Individual differences in procedural learning are associated with fiber specific white matter microstructure of the superior cerebellar peduncles in healthy adults

Functional neuroimaging has consistently implicated the fronto-basal ganglia-cerebellar circuit in procedural learning-defined as the incidental acquisition of sequence information through repetition. Limited work has probed the role of white matter fiber pathways that connect the regions in this network, such as the superior cerebellar peduncles (SCP) and the striatal premotor tracts (STPMT), in explaining individual differences in procedural learning. High angular diffusion weighted imaging was acquired from 20 healthy adults aged 18-45 years. Fixel-based analysis was performed to extract specific measures of white matter microstructure (fiber density; FD) and macrostructure (fiber cross-section; FC), from the SCP and STPMT. These fixel metrics were correlated with performance on the serial reaction time (SRT) task, and sensitivity to the sequence was indexed by the difference in reaction time between the final block of sequence trials and the randomized block (namely, the 'rebound effect'). Analyses revealed a significant positive relationship between FD and the rebound effect in segments of both the left and right SCP (pFWE < .05). That is, increased FD in these tracts was associated with greater sensitivity to the sequence on the SRT task. No significant associations were detected between fixel metrics in the STPMT and the rebound effect. Our results support the likely role of white matter organization in the basal ganglia-cerebellar circuit in explaining individual differences in procedural learning.


