Parallel processes of temporal control in the supplementary motor area and the frontoparietal circuit

: 1 Durations in the several seconds' range are cognitively accessible during active timing. 2 Functional neuroimaging studies suggest the engagement of basal ganglia (BG) and 3 supplementary motor area (SMA). However, their functional relevance and 4 arrangement remain unclear because non-timing cognitive processes temporally 5 coincide with the active timing. To examine the potential contamination by parallel 6 processes, we introduced a sensory control and a motor control to the duration 7 reproduction task. By comparing their hemodynamic functions, we decomposed the 8 neural activities in multiple brain loci linked to different cognitive processes. Our 9 results show a dissociation of two cortical neural circuits: the SMA for both active 10 timing and motor preparation, followed by a prefrontal-parietal circuit related to 11 duration working memory. We argue that these cortical processes represent duration 12 as the content but at different levels of abstraction, while the subcortical structures 13 including BG and thalamus provide the logistic basis of timing by coordinating 14 temporal framework across brain structures.

Abstract: 1 Durations in the several seconds' range are cognitively accessible during active timing. 2 Functional neuroimaging studies suggest the engagement of basal ganglia (BG) and 3 supplementary motor area (SMA). However, their functional relevance and 4 arrangement remain unclear because non-timing cognitive processes temporally 5 coincide with the active timing. To examine the potential contamination by parallel 6 processes, we introduced a sensory control and a motor control to the duration 7 reproduction task. By comparing their hemodynamic functions, we decomposed the 8 neural activities in multiple brain loci linked to different cognitive processes. Our 9 results show a dissociation of two cortical neural circuits: the SMA for both active 10 timing and motor preparation, followed by a prefrontal-parietal circuit related to 11 duration working memory. We argue that these cortical processes represent duration 12 as the content but at different levels of abstraction, while the subcortical structures 13 including BG and thalamus provide the logistic basis of timing by coordinating 14 temporal framework across brain structures. 15 Introduction: 1 Timing is a crucial aspect of sensory processing and motor planning in the brain. 2 Durations in the range of seconds to minutes are relevant for cognitively controlled 3 behavior, requiring active mental engagement, usually referred to as Interval Timing. 4 With the help of functional imaging techniques, researchers have found 5 timing-associated activities across multiple brain regions including subcortical . However, the 11 functional role of these regions and their inter-regional organization during interval 12 timing remain unclear (Pöppel, 2004;Zhou et al, 2014). One difficulty of conducting 13 neuroimaging studies for interval timing tasks presumably comes from parallel 14 cognitive processes that are hard to be temporally disentangled. 15 16 The accumulation of blood-oxygen-level-dependent (BOLD) signal has been taken as 17 the neural substrate of temporal encoding in many studies (Wittmann et al., 2010; 18 Casini & Vidal, 2011), thus treating the encoding of duration as an evidence 19 accumulation process, similar to other decision-making tasks (Wittmann, 2013; Balci 20 & Simen, 2016). However, the link between ramping BOLD signal and timing is 21 under-specific: no physiological evidence on the neuronal or circuit level has been 22 established in support of the link between climbing hemodynamic signal and 1 accumulation of neural information. More importantly, it is unclear whether the 2 climbing signal is a result of persistent non-temporal processes or the dedicated 3 timing. Time acts as the context of all neural and cognitive processes. There is no 4 guarantee that all temporally evolving neural activities, even when decoding of time is 5 possible, are relevant for devoted timing. 