The right inferior frontal gyrus as pivotal node and effective regulator of the basal ganglia-thalamocortical response inhibition circuit

Abstract Background The involvement of specific basal ganglia-thalamocortical circuits in response inhibition has been extensively mapped in animal models. However, the pivotal nodes and directed causal regulation within this inhibitory circuit in humans remains controversial. Objective The main aim of the present study was to determine the causal information flow and critical nodes in the basal ganglia-thalamocortical inhibitory circuits and also to examine whether these are modulated by biological factors (i.e. sex) and behavioral performance. Methods Here, we capitalize on the recent progress in robust and biologically plausible directed causal modeling (DCM-PEB) and a large response inhibition dataset (n = 250) acquired with concomitant functional magnetic resonance imaging to determine key nodes, their causal regulation and modulation via biological variables (sex) and inhibitory performance in the inhibitory circuit encompassing the right inferior frontal gyrus (rIFG), caudate nucleus (rCau), globus pallidum (rGP), and thalamus (rThal). Results The entire neural circuit exhibited high intrinsic connectivity and response inhibition critically increased causal projections from the rIFG to both rCau and rThal. Direct comparison further demonstrated that response inhibition induced an increasing rIFG inflow and increased the causal regulation of this region over the rCau and rThal. In addition, sex and performance influenced the functional architecture of the regulatory circuits such that women displayed increased rThal self-inhibition and decreased rThal to GP modulation, while better inhibitory performance was associated with stronger rThal to rIFG communication. Furthermore, control analyses did not reveal a similar key communication in a left lateralized model. Conclusions Together, these findings indicate a pivotal role of the rIFG as input and causal regulator of subcortical response inhibition nodes.

Consistent findings from animal model and human neur oima ging studies show that the globus pallidus (GP) also plays an essential role in action execution and response inhibition (Casey et al., 1997 ;Mallet et al., 2016 ;Pan et al., 2018 ;Wei and Wang, 2016 ).
A pr e vious structur al ima ging study r e v ealed that a better behavioral performance during a response inhibition task was related to a larger GP volume (Casey et al., 1997 ).In ad dition, a stud y from W ei and W ang sho w ed that GAB Aer gic inhibitory pr ojections fr om the external segment of the GP to the striatum are crucial for inhibiting a planned response (Wei and Wang, 2016 ).
Se v er al studies have explored sex differences in response inhibition performance and the associated neural activity (Chung et al., 2020 ;Ribeiro et al., 2021 ;Rubia et al., 2013 ;Sjoberg and Cole, 2018 ).While the existing e vidence fr om most studies and metaanalyses sho w ed no significant sex difference on behavioral performance (Chung et al., 2020 ;Cross et al., 2011 ;Gaillard et al., 2021 ;Gar av an et al., 2006 ;Li et al., 2006 ), some other studies sho w ed that female individuals demonstrate higher accuracy and faster stop signal reaction times compared to male participants (Ribeiro et al., 2021 ;Rubia et al., 2013 ;Sjoberg and Cole, 2018 ) and one study reported that males demonstrate better response inhibition compared to females (Gaillard et al. , 2020 ).W ith respect to neural differ ences the pr e vious liter atur e r emained inconsistent and the direction of sex differences may additionally vary depending on the task administered (Go/NoGo task or stop signal task) and the age of the participants (Chung et al., 2020 ;Rubia et al., 2013 ;Weafer, 2020 ).Such as, some studies reported that male participants tend to display greater brain activity in frontal as well as motor controlr elated r egions suc h as the GP and thalam us during r esponse inhibition on stop signal tasks when inhibiting an already-initiated response (Li et al., 2006(Li et al., , 2009 ) ), while female participants tend to display greater brain activity during inhibition on Go/NoGo tasks when inhibiting the initiation of a response (Chung et al., 2020 ;Gar av an et al., 2006 ).
