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

Periodic features of neural time-series data, such as local field potentials (LFPs), are often quantified using power spectra. While the aperiodic exponent of spectra is typically disregarded, it is nevertheless modulated in a physiologically relevant manner and was recently hypothesised to reflect excitation/inhibition (E/I) balance in neuronal populations. Here, we used a cross-species in vivo electrophysiological approach to test the E/I hypothesis in the context of experimental and idiopathic Parkinsonism. We demonstrate in dopamine-depleted rats that aperiodic exponents and power at 30–100 Hz in subthalamic nucleus (STN) LFPs reflect defined changes in basal ganglia network activity; higher aperiodic exponents tally with lower levels of STN neuron firing and a balance tipped towards inhibition. Using STN-LFPs recorded from awake Parkinson’s patients, we show that higher exponents accompany dopaminergic medication and deep brain stimulation (DBS) of STN, consistent with untreated Parkinson’s manifesting as reduced inhibition and hyperactivity of STN. These results suggest that the aperiodic exponent of STN-LFPs in Parkinsonism reflects E/I balance and might be a candidate biomarker for adaptive DBS.

between 30 and 100 Hz in STN-LFP was smaller during low STN spiking epochs compared to high 77 STN spiking epochs (LME: estimate = -0.02, t = -2.34, p = .02; Figure 1E). Furthermore, the lack of 78 correlations between power and aperiodic exponents suggests that both power and exponents from the 79 same frequency range are dissociable and might contain different information (Spearman; ρ = -.07, p = 80 .56 and ρ = -.18, p = .14 for high and low STN spiking epochs respectively). 81

Figure 1. Aperiodic exponents and power of STN-LFPs between 30 and 100 Hz reflect STN excitation and inhibition in lesioned animals. A.
Example traces of ECoG and single-unit spiking activity of STN and GPe-Ti neurons during slow-wave activity (SWA) in anaesthetised 6-OHDAlesioned animals. Note the rhythmic spiking pattern of both neuron types, which either aligns with peaks or troughs of cortical slow (~1 Hz) oscillations. B. We identified 250 ms epochs of relatively high spiking (> 75 th percentile) and epochs of low spiking (< 25 th percentile) based on STN neuron activity during cortical SWA. The distribution of STN (i) and GPe-Ti (ii) spiking activity is shown for one example animal, which confirms that spiking rates are clearly differentiable for the two high and low STN spiking states. GPe-Ti neurons are most active when STN neurons are relatively inactive and vice versa (iii; ***p < .001, Wilcoxon rank sum test). C. Average PSDs of STN-LFPs in the two states identified above (mean ± SEM, n = 8 animals). The black dotted lines denote the aperiodic fits (exponent values (exp) are colour-coded) for the respective PSDs between 30 and 100 Hz. D. Aperiodic exponents are high during low STN spiking epochs corresponding to more GPe-Ti activity and, by inference, more inhibition of STN. Inversely, aperiodic exponents are low during high STN spiking epochs associated with less GPe-Ti activity and, by inference, disinhibition (LME: estimate = 0.12, t = 3.92, p < .001). E. Average power between 30 and100 Hz in the STN-LFPs is higher when STN neurons are highly active than when STN spiking is low (LME: estimate = -0.02, t = -2.34, p = .02). F. Power at 30-100 Hz of STN-LFP and aperiodic exponents of the same frequency range are not correlated during high (ρ = -.07, p = .56) and low (ρ = -.18, p = .14) STN spiking states (n = 70 LFP channels). D & E: Large dots denote the mean per animal and are colour-coded. Small dots denote individual LFP channels. n = 8 animals, *p < .05, **p < .01, ***p < .001, LME.
Overall, these results from 6-OHDA-lesioned rats suggest that the aperiodic exponent of STN-LFPs is 82 altered according to different levels of STN spiking. The high and low spiking epochs of single STN 83 neurons can in turn be ascribed with confidence to an E/I balance that is tipped in favour of excitation 84 and inhibition, respectively. As such, these results support the notion that STN-LFP aperiodic exponents 85 may become valid markers of overall E/I balance in STN. 86 87