6 7 In interval timing, time is at the same time the logistic, contextual framework, and the 8 content of the neurocognitive processes (Pöppel, 1997). Therefore, it is hard to tell 9 from the data whether the temporally evolving neural activity represents an active 10 involvement in measuring time or whether it is simply an artifact of persisting 11 non-timing parallel processes that lasts the same period being timed. Take the 12 example of the duration reproduction task (e.g., Shi et al., 2013;Maass, Schlichting & 13 van Rijn, 2019), in which the subjects are asked to firstly remember the duration of an 14 interval, i.e., 'encode' the interval duration, and 'reproduce' the duration by holding a 15 key or terminate an external display after a proper duration. During encoding, the 16 internal events actively engaged in sensory timing share identical time courses with 17 the external presentation of stimuli, thus temporally collide with sensory processing, 18 along with other task-general components like elevated attention. For reproduction, 19 the motor timing is similarly contaminated by sensory processing, attention, or motor 20 preparation. 21 22 One physiological model of interval timing is the basal ganglia (BG)-SMA circuit 1 (Wittmann, et al., 2010;Kotz, Brown & Schwartze, 2016). The basal ganglia, 2 especially the putamen, are considered as the subcortical clock governed by midbrain 3 dopaminergic inputs and synchronize the cortical processes across multiple regions 4 (Meck, 2005;Cheng et al., 2016). This is supported by pharmacological interference these assumptions, hemodynamic changes in the BG structures and SMA during 12 timing tasks are often attributed to timing without closer inspection. 13 14 However, considering the more general role that the BG-SMA circuit plays in 15 goal-directed, task-context-sensitive behavior (Haber, 2003;Korb et al., 2017), it is 16 questionable whether the hemodynamic elevations in functional imaging studies are 17 relevant for active timing, or are simply artifacts of non-timing parallel processes (e.g. 18 attention and motor preparation). Since an explicit motor response is required in all 19 timing tasks, the preparation for the response is always concurrent with the active 20 timing, thus indistinguishable in the data. This possible confounding has not been 21 considered in previous studies. 22 1 One way to disentangle intermixed components is to perform subtraction with control 2 conditions containing only the non-timing elements. We therefore introduced two 3 controls to the duration reproduction task: a motor control requiring simple reaction 4 and a sensory control with only passive viewing. By comparing the time course of 5 BOLD signals in task epochs with identical sensory input and motor output, we were 6 able to decompose the neural activities in multiple brain loci linked to different 7 cognitive processes. We confirmed that the SMA is bifunctional, participating in both motor planning and 10 timing, with an additive hemodynamic response when both components are present. 11 The fluctuation of hemodynamic signals in subcortical structures including putamen 12 and thalamus are less specific and more likely motion-related. In addition, 13 working-memory associated activities were observed in another group of loci 14 including the left dorsal lateral prefrontal cortex and the bilateral intraparietal sulcus. 15 Activity in the SMA leads the frontoparietal circuit during encoding of the temporal 16 duration, while the sequence is reversed during reproduction. Our results dissociate 17 the interval timing mechanism into an encoding stage in the SMA and a following  Results: 21 Behavior verification of duration reproduction task 22 Duration reproduction task is popular in interval timing research partially because of 1 its complex cognitive spectrum. In a typical scenario, subjects are first presented with 2 an external event that lasts for a while, the duration of which is the sample to be 3 encoded and memorized. Following a delay, the subjects perform an anticipatory 4 timing task based on the reference memory of this sample duration (for a review, see 5 Mioni et al., 2014). To better disentangle the brain activities related to encoding, 6 working memory, and retrieval of interval duration, and for the sake of better 7 signal-to-noise ratio, a longer inter-stimuli interval (ISI) is required in functional 8 imaging. Considering the relatively long repetition time (TR) of fMRI scanning and 9 slow decay rate of the blood-oxygen-level-dependent (BOLD) signal, the ISI has to be 10 extended up to several seconds, which is much longer than what is usually 11 implemented. 12

