Basal ganglia and cerebellar lesions causally impact the neural encoding of temporal regularities

Time is a fundamental dimension of human cognition. Every decision, every action, every sensory stimulus around us happens in time and at multiple timescales. Our capacities to encode the precise timing of events and to time our (re-)actions to them are pivotal for acting in and adapting to a continuously changing dynamic environment. The environment displays some gradient of temporal regularity (Greenfield, Honing, et al., 2021): there are various periodicities within the body (e.g., the heartbeat and respiration; Criscuolo, Schwartze, et al., 2022) as well as in simple and complex sensory input (e.g., music, speech) and in behavior (e.g., interpersonal interactions in the animal and human world; Greenfield, Aihara, et al., 2021). These temporal regularities (or rhythm) can facilitate the processing of the timing of sensory events and further enable individuals to anticipate the when of next sensory events. In turn, temporal anticipation can benefit adaptive behavior: we can dance to music because we know when the next beat falls, and we can synchronize with others because their movement timing is predictable. Yet what determines our capacity to adapt behavior in time? Do we differ in the if and how we adapt and synchronize with auditory rhythms?

Human (e.g., Schroeder & Lakatos, 2009) as well as nonhuman animals (e.g., Criscuolo, Schwartze, Prado et al., 2023; Lakatos et al., 2008) encode and synchronize with temporal regularities by generating temporal predictions (Criscuolo, Schwartze, Prado et al., 2023; Lakatos et al., 2005). Temporal predictions allow to estimate the when next events occur, thus enabling dynamic attending (Large & Jones, 1999) of event onsets. Temporal predictions materialize as anticipatory neural activity (Arnal, 2012; Breska & Deouell, 2017; Fujioka et al., 2009, 2012, 2015; Ross et al., 2018; Snyder & Large, 2005), which supports the predictive alignment of neural oscillations to event onsets, fosters sensory processing (Lakatos et al., 2013), and further allows for production and synchronization of behavior in a predictive manner (Bartolo & Merchant, 2015; Gámez et al., 2018). Thus, ‘adaptation by anticipation’ (Fraisse, 1963; p. 18) is a mechanism for optimizing behavior and operates across sensory modalities (Arnal & Giraud, 2012; Cravo et al., 2013; Friston, 2005; Morillon et al., 2016; Nobre et al., 2012).

Fundamental to predictive temporal processes is the engagement of an extended motor system (Arnal, 2012; Fujioka et al., 2012, 2015; Schwartze & Kotz, 2013), recruited to prepare and execute predictive and synchronized behavior. The cerebellum (CE) and the basal ganglia (BG) are key structures in an extended cortico-subcortico-cortical brain network that plays a pivotal role in temporal processing (Merchant, Harrington, et al., 2013; Schwartze & Kotz, 2013). The CE encodes the precise timing (when an event onsets) of sensory events in the subsecond range (Bareš et al., 2018; Ivry et al., 1988; Ivry & Keele, 1989; Ivry & Schlerf, 2008) and thus allows estimating the duration of temporal intervals (Breska & Ivry, 2020, 2021; Grube, Cooper, et al., 2010; Grube, Lee, et al., 2010; Teki, Grube, & Griffiths, 2011; Teki, Grube, Kumar, et al., 2011) by quantifying the time elapsed between event onsets. The BG support the generation of temporal predictions (when the next event occurs) and use relative timing to process the beat (Grahn, 2009; Grahn & Brett, 2009; Schwartze et al., 2011; Teki, Grube, Kumar, et al., 2011).

CE lesions alter the encoding of event onsets in complex sound sequences (Nozaradan et al., 2017), as well as responses to single acoustic events, as evidenced by delayed and variable early event-related responses in the EEG (Schwartze & Kotz, 2021). CE lesions also affect the capacity to predict temporal intervals (Breska & Ivry, 2018, 2020, 2021; Grube, Cooper, et al., 2010) and impact the ability to produce and synchronize with rhythms (Ivry & Keele, 1989; Ivry et al., 1988). However, temporal predictions are comparable to healthy controls when tested in rhythmic contexts (Breska & Ivry, 2018, 2020, 2021).

A reversed pattern was observed in BG lesion patients: while their interval discrimination seems intact, their performance deteriorated in rhythmic contexts (Breska & Ivry, 2018). This observation suggests a fine, yet fundamental dissociation between rhythm- and interval-based temporal predictions in BG and CE lesion patients (Breska & Ivry, 2018). In fact, patients with BG lesions are less sensitive to temporal regularity in auditory sequences, have difficulties in generating temporal predictions in both basic (Schwartze et al., 2015) and complex (syncopated rhythms; Nozaradan et al., 2017; music (Grahn & Brett, 2009) and speech (Kotz & Schmidt-Kassow, 2015)) auditory sequences, and in coordinating and adjusting their tapping to tempo changes (Schwartze et al., 2011). Altogether, observations suggest intact single interval-based timing in the BG patients (Breska & Ivry, 2018; Grube, Cooper, et al., 2010; Teki, Grube, Kumar, et al., 2011), but impaired processing of temporal regularity in complex sequences.