Introduction
Procedural learning refers to the process of acquiring and retrieving information in an automated, unconscious manner (Nicolson & Fawcett, 2007). The procedural learning mechanism is typically slow, requiring considerable repetition before skills and knowledge are learned and can be retrieved automatically. This process is fundamental to the learning and expression of a range of motor (e.g., tying shoelaces), cognitive (e.g., producing language) and social functions (e.g., human interaction).
Procedural learning has been widely studied using the serial reaction time (SRT) task (Nissen & Bullemer, 1987). In this task, a visual stimulus appears repeatedly in one of four spatial locations on a computer screen. Participants are asked to respond to the location of the stimuli by pressing corresponding keys on keyboard. Unbeknown to participants, the stimuli are presented in a predefined, repeating visuospatial sequence. Despite a lack of awareness of the sequence, participants exhibit progressively faster reaction times across successive blocks of sequence trials, which indicates that the sequence is being implicitly learned. After multiple sequence blocks, participants are then presented with stimuli in a random visuospatial order. Here, participants typically exhibit an increase (or slowing) in reaction time. The magnitude of the increase in reaction time between the final sequence block and the random block is referred to as the 'rebound effect' and is often used to infer qualitative properties of the procedural learning process (Janacsek & Nemeth., 2013;Robertson, 2007). Participants who are more sensitive to the sequence embedded in the task typically exhibit a larger rebound effect, since taking the sequence away causes them to slow down their responses significantly. In this way, a larger rebound effect is typically thought to indicate higher levels of proficiency with respect to learning the sequence.
Properties of the fronto-basal ganglia-cerebellar circuit have been implicated in procedural learning. A recent functional neuroanatomical Activation Likelihood Estimation (ALE) meta-analysis revealed robust activation in the basal ganglia, cerebellum, and premotor regions during SRT task performance in healthy adults (Baetens et al., 2020;Janacsek et al., 2020). The implication of the involvement of these regions in sequence learning is broadly consistent with previous models (Doyon et al., 2003;Penhune & Steele, 2012), as well as with empirical findings in neuroimaging studies (Daselaar et al., 2003;Willingham et al., 2002). Evidence from lesion studies also reveal that patients with neurological diseases of basal ganglian circuitry (Parkinson's Disease e.g., Siegert et al., 2006; Huntington's Disease e.g., Knopman & Nissen, 1991), and cerebellar damage (e.g., Morgan et al., 2021) present with procedural learning impairments. Specifically, these patients tend to exhibit a smaller (or absent) rebound effect on the SRT task, relative to healthy controls (Clark et al., 2014;Knopman & Nissen, 1991;Pascual-Leone et al., 1993;Siegert et al., 2006). Altogether, this work underscores the role of frontobasal ganglia-cerebellar circuitry in procedural learning.
Despite these interesting findings, the fMRI studies have not considered the white matter tracts connecting these regions. Functional brain activations are likely to be subserved by the organization of the white matter fiber tracts that make up the connections of the fronto-basal ganglia-cerebellar circuitry (Filley, 1998). Indeed, there is a growing body of evidence demonstrating that microstructural organization within white matter tracts is not only susceptible to the effects of experience and practice (e.g., Scholz et al., 2009), but may provide a reliable predictor of individual differences in behavior and cognition across the lifespan (Filley & Fields, 2016;Forkel et al., 2021). Therefore, investigating white matter organization is just as important as identifying gray matter regions involved in procedural learning. This may further our understanding of the role played by the tracts that connect and mediate communication between regions in explaining, at least in part, individual differences in procedural learning.
To our knowledge, only one study has examined the role of white matter connectivity in procedural learning in healthy adults. Bennett et al. (2011) used diffusion tensor imaging (DTI) to model white matter microstructure in the caudatedorsolateral prefrontal cortex (DLPFC) and the hippocampus-DLPFC in healthy younger and older adults (N ¼ 28). Using a variant of the traditional SRT task to measure procedural learning (Howard & Howard, 1997), they found a positive relationship between learning on this task and fractional anisotropy (FA) in both tracts. The authors suggest that higher FA values indicate more consistent diffusion, and thus better integrity of the underlying tract. However, we now know that this interpretation is problematic (see below). And, whilst the regions explored by these authors included the caudate (which forms part of the basal ganglia), there is limited overlap between the tracts probed in this study and the regions which more recent work has implicated in procedural learningdthese being properties of the fronto-basal ganglia-cerebellar circuitry (Baetens et al., 2020;Janacsek et al., 2020). Since no study has directly probed the association between procedural learning and white matter organization within fronto-basal ganglia-cerebellar circuitry, the broader role of the microstructure supporting this network in procedural learning is still yet to be elucidated.
Whilst the DTI method adopted by Bennett et al. (2011) remains most common for reconstructing white matter tracts in vivo and generating metrics with which to infer underlying white matter microstructure (O'Donnell & Westin, 2011), this technique has been criticized for its inability to account for the presence of complex fiber orientations within a given voxel (Tournier et al., 2011). This is problematic, since 90% of white matter voxels contain crossing fibers (Jeurissen et al., 2013). Because of this limitation, the metrics that result from DTI (e.g., FA) are non-specific to the underlying biophysical properties that drive inter-individual variations in white matter microstructure. Accordingly, we cannot be confident that the effects found in prior work are a valid representation of white matter organization and its relevance to performance differences in procedural learning.
Constrained spherical deconvolution (CSD) is an alternative method for characterizing white matter organization in vivo which, unlike DTI, is sensitive to the presence of multiple fiber orientations within a single voxel (Dell'Acqua & Tournier, 2018). Consequently, tractography based on CSD affords greater biological plausibility compared to DTI modelling. As well as this, Fixel-Based Analysis (FBA) is a fiber-c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2 specific analysis framework that can be used to analyze CSD data (Dhollander et al., 2021). By generating metrics at a fiberpopulation level within a voxel (i.e., fixel), resultant FBA metrics can be more accurately attributed to fiber populations of interest (compared to tensor-derived metrics e.g., FA). These metrics include fiber density (FD), a measure of the microscopic density of a given fiber population, and fiber crosssection (FC), a measure of the macroscopic cross-sectional region occupied by a given fiber bundle (Raffelt et al., 2017). Considering the increased specificity, FBA offers promise for characterizing white matter organization within tracts that facilitate communication between fronto-basal ganglia-cerebellar regions, and their putative association with procedural learning.
The current study aimed to be the first to clarify the role of the fronto-basal ganglia-cerebellar systems in procedural learning using the novel FBA framework. By using more specific measures of white matter organization, we hoped to achieve higher sensitivity and specificity identifying significant associations with inter-individual variability in procedural learning. Specifically, we targeted the superior cerebellar peduncles (SCP), which support communication between the cerebellum and basal ganglia; and the striatal premotor tracts (STPMT), which connect the premotor and basal ganglia network. These tracts were chosen since they subserve regions previously implicated in functional imaging studies (Baetens et al., 2020;Janacsek et al., 2020). The SRT task was administered to measure procedural learning, and the rebound effect was calculated for each participant. We hypothesized that higher FD and FC in the SCP and STPMT would be associated with better performance on the SRT task, as indexed by the magnitude of the rebound effect.