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A behavioral pilot experiment was conducted in search of an optimal length of ISI as 14 well as reaffirming the temporal reproduction accuracy of the 3-second sample 15 interval. The uniqueness of 2-3s interval presumably represents a borderline of the 16 logistic capacity of interval timing as it is observed in many cognitive processes (Bao  in its optimal range to minimize the noise of low-level processing. The pilot task 21 design closely imitated the scanning experiment, except that the ISIs were randomly 22 chosen from either 4.5 or 9.0 seconds for each block, and the sample duration from 4 1 conditions (1.5, 3.0, 4.5, or 6.0 seconds), randomized within-block.   12 Duration reproduction and simple reaction time 13 During scanning, participants were asked to reproduce a duration to match the sample 14 (See Fig. 1 and Methods). Reproduced durations of all 15 participants in the scanner 15 were analyzed: subject means were in a range of 2.42 ~ 3.54s. Among the 16 participants, reproduced duration of 3 subjects were not significantly variated from 17 the sample (p > .05), another 2 tended to over-reproduce (i.e., 18 reproduced duration > 3s, all with p < .001), while all the other 10 participants 19 showed a tendency to under-reproduce (all with p < .005). Even though identical 20 sample duration was implemented in all trials without explicitly indicated, most of the 21 participants reported variations in the perceived duration during a short 22 post-experiment interview. Group mean of reproduced duration = 2.775s (95% CI 1 [2.628, 2.921]); one-sample T-test revealed that the reproduced duration was 2 significantly smaller than the sample duration of 3 seconds ( = .003, one-tailed). 3 See Table. 1. Considering that the difference between reproduced duration and the 4 sample (Mean = 0.225s) was much smaller than the sampling rate of fMRI (TR = 5 2s), this did not alter the temporal envelope of BOLD signals remarkably (see 6 Supplementary Fig.1). Therefore, all the following analyses were performed pooling 7 over all valid trials. In the motor control phase of the task, participants were asked to make a simple 10 reaction to the offset of the visual stimulus (see Methods). The mean reaction time 11 (RT) of participants range from 0.253s to 0.515s; group mean = 0.346s (95% CI 12 [0.311, 0.381]). See Table. 1. Since the fluctuation of reaction time is also much 13 smaller than the TR, the following analyses were performed pooling over trials with 14 different reaction time. 15 16 Comparisons between task phases 17 Taking together the two additional control tasks, the behavior paradigm can be split 18 into four task phases: the Encoding Phase (EP) when subjects were presented with a 3 19 s visual stimuli; the Reproduction Phase (RP) when subjects were required to 20 terminate another stimulus when its duration subjectively matched the sample; the 21 Visual Control (VC) phase when the same 3s visual stimulus was just passively 22 viewed, and the Motor Control (MC) phase when subjects were required to press the 1 key (identical motor response as the RP) following the removal of visual stimuli.
2 Therefore, each trial can be evenly divided into four task epochs with identical lengths 3 (12s). 4 5 For the first part of fMRI data analysis, simple contrasts were performed with a 6 general linear model (GLM, see Methods) on the whole-brain activation maps for the 7 period of stimuli presentation across four phases (see Methods for the experimental 8 design). Since overlapping compositions of cognitive processes were present in four 9 task phases, active timing and time-irrelevant activities can be disentangled by 10 psychological subtraction: comparison between EP and VC reveals timing-only 11 activities free from contamination by motor components; while comparing RP with 12 VC reveals duration working memory, decision-making, and motion preparation 13 activities in addition to those specific for timing. Comparison between MC and VC 14 was also performed in search of motor-specific components. 15 16 Subtracting visual components from the encoding phase, i.e., EP > VC, resulted in 17 significantly activated clusters mainly in the SMA, together with a small proportion of 18 medial superior frontal gyrus (See Table.1 for details; also see  Comparison RP > VC revealed a similar cluster at SMA and medial superior frontal 1 gyrus, as well as additional clusters spreading across bilateral thalamus, putamen, 2 pallidum, precentral gyrus, insula, and operculum (Fig.3, upper-middle). An 3 important difference between reproduction and encoding was the additional 4 involvement of bilateral Inferior Parietal Lobule, including structures alongside the 5 postcentral sulcus and intraparietal sulcus. These reproduction-specific brain activities 6 can be attributed to the duration working memory: maintenance of duration 7 information (reference memory) and its utilization in anticipatory timing (executive 8 control). Reverse comparison VC > RP revealed no significant cluster.