What underlies these dysfunctions? Can the analysis of neural oscillatory activity causally show in what way the cortico-subcortical timing network differentiates the processing of temporal regularities?

We addressed these questions in an EEG experiment involving healthy ageing controls (HC) and patients with focal lesions in either the CE or BG. Participants listened to isochronous auditory sequences while EEG was recorded. We expected CE patients to show increased variability in the temporal encoding of tone onsets, while we hypothesized BG patients to have difficulties in generating temporal predictions. Single-trial event-related potential (ERP) and inter-trial phase coherence (ITPC) analyses allowed testing if the participants’ neural activity responded in time to sound onsets, thus encoding their precise timing. Next, we employed a time-resolved metric of ITPC (t-ITPC) to quantify the build-up of phase-coherence over the course of the auditory sequence, an indicator of temporal prediction (Breska & Ivry, 2020) and auditory processing (Ten Oever et al., 2017). Finally, we quantified the tuning of delta-band neural oscillatory activity toward the stimulation frequency (Sf). Thus, we estimated trial-level instantaneous frequency (IF), its dynamics of acceleration while tuning- and de-tuning to the Sf, its Stability (S), and Deviation (Dev) from the Sf. These newly introduced metrics would allow to estimate if and how much endogenous neural activity in the delta-band fluctuates around the prominent frequency in the acoustic stimulation. As such, it would provide new insights on the time-varying neural dynamics of entrainment while listening to temporally regular auditory rhythms.

Thirty-three participants took part in the study and signed written informed consent in accordance with the guidelines of the ethics committee of the University of Leipzig and the declaration of Helsinki. Participants comprised two patient groups and one age- and gender-matched control group: 11 patients with focal lesions in the basal ganglia (BG; mean age 50.9, range = 30–64 years; 5 males), 11 patients with focal lesions in the cerebellum (CE; mean age 52.6, range = 37–64 years; 5 males), and 11 healthy controls (HC; mean age 52.1, range = 28–63 years; 5 males). Patients’ demographics and lesion information are provided in Table 1, and their anatomical MRI is provided in Figure 1.

The HC group was recruited via a database at the Max Planck Institute for Human Cognitive and Brain Sciences (Leipzig, Germany). All participants were right-handed and matched for years of education. None of the participants were professional musicians, and they reported no history of hearing or psychiatric disorders. All participants received monetary compensation for taking part in the study. Further information on the participants and lesions characteristics can be found in Nozaradan et al. (2017).

Participants listened to 96 sequences comprising 13-to-16 tones in a recording session of approximately 25 min. Each sequence contained frequent standard tones (STD; F0 = 400 Hz, duration = 50 ms, rise and fall times = 10 ms, amplitude = 70 dB SPL) and one or two amplitude-attenuated deviant tones (DEV; amplitude 66 dB). The inter-onset-interval between successive tones was 650 ms, resulting in a stimulation frequency (Sf) of 1.54 Hz, and a total sequence duration of 8.45–10.4 s (13 to 16 tones * 650 ms; Fig. 2A).

Participants were seated in a dimly lit soundproof chamber facing a computer screen. Every trial started with a fixation cross (500 ms), followed by the presentation of an auditory sequence. The cross displayed on the screen served to prevent excessive eye movements during the presentation of the tone sequences. After each sequence, there was an inter-trial interval of 2000 ms. A session was divided into two blocks of approximately 10 min each, with a short pause in between. At the end of the experiment, participants indicated how many softer tones they heard.

The EEG was recorded by means of 59 Ag/AgCl scalp electrodes positioned according to the International 10-10 system with the ground placed on the sternum. Four additional vertical and horizontal electrodes monitored eye movements and were positioned on the outer canthus of each eye, and on the inferior and superior areas of the left orbit. The signals were amplified, low-pass filtered at 512 Hz, and digitized using a sampling rate of 1024 Hz (64-channel high-speed amplifier, Biosemi, the Netherlands). Electrode impedances were kept below 5 kΩ, and the left mastoid served as online reference. Data were referenced to an average reference offline.