Participants
Participants were 22 healthy adults aged 18e45 years (M Age ¼ 27.41 ± 6.98, 10 female), recruited via social media, and advertisements placed at Deakin University. Exclusionary criteria were a known serious medical or neurodevelopmental condition that might be expected to impact procedural learning (e.g., autism spectrum disorder or dyslexia), and contra-indications of MRI (e.g., claustrophobia or metal in the body). These criteria were implemented at the recruitment stage. As noted later, a sample of 20 participants were included in our final analyses, since two participants were excluded based on SRT task data. All participants gave informed consent and were reimbursed for their time. The Deakin University Human Research Ethics Committee approved the experimental procedures. No part of the study procedures or analyses were pre-registered prior to the research being conducted. Sample size was based on recent meta-analyses which show that effects between the rebound measure and neurophysiological metrics are often detected where z20 participants or more are included (e.g., Janacsek et al., 2020).

SRT task
Participants completed the SRT task while in the MRI scanner. The task involved a visual stimulus appearing in one of four horizontal locations on a computer display, which participants viewed via a tilted mirror located on the head coil. At the beginning of a trial, participants viewed a black screen with four white squares, indicating the spatial locations that the visual stimulus could appear. Then, a visual stimulus appeared on the screen. Unlike most versions of the SRT task which typically use a dot or asterisk as visual stimuli, we chose to present participants with abstract wingdings characters that changed on each trial. This modification to the presentation of stimuli appears to mask the embedded sequence (Koch et al., 2020;Lum, 2020), which is important in ensuring that participants engaged with implicit (and not explicit) learning. When the wingdings stimuli appeared, participants were instructed to use their dominant hand to press one of four buttons on an MRI compatible response box that corresponded to the stimuli's location: the left-most button corresponded to the left-most location on the screen, and so forth. Participants were instructed to respond to each stimulus as quickly and as accurately as possible. Following each response, participants were given feedback in the form of a box appearing over the position they indicated. These events represented one trial. The task consisted of eight blocks of 50 trials. To ensure each trial and block were the same length, the wingdings characters and feedback stayed on the computer display until 550 ms had elapsed. Failure to respond within this time frame was coded as an incorrect response. Each block was separated by a 15s rest period in which only the four white squares appeared on the display. The SRT task is publicly available on the Open Science Framework: https://osf.io/n4cme/. A schematic overview of the SRT task and stimuli can be viewed in Fig. 1. Participants were not informed that on Blocks 1e6, the presentation of stimuli followed a 10-item circular sequence (repeated 5 times to equal 50 trials per block). The sequence used was "3-4-1-2-4-1-3-4-2-1", with "1" representing the left-most position on the screen, and "4" representing the right-most position. On Blocks 7e8, the visual stimulus appeared pseudo-randomly in one of the four spatial locations adhering to the following constraints. First, the visual stimulus appeared in each spatial location as per the blocks comprising sequence stimulus presentations. Second, the visual stimulus could not appear in the same location on two consecutive trials. Specifically, one of ten wingding characters were randomly selected, without replacement, to appear on each trial. The randomization was reset at the end of each ten trials.
The behavioral data analyzed from the SRT task were manual reaction times (RTs), which measured the time taken to provide a manual response following stimulus onset. Only RTs associated with a correct response were analyzed. The RT data were averaged over consecutive pairs of blocks to create three blocks of sequence trials (S1, S2 and S3) and one block of random trials (herein, R1). For example, RT data from Blocks 1 and 2 were averaged to create the first sequence block (herein, S1), data from Blocks 3 and 4 were averaged to create the c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2 second sequence block (herein, S2) and so on. Finally, RT data from Blocks 7 and 8 were averaged to create R1. The dependent measure of sequence learning adopted in this studydthe rebound effectdwas computed by calculating R1 minusS3. Positive values indicated that participant's RT slowed down following the introduction of R1, and larger values indicate greater sensitivity to the change from sequence to random blocks (Clarke et al., 2014;Robertson, 2007). Importantly, as detailed below, the main analysis utilized a standardized value for the rebound effect to control for individual differences in processing speed (see section 2.5.1 for a detailed explanation of the calculation). contiguous slices. A total of 64 gradient directions with b ¼ 3000 sec/mm 2 and one non-weighted image (b ¼ 0 sec/mm 2 ) were captured. A pair of reverse phase-encoded b ¼ 0 images were also collected to correct for susceptibility-induced EPI distortions.