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To control for non-timing motor components, a comparison MC > VC was performed 11 (Fig.3, lower left). Significant clusters spread in a similar set of regions as in RP, 12 including subcortical structures in bilateral thalamus, putamen, pallidum, and caudate, 13 as well as cerebral activations in bilateral insula and SMA. Another cluster was in the 14 superior lobes of the left cerebellum. The operculum cortex, inferior frontal lobule, 15 and precentral gyrus were lateralized to the left hemisphere. Since no explicit timing 16 was required in this phase of the task, these activities should be caused by non-timing 17 motion preparation and motor initiation. Reverse comparison VC > MC revealed 18 significant clusters mainly in the occipital visual areas (Supplemental Fig.2). 19 20 To disentangle motor components from active timing which were intermingled during 21 reproduction, the comparison RP > MC was also performed, revealing higher 22 activation levels in the putamen, pallidum, insula, and precentral cortex, all lateralized 1 to the left. Operculum activation was found to be higher during reproduction in both 2 hemispheres. SMA also displayed elevated activity, indicating its participation in both   In addition to the SMA and the basal ganglia, significant clusters located in the right 11 middle frontal gyrus and bilateral structures alongside the intraparietal sulcus were 12 unique for duration reproduction; again, indicating their role in active and explicit 13 timing rather than motor planning. Reverse comparison MC > RP revealed clusters in 14 the cingulate cortex and left medial superior frontal gyrus (Supplemental Fig.2). 15 16 Reference memory of duration 17 To reproduce a duration in match of a previously given sample, information about the 18 sample duration must be kept in reference memory throughout the response delay. A  Hemodynamic function in regions of interest 6 Since the GLM model provides a trend-line analysis between the observed signal and 7 the pre-hoc defined task design matrix, the reliability of the interpretation depends on 8 the neuropsychologic understanding of the task itself. However, in a timing task 9 where time itself is the information to be encoded, it is unknown what cognitive 10 progress is taking place at when. Therefore, the task design matrix of the GLM model 11 is based on hypothetical prior assumptions about the temporal profile of cognitive 12 processes. From a statistical perspective, the results cannot be more reliable than the 13 assumptions, neither can they justify these assumptions. A data-driven, 14 hypothesis-free approach is preferential in this case. 15 16 We then took a data-driven approach by comparing the temporal envelope of BOLD 17 signal across different loci. Our behavior task was designed in a way that the BOLD 18 signal sampling can be temporally aligned across all the trials. All four task epochs 19 were extended to 12s, corresponding to 6 sampling points. The whole trial added up to 20 48s or 24 sampling-point lengths of the BOLD envelope. Overlapping between the 21 BOLD signal of adjacent events is optimally balanced between each phase of the task. 22 The mean BOLD envelop is thus a reliable approximate of the task-evoked 1 hemodynamic functions (HDF) in each region-of-interest (ROI). In bilateral SMA (Fig.4A), the HDF showed three peaks following the encoding, 4 reproduction, and motor control phase. Interestingly, only in the right SMA, the last 5 peak of HDF during motor control came later than prediction and its left-hemisphere 6 counterpart (estimated with 6s offset, see Methods). Considering the delay by reaction 7 time and the left-hand response, the delayed activity of right SMA might be better 8 explained by the motor response. In addition, the peak amplitude following 9 reproduction was higher than both encoding and motor control phase (paired t-test, all 10 with < .001). Confirming the simple contrast between RP > MC. This again 11 supports the bifunctionality of SMA, with additive BOLD signals when both 12 functionalities are called.  The HDF in the thalamus (Fig.4C) suggests that its function might be more 21 motor-related, with peaks only in the two phases with a motor response, i.e. 22 reproduction and motor control. It is thus consistent with the results of simple 1 comparisons. The right thalamus ROI revealed more dramatic signal fluctuation 2 compared to the left side, in line with the left-handed motor response. 3 4 The BOLD signal changes during the timing task in basal ganglia structure putamen 5 (Fig.4D), on the other hand, was smaller in size compared to other ROIs. Signal 6 remained high throughout the first two phases (encoding, reproduction compared to 7 visual control); as well as during motor control but was delayed and much steeper. It generation as compared to explicit timing. 10 11 In the inferior parietal lobule (IPL, Fig.4E), the HDF followed a similar pattern like 12 the SMA, with three peaks in encoding, reproduction, and motor control, and the 13 highest response was reached during reproduction. Interestingly, a plateau of activity 14 between encoding and reproduction was observed only in the left IPL ( Fig.4E-left), 15 probably related to the maintenance of duration reference memory. Although activities 16 in bilateral IPL were both significantly altered by the task, it seemed that the reference 17 memory of duration information was leftward lateralized as suggested by its activity 18 pattern.