Aperiodic exponents from 40 to 90 Hz separate levodopa medication states in PD patients 88
After corroborating the link between aperiodic exponents in STN-LFPs and changes in E/I balance in 89 the STN in an animal model under anaesthesia, we sought to apply the same concept to clinical data 90 from awake PD patients. According to the classical direct/indirect pathways model of basal ganglia 91 functional organisation, the parkinsonian STN is overactive (reduced inhibition), which is alleviated by 92 dopaminergic stimulation (Albin et al., 1989;DeLong, 1990). Therefore, we hypothesised that aperiodic 93 exponents of STN-LFPs are relatively low in the untreated Parkinsonian state, and would be increased 94 with dopaminergic medication. To test this hypothesis, we estimated aperiodic exponents in STN-LFPs 95 recorded from 30 hemispheres in 17 patients both ON and OFF levodopa ( Figure 2A+B). Aperiodic 96 exponents at 40-90 Hz successfully distinguished dopaminergic medication states (paired samples 97 permutation t-test; t = -3.31, p = .0015, Cohen's d: 0.60) and were larger ON medication (in 66% of 98 hemispheres), suggesting a faster drop of power with increasing frequencies and in keeping with more 99 inhibition of STN ( Figure 2C). The levodopa effect on aperiodic exponents was robust against different 100 settings for FoooF parameterisation ( Figure S2). Note that for human data, the frequency range was 101 adjusted to 40-90 Hz (the lower bound due to high-amplitude beta peaks crossing the fitting range and 102 the upper bound due to the harmonic of mains interference; see section 4.2.3. for more details). 103

104
In addition, we quantified periodic beta power identified using the FoooF parameterisation ( Figure 2B) 105 and average power of six different frequency bands and compared them between conditions ON and 106 OFF levodopa. Periodic beta power differed between the two medication states (paired samples 107 permutation t-test, t = 2.50, p = .0168), with higher power in the OFF medication state consistent with 108 previous studies (Brown et al., 2001;Neumann et al., 2017) (Figure 2C). Of the six frequency ranges, 109 only beta power distinguished medication states ( Figure S3A). However, neither periodic beta 110 (Spearman; ρ = -.023, p = .91) nor average beta power (Spearman; ρ = -.08, p = .67) correlated with 111 aperiodic exponents ( Figure S3B). In 10 of 20 cases in which the aperiodic exponent was higher ON 112 medication, there was either no clear beta peak in the OFF state or no clear beta reduction with levodopa. 113 This underlines the benefit of multi-biomarker aDBS compared to an algorithm that only relies on beta 114 power as a feedback signal. In 8 of 10 hemispheres in which aperiodic exponents were not higher ON 115 medication, exponents were either very similar and the difference between medication states was < 0.1 116 (4 cases) or beta power was not affected by levodopa either (4 cases). 117 We analysed 60-s segments of bipolar STN-LFP recorded from Parkinson's patients at rest while leads were externalised (iii). Recordings were performed ON and OFF dopaminergic medication. Directional contacts were fused (i) and bipolar recordings were conducted from contacts adjacent to the stimulation contact (red; ii). B. Average PSD from 30 hemispheres (17 patients) ON and OFF medication of 60-s recordings using Morlet Wavelet transforms (mean ± SEM). Aperiodic exponents were computed between 40-90 Hz to avoid highamplitude beta peaks and harmonics of mains noise at 100 Hz and the PSD was relatively linear in loglog space within this range. To obtain periodic beta power, we fit the FoooF algorithm between 5-90 Hz and picked the power of the largest oscillatory component within the beta range (13-35 Hz, green rectangle). C. Aperiodic exponents and periodic beta power differ between medication states (p = .0015 and p = .0168). †p-values were computed using a paired samples permutation t-test with multiple comparison correction on 30 hemispheres recorded from 17 PD patients. D. Aperiodic exponent and periodic beta power changes with levodopa are not correlated (Spearman; ρ = -.023, p = .91, n = 29). E & F. Neither periodic beta power (E) nor the aperiodic exponent (F) changes with medication are correlated with contralateral appendicular bradykinesia and rigidity UPDRS part III sub-scores OFF-ON levodopa (Spearman: ρ = -.07, p = .73, n = 25 hemispheres for periodic beta; Spearman: ρ = .07, p = .73, n = 26 hemispheres for aperiodic exponents).
Medication-induced changes of aperiodic exponents and periodic beta power were not correlated 118 hemispheres from 17 PD patients. Compared to previous analyses, we lowered the frequency range for 136 parameterisation to avoid a spectral plateau starting > 50 Hz when stimulation was on ( Figure 3A). We 137 found increased aperiodic exponents ON DBS (paired samples permutation t-test; t = -6.27, p < .001, 138 Cohen's d: 1.23, Figure 3B), a similar effect as levodopa, in keeping with the E/I hypothesis and of the 139 notion that DBS supresses STN firing to some degree. 140 in that range ( Figure 3A). Aperiodic exponent changes with DBS were not correlated with spectral 145 changes of any frequency ( Figure S3D). Again, this implies that the aperiodic exponent is independent 146 of spectral changes averaged over pre-defined frequency ranges or periodic beta power and might 147 provide additional information. 148