Fiber orientation distribution calculation
Response functions were estimated for gray matter, white matter, and cerebrospinal fluid, and then averaged across participants to generate group-level response functions for each tissue type . Using these group average response functions, Single-Shell 3-Tissue CSD (SS3T- Fig. 1 e Schematic overview of the serial reaction time (SRT) task. The task contained 8 blocks of 50 trials. Each trial consisted of a blank screen, followed by stimulus presentation, then visual feedback of the participant's response. Blocks 1e6 were composed of a predefined 10-item repeating circular sequence. Blocks 7e8 presented the visual stimuli in a random visuospatial order. Participants used their dominant hand to press the button on the response box that matched the visuospatial location of the stimulus. The left-most button corresponded to the left-most location on the screen (i.e., "1" in the sequence), and so forth. SEQ ¼ sequence block; RAND ¼ random block.
CSD) was performed for each participant to generate individual fiber orientation distribution (FOD) maps (Dhollander & Connelly, 2016). FOD maps then underwent intensity normalization to make the FOD magnitudes comparable between participants (Raffelt et al., 2017). A study-specific population template using FOD maps from all 22 participants was then generated. Each participant's individual FOD map was subsequently registered to the population template and segmented to produce individual fixel maps for each participant (Raffelt et al., 2017).

Fixel metric calculations
Fixel metrics including FD and logFC were computed for each participant across all white matter fixels in their fixel map, as described in Raffelt et al. (2017). This produced a whole-brain FD and logFC fixel map for each participant. Of note, FC was logtransformed as per the MRtrix3 suggestion for FC-based statistical analyses to ensure data is normally distributed (see www.mrtrix.org). These two metrics were used for further analyses.

Tracts of interest generation
We used TractSeg to delineate the SCP and STPMT, which is a novel semi-automated probabilistic tractography tool (Wasserthal et al., 2018(Wasserthal et al., , 2019. This approach provides fast and accurate segmentation of white matter bundles from diffusion MRI, and provides a robust balance between manual delineation and automated atlas-based tracking approaches (Wasserthal et al., 2018(Wasserthal et al., , 2019. Specifically, we applied Tract-Seg to the study-specific population template to segment those voxels corresponding to the SCP (left and right) and STPMT (left and right). These tractograms were subsequently concatenated across hemispheres to generate a single bilateral tractogram for each tract, in an effort to reduce the number of comparisons (Fig. 2). The corresponding SCP and STPMT tractograms were then applied to each individual participant's whole-brain FD and logFC fixel maps, to specifically crop the fixels belonging only to the SCP and STPMT (using the 'tck2fixel' command [Tournier et al., 2019]). These individual fixel maps, cropped to the SCP and STPMT, were submitted for statistical analysis.

Statistical analyses
We obtained MRI and behavioral data from 22 participants. However, because of missing behavioral data for two participants, final analyses included the 20 participants for whom we had complete data. Data were checked for violations of normality and sphericity.