EEG data were analyzed in MATLAB with a combination of custom scripts and functions and the FieldTrip toolbox (Oostenveld et al., 2011). Data were band-pass filtered with a 4th order Butterworth filter in the frequency range of .1–50 Hz (ft_preprocessing). Eye-blinks and other artifacts were identified using independent component analysis. This semi-automated routine is composed of two steps: in the first iteration, ‘fastICA’ (implemented in FieldTrip) was applied to decompose the original EEG signal into independent components (N = number of EEG channels -1). Components with a strong correlation (>.4) with the EOG time-courses were automatically identified and removed with ‘ft_rejectcomponent’ before reconstructing the EEG time-course. In a second step, ‘fastICA’ was used again, now with a dimensionality reduction to 20 components. These components were visually inspected via ‘ft_rejectvisual’ and marked as ‘outliers’ if their max values and z-scores were far from the distribution of other components. The 20 components were further visually inspected by plotting their topographies and time-series, and a second selection of ‘outliers’ was made. Taking into consideration the two visual inspections, we made a final decision on which components to remove. On average, two components were removed (‘ft_rejectcomponent’) before reconstructing the EEG time-series. In the next preprocessing step, artifact subspace reconstruction was performed as implemented in the ‘pop_clean_rawdata’ function in EEGlab, and with the ‘BurstCriterion’ parameter set to 20 (as recommended in the online EEGlab tutorials; all other parameters were set to ‘off’). To further ensure the removal of potentially noisy channels and time-points, we implemented an automatic channel rejection and an artifact suppression procedure. To this end, the median variance across channels was calculated (excluding EOG channels), and channels exceeding 2.5*median variance were defined as ‘outliers’ and removed. Similarly, the artifact suppression procedure (see Criscuolo, Schwartze, Henry, et al., 2023) interpolated noisy (>4*absolute median) time-windows on a channel-by-channel basis. Lastly, data were low-pass filtered at 40 Hz via ‘ft_preprocessing’, segmented to each auditory sequence (starting 4 s before the first tone onset and ending 4 s after the last tone onset), and downsampled to 250 Hz. All the following analyses focused on a region of interest. As in prior work (Criscuolo, Schwartze, Henry, et al., 2023), a fronto-central channel (FC) cluster was used, encompassing the sensor-level correspondents of prefrontal, pre-, para-, and post-central regions highlighted in (Fujioka et al., 2012, 2015) and further highlighted in similar EEG work on rhythm processing (Nozaradan et al., 2012). The cluster included 14 channels: ‘AFz’, ‘AF3’, ‘AF4’, ‘F3’, ‘F4’, ‘F5’, ‘F6’, ‘FCz’, ‘FC3’, ‘FC4’, ‘FC5’, ‘FC6’, ‘C3’, ‘C4’.

To perform ERP peak analyses, preprocessed data were low-pass filtered at 30 Hz via ‘ft_preprocessing’ and averaged across FC channels. ERP time-series are provided in Figure 2B, and are color-coded for each group. Next, these time-series were segmented to each tone onset in the auditory sequences (average over trials provided in Fig. 2C) and mean corrected. The mean correction uses a global mean calculated across the whole segment (-.1 to .4 s relative to tone onset) and averages across all trials (Criscuolo, Schwartze, Henry, et al., 2023, Criscuolo, et al., 2024). To perform peak analyses, we set out to identify, at the single participant level, the N100 peak amplitude and its latency for each tone onset, after averaging across sequences. We created a window of interest in the time interval between .07 s and .13 s relative to tone onsets and identified the most negative amplitude value (N100 peak amplitude) and its latency (N100 peak latency). Finally, we calculated, at the single-participant level, the variance in N100 amplitude and latency across tone positions. Peak amplitude, latency, and variance are provided in Figure 2D, pooling single-participant data per group. Analyses focused on the 3rd to the 7th tone: the first two sound onsets were excluded as they are known to trigger much stronger ERPs; the later tones are excluded because they occur in proximity of the DEV (8th position onward). Analyses on the first two tones in the sequence, where no group differences were expected, are provided in Suppl. Figure 1.

We assessed group differences in the N100 peak amplitude and latency via Mixed effect models (‘fitlme’ function in MATLAB, version 2024). The model included ‘Group’ as a fixed factor and a random intercept per participant. When the fixed effect was significant, we performed post-hoc pairwise group comparisons via permutation testing. Pair-wise comparisons were thus performed by randomly permuting data points belonging to one or the other group, with a total of 1000 permutations. This iterative procedure would ultimately assess the p-value from the original groups against the p obtained from permutations. Model information and results are reported in Suppl. Tables 1-2.

We assessed the variability in the N100 peak amplitude and latency across groups. For these two analyses, we first performed Levene’s test to assess the homogeneity of variance and later employed ANOVA. With a significant group effect, we later performed post-hoc pairwise comparisons via simple t-tests and implementing the Tukey-Kramer correction. Analyses details and results are provided in Suppl. Tables 3-4.

Inter-trial phase coherence (ITPC) analyses were conducted to test whether healthy participants and patients encoded temporal regularities in the auditory sequences. To estimate ITPC, we first performed Fast-Fourier transform (FFT). FFT analyses were performed at the single-participant, -channel, and -trial level on 8-s-long segments starting from the onset of the first tone in the auditory sequence and including a total of 12 tones. The resulting frequency resolution was .125 Hz (1/8 s = .125 Hz). As in prior work (Criscuolo, Schwartze, Henry, et al., 2023), and for the ERP analyses described above, a fronto-central channel (FC) cluster was used, including the following 14 channels: ‘AFz’, ‘AF3’, ‘AF4’, ‘F3’, ‘F4’, ‘F5’, ‘F6’, ‘FCz’, ‘FC3’, ‘FC4’, ‘FC5’, ‘FC6’, ‘C3’, and ‘C4’. Data from this FC cluster were not averaged at this stage. Next, the complex part of the Fourier spectrum was used to calculate ITPC (Fig. 3A left). ITPC was obtained by dividing the Fourier coefficients by their absolute values (thus, normalizing the values to be on the unit circle), averaging, and finally taking the absolute value of the complex mean (for further documentation see https://www.fieldtriptoolbox.org/faq/itc/). For illustration purposes, the ITPC plot in Figure 3A is restricted to 1–4 Hz. The full frequency spectrum is provided in Suppl. Figure 2, along with the Fourier spectrum in the frequency-range of 4–30 Hz.