Conv er gent e vidence fr om human lesion studies and neur oima ging meta-anal yses demonstr ates a right-later alized inhibitory control network encompassing the right IFG (rIFG), right caudate nucleus (rCau), right GP (rGP), and right thalamus (rThal) (Aron et al., 2003 ;Chevrier et al., 2007 ;Garavan et al., 1999 ;Hung et al., 2018 ;Jahfari et al., 2011 ;Thompson et al., 2021 ).Ho w e v er, while extensive research has highlighted the critical role of these regions within a right-lateralized inhibitory control circuitry, the causal information flow and critical contribution of single nodes within this network as well as the modulatory effect of sex have not been determined.
We ther efor e ca pitalized on a nov el dynamic causal modeling (DCM) a ppr oac h based on a priori specification of biologically and anatomically plausible models that allows estimation of directed causal influences between nodes and their modulation by changing task demands (Friston et al., 2003 ;Stephan et al., 2010 ) in the largest sample to date ( n = 250).The DCM approach conceptualizes the brain as a nonlinear dynamical input-state-output system and was de v eloped to provide a more biologically informed a ppr oac h to test a hypothesis about experimental manipulationdependent interactions between brain regions based on differential equations describing interactions between neural populations that may dir ectl y or indir ectl y giv e rise to the observ ed functional magnetic resonance imaging (fMRI) data.The estimated parameters in these models are considered as directed or effective connectivity between brain regions.DCM further allows comparison of modulatory effecti ve connecti vity str ength acr oss different experimental conditions using Bayesian contrasts (Dijkstra et al., 2017 ) and, in combination with the r ecentl y de v eloped par ametrical empirical Bayes (PEB) hier arc hical fr ame work (DCM-PEB method), it allows modeling of both commonalities and differences in effecti ve connecti vity between participants , e .g. to determine the neurobiological basis of sex and behavioral performance variations (Friston et al., 2016 ;Zeidman et al., 2019aZeidman et al., , 2019b ) ).
To determine the causal information flow and critical nodes in the basal ganglia-thalamocortical circuits and whether these are modulated by biological factors (i.e.sex) and show functional rele v ance in terms of associations with performance we capitalized on DCM-PEB in combination with fMRI data collected in a large sample of healthy individuals ( n = 250) during a well-established r esponse inhibition par adigm (emotional Go/NoGo task, see also Zhuang et al., 2021 ).To unr av el the k e y nodes and causal influences within the inhibitory control netw ork, w e first estimated the effecti ve connecti vity between and within k e y r egions involv ed in response inhibitory control within the rIFG-rCau-rGP-rThal functional circuit (right lateralized model) and, second, we estimated sex differences and behavioral performance effects on connectivity par ameters.Furthermor e, to v alidate the hemispheric asymmetry of the inhibitory control network, an identical model of nodes was tested in the left hemisphere (left lateralized model).
Giv en conv er gent e vidence on a pivotal r ole of the right IFG in mediating top-down cortical-subcortical control via connectivity pathways with striatal and thalamic areas during response inhibition (Aron et al., 2003 ;Dambacher et al., 2014 ;Hampshire et al., 2010 ;Maizey et al., 2020 ), we predicted a greater modulatory effect on rIFG and its directed connectivity to both rCau and rThal in the NoGo compared to Go condition.Additionally, based on pr e vious studies r eporting sex differ ences in both, behavior al r esponse inhibition and associated neur al pr ocessing in cortical-subcortical circuits (i.e.sex, Li et al., 2006 ;Ribeiro et al., 2021 ;Sjoberg and Cole, 2018 ), as well as a significant correlation between enhanced inhibitory control and increased frontalstriatal connectivity (Chang et al., 2020 ;Jahfari et al., 2011 ;Wei and Wang, 2016 ;Xu et al., 2016 ), we hypothesized a modulation of the k e y pathw ays b y biological and performance variations with better response inhibition being associated with stronger causal regulation in the inhibition circuitry, especially in the IFG-Cau pathway .Finally , in line with consistent evidence that sho w ed right-later alized br ain ar eas and neur al cir cuits inv olved in the r esponse inhibition (Ar on et al., 2003 ;Che vrier et al., 2007 ;Hung et al., 2018 ;Jahfari et al., 2011 ;Thompson et al., 2021 ), we proposed a differ ent causal structur e for the left and right models given the hemispheric asymmetry in the inhibitory network.

