Cognitive processing speed (PS-C) refers to the time required to encode an incoming stimulus and connect it with the existing experience in the brain (Kail and Salthouse, 1994). Previous fMRI studies revealed that PS-C is subserved by extensive neural networks. Silva et al. (2018) revealed that performance on a symbol-to-digit task was subserved by an extensive network of middle frontal gyri, superior parietal lobule, precuneus, inferior frontal gyrus, cuneus, and lingual gyrus (Silva et al., 2018). Previous studies quantified processing speed with complex cognitive tests, such as the Symbol Digit Modalities Test (SDMT). A review of these studies indicates their results are inconsistent. For instance, Silva et al. (2019) reported the fronto-parietal and fronto-occipital networks subserved participants’ performances in the SDMT (Silva et al., 2019). Savini et al. (2019) revealed that the connectivity between the cerebellum and the default mode network (DMN) was related to the reaction time decline in the SDMT among multiple sclerosis patients (Savini et al., 2019). Manca et al. (2018) conducted a systematic review of multiple sclerosis patients that connectivity of the frontal areas and microstructural integrity of the anterior corpus callosum accounted for processing speed tasks, including SDMT (Manca et al., 2018). The inconsistent results mentioned above could have been confounded by varying contents and task-taking processes of the complex cognitive tasks used in these studies, such as the SDMT.

In a recent study, our research team designed a simple multimodality reaction time task to revisit the PS-C (Wong et al., 2021). This custom-designed task was developed to minimize the potential task-specificity confounds observed in previous studies. The results indicated a fronto-cerebellar connective network, especially long-range effective connectivity in the right medial frontal cortex on the medial cerebellar vermis VI [i.e., Right medial frontal cortex (RMFC) → medial cerebellar vermis VI (MCV6)] subserving PS-C. We further proposed that PS-C is the outcome of an interplay between automaticity and effortful top-down attentional control processes (Wong et al., 2021).

In this study, we aimed to gain a deeper understanding of the roles of the RMFC and MCV6 within the fronto-cerebellar connective network in subserving PS-C. The reason for selecting the RMFC–MCV6 couple for the study is because it was the strongest effective connective predictor of faster reaction times (with the largest β value of −0.330) among the six significant paths (Wong et al., 2021). The RMFC–MCV6 couple is one of the three long-range functional connectivities between the frontal cortex and cerebellum, which involve automaticity and top-down attentional control interplay. The changes in task-based reaction times due to external stimulations applied to the RMFC–MCV6 couple would yield stronger modulation of the fronto-cerebellar connective network than other couples that showed weaker prediction power or belonged to short-range such as the RMFC–LIPS (LIPS refers to left intra-parietal sulcus; β value of 0.301).

We employed transcranial magnetic stimulation (TMS) to separately modulate the neural activities of the RMFC and MCV6. Previous studies have demonstrated the effects of TMS on regulating brain activation (Burke et al., 2019) and inducing functional and structural plastic changes (Jung and Lambon Ralph, 2021). The intermittent theta-burst stimulation (iTBS) protocol induced excitatory effects, while the continuous theta-burst stimulation protocol (CTBS) induced inhibitory effects. Other literature employed stimulation to a single neural substrate method to modulate the connectivity of neural networks. For instance, intermittent TBS of the left superior parietal lobule was revealed to enhance cognitive speed and resting-state connectivity of the dorsal attention network (DAN) (Anderkova et al., 2018). Intermittent theta-burst stimulation at the midline cerebellar node of the DAN resulted in improved performances in both sustained and transient attentional control functions, which subserved by the respective connective network (Esterman et al., 2017). High-frequency rTMS of the lateral parietal region was found to effectively improve generic cognitive function via activating the default mode network (DMN) (Wei et al., 2022). The significant single substrate-to-network modulation effects reported in the previous studies lend support to our use of such a method in this study.