As the stimulation frequency of the auditory sequences was 1.5 Hz, we restricted the main ITPC analyses to 1.5 Hz only. We did not conduct statistical analyses on any other frequencies (e.g., (sub)harmonics of the stimulation frequency) because we were specifically interested in assessing the neurophysiological encoding of the auditory rhythm at the stimulation frequency as previously reported in (Criscuolo, Schwartze, Henry, et al., 2023, Criscuolo, Schwartze, Prado, et al., 2023). Thus, single-participant data were pooled per group after averaging across channels and visualized as violin plots in Figure 3A (right).

Group differences were statistically assessed by means of a 1-way ANOVA with a group factor (anova1 built-in in MATLAB), followed by post-hoc simple tests corrected for multiple comparisons via Tukey-Davis correction (multcompare built-in in MATLAB) in case of a significant (p < .05) main effect (Suppl. Table 5). Simple effects with a p-value below an alpha-corrected .05 were considered statistically significant. The choice of the parametric test was informed by Levene’s test for homogeneity of variance (Suppl. Table 5).

Additional analyses were performed to test the hypothesis that group differences are specific to the rhythm of the auditory sequences. We statistically assessed group differences in the alpha (8–12 Hz) frequency band following the same statistical procedure as detailed above, for both the ITPC and Fourier spectrum (Suppl. Fig. 2).

A time-resolved metric of ITPC (t-ITPC) was estimated to quantify the build-up of phase-coherence over the course of an auditory sequence. For doing so, we first employed time-frequency transform (TF data), then calculated the t-ITPC using the complex spectra of TF data (same procedure as in the ITPC above), and finally calculated the slope of the t-ITPC at the single-participant level. More details are provided in the respective paragraphs below.

After preprocessing, single-trial EEG data underwent time-frequency transformation (‘ft_freqanalysis’) by means of a wavelet-transform (Cohen, 2014). The bandwidth of interest was centered around the stimulation frequency (+/- 1 Hz, i.e., .54 - 2.54 Hz, thus obtaining a 1.54 Hz center frequency), using a frequency resolution of .2 Hz. The number of fitted cycles was set to 3. The single-trial approach results in ‘induced’ (as compared to ‘evoked’) responses. The output was a complex spectrum; no averaging over channels, trials, or participants was performed at this stage.

As for the ITPC above, t-ITPC was obtained by dividing the complex coefficients of TF-data by their absolute values (thus, normalizing the values to be on the unit circle), averaging, and finally taking the absolute value of the complex mean. Next, we calculated the slope of each t-ITPC time-series by fitting a first-order polynomial (‘polyfit’ function in MATLAB; p) and then deriving a first-order approximation (p(1)*Time+p(2)). The calculation of the slope was performed on a 5-s-long interval starting from the 3rd tone onset.

Before assessing group differences in the t-ITPC, we performed Levene’s test for homogeneity of variance. As the p returned significant, we implemented non-parametric group comparisons via a Kruskal-Wallis test. With a significant group effect, we later assessed pairwise group comparisons via permutation testing and with a total of 1000 permutations. This iterative procedure would ultimately assess the p value from the original groups against the p obtained from permutations. Analysis steps and results are reported in Suppl. Table 6.

We aimed at assessing the tuning of endogenous delta-band neural oscillatory activity towards the stimulation frequency (Sf). A self-sustained endogenous oscillator capable of entrainment should adjust its frequency and phase so to align to external temporal regularities, or rhythms. Such an active process is displayed in tuning dynamics during which the endogenous oscillator accelerates and decelerates to align its period to an external rhythm. Thus, we calculated the instantaneous frequency (IF) and quantified acceleration (Acc) dynamics. While processing the auditory rhythm, oscillations may be fluctuating around the Sf with various magnitude and deviating from the Sf. We consequently calculated metrics of stability (S) and deviation. Each metric was estimated at the single-participant and -trial level as illustrated in Figure 4A: on top, the time-course of delta-band filtered Hilbert-transformed data; in the middle, IF as the derivative of phase evolution over time, considering the sampling frequency; at the bottom, Acc was calculated as the derivative of IF. The dashed pink line on the IF plot indicates the Sf. On the right side, the distribution of IF and Acc in the ‘Pre-’, ‘Post-’, and ‘Dur-(ing)’ the listening periods (color-coded in shades of blues), and pooling across the FC channel cluster. The time-series of IF and Acc were further used to estimate S, the stability of the neural signal. Finally, we obtained the Latency and Deviation (not visualized in the top panel): the first corresponds to the first crossing point of IF through the horizontal Sf line; the latter is the standard deviation from the Sf. Individual data were then pooled into three groups: HC, CE, and BG patients. Details for each of the metrics are provided in the respective sections below.

