stimulation was applied and multiple bipolar configurations were available, we selected the bipolar channel with the largest beta peak at rest. If only one hemisphere was recorded per patient, it was the hemisphere contralateral to the most affected upper limb.

32Analyses were performed on 60 s of data while patients were awake and at rest. LFP time series were highpass filtered at 1 Hz. Complex Morlet wavelet convolution was used for time-frequency decomposition with 50 wavelet cycles between 1 and 90 Hz as described in section ‘Spectral decomposition’. To exclude artefacts from mains interference at 50 Hz before isolating the aperiodic component, frequencies between 47 and 53 Hz were removed and the gap was linearly interpolated using the fillmissing function. To run the FoooF algorithm, the same settings were used as described in ‘FoooF parameterisation’, and power spectra were parameterised across the frequency range 40–90 Hz. The lower bound was increased to avoid high-amplitude beta peaks crossing the fitting range (see Figure 2B). The upper bound was lowered to avoid the harmonic of mains interference. When a broad frequency band (e.g. 1–100 Hz) was considered, the PSD was not linear in log-log space. However, within the selected frequency band, the power spectrum followed an almost perfect linear line as illustrated in Figure 2B (bottom-right plot). Therefore, we used the ‘fixed’ mode for parameterisation of the selected frequency range. To isolate periodic beta activity, the PSD was parameterised using FoooF between 5 and 90 Hz (‘knee’ mode in this case as such a wide frequency range is unlikely to only have a single aperiodic component, all other FoooF settings were identical to what was used in animal data). After removing the aperiodic component, the largest peak within the canonical beta range from 8 to 35 Hz was selected (Figure 2B). All other FoooF fittings presented elsewhere in this study were performed using the ‘fixed’ mode. In the stimulation ON condition, stimulation artefacts led to a plateau at frequencies >50 Hz in the spectra (Figure 3A). Therefore, aperiodic exponents were estimated between 10 and 50 Hz to evaluate the effect of DBS. A similar frequency range (5–45 Hz) was used in a previous study. Beta (13–35 Hz), low beta (13–20 Hz), high beta (21–35 Hz), gamma (35–90 Hz), low gamma (35–50 Hz), and high gamma (51–90 Hz) power were computed as the mean power of the normalised (divided by the mean power from 1 to 90 Hz), 50 Hz removed and 1/F-corrected PSD across the respective frequency range.

33Statistical analyses were performed using custom-written scripts in MATLAB (R2020b). To perform paired comparisons between the two medication or stimulation conditions, we used a paired samples permutation t-test with multiple comparison correction (50,000 permutations each) as implemented in. When correlations were reported, we calculated Spearman’s rank coefficients because the non-baseline-transformed power data are non-normally distributed and contain outliers. When multiple channels within one animal were available, hierarchical comparisons of aperiodic exponents and power across different epochs was performed using linear mixed-effects models to take repeated measures from multiple electrodes for each animal into account. The exponent or power data was set as dependent variable and different STN spiking conditions (e.g. high STN spiking epochs, low STN spiking epochs) as fixed effects. The normal distribution of each variable and the residuals were visually inspected with quantile-quantile plots and histograms of distribution. All models were estimated by the method of maximum likelihood and included random intercept for subjects to allow different intercepts for each subject, thereby capturing individual differences. Multiple statistical tests were performed in this study under FDR control at 5% using the adaptive linear step-up procedure, a modification of the original Benjamini and Hochberg procedure. This ensures that the expectation of the number of false positives over the total number of positives is less than 5% when many statistical tests are performed. When histograms of distribution are shown, the optimal number of histogram bins was determined using the Freedman–Diaconis rule. All data are shown as mean ± standard error of the mean (SEM) unless mentioned otherwise.

34Due to the explorative nature of this study, we did not perform prospective sample size estimations but included all animal data with wideband recordings from STN that were available to us (n = 8). Since 6-OHDA-lesion was performed unilaterally, only one STN was recorded per animal. Similarly, we did not perform prospective sample size calculations for human data, but included all STN recordings we had available (37 STNs from 24 patients). This approach was chosen as postoperative LFP recordings from DBS electrodes are rare research opportunities. Fortunately, due to the relatively high signal-to-noise ratio of LFP recordings, a small number of patients between 7 and 12 is considered sufficient to detect robust effects in LFP studies.

35In our study, each STN was treated as one independent sample. In doing so, we follow the definition that ‘biological replicates are parallel measurements of biologically distinct samples that capture random biological variation’. It should be recognised that the variations we observed in our sample can be caused by variability in the phenotype of PD, of the target location of the electrode, or in the temporary lesion effect of DBS surgery.

36This was not a clinical study. We used a within-subject design to test the effects of DBS and dopaminergic medication. All available animal and human data recordings were included in the analysis (no attrition).