The RMFC→MCV6 couple connectivity was a negative relationship (denoted by the →) between the two neural substrates (Wong et al., 2021). That is, the RMFC exerted an inhibitory influence on the MCV6. The negative β value of −0.330 in the regression model suggested that lowering the inhibitory RMFC→MCV6 influence would produce faster PS-C. First, we aimed to increase the inhibitory influence of the RMFC on the MCV6 by applying an excitatory iTBS protocol to the right pre-supplementary motor area (RpSMA). The RpSMA, a subregion of the RMFC (De La Vega et al., 2016), is located in the right prefrontal cortex as part of the salient network (Wang et al., 2020). The RpSMA was found to be related to resource allocation in processing salient information (Weigard et al., 2019) and cognitive control (Wolpe et al., 2022). A previous study of six sessions of excitatory stimulation over the frontal cortex showed increased cognitive performance in patients with Parkinson’s disease (Trung et al., 2019). Other studies (Viejo-Sobera et al., 2017; Chung et al., 2019; Dumitru et al., 2020; Wu et al., 2021) reported that the excitatory effects promoted general cognitive functions among healthy subjects and modulated cerebellar-cortical connectivity in patients with progressive supranuclear palsy (Brusa et al., 2014). Second, to produce contrasting effects, an inhibitory CTBS protocol was applied to the MCV6 to suppress its activity. The cerebellar vermis is related to automation, cognitive optimization, and implicit learning (Cheng et al., 2014; Moroso et al., 2017) and modulates neural synchronization in the non-motor frontal cortex (Tremblay et al., 2019). Multiple sessions of inhibitory stimulation over the cerebellar vermis have been revealed to promote synaptic connections (Colnaghi et al., 2017a). In contrast to the facilitative effects mentioned above, other studies reported mixed results of the inhibitory stimulation to the cerebellum.

We hypothesized that iTBS to the RpSMA, which is excitatory in nature, would further increase the negative influence on the MCV6, resulting in higher neural activity to mediate faster reaction times in the participants’ post-intervention task performances. In contrast, as the MCV6 receives negative influence from the RMFC (i.e., RMFC→MCV6) to produce faster reaction time, CTBS to the MCV6, which would inhibit its activity, was hypothesized to produce slower reaction times. We employed a two-task contrast method to quantify the post-stimulation effects. They were the simple reaction time task (SRT), vs the SDMT, a complex reaction time task. The TMS effects were analyzed with repeated measure analysis of covariance (RM-ANCOVA) for the Group × Time on the changes in the task-based reaction times. Structural equation modeling (SEM) was used to model the differences in the TMS modulations of the participants’ reaction times on the simple vs complex tasks.

This study aimed to test the roles of the RpSMA and MCV6 effective connectivity within the fronto-cerebellar network to subserve cognitive processing speed. The five-session TMS excitatory and inhibitory protocols were intended to initiate changes in the participants’ task-based reaction times. Despite the changes in the reaction times that had been observed across the stimulation sessions, they were at best regarded as marginal because they did not reach statistical significance. However, the results of structural equation modeling revealed systematic significant stimulation effects on both the RpSMA and MCV6, resulting in significant paths on the reaction time change factors. More importantly, the significant paths from the stimulation to the faster reaction time factors were only observed in the simple but not in the complex tasks. Excitation to the RpSMA relating to the faster reaction times in the simple task supports its “increase in the negative influence” role in the RpSMA➔MCV6 effective connectivity. Counterintuitively, inhibition of the MCV6 relating to the faster reaction times in the simple task did not support its unique role in the effective connective network to subserve processing speed. In other words, the iTBS protocol on the MCV6, which was supposed to reverse the “increase in the negative influence” originally received from the RpSMA, did not produce slower reaction times. The contradictory results obtained from the MCV6 are plausibly due to the influences exerted by the available short-range connective networks within the cerebellum.

Excitatory stimulation on the RpSMA did not produce significantly faster reaction times when compared with the sham condition. The non-significant results were yielded from conducting conventional Group × Time comparisons. Our findings are consistent with those reported in two previous studies, reporting the effects of excitatory stimulations on the RpSMA. One study employed quadripulse transcranial magnetic stimulation over the pre-SMA, which did not produce significant effects on participants’ performances in the simple choice reaction time task (Shimizu et al., 2020). Another study adopted a similar stimulation protocol to this study on the RpSMA, which showed significant modulation effects on the biceps brachii corticomotor excitability in individuals with tetraplegia (Mittal et al., 2022). However, several studies on similar topics involved excitatory stimulations applied to the dorsolateral prefrontal cortex. The results of these studies were largely equivocal on excitatory stimulations producing faster reaction times (Curtin et al., 2019; Song et al., 2020; Ngetich et al., 2022). Future studies can modify the stimulation protocols, such as increasing the dosage of the stimulation (intensity or duration) and enlarging the sample size. These strategies would increase the effect size of the stimulation, hence the chance of showing significant post-stimulation changes.