Participants
In this study, n = 250 healthy right-handed participants were enrolled and underwent a validated Go/NoGo fMRI paradigm.The data have been previously used to examine undirected functional connectivity within domain-general and emotion-specific inhibitory brain systems (Zhuang et al., 2021 ), and were part of a lar ger neur oima ging pr oject examining pain empathy (Li et al ., 2019 ;Zhou et al., 2020 ), emotional face memory (Liu et al., 2022 ), and mirr or neur on pr ocessing (Xu et al., 2022 ).After quality assessment during the processes of data collection and preprocessing n = 218 participants were included (104 males, details see Supplementary Materials).During the model estimation processes, explained variance by the specified model on the individual le v el was calculated with higher values reflecting better model inversion (Zeidman et al., 2019a ).In line with previous studies (Bencivenga et al., 2021 ;Rupprechter et al., 2020 ), participants with < 10% of explained variance were excluded and finally a total of 118 participants (56 males, age: mean ± SEM = 21.57± 0.21 y ears) w er e included into further anal yses .T he study was appr ov ed by the local ethics committee and in accordance with the latest version of the Declaration of Helsinki.

Response Inhibition Paradigm
A v alidated mixed e v ent-r elated bloc k design linguistic emotional Go/NoGo fMRI paradigm w as emplo y ed (Goldstein et al., 2007 ;Protopopescu et al., 2005 , for details see Zhuang et al., 2021 ).Notably, although both the Go/NoGo and stop signal paradigm are commonly used to examine response inhibition control and associated brain function, the former paradigm captures action r estr aint while the latter primarily involves action cancellation (Raud et al., 2020 ;Sc hac har et al., 2007 ).During the pr esent Go/NoGo task, participants were required to make responses as accur atel y and quic kl y as possible based on orthogr a phical cues, i.e. w or ds w er e pr esented in normal or italic font.For w or ds in a normal font, participants were instructed to perform a buttonpress (Go trials), while inhibiting their response to w or ds presented in italic font (NoGo trials).Omission err ors wer e defined when no r esponses wer e made for Go trials, while commission err ors wer e defined when r esponses wer e made to NoGo trials .P ositi ve, negati ve, and neutral w or ds w ere included into the paradigm as stimuli.Ho w ever, given that the main aim of the present study was to examine the causal influence within the general inhibition network as proposed by Alexander et al. ( 1986Alexander et al. ( , 1991 ; ;Alexander and Crutcher, 1990 ) and to increase statistical po w er in this respect the different emotional valence conditions (e.g.positive Go condition, positi ve NoGo condition, negati ve Go condition, negativ e NoGo condition, neutr al Go condition, and neutr al NoGo condition) were not further accounted for in the DCM analysis.Stimuli wer e pr esented in two runs and each run included 12 blocks (six blocks: Go; six blocks: NoGo).Each Go block encompassed 18 normal font w or ds (100% Go trials) while each NoGo block encompassed 12 normal font w or ds (66.7% Go trials) and six italicized font w or ds (33.3% NoGo trials).Further details can be found in Zhuang et al. ( 2021 ) and the Supplementary Materials.

Behavior al Da ta Anal ysis
In our pr e vious study, we demonstrated that participants exhibited more commission errors during inhibitory control (i.e.NoGo > Go) as well as faster responses in positive Go contexts and lo w er accurac y in positive NoGo contexts (Zhuang et al., 2021 ).Given that sex-differences were examined in the DCM model, the pr esent anal yses additionall y examined sex-differ ences on accuracy and reaction times (Supplementary Materials).Given previous studies have sho w ed age-related effects on inhibition (Rey-Mermet et al., 2018 ;Rubia et al., 2007 ) age was included as covariate.

MRI Data Acquisition and Preprocessing
MRI data were collected on a 3T MRI system using standard sequences and were initially preprocessed using validated protocols in SPM 12 (for details see Supplementary Materials).

GLM Analysis
An e v ent-r elated gener al linear model (GLM) was established in SPM12.To examine domain general inhibitory control (irrespective of emotional context) the overarching inhibitory control contrast was modeled (e.g.all NoGo > all Go trials) and convolved with the canonical hemodynamic response function.Six head motion par ameters wer e included in the design matrix to control mov ement-r elated artifacts and a high-pass filter (1/128 Hz) was a pplied to r emov e low fr equency components .T he contrast of inter est (contr ast: NoGo > Go) was cr eated and subjected to onesample t -test at the second le v el.In line with pr e vious studies (Ar on et al., 2003 ;Che vrier et al., 2007 ;Hung et al., 2018 ;Jahfari et al., 2011 ;Thompson et al., 2021 ), gr oup-le v el (contr ast: NoGo > Go) peaks in the IFG, Cau, GP, and Thal within the identified general inhibition network were then used to define individual-specific regions of interest (ROI) for the DCM analysis.Additionally, a twosample t -test was conducted (contrast: NoGo > Go) to examine sex-dependent effects on the response inhibition network.Analyses wer e corr ected for m ultiple comparisons using a conserv ativ e peak-le v el thr eshold on the whole br ain le v el ( P < 0.05 famil y-wise error, FWE).

DCM and Node Definition
A DCM analysis w as emplo y ed to determine directed causal influences according to the circuitry model proposed by Alexander et al. ( 1986Alexander et al. ( , 1991 ; ;Alexander and Crutcher, 1990 ).The DCM appr oac h allows construction of a realistic neuronal model of inter acting r egions and the prediction of the underl ying neur onal activity from the measured hemodynamic response (Friston et al., 2003 ;Stephan et al., 2007 ).To this end, directed causal influences between the k e y regions including IFG, Cau, GP, and Thal in the basal ganglia-thalamocortical loop and their modulation via experimental manipulations (engagement of motor inhibitory contr ol) wer e examined.In line with pr e vious neur oima ging studies and meta-analyses demonstrating a right-lateralized inhibition model (right model) encompassing the rIFG, rCau, rGP, and rThal (Ar on et al., 2003 ;Che vrier et al. , 2007 ;Hung et al. , 2018 ;Jahfari et al. , 2011 ;Thompson et al., 2021 ), our main hypothesis testing focused on the right lateralized network.To further validate the hemispheric asymmetry of the inhibitory control network an identical model was tested for the left hemisphere including the lIFG, lCau, lGP, and lThal.In line with pr e vious studies, we combined atlas-based masks (Human Brainnetome Atlas, Fan et al., 2016 ) with gr oup-le v el and individual le v el activity ma ps to gener ate the corresponding nodes (Fernández-Espejo et al., 2015 ;Holmes et al., 2021 ;Qiao et al., 2020 ;Van Overwalle et al., 2020 ).Among this, the caudate is limited to a mask that combines the v entr al and dorsal caudate but not the putamen (Fan et al., 2016 ).