Behavioral analyses
Preliminary analyses were conducted to confirm that the predicted procedural learning effects took place during SRT task performance. The effect of block (S1, S2, S3, R1) on RT was examined using a one-way repeated measures ANOVA. Next, as per our previous work adopting the SRT task (Lum et al., 2019), planned comparisons using paired samples t-tests were undertaken to examine sequence learning effects. The first comparison tested for a difference in RT between the first and last sequence blocks (i.e., S1 vs. S3), with a significant reduction expected where sequence learning had taken place. The second comparison examined whether there was a significant increase in RT from the final sequence block (S3) to the random block (R1) e viz., the rebound effect. Due to violations of normality, Wilcoxon's W was used in place of Student's t.
In subsequent analyses, the rebound effect was calculated for each participant and used as the dependent measure of procedural learning (Knopman & Nissen, 1991;Robertson, 2007;Siegert et al., 2006). First, raw RTs for each trial were transformed to z-scores to control for general processing speed (Janacsek et al., 2012;Koch et al., 2020). This was Fig. 2 e Glass brain depicting the SCP and STPMT, delineated using TractSeg (Wasserthal et al., 2018(Wasserthal et al., , 2019. The tractograms from the left and right hemispheres were combined to generate one single bilateral tractogram for each tract (SCP in purple, STPMT in green). Labels indicate the cortical and subcortical regions that the white matter tracts connect. Glass brain created in MRtrix3Tissue (Tournier et al., 2019). c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2 calculated for each participant based on their mean and standard deviation RT for all trials across all blocks. This transformation ensured that, across participants, the shortest and longest RTs had similar values. This allowed us to attribute participant differences in the magnitude of the rebound effect to procedural learning only, rather than individual difference effects in general processing speed (i.e., reaction time, alone). Then, mean z-scores were calculated for each block, resulting in a mean z-score for RT for each block, for each participant. The magnitude of the rebound effect was calculated for each participant by subtracting the mean z-score for RT for S3 from the mean z-score for RT for R1.

Fixel-based analysis
To investigate the relationship between individual differences in procedural learning and white matter organization within the SCP and STPMT, we used the connectivity-based fixel enhancement (CFE) method in MRtrix3Tissue to probe the relationship between the rebound effect on the SRT task and fixel-based metrics in the SCP and STPMT. CFE provides a permutation-based, family-wise error (FWE) corrected p-value for every individual fixel in the population template space (Raffelt et al., 2015). Sex was included as a covariate, and we further controlled for intracranial volume (ICV) for analyses involving FC . ICV was derived from each subject's structural T1 image using FreeSurfer (Fischl et al., 2012). Statistical significance for correlations was set at p FWE < .05, though a more liberal threshold of p FWE < .10 was adopted to visualize the spatial extent of effects. Lastly, for visualization purposes, in tracts where CFE detected significant relationships between fixels and the rebound effect, we extracted mean values for all significant fixel-based metrics from each subject (p FWE < .05) and plotted the linear relationship between these values and the rebound effect. This was conducted separately for the left and right hemispheres.

Exploratory analyses
As noted below, we observed some non-significant associations between fixel-based metrics and the rebound effect. However, due to the modest sample size, we questioned whether we lacked the power to detect small, significant effects. To gain further insight into the strength and pattern of effects, we conducted exploratory analyses where, for each participant, we calculated the average FD and logFC across the entire white matter tract and correlated this with participants' standardized rebound effect. Covariates included sex, and ICV (for analyses involving FC only). Lastly, after inspecting the results of the main CFE analysis and scatterplots, we observed that FD values appeared to differ between the left and right SCP. This prompted post-hoc consideration of whether microstructural laterality across the SCP might impact our effects of interest. Accordingly, we ran a post-hoc exploratory analysis to investigate this possibility. Consistent with common approaches to generating lateralization indices for neuroimaging data (Agarwal et al., 2018;Nagel et al., 2013;Othman et al., 2020), we calculated a lateralization metric for FD within the bilateral SCP as follows: lateralization ¼ (average FD in right SCPdaverage FD in left SCP)/(average FD in right SCP þ average FD in left SCP). In this way, a negative lateralization metric indicates left hemisphere dominance for FD, and positive values indicate right hemisphere dominance for FD. For each participant, their lateralization value was correlated with their rebound effect value, to see whether there was an association between procedural learning and hemispheric dominance for FD within the SCP.