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A similar pattern as IPL was found in the middle frontal gyrus (MFG, Fig.4F), with a 21 more prominent signal fluctuation in the right hemisphere and a plateau-like activity 22 in the left. Concerning results of simple contrasts that the left MFG was found 1 significant during the memory phase and the right MFG significantly activated during 2 reproduction, bilateral MFG might play a different role in duration reference memory 3 (left) and executive control (right). 4 5 In contrast, no such plateau-like activity was found in the left inferior frontal 6 operculum (Supplemental Fig.3), another significantly activated region in both the 7 reproduction and memory phase. It also illustrates that comparing the temporal 8 envelope of the BOLD signal can reveal more than the common hypothesis-driven 9 way. 10 11 Inter-regional cross-correlation 12 To further investigate the strength and direction of inter-regional interaction, a 13 cross-correlation analysis was performed on the HDF for each pair of ROIs within the 14 four task epochs. The peak of activity was estimated by fitting a quadratic function to 15 the more sparsely sampled data. This allows interpolation beyond the 2s sampling rate 16 of the fMRI (see Methods and Fig.6A). Dramatic changes in the direction of 17 inter-regional correlation were observed in the inter-regional time lag matrix (see  phase when significant activity is missing in most subjects, the interpolation method 10 we used for inter-regional temporal lag estimation is not as reliable as the other three 11 phases. 12 13 Discussion: 1 Disentangling parallel cognitive processes is the core challenge in neurocognitive 2 research on timing. All physical events, including those that take place in the brain,  This problem is especially eminent when the duration of time itself is the input to the 9 neuronal system, as in interval timing research. 10 11 In previous imaging studies on interval timing, researchers either look for 12 accumulating signals that correlate with the passage of time or simply compare brain 13 activities between a timing task and a non-timing task in a block design. However, 14 both ways fail to address whether these observed activities are truly relevant for 15 dedicated timing in the brain. The same problem persists even when temporal  ). The subtraction method was first implemented on reaction time, following the 5 idea of sequential processing, but has been frequently revisited in modern 6 neuroscience with measurements far more advanced than the reaction time paradigm.