Model Specification and Estimation
A two-step DCM analysis was performed using the DCMparametric empirical Bayes (PEB) approach (Zeidman et al., 2019a(Zeidman et al., , 2019b ) ).On the first-le v el, time-series fr om four ROI (rIFG, rCau, rGP, rThal) were extracted.A full DCM model was specified for each participant and all connectivity parameters in both forw ar d (e .g. rIFG-rT hal-rGP-rCau-rIFG) and backw ar d (e.g.rIFG-rCau-rGP-rThal-rIFG) dir ections wer e estimated.We estimated three k e y DCM parameters: (i) the matrix A reflecting all connections including forw ar d and backw ar d connectivity betw een R OI and selfinhibitions in each ROI, (ii) the matrix B representing modulatory effects of Go and NoGo condition on all connections, and (iii) the matrix C r epr esenting the driving inputs into ROI fr om Go and NoGo conditions separ atel y.Giv en that all inputs in the model wer e mean-center ed, intrinsic connectivity in the matrix A indicates mean effective connectivity independent of all experimental conditions .T he model was estimated using v ariational La place (Friston et al., 2007 ).Further details are presented in the Supplementary Material.At the second (group) level, we constructed a PEB model over the first-level estimated parameters.In accordance with pr e vious studies (Benciv enga et al., 2021 ;Ruppr ec hter et al., 2020 ), we e v aluated the explained variance by the model on the individual le v el (Zeidman et al., 2019a )-and then we only included participants with > 10% of explained variance in the PEB model.Finally, 118 participants were included for further analyses .T he number of excluded participants is similar to a pr e vious study (Ruppr ec hter et al., 2020 ).The differ ences on behavior al performance were examined between the excluded and included participants and no significant differ ences wer e found (all P ≥ 0.23, for details see the Supplementary Material), suggesting no evidence of biased selection.
The primary aim of the present study was to establish a causal neurobiological model for response inhibition and to determine the interaction between k e y players in this circuitry.To e v aluate the model three PEB analyses were carried out separately for A, B, and C matrices.Separate analyses examined sex and performance variations (for details, see the Supplementary Materials).
Next, to identify the model that best r epr esented our data, Bayesian model reduction was performed to compare the free energy of the full model with numerous reduced models for which specific par ameters wer e "switc hed off" (Friston et al., 2016 ).An automatic gr eedy searc h pr ocedur e (iter ativ e pr ocedur e) was emplo y ed to facilitate an efficient comparison of thousands of models.In this pr ocedur e, par ameters that do not contribute to free ener gy wer e pruned a wa y.Next, the Ba yesian model a v er a ge, performing a weighted av er a ge of the parameters of each model, was calculated over the 256 models obtained from the final iteration (Friston et al., 2016 ).
Finall y, to compar e the effectiv e connection str ength, especiall y the cortical-subcortical connectivity and driving inputs into each r egion fr om differ ent experimental conditions (NoGo and Go conditions), Bayesian contrasts (Dijkstra et al., 2017 ) were computed ov er par ameters fr om the B and C matrices.Gr oup-le v el estimated par ameters wer e thr esholded at posterior pr obability > 95% (indicating strong evidence: Kass and Raftery, 1995 ) based on free energy.

BOLD Activ a tion (GLM) Anal ysis
Examination of domain general inhibition (contrast: NoGo > Go) r e v ealed a widespr ead fr onto-parietal cortical and thalamostriatal subcortical network including the IFG, striatal, pallidal, and thalamic regions (Fig. 1 and Table 1 ) during response inhibition.Gr oup-le v el peaks in the rIFG, rCau, rGP, and rThal were selected as centers of the ROI for model testing (Fig. 2 a and Table 2 ).No significant sex difference was observed in blood oxygen le v el-dependent (BOLD) activation.