2.6.
Data and code availability The conditions of our ethics approval do not permit public archiving of anonymized study data. Readers seeking access to the data should contact the lead author. Access will be granted to named individuals in accordance with ethical procedures governing the reuse of clinical data, including completion of a formal data sharing agreement and approval of the local ethics committee. Code used for data processing and analysis is publicly available and provided on the MRtrix3 website (https://mrtrix.org). Our analysis script and SRT task is publicly available on the Open Science Framework: https:// osf.io/n4cme/. Where code is not explicitly provided, the analysis was not conducted using code.

SRT task performance
Mean RTs for each block are presented visually in Fig. 3. The general trend observed was a decrease in RT (i.e., faster responses) across the sequence blocks (S1eS3), followed by an increase in RT in the random block (R1). The ANOVA revealed a significant main effect of block on RT, F(3,57) ¼ 15.78, p < .001, h 2 p ¼ .45. Subsequent Wilcoxon's tests revealed that RTs in S3 (M ¼ 343 ms) were significantly faster compared to S1 (M ¼ 356 ms), W ¼ 159, p ¼ .044, r ¼ .51. There was also a significant increase (i.e., slowing) in RT from S3 (M ¼ 343 ms) to R1 (M ¼ 392 ms), W ¼ 17, p < .001, r ¼ À.84. Descriptive statistics for reaction time, reported by block, can be found in Table 1.

Association between the rebound effect and fixelbased metrics in the SCP and STPMT
The results of our tracts-of-interest FBA are presented in Fig. 4. Overall, CFE revealed a significant positive association between FD and the rebound effect on the SRT task in segments of both the left and right SCP (p FWE < .05). We also report a trend towards significance (p FWE < .10) in more distributed areas of the SCP. No significant relationships were observed between the rebound effect and FD in the STPMT, or logFC in either tracts-of-interest. To visualize the effects at the hemispheric-level, Fig. 5 presents the correlations between mean FD of significant fixels in the left (a) and right (b) SCP against the rebound effect.

Results of exploratory analyses
Since the CFE analysis did not detect a significant relationship between fixel-based metrics in the STPMT and the rebound effect, we ran exploratory correlations between participants' average FD and logFCdcalculated across the entire STPMTdand the standardized rebound effect. No effect c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2 reached statistical significance (mean FD in right STPMT: r ¼ .34, p ¼ .161; left STPMT: r ¼ .15, p ¼ .545; mean logFC in right STPMT: r ¼ À.22; p ¼ .380; left STPMT: r ¼ À.21, p ¼ .396). See Fig. 6 for relevant scatterplots. Results of the lateralization analysis indicate a trend towards a negative association between the standardized rebound effect and lateralization of FD in the SCP (r ¼ À.40, p ¼ .082). All participants returned positive lateralization metrics, suggesting higher average FD of significant fixels in the right SCP. However, as the degree of right lateralization increased, the rebound effect decreased. As such, it appears that the rebound effect was strongest in those individuals where rightward lateralization of FD in the SCP was weakest. See Fig. 7 for scatterplot.

Discussion
The current study was the first to use a novel FBA framework to probe the microstructural basis of procedural learning within fronto-basal ganglia-cerebellar circuitry in healthy adults. Our results found that increased FD in the SCP was associated with better procedural learning on the SRT task, as indexed by the magnitude of the rebound effect. In contrast, we did not observe an association between logFC in the SCP and the rebound effect. We also found no relationship between procedural learning and microstructure in the fronto-basal ganglia network, since no significant association was observed between the rebound effect and FD or logFC in the STPMT. Taken in the context of available functional neuroimaging evidence, our work supports recent arguments that white matter fiber properties along basalganglia-cerebellar networks may be associated with individual differences in procedural learning. These conclusions, their implications and limitations are discussed below.

SRT task indicates procedural learning
As expected, behavioral analysis of SRT task performance indicated that procedural learning took place (Nissen & Bullemer, 1987). Participant RTs decreased (i.e., became faster) across blocks comprising sequenced trial presentations, and then increased (i.e., became slower) when a block of random trials were presented. This trend is the hallmark of performance on the SRT task in healthy populations, and suggests that knowledge of the sequence was obtained across sequenced blocks but could no longer be used to anticipate the stimulus' location during the random block (Robertson, 2007). In the current study, the difference between sequence and random RTs (i.e., the rebound effect) thus provided a specific and sensitive measure of procedural learning on the SRT task. . RT data from Blocks 1 and 2 were averaged to create S1. Data from Blocks 3 and 4 were averaged to create S2. Data from Blocks 5 and 6 were averaged to create S3. Data from Blocks 7 and 8 were averaged to create R1. The first three blocks (S1, S2 and S3) presented stimuli in a visuospatial sequence. The fourth block (R1) presented stimuli in a random visuospatial order. Note. S1, S2 and S3 refer to sequence blocks 1, 2 and 3. R1 refers to the fourth block, which presented stimuli in a random visuospatial order.