After preprocessing, single-trial EEG data were bandpass-filtered with a 3rd-order Butterworth filter centered around the stimulation frequency (plus and minus 1 Hz, .54–2.54 Hz, obtaining a 1.54 Hz center frequency; ft_preprocessing) and Hilbert-transformed to extract the analytic signal. Next, the instantaneous frequency (IF) at each time point (t), and for each channel, trial, and participant, can be calculated with the following formula:

Where $ω$(t) is the derivative of the unwrapped phase (⁠$θ$⁠) at each time point (t), given the time-steps (⁠$dt$⁠) and FS is the sampling frequency. IF can also be obtained in MATLAB using the ‘instfreq’ function.

Once calculated the single-participant, -trial, and channel-level IF, acceleration (Acc) was calculated as the first derivative of IF. Thus, we employed the following formula:

After the single-participant, -trial, and channel-level Acc was obtained, Stability (S) was calculated as the inverse of the sum of absolute changes in Acceleration. Thus, we employed the following formula:

Once the single-participant, -trial, and channel-level IF was obtained, we quantified the standard deviation (D) from the stimulation frequency. D was calculated as the square-root of the mean squared difference between the IF and the stimulation frequency (Sf):

For each participant, trial, and channel, we estimated how long it took for the IF to tune to the Sf (1.5 Hz). The search was performed within the first 8 s of listening (–8 s) of each trial, and by using a narrow frequency criterion (Sf± .2 Hz).

Group differences were statistically assessed for each of the above-mentioned metrics by means of a one-way ANOVA with a group factor (anova1 built-in into MATLAB), followed by post-hoc simple tests corrected for multiple comparisons (Tukey-Davis correction) (multcompare built-in into MATLAB) in case of a significant (p < .05) main effect. Simple effects with a p-value below an alpha-corrected .05 were considered statistically significant and are depicted as horizontal black lines on top of Figure 4B. The ANOVA tables and simple tests for significant effects are provided in Suppl. Table 6.

In this EEG study, we adopted two complementary methodological approaches.

First, we reproduced typical event-related potential (ERP) and inter-trial phase coherence (ITPC) analyses to test if and how participants’ neural activity encoded the temporal regularity of sound onsets. In the second analysis step, we employed a time-resolved metric of ITPC (t-ITPC) to quantify the build-up of phase-coherence over the course of the auditory sequence. The t-ITPC slope could indicate a mechanism of phase-alignment toward next sound onsets (Breska & Ivry, 2020; Ten Oever et al., 2017). Next, we introduced a new method to assess the tuning of endogenous delta-band neural oscillatory activity toward the Sf. We quantified trial-level instantaneous frequency (IF), its dynamics of acceleration while tuning- and de-tuning to the Sf, its Stability (S), and Deviation (Dev) from the Sf.

Details for each methodological approach can be found in the respective methods section above. Results for each method are discussed below.

After computing the sequence-level (Fig. 2B) and tone-level ERPs (Fig. 2C), we obtained single-participant N100 peak amplitude, latency (Fig. 2D, top) and later estimated the variance across tone positions (Fig. 2D, bottom). Participant-level N100 peak amplitude and latency separately entered a Mixed-Effect Model with a Group Factor and a random intercept per participant. The first model reported a significant group effect for N100 peak amplitude (F(2,165) = 2.33, p = .02; (Suppl. Table 2). Post-hoc pairwise comparisons showed that CE had a lower N100 amplitude peak than HC (Obs Diff = -3.23, p = .01, Eff size = -1.33). There were no significant differences between HC and BG, nor between CE and BG (Suppl. Table 1).

The second model reported no significant group effect for N100 peak amplitude latency (F(2,165) = -.16, p = .88). Next, we assessed the variability in the N100 peak amplitude via a one-way ANOVA with a group factor. The ANOVA reported a significant group effect (F(2,30) = 21.26, p < .001; Suppl. Table 2, middle), and pairwise post-hoc comparison revealed that HC had higher variance than either CE or BG, but there was no difference between CE and BG (Suppl. Table 2, bottom). Finally, we assessed the variability in N100 peak amplitude latency. The ANOVA reported a significant group effect (F(2,30) = 22.14, p < .001; Suppl. Table 3, middle) and pairwise post-hoc comparison revealed that both CE and BG had higher variance than HC but there was no difference between CE and BG (Suppl. Table 3, bottom).

Additional analyses confirmed that there were no group differences in the amplitude and variance of P50, N100, and P200 peaks in the first two tones of the auditory sequence (Suppl. Fig. 1).

While participants listened to isochronous auditory sequences presented at an Sf of 1.5 Hz (Fig. 2A), their neural activity responded timely to tone onsets, as shown by the coherence peaks at 1.5 Hz in the ITPC spectrum (Fig. 3A, left). A distinct peak at 1.5 Hz was present in the ITPC spectrum for all groups. However, statistical analyses revealed significant group differences (Fig. 3A, right): HC (dark blue) showed stronger coherence at the Sf than both CE and BG groups (lighter shades of blue). The one-way ANOVA revealed a significant group effect (F(2,30) = 5.25, p = .01; Suppl. Table 4), and post-hoc simple t-tests revealed higher coherence in HC than in both CE (p = .04) and BG (p= .02) groups, but no significant difference between CE and BG (Suppl. Table 4; corrected for multiple comparisons via Tukey-Kramer). To confirm the specificity of the effects to neural dynamics centered at the stimulation frequency, we conducted additional statistical analyses on rhythm-unrelated frequency-bands. Following the same statistical procedure detailed above, we showed no group differences in the alpha (8–12 Hz) frequency band, neither for the ITPC nor the Fourier spectrum (Suppl. Fig. 2).