Discussion 151
In this study, we validated the aperiodic exponent of STN-LFPs as a marker of E/I balance using single 152 unit activity from the basal ganglia in 6-OHDA-lesioned animals, under conditions of where the activity 153 levels of neurons providing major excitatory and inhibitory inputs to STN neurons are well defined. 154 Having validated the approach with single unit activities under these controlled conditions in rodents, 155 we found that the aperiodic exponent of STN-LFPs recorded from awake PD patients distinguishes 156 medication and stimulation states. Its sensitivity to levodopa and DBS underlines the notion that the 157 aperiodic exponent of the STN-LFP may indicate pathological states of PD and can potentially serve as 158 a feedback signal for adaptive DBS. 159 160

The aperiodic exponent as a marker of E/I balance 161
Our results support that the aperiodic exponent of STN-LFPs changes with excitatory and inhibitory However, there are some obstacles to its use as a feedback marker. First, we could not show a direct 216 link between the aperiodic exponent and clinical symptoms, but in our data set UPDRS part III scores 217 were not correlated with periodic beta power either ( Figure 2E+F). To unequivocally assess clinical 218 relevance of aperiodic exponents, motor tests with higher discriminatory power than UPDRS motor 219 sub-scores such as the BRAIN TEST may be useful (Giovannoni et al., 1999). Second, the aperiodic 220 exponent would present a feedback signal with low temporal resolution. We averaged PSDs over 60 s 221 to isolate exponents of STN-LFPs. Shortening this time window will introduce noise into the PSD and 222 increase the error of aperiodic estimates. While these temporal dynamics prevent aperiodic exponents 223 from targeting beta bursts, they may provide additional information about the E/I balance with slower 224 temporal dynamics. Third, the frequency range is critical for isolating the aperiodic exponent and results 225 may vary considerably depending on this. Moreover, for some PSDs with large oscillatory components 226 and a spectral plateau at low frequencies, it may even be impossible to obtain an unequivocal linear fit 227 longevity. If aperiodic exponents can be combined with other LFP parameters to improve optimal DBS 230 settings, will depend on if they can add additional clinical information than beta power alone, which 231 our results imply (Figure S3). 232

Limitations 235
The chosen frequency band for linear fitting can affect FoooF parameterisation. In the past, many 236 different fitting ranges were applied to extract the aperiodic exponent (reviewed in Gerster et al., 2022). 237 Most of these frequency ranges comprise low frequency oscillations and start in the delta, theta, alpha 238 or beta range. If prominent low frequency oscillations are present, this may lead to steepening of the 239 spectrum and error-prone aperiodic fits (Gerster et al., 2022). In this study, when parameterising PSDs 240 from rodent data recorded using high-impedance microelectrodes, we chose the frequency band from 241 30 to 100 Hz to avoid false-high exponents due to high power in the lower frequency bands. The lower 242 fitting bound of 30 Hz was chosen to exclude overlap of the lower fitting bound with the rising or falling 243 arm of alpha or beta oscillations ( Figure 1D). A similar frequency range has been recommended to 244 estimate the E/I ratio before (from 30 to 70 Hz, if this range is uncorrupted by oscillatory peaks) (Gao 245 et al., 2017). To asses differences with medication in clinical data recorded using macro-electrodes, we 246 narrowed the fitting range to 40 to 90 Hz to avoid overlap and false-high estimates due to peaks in the 247 high beta range (Figure 2B), and to avoid the harmonic of mains interference. These results are robust 248 as long as the selected frequency range covers 40-70 Hz (Figure S2). For DBS data analysis, we adapted 249 the fitting range to avoid a spectral plateau (Figure 3A) which would have resulted in false-low 250 exponents had we used the same fitting range as for the previous analysis. We observed this prominent 251 plateau at frequencies larger than 50 Hz when DBS was switched ON in addition to prominent peaks at 252 half stimulation frequency and other harmonics ( Figure 3A). However, we did observe reduced power 253 in the high beta and low gamma frequency bands (21-50 Hz) with stimulation, suggesting that the signal 254 to noise ratio is sufficient to detect physiological signals in this frequency band. Therefore, we have 255 focused on the lower frequency bands (10-50 Hz) for quantifying aperiodic exponents ON and OFF 256 stimulation. In addition, in our dataset we did not see a link between medication-induced changes of 257 either the aperiodic exponent or periodic beta power and contralateral bradykinesia and rigidity scores 258 OFF-ON levodopa ( Figure 2E+F) and further studies will be required to investigate if and to what 259 extent aperiodic exponents of STN-LFPs correlate with parkinsonian symptoms. 260