4.2.
Procedural learning is associated with FD in the SCP Results showed a positive association between procedural learning and microstructural organization within the basal ganglia-cerebellar network. Microstructure in the SCP was associated with SRT task performance, whereby greater FD in this tract was associated with a larger rebound effect. Given that performance on the SRT task was standardized at the individual level to control for the effect of individual differences in RT, we can be confident that the observed relationship between FD and the rebound effect are specific to the rebound effect (and not RT more broadly).
In the context of the FBA framework, FD is thought to reflect the density or volume of axons within a voxel, such that higher values are likely to reflect a more densely packed bundle, or greater axonal count, within a voxel (Raffelt et al., 2017). Given that intra-axonal volume is related to the white matter's 'ability to relay information' (Raffelt et al., 2017), it may be that higher FD within white matter pathways endows a bundle with greater information processing capacity, making it more efficient (Fletcher et al., 2021;Horowitz et al., 2015). This is supported by evidence that cognitive processing is slowed if signals must travel via connections with low axon density (e.g., Tolhurst & Lewis, 1992). With this in mind, Fig. 4 e Glass brain representation of streamline segments showing a positive association between the rebound effect and FD within the left and right SCP. Colored streamlines represent streamlines passing through significant fixels with p FWE < .05 (red). To show the greater spatial extent of effects, we further present these results using a more liberal threshold of p FWE < .10 (yellow). R ¼ right; L ¼ left; A ¼ anterior; P ¼ posterior. Glass brain created in MRtrix3Tissue (Tournier et al., 2019). Fig. 5 e Scatterplots (N ¼ 20) show the association between the mean FD for each participant (averaged across the significant fixels from the CFE analysis investigating the association between FD in the SCP and the rebound effect) and the standardized rebound effect for the (a) left and (b) right SCP. A larger rebound effect indicates greater sensitivity to the sequence. The shaded area represents standard error. The solid line represents the line of best fit. c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2 increased FD (or, higher axon density) within the SCP pathway may facilitate transmission of information between the cerebellum and basal ganglia, leading to better procedural learning performance on the SRT task. And, as we found no relationship between logFC in the SCP and the rebound effect, results imply that procedural learning may be predominantly driven by microstructural properties within the basal gangliacerebellar circuit, rather than overall tract macrostructure.
Lastly, we found that all participants presented with higher average FD in the right SCP, but that there was a trend towards a negative association between the rebound effect and lateralization of FD in the SCP. This finding demonstrates that procedural learning may be more efficient in those individuals where rightward lateralization of SCP FD is weakest. While a linear relationship has traditionally been assumed between hemispheric asymmetry and cognitive function, this view has been criticised in the wake of mixed evidence. More recent behavioral work suggests an inverted U-shaped relationship, whereby a small to moderate level of hemispheric asymmetry is associated with optimal cognitive processing, and greater asymmetry results in deteriorating performance (e.g., Hirnstein et al., 2010). Our findings are in-keeping with this interpretation, since greater procedural learning effects were  observed in those with weaker right lateralization of FD. However, given the exploratory nature of our analyses here, we suggest future work adopt a longitudinal design to better clarify the observed relationship between procedural learning and lateralization of FD in the SCP.