We estimated a time-resolved metric of ITPC (t-ITPC) to quantify the build-up of phase-coherence over the course of the auditory sequence. T-ITPC was obtained by quantifying phase coherence from the complex spectra of continuous wavelet transformed data in the delta frequency band. The group-level time course is displayed in Figure 3B, color-coded per group. Next, we calculated, at the level of the single-participant, the slope of t-ITPC over a 5 s interval starting from the third tone onset. Participant data were pooled into groups (Fig. 3B, right), and we later performed group comparisons via non-parametric analysis of variance via a Kruskal-Wallis test. The Group effect was significant (Chi-sq (2,30) = 15.4, p < .001), and pairwise group comparisons performed via permutation testing (1000 permutations) revealed a significantly steeper t-ITPC slope for HC than for both CE and BG patients (Suppl. Table 5).

To assess the tuning of endogenous delta-band neural oscillatory activity toward the Sf, we quantified trial-level instantaneous frequency (IF), its dynamics of acceleration while tuning- and de-tuning to the Sf, its Stability (S), and Deviation (Dev) from the Sf. The group-level data are provided in Figure 4B. On the right side, the violin plots show (in order) the IF and Acc, obtained by averaging data during the listening window (0-8 s) and across channels and trials. Next to it are the distributions of Dev, S, and latency.

We performed independent comparisons for the metrics mentioned above and focused on the listening period only (‘Dur’). The only group comparison showing a significant effect was for Stability: F(2,30) = 4.36, p = .02. Post-hoc simple tests showed that CE had lower Stability than HC (p = .016; Suppl. Table 6), while no difference was found between HC-BG nor between CE-BG (p> .05). The reduced Stability in CE patients reflects high variability in acceleration dynamics of delta-band activity, ultimately suggesting a poorer neural representation of temporal regularity displayed in the auditory sequences. No group difference was detected for Dev nor other metrics (p> .05).

In this EEG study, we investigated the causal contributions of the cerebellum (CE) and the basal ganglia (BG) to the capacities to encode and predict temporally regular auditory streams.

We first assessed the encoding of sound onset timing via event-related (ERP) and inter-trial phase coherence (ITPC) analyses. The assessment of the N100 amplitude and latency along with the ITPC amplitude at the Sf (1.5 Hz) allowed testing whether the participants’ neural activity responded in time to sound onsets, thus encoding their precise timing. In line with previous evidence, we expected CE but not BG patients to show altered encoding of sound onsets: this would result in increased N100 latency variability and reduced ITPC.

While ITPC and similar phase concentration measures are typically interpreted as a proxy of entrainment, it is generally hard to disentangle true entrainment from a series of evoked responses (Breska & Deouell, 2017; Haegens & Zion Golumbic, 2018; Obleser et al., 2017; Zoefel et al., 2018). In fact, simulations showed that evoked responses drive high-phase coherence (Breska & Deouell, 2017; Obleser et al., 2017), ultimately weakening its functional link with temporal prediction. Thus, in a second analysis step, we introduced a novel approach to assess finer-grained measures of neural dynamics of temporal processing. First, we employed a time-resolved metric of ITPC (t-ITPC) to quantify the build-up of phase-coherence over the course of the auditory sequence. Such a metric was previously shown to be a good indicator of temporal prediction (Breska & Ivry, 2020) and auditory processing (Ten Oever et al., 2017). Next to event-related t-ITPC peaks, which are induced by the phase rest of oscillations at tone onsets, the t-ITPC slope could indicate a mechanism of anticipation of next sound onsets. Thus, we expected BG but not CE patients to show a shallower slope of t-ITPC along the auditory sequence, potentially indicating altered temporal predictions.

Next, we showcased new metrics to assess the tuning of endogenous delta-band neural oscillatory activity toward the Sf. We quantified trial-level instantaneous frequency (IF), its dynamics of acceleration while tuning- and de-tuning to the Sf, its Stability (S), and Deviation (Dev) from the Sf. We expected BG and CE patients to show reduced S and greater Dev than HC, indicating their altered capacity to align neural dynamics to predictable onsets.