Causal Connectivity (DCM) Analysis
For the matrix A, the diagonal cells r epr esent self-connections that are unitless log scaling parameters and were multiplied with the default value of −0.5 Hz (Zeidman et al., 2019a ).Positive values indicate increased self-inhibition due to task condition and  decr eased r esponsivity to the inputs fr om the other r egions of the network, while negativ e v alues indicate decr eased self-inhibition and incr eased r esponsivity to the inputs from other nodes of the network (Zeidman et al., 2019a ).Our findings r e v ealed negativ e self-inhibition values for the rIFG, rCau, and rThal but a positive value for the rGP (Fig. 2 b,f), indicating that the GP increased selfconnection while the other nodes increased interaction with other nodes in the network.For the off-diagonal cells in the matrix A, the values (in Hz) reflect the rate of change in the activity of the tar get r egion caused by the source region per second.Positive values reflect excitatory effects while negative values indicate inhibitory effects.In the forw ar d direction (e .g. rIFG-rT hal-rGP-rCau-rIFG), we found a significant negati ve connecti vity from rIFG to rThal and positi ve connectivity from rThal to rGP as well as rCau to rIFG.In the backw ar d direction (e .g. rIFG-rCau-rGP-rT hal-rIFG), rIFG exhibited a negative inhibitory influence onto rCau, alongside an excitatory connection from rCau to rGP and rGP to rThal (Fig. 2 b,f).Although the connectivity from rThal to rIFG was not significant, a weak evidence (posterior probability of 57%) for this connection was observed with a more lenient threshold.
Values in the matrix B r epr esent the r ate of change, in Hz, in the connectivity from source area to target area induced by the experimental conditions (Zeidman et al., 2019a ).During inhibitory control (NoGo condition) the rIFG exerted a negative influence onto the rCau and rThal whereas the rGP exerted a negative influence on the rCau (Fig. 2 c,g).In addition, we found negative selfinhibition values in both rCau and rThal, r espectiv el y.During the Go condition a negative influence of the rIFG on both rCau and rThal was observed (Fig. 2 d,h), while the positive influence was observ ed fr om the rGP to rCau and fr om rThal to rIFG.Mor eov er, we found a positive self-inhibition value in rIFG and a negative value in rCau.A Bayesian contrast (NoGo > Go) allo w ed us to compare the connectivity strength modulation during the different experimental conditions and r e v ealed a v ery str ong e vidence (posterior probability > 99%) that the causal influence of the rIFG to both, the rCau and rThal was stronger during inhibitory control (NoGo vs Go condition).This reflects that response inhibition criticall y r equir es a causal top-down cortical-subcortical regulation via the right IFG.We additionally found a v ery str ong e vidence (posterior probability > 99%) for a consider abl y str onger inhibitory connectivity from rGP to rCau in the NoGo compared to Go condition.
The matrix C r epr esents the r ate of c hange in neur al r esponse of one brain region due to the driving input from an experimental condition (Zeidman et al., 2019a ).During inhibitory control (NoGo) all regions (rIFG, rCau, rGP, and rThal) exhibited excitatory driving input while during the Go condition only the rIFG exhibited excitatory input (Fig. 2 e ,i).Ba yesian contr asts dir ectl y comparing the conditions (NoGo > Go) demonstrated an increasing driving in-put specifically in the rIFG during engagement of cognitive control (NoGo > Go condition) with a 100% posterior probability.

Sex Differences in Connectivity Parameters
Examining sex effects on intrinsic connectivity sho w ed a negative influence from rThal to rGP in female compared to male participants across all experimental conditions (Fig. 3 a).For the modulatory effects on connectivity, we found a greater self-inhibition in rThal in female than male participants in the NoGo condition (Fig. 3 b).This suggests that for female participants, rThal exhibits reduced sensitivity to inputs from the other regions of the selected network during response inhibition.

Brain Behavior Associations: Inhibitory Beha vioral P erformance and Connectivity Parameters
Examining associations between inhibitory performance on the behavior al le v el (NoGo performance) and connectivity par ameters r e v ealed a v ery str ong e vidence (posterior pr obability > 99%) that NoGo accuracy was positiv el y associated with the directed connectivity from rThal to rIFG.

DCM Analyses in the Left Hemisphere
To further validate the hemispheric asymmetry of the inhibitory control network, an identical model for the left hemisphere including lIFG, lCau, lGP, and lThal was tested ( Fig. 4 a).Participants with < 10% explained variance were excluded and finally 82 participants (40 males, age: mean ± SEM = 21.24 ± 0.27 years) were included for the final DCM analyses.In contrast to the right model, no directed influences from IFG to subcortical regions were observed in terms of matrix A in the left model ( Fig. 4 b,f).Although the results sho w ed modulatory effects of NoGo and Go conditions on the connectivity from IFG to Cau and Thal in both left and right models, the modulation effect of experimental condition on GP to Cau connectivity was only found in the right model ( Fig. 4 c,d,g,h).Additionally, the NoGo condition sho w ed an inhibitory modulatory effect on the connectivity from Cau to GP in the left but not the right model and the Go condition sho w ed an excitatory modulatory effect on the connectivity from Thal to IFG in the right but not the left one .Moreo ver, the two models had a similar pattern for the driving inputs of the NoGo condition on regions but The A matrix: intrinsic connectivity independent of experimental conditions ( B , F ).The B matrix: modulatory effect on effective connectivity between regions and self-connections in the NoGo ( C , G ) and Go condition ( D , H ). The C matrix: driving inputs into ROI of NoGo and Go conditions ( E , I ).Values in matrices reflect the connectivity parameters.Effective connectivity strengths are displayed by the color ranging from y ello w to dark red (i.e.excitatory connectivity) and from turquoise to dark blue (i.e.inhibitory).P ar ameters with str onger e vidence (posterior pr obability > 95%) ar e pr esented and subthreshold parameters marked with "n.s.".not the Go condition ( Fig. 4 e,i).The different causal structure in the left and right model indicated a hemispheric asymmetry in the inhibition network.Additional Bayesian analyses confirmed the lack of a robust cortical-subcortical pathway in the left hemisphere (Supplementary Materials).