4.3.
Procedural learning and the STPMT Contrary to expectations, we did not detect a correlation between white matter organization in the fronto-basal ganglia networks and procedural learning, as shown by the nonsignificant associations between the rebound effect and FD or logFC in the STPMT. There are several possible reasons for the lack of effect observed here. Firstly, this finding (or lack thereof) may suggest that white matter organization in these regions is not linked to individual differences in procedural learning. However, given our sample size, we feel it prudent to consider the power of the present study. To investigate this further, we conducted exploratory analyses to gain insight into the strength and pattern of effect between microstructure in fronto-basal ganglia tracts and the rebound effect. For each participant, we correlated the standardized rebound effect on the SRT task with the average FD and logFC across the entire STPMT. While no effect reached statistical significance, the scatter of scores and correlation values (especially r ¼ .34 for the association between the rebound effect and FD in the right STPMT) may suggest a non-significant trend (or at least, call into question a true null effect). Thus, while our work failed to provide evidence that white matter organization within the STPMT is associated with procedural learning, we recommend that future work replicates our study with a larger sample to clarify the true nature of this effect.

Limitations and future directions
Despite our encouraging results, this study is not without limitations. First, while we report compelling evidence of cerebellar microstructural involvement in procedural learning here, we also acknowledge that our sample size is somewhat modest. As suggested, future studies should examine larger cohorts to better ascertain relationships between FBA metrics and procedural learning in healthy adults. This may assist in discerning whether our lack of effect for the fronto-basal ganglia circuit reflects a true null effect, or that a weaker (though valid) effect was present that our study did not have the power to detect. Second, our results don't allow us to draw causal or directional inferences about the relationship between white matter organization and procedural learning. Whilst we make the point that higher FD in the SCP may result in more efficient procedural learning, it is equally possible that increased tract FD is the consequence of better procedural learning (or exposure to it). Clarifying the direction of this relationship through longitudinal work might help to explain developmental trajectories in procedural learning, and its pathology. Finally, we investigated the role of the SCP in procedural learning based on evidence that the cerebellum, basal ganglia, and frontal regions may be implicated in procedural learning (Baetens et al., 2020;Janacsek et al., 2020). While the SCP was a primary candidate for a white matter pathway connecting these regions, we acknowledge that other white matter tracts are involved in the transmission of information between these sites. For example, the cerebellum and prefrontal regions are also connected via the middle cerebellar peduncle (MCP) (Kelly & Strick, 2003;Palesi et al., 2017). In order to minimize the number of comparisons and maintain study sensitivity, we did not include this tract in our analyses (nor other candidate white matter tracts). In order to better understand the broader role of white matter connectivity in procedural learning, future work, with a larger sample size, should consider the role of the MCP in SRT task performance. Our findings hold broader implications for understanding the expression and development of procedural learning. Since white matter has shown to predict developmental and patient outcomes (Forkel et al., 2021), it is possible that white matter microstructure may explain developmental progressions in procedural learning, and pathology of the latter. Indeed, impaired procedural learning is a common phenotype of several neurodevelopmental disorders, including developmental coordination disorder, specific language impairment, attention-deficit hyperactivity disorder, autism spectrum disorder and Tourette Syndrome (Clark & Lum., 2017;Tak acs et al., 2017;Ullman et al., 2020). In most of these disorders, atypical development of cortico-subcortical networks, particularly cortico-striatal and cortico-cerebellar circuits, have been reported in their pathophysiology (Langen et al., 2012;Nayate et al., 2005;Ullman & Pierpont, 2005, van Ewijk et al., 2012Zwicker et al., 2011). As such, atypical microstructure within fronto-basal ganglia-cerebellar circuits may explain some of the symptom expression in these disorders. Our preliminary results suggest that this might be a worthwhile area for future research.

Conclusion
This study is the first to investigate the role of white matter properties in procedural learning in healthy adults using a novel fixel measure of white matter microstructure. To do this, we adopted FBA, which allowed us to provide biological specificity for the link between procedural learning and white matter organization within the front-basal ganglia-cerebellar network. We observed that increased FD in basal gangliacerebellar networks was associated with greater sensitivity to the sequence on the SRT task. This work builds on an earlier ALE meta-analysis of functional work (Baetens et al., 2020;Janacsek et al., 2020) by demonstrating that the role of basal ganglia-cerebellar circuitry in explaining individual differences in procedural learning may also be present at a microstructural level. c o r t e x 1 6 1 ( 2 0 2 3 ) 1 e1 2