We found that CE patients showed lower N100 amplitudes, and increased N100 latency variability than healthy controls (HC). Furthermore, they displayed a reduced ITPC at the Sf, and a nearly flat t-ITPC slope. In contrast, HC showed an increasing slope over the course of the isochronous tone sequence, indicating increased alignment of oscillatory activity to the temporal regularity. Finally, analyses of neural dynamics revealed a tendency toward an increased deviation from the Sf, and a significant reduction in stability in CE compared to HC. Thus, while not deviating largely from the Sf, reduced stability might reflect abundant fluctuations in acceleration dynamics. Altogether, increased variability in ERPs, reduced delta-band phase coherence, reduced slope of t-ITPC, and reduced stability of delta-band dynamics observed in CE patients suggest altered neural encoding of temporally regular sound onsets and impaired temporal predictions. These observations align with previous evidence linking the CE to the encoding of the precise timing of sensory events (Bareš et al., 2018; Ivry et al., 1988; Ivry & Keele, 1989; Ivry & Schlerf, 2008) and to the processing of temporal intervals (Breska & Ivry, 2020, 2021; Grube, Cooper, et al., 2010; Grube, Lee, et al., 2010; Teki, Grube, & Griffiths, 2011; Teki, Grube, Kumar, et al., 2011). Thus, these results confirm that CE lesions affect the capacity to predict temporal intervals (Breska & Ivry, 2018, 2020, 2021; Grube, Cooper, et al., 2010), potentially impacting the capacity to synchronize ongoing neural activity with external rhythms (Ivry & Keele, 1989; Ivry et al., 1988). However, differently from previous literature (e.g., Breska & Ivry, 2018, 2020, 2021), we show that timing processes in CE lesion patients is not comparable to healthy controls when processing isochronous tone sequences. Possible interpretations for this and other discrepancies related to prior research are provided in the following.

Regarding BG lesion patients, we found increased variability in the N100 peak amplitude latency and a significant reduction in ITPC peak at the Sf. Furthermore, BG lesions were associated with a reduced slope of the t-ITPC. No differences were found in the neural dynamics metrics (stability and deviation) which indicates similar tuning dynamics toward the Sf (stability) and small deviations from the Sf (deviation) in delta-band activity, as observed in HCs. The increased latency variability observed in ERPs and the reduction of the ITPC peak at the Sf suggest altered encoding of temporal regularity in auditory sequences (Breska & Ivry, 2020; Nozaradan et al., 2017; Schwartze et al., 2015). The reduction in the t-ITPC slope suggests that BG lesions causally impacted the generation of expected tone onsets, thus aligning with and supporting prior evidence linking the BG with temporal prediction (Grahn, 2009; Grahn & Brett, 2009; Schwartze et al., 2011; Teki, Grube, Kumar, et al., 2011).

While most of the employed metrics (variability in ERPs, ITPC, t-ITPC) did not dissociate specific contributions of BG and CE to sound processing in isochronous sequences, CE but not BG patients clearly displayed reduced ‘stability’. Both ‘stability’ and ‘deviance’ are new metrics to quantify fine-grained fluctuations in delta-band dynamics while tuning- to and de-tuning from the temporal regularity (1.5 Hz; the Sf) in isochronous tone sequences. ‘Deviance’ indicates the degree of deviation from the Sf: in both patient groups, instantaneous delta-band activity fluctuated around the Sf, comparable to HCs. The ‘stability’ metric quantifies fluctuations in acceleratory dynamics while tuning-in and -out of Sf. Change in this metric only showed in CE patients, and the reduction in ‘stability’ likely highlights a poorer neural encoding of event onsets in isochronous tone sequences and of temporal intervals. This observation supports the fundamental role of the CE in generating and maintaining stable neural representations of temporal regularities in the sensory environment.

Most of the current results, however, fail to reconcile with previous literature showing fundamental dissociations between rhythm- and interval-based temporal predictions in BG and CE lesion patients (e.g., Breska & Ivry, 2018; Schwartze & Kotz, 2013), and with evidence showing that temporal predictions in CE lesion patients are comparable to healthy controls when tested in rhythmic contexts (Breska & Ivry, 2018, 2020, 2021).

How can these differences be explained? A few factors might have mediated these differences: the experimental paradigm, attention, sample size, and the exclusive focus on delta-band activity. Furthermore, compensatory strategies may further mask results. In fact, in contrast to prior work employing a few repeated temporal intervals and active task settings (e.g., Breska & Ivry, 2018), here we tested endogenous timing: participants were exposed for 20 min to 8-to-11 s long auditory sequences, and their attention was diverted from the temporal aspects of the sequence as they were asked to count the N of deviant (amplitude attenuated) tones. Thus, the long exposure to an auditory isochronous stream and the absence of an explicit timing task allowed us to test temporal processing in absence of attention. Consequently, we might argue that, at least in passive listening, we cannot dissociate the roles of BG and CE. The use of isochronous auditory sequences, as opposed to complex auditory rhythms, might represent another limitation as these stimuli may have been suboptimal to dissociate CE-related sensory timing computations from BG-related temporal predictions. The small sample size may represent another limitation, as it might have not provided the adequate statistical power to discern such fine dissociations. In addition, it is possible that both patient populations employed compensatory mechanisms, thus masking out existing differences. In fact, we have previously discussed that BG and CE are part of a widespread cortico-subcortical network engaged in rhythm processing. Animal literature shows that there are neurons in the cortex acting as ‘neural chronometer’ encoding the passage of time and the precise timing of sensory events (Merchant et al., 2011; Merchant, Harrington, et al., 2013; Merchant, Pérez, et al., 2013). These cortical neurons may take over timing computations as a functional reorganization mechanism after subcortical brain lesions, ultimately preventing to dissociate BG and CE’s roles in basic timing functions.