Discussion
We capitalized on a combination of recent progress in biologically plausible causal hierarchical modeling (DCM-PEB) and a compar abl y lar ge fMRI r esponse inhibition dataset to determine causal information flow and k e y nodes within the extensiv el y described basal ganglia-thalamocortical response inhibition circuits (Alexander et al., 1986(Alexander et al., , 1991 ; ;Alexander and Crutcher, 1990 ;Aron et al., 2007 ;Jahfari et al., 2019 ;Morein-Zamir and Robbins, 2015 ;Pfeifer et al., 2022 ;Schall and Godlo ve , 2012 ;Stuphorn, 2015 ;V erbruggen and Logan, 2009 ;W ei and W ang, 2016 ).Our neurocomputational model successfully validated a right-lateralized inhibitory control causal circuit and the best model sho w ed significant intrinsic connectivity within this functional loop and cap-tur ed an incr easing causal influence of the cortical rIFG node on both the rCau and rThal as well as from the rGP to the rCau during inhibition.Direct comparison between different experimental conditions (e.g.NoGo and Go) r e v ealed enhanced input into rIFG in terms of matrix C and increased connectivity from rIFG to rCau and rThal in the NoGo compared to the Go condition in terms of matrix B, suggesting a higher engagement of causal top-down cortical-to-subcortical control via the rIFG during inhibitory control.Although no sex differences were observed in inhibitory performance or BOLD activation, females exhibited decreased intrinsic connectivity from rThal to rGP and increased self-inhibition in rThal during the NoGo condition as compared to males.This indicates that a similar behavioral performance in response inhibition might be mediated by different brain processes in men and women, particularly in thalamic loops .Moreo ver, a higher NoGo r esponse accur ac y w as associated with stronger causal information flow from the rThal to rIFG in the NoGo condition, suggesting a particular behavioral inhibitory relevance of this pathway .Finally , our findings showed different left and right model structures, suggesting a hemispheric asymmetry in the inhibitory control network and confirming a critical role of the rIFG in implementing response inhibition.Together, these findings identified a pivotal role of the rIFG and its effective connectivity with the rCau/rThal within the basal ganglia-thalamocortical circuit during r esponse inhibition.Giv en that r esponse inhibition deficits have been observed across a wide range of mental and neurological disorders, such findings may allow a mor e pr ecise determination of target regions and circuits for neuromodulation strategies and personalized intervention.
Pr e vious studies have underscored the predictive validity of the DCM a ppr oac h based on hemodynamic r esponses c hanges (Bernal-Casas et al., 2017 ).A study by Bernal-Casas et al. combined optogenetic fMRI with DCM to examine cell-typespecific causal pathways among regions within the basal gangliathalamocortical network and found that effective connectivity pathways during D1-and D2-r eceptor-expr essing medium spin y neur on stim ulation significantl y differ ed (Bernal-Casas et al., 2017 ).Furthermor e, the DCM a ppr oac h has also been validated based on electrophysiological time series with respect to estimating activity on the synaptic or neuronal level in both animal models (Moran et al., 2011 ;Papadopoulou et al., 2017 ;Rosch et al., 2018 ) and clinical studies in humans (P a padopoulou et al., 2015 ).
In the current study, causal modeling successfully determined a right lateralized inhibitory control causal circuit encompassing the rIFG, rCau, rGP, and rThal (Aron et al., 2003 ;Chevrier et al., 2007 ;Hung et al., 2018 ;Jahfari et al. , 2011 ;Thompson et al. , 2021 ).In terms of the matrix A, a significant rIFG-rCau-rGP-rThal loop was observed with rIFG exhibiting a negative influence onto rThal, alongside a positive information flow from from rThal to rGP and rCau to rIFG in the forw ar d direction.In the backw ar d direction, we found significant negative connectivity from rIFG to rCau and positi ve connecti vity from rCau to rGP as well as rGP to rThal.A mor e lenient thr eshold additionall y r e v ealed rThal to rIFG connections (posterior probability of 57%).Importantly, accounting for behavioral task context revealed a significant positive modulatory effect on rIFG in both NoGo and Go condition in terms of matrix C, which was considerably stronger during response inhibition.The direct driving inputs into the rIFG are in line with its role in top-down target detection and attentional control in the context of response inhibition (Hampshire et al., 2010 ;Krämer et al., 2013 ) and indicate that the rIFG r epr esents the key regulator of other nodes.Response inhibition impairments have been observed in several disorders and identification of the rIFG as critical input and top-down regulator for response inhibition opens ne w tar gets for r egional or connectivity-based neur omodulation suc h as r eal-time neur ofeedbac k, whic h has been established for these regions (Li et al., 2019 ;Weiss et al., 2022 ;Zhao et al., 2019 ).For instance, rIFG and response inhibition deficits have been determined in ADHD (Clark et al., 2007 ;Morein-Zamir et al., 2014 ) and targeting the rIFG in ADHD may be a promising treatment.
In line with our hypothesis, the best model in terms of matrix B r e v ealed str ong e vidence for causal effectiv e connectivity from the rIFG to both rCau and rThal during response inhibition (posterior probability > 95%).This inhibitory pathway is consistent with pr e vious r e ports on negati ve coupling between the rIFG and striatal regions during behavior control (Behan et al., 2015 ;Diekhof and Gruber, 2010 ).Notably, direct comparison using Bayesian contrast revealed a very strong evidence (posterior probability > 99%) for increased modulatory connectivity from rIFG to rCau and rThal in the NoGo condition compared to the Go condition, suggesting the rIFG's driven engagement of corticalto-subcortical top-down control during response inhibition.Previous animal models and human neur oima ging meta-anal yses hav e consistentl y identified the rIFG as a k e y region implicated in dopaminergic and noradrenergic modulated inhibitory regulation (Bari et al., 2011 ;Hauber, 2010 ;Ott and Nieder, 2019 ;Pfeifer et al. , 2022 ;Terra et al. , 2020 ;Vijayr a ghav an et al., 2016 ;Zhuk ovsky et al., 2022 ), in particular during motor control and inhibition (Aron et al., 2003 ;Chamberlain and Sahakian, 2007 ;Puiu et al., 2020 ;Xu et al., 2016 ).Furthermore, both fr onto-striatal and fr onto-thalamic pr ojections hav e also been extensiv el y involv ed in r esponse inhibition (Ahissar and Or am, 2015 ;Bosc h-Bouju et al., 2013 ;Marzinzik et al., 2008 ;Phillips et al., 2021 ;Schmitt et al., 2017 ;Sommer, 2003 ;Tanaka and Kunimatsu, 2011 ).