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The underlying idea is the same: as long as the detected signal is systematically 8 modulated by each additional cognitive process, subtraction of the data can 9 presumably disclose the difference between cognitive compositions. The simple 10 contrast between whole-brain activity maps of different tasks is a typical example of 11 subtraction. It has the potential to differentiate activities even when they share the 12 same time course. 13 14 The duration reproduction paradigm is widely used in interval timing research 15 partially due to its rich cognitive composition. It consists of a near-complete 16 spectrogram of cognitive components: encoding, memory, and retrieval of duration 17 information, for both external sensory input and prospective motion planning. 18 However, its complexity also adds to the difficulty of interpreting the task-data 19 temporal correlation. Linking any activity that is temporally evolving with the timing 20 mechanism risks contamination from non-timing parallel components. In this study, 21 we tried to dissect the duration reproduction task by comparing the hemodynamic 22 function of the timing task with control tasks, in both hypothesis-driven and 1 data-driven ways.  Our result shows that the SMA is involved in both timing and motor planning, with an 14 additive BOLD response when both cognitive components are present during 15 reproduction. Similar signatures of activity were observed in the insula but turned out 16 to be statistically insignificant during encoding, as shown in the simple contrasts. 17 Comparatively, the BOLD signal in part of the dorsal striatum, the putamen, was 18 subtle during encoding and reproduction but had a clear and sharp response during 19 motor control. However, given its elevated response throughout EP and RP compared 20 to VC, putamen may also be bifunctional, only less specific during timing than its 21 well-known function in motion initiation (Turner & Desmurget, 2010). We also found 22 in temporal cross-correlation that the direction of connectivity went from BG to SMA 1 during encoding but from SMA to BG and thalamus during reproduction, suggesting 2 some information might have been passed from BG to SMA during encoding. We  The most persuasive evidence on timing in the BG comes from clinical research (e.g., 12 Dušek et al. which is located at a higher hierarchy in the cortex. 20 21 In addition to the SMA, a working memory network was observed in a different group   In conclusion, by comparing BOLD signals between different tasks in multiple brain 22 areas, we were able to disentangle different cognitive components of the duration 1 reproduction task. Based on differentiating the logistic function and the semantic 2 function of time, we attribute the devoted timing mechanism to the cortex. More 3 specifically, two distinct cortical circuits were discovered: the supplementary motor 4 area which displayed additive BOLD signal for both timing and motor planning, 5 probably result from involvement of independent subpopulations in different tasks; 6 and a working-memory related frontoparietal circuit. The plateau BOLD signal 7 observed in these working memory regions may suggest a different coding strategy 8 and thus different levels of abstraction for the semantic duration information.

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Activities in the subcortical regions such as the putamen and thalamus are less 10 specific. This may be because of overlapping populations realizing different functions 11 or simply the lack of functional differentiation in these subcortical regions. Thus, we 12 propose the distinction between a subcortical logistic function of time and a cortical 13 semantic function of time. 14 15 However, although we succeeded in attributing different processing stages to different   (Pöppel, 1972). 11 12 In the next phase of task (RP), participants were asked to reproduce the sample 13 duration by terminating a comparison stimulus with a keypress. In the third phase 14 (VC), the same square was presented again for 3 seconds, only passive viewing was 15 required. In the last phase (MC), the square was presented for the same duration as 16 reproduced in RP. To control for timing-irrelevant brain activities, e.g., motion 17 preparation and initiation, participants were asked to make a keypress following the 18 disappearance of the stimulus as soon as possible. They were instructed not to 19 deliberately time the stimuli in the MC phase but only react when the square was gone. 20 In case participants failed to press a key in RP, the stimulus was presented for 11 21 seconds and then turned off; the missing trial would be excluded from the analysis. 22 All key presses were performed with the left index finger. Each task phase was extended to exactly 12 seconds with a blank screen, allowing 3 hemodynamic response back to baseline. With identical lengths for each task phase, it 4 is possible to obtain trial-average hemodynamic curves for each region of interest 5 (ROI). 6 Trials were first screened by the reproduced duration during the RP phase to ensure 7 that participants were attending and following the instructions; further screening was 8 conducted on the reaction time in MC, ensuring no anticipation or active timing.