Finally, another limitation lies in the difficulty to distinguish fine-grained timing processing in the absence of spatiotemporally resolved data. In this perspective, this research field would benefit from a more accurate characterization of the time-course, strength, and directionality of information flow during rhythm processing. Such an approach would allow to monitor the interplay and the causal relationship between cortico-subcortical regions, as well as between the BG and CE. Furthermore, it would enable to characterize the frequency-specificity and directionality of influence of some timing computations. In fact, while we here focused on delta-band activity only, literature suggests beta-band activity to also be prominent in subcortical and cortical brain regions (Bartolo et al., 2014; Bartolo & Merchant, 2015; Keitel et al., 2017; Keitel & Gross, 2016) and to further be linked to predictive priming of sensory regions (Arnal, 2012; Engel & Fries, 2010). In other words, the anticipatory alignment of beta-band activity to the when of salient events (Fujioka et al., 2012, 2015) couples with bottom-up delta-band activity (Abbasi et al., 2018; Arnal et al., 2015; Merchant et al., 2015; Saleh et al., 2010) to instantiate motor-to-auditory predictions in support of adaptive behavior. Accumulating evidence links cerebellar beta-band activity to temporal and spatial predictions, as well as to the fine processing of the timing of stimuli and action (Andersen & Dalal, 2024). In fact, beta-band activity from the cerebellum was associated with sensory predictions in temporally regular contexts (Andersen & Lundqvist, 2019). Cerebellar beta-band strength is modulated by the temporal predictability of sensory streams (Andersen & Dalal, 2021), and might have a general, modality-independent, role in building temporal expectations during sensory and sensorimotor processes (Herrojo Ruiz et al., 2017). Thus, our focus on scalp activity and on delta-band activity only may have prevented a full characterization of bottom-up and top-down mechanisms of temporal processing and prediction in BG and CE lesion patients. We encourage future studies to better elucidate the link between the observed alterations in delta-band dynamics and top-down beta-band modulatory activity.

Overall, the newly employed metrics allowed characterizing dynamics of delta-band oscillations in basic rhythm processing: we showed that delta oscillations fluctuate over time, tuning in and out of perceived acoustic regularity in auditory sequences by dynamically accelerating and slowing down from silence to listening periods, and further increasing phase coherence over time. These observations support the dynamic attending hypothesis (Jones & Boltz, 1989; Large & Jones, 1999), and confirm the role of low-frequency oscillations (Schroeder & Lakatos, 2009) in encoding and predicting temporal regularities in the auditory environment. On the other hand, the current approach also confirmed the fundamental role of the BG and CE in an extended cortico-subcortical-cortical network underlying rhythm and timing processing (Criscuolo, Pando-Naude, et al., 2022; Kasdan et al., 2022; Kotz et al., 2018; Schwartze & Kotz, 2013).

In fact, we showed that while the healthy brain could flexibly and dynamically respond to and synchronize with sensory inputs, patients with lesions in the BG and CE did not. Patients showed a degree of heterogeneity and deteriorated capacity to synchronize ongoing neural activity to temporal regularities in the acoustic environment. Differently from our hypotheses, however, our EEG data did not clearly dissociate CE from BG timing functions in isochronous contexts. While we delineate potential limitations in our experimental paradigm, these observations motivate novel research on the causal role of subcortical circuitries in basic timing processing. We encourage future studies to complement the current findings with spatiotemporally resolved assessments of delta-, beta-band activity and their dynamic interaction. Such a complementary approach would deepen our understanding of the neurophysiological mechanisms underlying intra- and inter-individual variabilities in the capacities to detect, produce and synchronize with temporal regularities in the sensory environment, and to ultimately produce adaptive behavior.

The capacities to encode the precise timing of the sensory events around us, and to time our (re-) actions to changes in the environment are pivotal to act and adapt in a dynamically changing environment. In this study, we explored the rich and variegated landscape of neural oscillatory dynamics, and assessed if, when, and how neural oscillations processed the temporal regularity in acoustic sequences. BG and CE lesions causally impacted the neurophysiological encoding of the rhythm, as demonstrated by reduced capacities to encode precise tone onsets and predict the timing next events.

The data and analysis code in use will be made available upon reasonable request by the corresponding author.

S.A.K., M.S., and S.N., conceptualized the study. S.A.K., M.S., collected the data. A.C. designed and performed data analyses. A.C., S.A.K., M.S., and S.N. interpreted the results and wrote the manuscript.

The work was funded by KNAW Van der Gaag beurs (WF/1627) to A.C.

The authors declare no competing interests.

The authors would like to thank Anne-Kathrin Franz, Christian Obermeier, and Heike Boethel for support during data acquisition; Anika Stockert for support in the preparation of the clinical data; and Julio Rodriguez-Larios for initial data discussion and analysis exploration. The authors would also like to thank the anonymous reviewers for their help in improving the overall quality of this article.

Supplementary material for this article is available with the online version here: https://doi.org/10.1162/imag_a_00492.