Conclusions 263
We showed that aperiodic exponents of STN-LFPs reflect STN excitation and inhibition as evinced by 264 single neuron activity in states of extreme spiking differences in rodents. We further showed that

Electrophysiological recordings 291
Data was recorded as described in Mallet et al., 2008a from eight 6-OHDA-lesioned rats. Here, we 292 summarise key steps of the experimental procedure and data acquisition. Anaesthesia was induced with 293 isoflurane and maintained with urethane, ketamine and xylazine throughout the recording (Magill et al., 294 2006). Animals were placed in a stereotaxic frame where their body temperature was maintained at 295 37°C. ECoG, electrocardiograms (ECG) and respiration rate were monitored to ensure animal well-296 being. ECoG was recorded via a 1 mm steel screw juxtaposed to the dura mater above the frontal cortex 297 and referenced against another screw in the skull above the ipsilateral cerebellum ( Figure S1A). Raw 298 ECoG traces were bandpass filtered (0.3-1500 Hz) and amplified (2000x) before acquisition. 299 Extracellular recordings of unit activity and LFPs in the globus pallidus (GP) and STN were 300 simultaneously made using silicon probes with high-impedance microelectrodes ( Figure S1A). Each 301 probe had 1 or 2 vertical arrays (500 μm apart) with 16 recording contacts along the arrays with 100 302 μm spacing. Monopolar probe signals were referenced against a screw above the contralateral 303 cerebellum. Probes were advanced into the brain under stereotaxic control and extracellular signals 304 were lowpass filtered (6000 Hz). ECoG and probe signals were each sampled at 17.9 kHz using a Power 305 1401 Analog-Digital converter. Recording locations were verified after experiments using histological 306 procedures. STN was identified by comparison of recorded unit activity with the known characteristics 307 of STN neurons in urethane anaesthesia (Magill et al., 2001). 308 The ECoG measurements were used to assess if the rodent was in SWA state, which accompanies deep 309 anaesthesia and is similar to activity observed during natural sleep (Steriade, 2000). We analysed a total 310 of 28 extracellular LFP channels within STN during SWA (3.5 ± 0.18 channels per animal (mean ± 311 SEM)). STN single unit activity was isolated from 20 of these channels (2.5 ± 0.07 per animal). 312

Re-referencing 329
LFPs were downsampled to 2048 Hz. Target channels within STN were re-referenced by subtracting 330 the mean signal across the 6 neighbouring channels to reduce volume conduction ( Figure S1C). We 331 computed wavelet magnitude squared coherence between the target LFP channel in STN and ECoG to 332 control for volume conduction and opted for the above re-referencing approach with coherence < 0.1 333 for all frequencies > 10 Hz (Figure S1C). 334 we defined epochs with a spike rate > 75 th percentile as "high spiking" and all epochs with a spike rate 343 < 25 th percentile as "low spiking" (Figure S1B). We computed the mean PSD for every 250-ms epoch 344 and normalised it by dividing through the mean power from 1 to 100 Hz (Figure S1D).

Data recording and lead localisation determination 389
Recordings were made between 3 and 6 days postoperatively, while lead extensions were still 390 externalised and before implantation of the subcutaneous pulse generator. In total, 24 patients (37 391 hemispheres) were recorded for this study; 17 patients (30 hemispheres) were recorded on and off 392 dopaminergic medication and 17 patients (26 hemispheres) on and off stimulation. In patients with 393 directional leads, the 3 directional contacts were joined to form a ring contact (Figure 2Ai). All LFPs 394 were amplified and sampled at either 2048 Hz using a TMSi Porti (TMS International, Netherlands) or 395 at 4096 Hz using a TMSi Saga32 (TMS International, Netherlands). The ground electrode was placed 396 on the non-dominant forearm. High-frequency stimulation at 130 Hz was only tested at the middle 397 contacts to allow bipolar LFP recordings from the two surrounding contacts (Figure 2Aii). A self-398 adhesive electrode attached to the patient's back served as a reference for stimulation, which was 399 delivered using a custom-built highly-configurable in-house neurostimulator. Stimuli comprised 400 symmetric constant-current biphasic pulses (60 μs pulse width, negative phase first). The stimulation 401 current was started at 0.5 mA and increased in increments of 0.5 mA until first a benefit in Parkinsonian 402 motor symptoms was observed and second side-effect threshold was reached. The contact and current 403 associated with the best clinical improvement were selected. If no stimulation was applied and multiple 404 bipolar configurations were available, we selected the bipolar channel with the largest beta peak at rest. 405 If only one hemisphere was recorded per patient, it was the hemisphere contralateral to the most affected 406 upper limb. We analysed data from 17 patients (26 hemispheres) ON and OFF DBS. 407 408