The results of the significant structural paths suggested the excitatory RpSMA effects related to faster post-stimulation reaction times in the simple, not complex task. The first level path was the excitatory RpSMA, which showed direct and negative effects on the latent simple task speed factor, while the second level path was the latent speed factor, which continued with similar relationships with the reaction times. The evidence renders support for Wong et al. (2021)’s proposition on the RpSMA “lowering negative influence” relationships with the MCV6 in the RpSMA➔MCV6 effective couple. The RpSMA or pre-SMA, part of the motor cortex, primarily relates to motor functions (motor inhibition, visuomotor sequence learning, the control of motor sequences, and modulation of the balancing of speed vs accuracy) (Georgiev et al., 2016; Obeso et al., 2017; Hanoğlu et al., 2020; Shimizu et al., 2020; Nakajima et al., 2022). One previous study reported that RpSMA subserved cognitive control such as response inhibition (Obeso et al., 2013). Our findings are contrary to those reported by Obeso et al., who showed that RpSMA was associated with simple rather than complex cognitive operations. The simple reaction time task employed in our study required the participants to decode symbols presented but make mono responses. The complex task was the symbol digit modalities task, requiring participants to decode, match, and respond according to the different symbol-digit pairs. In other words, the cognitive control processes would have been a part of the complex task but not part of the simple task. Future studies will need to replicate simple vs complex tasks to generate more robust results on the observed role of the RpSMA.

Similar to the RpSMA, inhibitory stimulation to the MCV6 did not produce significant changes in the participants’ reaction times. Deliberation on the significant direct and negative paths from the inhibitory MCV6 to the latent speed factor only in the simple but not in the complex task sheds light on its role in the RpSMA➔MCV6 effective connectivity. The MCV6-induced latent speed factor showed significant direct and negative paths to the simple task reaction times. In other words, the inhibitory MCV6 related to faster rather than slower reaction times, which was inconsistent with the study’s hypothesis. One plausible explanation for the contradictory results could be that the inhibitory stimulation was over-spilled to other cerebellar sites. Two studies reported inhibitory stimulations resulting in faster reaction times involving sites different from the MCV6. They were the stimulation at the 1–2 cm below the inion (adjacent to MCV6) (Heleven et al., 2021) or the right Crus I/Crus II (adjacent to MCV6) (Gatti et al., 2020). Both studies revealed significantly faster reaction times in complex tasks: picture sequencing (Heleven et al., 2021) or word pairing (Gatti et al., 2020). These studies further explained that inhibitory stimulation possibly would have modulated the inherent sequence processing, semantic function in language, or semantic memory function required in the complex tasks. The over-spilled inhibition speculation does not seem to offer insight into the counterintuitive findings. Another plausible line of explanation is from a recent study that applied inhibitory stimulation over the left cerebellum (1 cm below and 3 cm lateral to the inion), resulting in faster reaction times in a lexical decision task (Allen-Walker et al., 2018). Allen-Walker et al. attributed the faster reaction time to activate the automatic and fast feedback loops in the left cerebellar hemisphere after CTBS was applied with the left cerebellum or contralateral cerebral cortex (right temporal cortex) as a result of left cerebellar rTMS. An earlier study using the same lexical decision task and applying inhibitory stimulation to the site similar to MCV6 revealed deterioration of reaction times (Argyropoulos, 2011). Argyropoulos (2011) explained that the participants’ deteriorated performance could have been attributable to disrupted oculomotor processes by the inhibitory MCV6 essential for the reading during the task (Argyropoulos, 2011). Their argument was supported by a later study suggesting that the cerebellar stimulation could have modulated the primary motor cortex via the efferent path of the fronto-pontine-cerebello-thalamo-cortical loop (Grimaldi et al., 2014). However, the fronto-pontine-cerebello-thalamo-cortical loop is different from the fronto-cerebellar network, which contains the RpSMA➔MCV6 in this study. The latter is a long-range connectivity between the frontal cortex and the cerebellum without the dentate and motor thalamus (Wong et al., 2021). The lexical decision task involved semantic processing and higher cortical function, which is different from the simple reaction task in this study. Taken together, the inhibitory effects on the cerebellum are likely to vary with the location of stimulation and the content of the tasks. Future studies would explore the mechanism of combined existing connectivity or new models for the roles of the cerebellum in subserving cognitive processing speed.