In addition to the cortical-subcortical pathways significant excitatory connectivity was observed from the rGP to rCau during the Go condition and switched to inhibitory connectivity when response inhibition was required during the NoGo condition.Direct comparison confirmed a considerably stronger inhibitory influence of the rGP on the rCau during response inhibition (posterior probability > 99%), suggesting that communication between basal ganglia nodes is crucial for context-a ppr opriate behavior al r esponse contr ol.T he in v olvement of this pathw ay is in line with extensiv e neur ophysiological e vidence sho wing that GAB A inhibitory pr ojections fr om the external segment of the GP to the striatum play an essential role in cancelling a planned response when it is ina ppr opriate (Mallet et al., 2016 ;Wei and Wang, 2016 ) (but see also subthalamic nucleus to substantia nigra pars reticulata pathways in Hikosaka et al., 2006 ;Mallet et al., 2016 ).In addition, while numer ous pr e vious studies consistentl y demonstr ated a right-lateralized fronto-striatal response inhibition circuit (Aron et al., 2003 ;Chevrier et al., 2007 ;Gar av an et al., 1999 ;Hung et al., 2018 ;Jahfari et al., 2011 ), the present study additionally observed an inhibitory modulation effect of the NoGo condition on the effecti ve connecti vity between the left Cau to GP, suggesting that a left lateralized basal ganglia pathwa y ma y pla y an important role in action r estr aint.
With respect to sex difference analyses, we observed that females exhibited a lo w er intrinsic connectivity from rThal to rGP compared to male participants in the absence of performance differ ences, suggesting a differ ent baseline basal ganglia-thalamic connectivity pattern independent of experimental contexts between males and females.In addition, we also found an increased modulatory effect of the NoGo condition on self-inhibition in the rT hal in female , which indicates that female participants exhibited a reduced thalamic connectivity with other regions among the inhibitory control network compared to male participants.Giv en that pr e vious studies r eported an important r ole of the thalam us in r elaying information and monitoring performance via r ecipr ocal connections with the basal ganglia and PFC (Guillery, 1995 ;Phillips et al., 2021 ;Xiao et al., 2009 ;Tanaka and Kunimatsu, 2011 ), our findings may reflect a higher neural efficiency of this basal ganglia-thalamocortical circuit during response inhibition in females compared to males in the context of comparable performance in both gr oups.Mor eov er, while pr e vious findings on sex differences in response inhibition performance and the underlying neural activity remained inconsistent (Chung et al., 2020 ;Gaillard et al., 2020Gaillard et al., , 2021 ; ;Li et al., 2006 ;Ribeiro et al., 2021 ;Sjoberg and Cole, 2018 ), similar findings have been reported in a previous study using a Go/NoGo task.This stud y re ported significant sex differences on the neural response level in terms of functional connectivity in the absence of behavioral performance differences (Chung et al., 2020 ).Ho w ever, it also has to be acknowledged that the findings by Chung et al., differ in important aspects from our findings, such as those authors observed greater functional connectivity between subcortical regions including thalamus and amygdala with other regions in females as compared to males .T his ma y reflect the influence of a ge-r elated factors (the pr e vious stud y was conducted in adolescents), gi ven that males and females exhibit different neuromaturation of the inhibitory control circuits (Weafer, 2020 ).In addition, although the present findings suggest that our model was sensitive to biological variables and that separable information processes may underly response inhibition in men and women (see also Chung et al., 2020 ;Li et al., 2006 ), further r esearc h is needed to firml y v erify the pivotal role of rIFG and its top-down control to subcortical rCau and rThal regions in response inhibition in the context of individual differ ences.Mor eov er, the functional r ele v ance of the identified pathw ays w as further underscored b y a significant association between response inhibition performance and the causal influence from the rThal to rIFG in the NoGo condition, which demonstrates that this pathway involved in motor inhibition critically mediates behavioral success during inhibition (Wei and Wang, 2016 ).
Finally, our modeling tests confirmed a hemispheric asymmetry and support the critical role of right IFG circuit in response inhibition (Hung et al., 2018 ;Jahfari et al., 2011 ;Maizey et al., 2020 ).The different causal structures suggest a strong corticalsubcortical intrinsic connectivity and rIFG control on the right side, although the left model r e v ealed a differ ent causal structure and null hypothesis tests sho w ed moder ate e vidence for the difference between NoGo and Go condition's modulatory effects on effecti ve connecti vity from lIFG to lCau and to rT hal (e .g. lIFG to lCau: Bayes factor = 5.47; lIFG to lThal: Bayes factor = 8.20).
Ther e ar e se v er al limitations in the current study.First, in line with our main aim we did not account for emotional valence in the DCM model, which may affect response inhibition (Schimmack and Derryberry, 2005 ).Second, we focused on specific nodes that were based on established basal ganglia-thalamocortical circuits proposed by Alexander (Alexander et al ., 1986(Alexander et al ., , 1991 ; ;Alexander and Crutcher, 1990 ) (see also neur oima ging meta-anal ysis: Hung et al., 2018 ).Other regions such as the STN (Aron et al., 2016 ;Ar on and Poldr ac k, 2006 ;Chen et al., 2020 ) could be integrated in future studies .T hird, although DCM has adv anta ges in testing directed connectivity and causal pathways between regions, it also has a number of limitations.For instance, the a ppr oac h uses a Bayesian information pr ocedur e and as such is stringently dependent on the priors (Friston et al., 2003 ).Mor eov er, the a ppr oac h assumes that activity in the neurons forming an assembly is conform which does not adhere to the actual physiological properties (Friston et al., 2003 ).