Signal processing 409
Analyses were performed on 60 s of data while patients were awake and at rest. LFP time series were 410 highpass filtered at 1 Hz. Complex Morlet wavelet convolution was used for time-frequency 411 decomposition with 50 wavelet cycles between 1-90 Hz as described in section 4.1.3.3. To exclude 412 artefacts from mains interference at 50 Hz before isolating the aperiodic component, frequencies 413 between 47-53 Hz were removed and the gap was linearly interpolated using the fillmissing function. 414 To run the FoooF algorithm, the same settings were used as described in 4.1.3.4., and power spectra 415 were parameterised across the frequency range 40 to 90 Hz. The lower bound was increased to avoid 416 high-amplitude beta peaks crossing the fitting range (see Figure 2B). The upper bound was lowered to 417 avoid the harmonic of mains interference. To isolate periodic beta activity, the PSD was parameterised 418 using FoooF between 5-90 Hz, otherwise using the same settings, and the largest peak within the 419 canonical beta range from 13-35 Hz was selected ( Figure 2B). In the stimulation ON condition, 420 stimulation artefacts led to a plateau at frequencies > 50 Hz in the spectra ( Figure 3A). Therefore, 421 aperiodic exponents were estimated between 10 to 50 Hz to evaluate the effect of DBS. Beta

Sample-size estimation, replicates and group allocation 448
Due to the explorative nature of this study, we did not perform prospective sample-size estimations but 449 included all animal data with wideband recordings from STN that were available to us (n = 8). Since 6-450 OHDA-lesion was performed unilateral, only one STN was recorded per animal. Similarly, we did not 451 perform prospective sample-size calculations for human data, but included all STN recordings we had 452 available (37 STNs from 24 patients). This approach was chosen as postoperative LFP recordings from 453 DBS electrodes are rare research opportunities. Fortunately, due to the relatively high signal-to-noise 454 ratio of LFP recordings, a small number of patients between 7-12 is considered sufficient to detect Epochs below the 25 th percentile were considered low spiking. C. Left: LFP was re-referenced by subtracting the mean of the 6 neighbouring LFP channels. Right: This approach was chosen to control volume conduction since coherence between the re-referenced LFP channel and ECoG recorded from a steel screw over the frontal cortex (red) was lower compared to no re-referencing (blue) and subtracting the mean of all channels (yellow). D. Complex Morlet Wavelet Transforms (50 cycles) were used for time-frequency decomposition of the full LFP time series. Afterwards, average power spectral densities (PSDs) were computed for non-overlapping 250-ms epochs. PSDs of all high spiking epochs (blue boxes) and low spiking epochs (red boxes) were averaged. E. Periodic and aperiodic components of the PSD were separated using the FoooF parameterisation (see Methods). The original PSD of all low spiking epochs (black) is shown for one example LFP channel with the FoooF model fit (orange) and the aperiodic fit (dashed green). The aperiodic exponent and goodness of fit metric for this example are shown. F. Example analysis of the aperiodic exponent for one STN-LFP channel in one subject. The blue and red lines show the average PSDs of 'high STN spiking' epochs and 'low STN spiking' epochs respectively. The black lines denote the aperiodic fit in the selected fitting range (30-100 Hz). Note the PSD is roughly linear across this frequency range in log-log space.  For the same frequency bands, changes between medication states were correlated with aperiodic exponent changes. Note that correlations with beta power were not significant, while there was a weak positive correlation between aperiodic exponents at 40-90 Hz and power changes in the gamma range. C. Average power of the same frequency bands and periodic beta power were compared before and during 130 Hz STN-DBS. Primarily high beta and low gamma power separated ON and OFF stimulation conditions. Note the power increase of the high gamma band ON DBS, which is driven by artefacts of stimulation in this frequency band. D. Spectral changes with DBS were not correlated with changes of the aperiodic exponent at 10-50 Hz.