A plausible explanation of the inhibitory MCV6 for the RpSMA➔MCV6 may be explained by the long- and short-range fronto-cerebellar effective connectivity revealed in our previous study (Wong et al., 2021). Long-range cerebellar connectivity plays a dominant role in subserving cognitive information processing (Deco et al., 2021). The RpSMA➔MCV6 couple is long-range connectivity. In the same study, Wong et al. revealed MCV6➔RCH6, a short-range connectivity, in which the MCV6 exerted a lower positive influence on the RCH6, predicting faster processing speed (Wong et al., 2021). Functional connectivity within the cerebellar networks was suggested to be associated with learning in young adults (Edde et al., 2020). The effect of RpSMA➔MCV6 on processing speed was found to be independent of that of MCV6➔RCH6 (Wong et al., 2021). We, therefore, speculate that the opposite effects manifested from the inhibitory MCV6 could have been intervened by the short-range cerebellar connectivity, such as the RCH6. However, the effect of short-range connectivity is outside the scope of this study. Further study should include both long- and short-range connectivities in building a comprehensive model for the cerebellum.

Another finding revealed in this study is stimulations at the RpSMA, and MCV6 showed effects on the simple but not complex tasks. These findings perhaps would have been confounded by the RpSMA➔MCV6 effective connectivity reported by Wong et al. (2021), which was based on the modified arrow test, which involved relatively simple cognitive operations. The simple reaction time task deployed in this study required basic information processes, such as encoding and discrimination of the figure “0,” and a one-to-one task rule of “press on a key” when seeing “0” (Deary et al., 2010). Our findings are consistent with an earlier study that a simple reaction time task involved activations of the premotor cortex, medial frontal gyrus, cerebellar vermis, and frontal–parietal cortex, which overlaps with the RpSMA and MCV6 (Kansaku et al., 2004). On the contrary, studies that employed more complex tasks, such as the SDMT deployed in this study, have been found to activate the other brain regions, including the frontal–parietal cortex, cingulate gyrus, and precuneus (Silva et al., 2018).

We attempted to understand the role of the individual neural substrates in the RpSMA➔MCV6 effective connective couple within the fronto-cerebellar network. The hypotheses set for the study were partly supported. Based on the structural equation modeling results, excitatory stimulation at the RpSMA showed significant paths to faster reaction times in the simple cognitive task. The results supported the RpSMA playing a lower negative effect role, as proposed in our previous study inhibiting the MCV6, which subserves faster processing speed. However, the results from the inhibitory MCV6 showed that significant paths to the faster reaction times in the simple cognitive tasks did not support the hypothesis. The anticipated inhibition of the MCV6, which was supposed to be associated with slower reaction times, could have been compromised by the short-range cerebellar connectivity, such as the RCH6.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving humans were approved by the Ethics Committee of the Rehabilitation Hospital affiliated with the Fujian University of Traditional Chinese Medicine. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

NZ: Data curation, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing, Visualization. JT: Project administration, Software, Supervision, Writing – review & editing, Investigation. CW: Methodology, Software, Writing – review & editing. JW: Methodology, Software, Writing – review & editing. JL: Methodology, Software, Writing – review & editing. LC: Conceptualization, Project administration, Supervision, Writing – original draft, Writing – review & editing, Methodology. TL: Conceptualization, Methodology, Writing – original draft, Writing – review & editing. YX: Writing – review & editing. CC: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Writing – original draft, Writing – review & editing.