Conclusions
In conclusion, our findings demonstrated a critical role of the rIFG as well as top-down cortical-subcortical control from the rIFG to rCau and rThal in response inhibition.The nodes and pathways of the model wer e sensitiv e to biological and performance variations .T he nodes and pathways may r epr esent pr omising tar gets to impr ov e r esponse inhibition in mental disorders.

Figure 1 :
Figure 1: Brain activation maps for general response inhibition on whole br ain le v el (contr ast: NoGo > Go; P < 0.05 FWE, peak le v el).L, left; R, right.The color bar r epr esents the t -values of the BOLD signal and reflect the significance level of the contrast.

Figure 2 :
Figure 2: Location of regions included in the right model and group-level connectivity parameters.( A ) Location of regions included in the right model.The A matrix: intrinsic connectivity across all experimental conditions ( B , F ).The B matrix: modulatory effect on effective connectivity between regions and self-inhibitions from NoGo ( C , G ) and Go condition ( D , H ). The C matrix: Driving inputs in ROI in the NoGo and Go condition ( E , I ).Values in matrices reflect the connectivity parameters.Effective connectivity strengths are displayed by the color ranging from y ello w to dark red (i.e.excitatory connectivity) and from turquoise to dark blue (i.e.inhibitory).Parameters with stronger evidence (posterior probability > 95%) are presented and subthr eshold par ameters ar e marked with "n.s.".

Figure 3 :
Figure3: Sex effect on connectivity parameters in terms of A matrix and B matrix.( A ) For intrinsic connectivity in A matrix, female participants sho w ed a more negative influence from rThal to rGP compared to male participants.( B ) In the NoGo condition, there is a greater self-inhibition in rThal in female than male participants in terms of B matrix.Effective connectivity strengths are displayed by the color ranging from y ello w to dark red (i.e.excitatory connectivity) and from turquoise to dark blue (i.e.inhibitory).Parameters with stronger evidence (posterior probability > 95%) are presented.

Figure 4 :
Figure 4: Location of regions included in the left model and group-level connectivity parameters.( A ) Location of regions included in the left model.The A matrix: intrinsic connectivity independent of experimental conditions ( B , F ).The B matrix: modulatory effect on effective connectivity between regions and self-connections in the NoGo ( C , G ) and Go condition ( D , H ). The C matrix: driving inputs into ROI of NoGo and Go conditions ( E , I ).Values in matrices reflect the connectivity parameters.Effective connectivity strengths are displayed by the color ranging from y ello w to dark red (i.e.excitatory connectivity) and from turquoise to dark blue (i.e.inhibitory).P ar ameters with str onger e vidence (posterior pr obability > 95%) ar e pr esented and subthreshold parameters marked with "n.s.".

Table 2 :
Activation and peak values for k e y regions included in the right model.