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Outlier trials were both defined individually as beyond 2 standard deviations from the 10 mean. This post-hoc data screening supplements the verbal instructions to guarantee 11 that all trials analyzed were performed as instructed. 12 13 Behavior verification of duration reproduction task: 14 6 right-handed college students (all males; mean age: 21.5 years; age range: 21-23 15 years) participated in the pilot behavioral experiment, all with normal or 16 corrected-to-normal vision, and reported no neurological, psychiatric or medical issue. 17 The experiment was conducted in a soundproofing chamber equipped with a computer. 18 The visual parameters were identical to the fMRI study. Sample durations were 19 randomly chosen from 1.5, 3.0, 4.5, or 6.0 seconds as the within-block variable; each 20 of the four alternatives was repeated four times, resulting in 16 trials per block. The 21 interstimulus interval (ISI) following the reference stimuli was either 4.5 or 9.0 22 seconds, randomized between blocks; each ISI was repeated three times, composing 6 1 blocks. Participants were instructed to terminate the second visual object with a press 2 on a 4-key reaction box (Sinorad Inc., China) when its duration matched the sample, 3 and not to apply any timing strategy such as counting or tapping. Each trial was 4 followed by a 7-second inter-trial interval with a blank screen.  MRI Participants: 12 16 college students (8 females and 8 males) were money-rewarded for participation in 13 the functional imaging study, with ages ranging from 19-28 ( = 21.7, = 2.6).
14 All participants were right-handed and with normal or corrected to normal vision. No 15 record of neurological, medical, visual, or memory issues was reported. Participants 16 were given written consent and several practice trials to familiarize themselves with 17 the task before the scanning session. They were asked to maintain a regular daily 18 schedule and not to consume any psychostimulants, drugs, or alcohol within 3 days 19 before the experiment. One Subject was excluded from data analysis due to bad signal 20 spatial alignment due to excessive head movement (> 4 mm). The study was approved 21 by the departmental ethical committee of Peking University.  Anatomical Labeling (AAL, http://www.gin.cnrs.fr/AAL-339) atlas. 14 15 ROI analysis: 16 To further investigate the temporal envelope of BOLD signal related to different 17 cognitive processes, region of interest (ROI) analysis was performed in a set of 18 regions derived from the group-level simple contrasts ( and then averaged across subjects and plotted with the between-subject variance 2 (Fig.4). All HRFs were baseline-corrected to the average BOLD signal during the  Temporal cross-correlation of regional HDF: 8 Trial averaged HDFs for each subject were then fed into an interregional temporal 9 cross-correlation analysis to investigate the connectivity pattern. The HDFs were 10 divided into 4 segments, corresponding to the delayed hemodynamic response for 4 11 task phases (start at 6s, 18s, 30s, and 42s after trial onset, see Fig.5A), resulting in a 12 cross-correlation function for each ROI pair. A quadratic function was fitted with the 13 highest 3 points around the peak in estimation for the inter-regional lag (Fig.5B). A 14 heatmap was created to visualize the inter-regional lag between selected ROIs during 15 each of the task phases (Fig.5C). 16 17 Reference of the Methods:     In each trial, four phases were in a continuous sequence with a fixed order, durations of all four phases were extended to 12 seconds. In each phase, a box appeared at the screen center following a visual cue of 1s. In the encoding and visual control, the visual stimuli persisted for 3s; while in the other two phases the duration was dependent on the subject-reproduced duration in that trial.

Fig.2 |
Reproduced duration for each sample duration in two different ISI conditions. Error bar marks the range of 95% confidence interval. No significant difference in reproduction performance was observed between different inter-stimulus intervals.
Reproduction for the 3s sample duration was more accurate than the over-reproduced 4.5 and 6 seconds.  The trial average HDF of each ROI was first obtained for each individual and then segmented into 4 phases. Cross-correlation functions were calculated for each pair of ROIs and then averaged across subjects. The temporal lag between each pair of ROIs was estimated by fitting a quadratic function to the highest 3 data points of the cross-correlation function.
(B) Inter-regional time lag matrix for each task phase. A negative value (-n) indicates that the region specified on the Y-axis leads the region on the X-axis by n seconds; while a positive value indicates the X-labeled region leading the Y-labeled region. In the encoding phase (EP), thalamus and putamen activities lead SMA and insula, while the relationship was partially reversed during reproduction (RP), in accordance with the direction of information flow.