Neural Substrates Related to Motor Memory with Multiple Timescales in Sensorimotor Adaptation
[['Behavioral and computational modeling studies , on the one hand , and neuroimaging studies , on the other hand , have greatly advanced our understanding of motor adaptation .', 'In particular , recent behavioral and computational modeling studies have shed light on the temporal structure of motor adaptation by showing that motor behavior is well accounted for by the sum of multiple motor memory states with different timescales .', 'For instance , models with two time constants can reproduce a number of adaptation phenomena such as anterograde interference , spontaneous recovery , and savings [1–4] .', 'A model with a larger number of time constants can account for adaptation occurring at multiple timescales , e . g . , fatigue and aging [5] .', 'In contrast , neuroimaging studies , using either functional magnetic resonance imaging ( fMRI ) [6–8] or positron emission tomography ( PET ) [9–12] , have investigated the spatial distribution of the neural correlates and plastic changes across different brain regions at specific times during and after adaptation , with the prefrontal cortex ( PFC ) , the posterior parietal cortex ( PPC ) , and the cerebellum consistently showing activation .', 'The PFC mostly contributes to the early , but not the late , stage of adaptation , which is consistent with its role in spatial working memory and in attention and arousal at the onsets of target presentation [13 , 14] .', 'The PPC is also important in the early stage of motor adaptation [6 , 9 , 15] , here again consistent with its role in working memory [13 , 14] , planning movements and early adaptation to a new visuomotor transformation [9 , 16 , 17] .', 'The activity of the cerebellum increases in a later stage of visuomotor adaptation [6 , 15 , 18] and correlates with the degree of savings at transfer of learning [19] .', 'Such activation is consistent with cerebellum learning from errors [20 , 21] , building internal models [22–24] , and storing multiple motor skills [25] .', 'However , these modeling and neuroimaging studies have been conducted independently of each other .', 'As a result , little is known about the neural correlates of the latent ( i . e . , nondirectly observable from the behavioral data ) motor memories at different timescales suggested by computational models .', 'In particular , it is unclear whether the multiple motor memories proposed by the models reside within a single system that contains a distribution of possible timescales or in a finite set of qualitatively distinguishable neural systems [1 , 26] .', 'In addition , because experimental behavioral data can be well accounted for by models with different number of time constants , it is unclear how many distinct memories the brain actually updates during a specific type of motor adaptation .', 'Finally , it is unclear whether the neural substrates identified in the early and late phases of adaptation in previous fMRI studies map onto putative “fast” and “slow” processes suggested by the computational models .', 'Here , we combined modeling and imaging approaches via a model-based fMRI study of the spatial and temporal distribution of multiple motor memories during adaptation .', 'Subjects adapted to two opposing visuomotor rotations in short alternating blocks .', 'We estimated the multiple memories via a multiple-timescale adaptation model that generalizes the two-state models to multiple states with a logarithmic distribution of time scales from seconds to hours , as in a previous study [5] .', 'A model-based approach based on regression analyses of brain activity would have insufficient power to dissociate multiple memories that are highly correlated with each other .', 'We therefore propose a novel two-step approach .', 'In a first step , we conducted exploratory multiple single regressions with individual memories , which avoids the problem of multicollinearity .', 'In a second step , we performed a sparse singular value decomposition ( SVD ) on the voxels identified in the first step , in order to select a small number of orthogonal components .', 'As a result , we identified four characteristic networks , each associated with formation of different time-scales of memories .'], ['The overall mean adaptation level of 21 subjects showed that fast adaptation occurred within task blocks , and slow adaptation occurred across the task blocks for each task ( Fig 2A ) .', 'Forgetting across blocks , which can be observed by comparing the last trial of a task block and the first trial of the next block of the same task , gradually decreased across blocks .', 'Thus , visual inspection of the behavioral data suggests the existence of multiple timescales in motor memory , initially dominated by faster memories and eventually dominated by slower memories .', 'We modeled adaptation as the sum of multiple memory states with different time constants .', 'As in a previous model [5] , a continuous distribution of timescales was approximated by multiple time constants .', 'We defined 30 time constants , ranging from 2 s to ~92 . 6 h , in a logarithmic scale ( S1 Table ) .', 'In addition , the contextual cue ( here the target color ) selects the states for a specific task , as in a previous study [2] .', 'Thus , the motor output at each trial n is given by', 'y ( n ) =∑k=130xk ( n ) Tc ( n ) ,', '( 1 )', 'where xk = [xk , 1 xk , 2] with time constant τk ( k = 1 , … , 30 ) .', 'The contextual cue vector is c = [1 0]T for Task 1 and c = [0 1]T for Task 2 .', 'This model thus assumes no interference between two tasks ,', 'i . e .', ', perfect switching ( please refer to S1 Text for the rationale of this choice of a model with no interference ) .', 'The states were updated by the error feedback , e = f − y , where f is , at each trial , one of the two visuomotor rotations , 40° or −40° .', 'Because the intertrial interval ( ITI ) was random ( see details in Materials and Methods ) , we modeled time decay as an exponential function of time [27] .', 'The update equation from trial n to n+1 for the state of motor memory with time constant τk is thus given by', 'xk ( n+1 ) =xk ( n ) e−T ( n ) /τk+βk⋅e ( n ) ⋅c ( n ) ,', '( 2 )', 'where T ( n ) is the ITI following trial n and βk is the learning rate .', 'The learning rates depend inversely on the time constant τk , as follows:', 'βk=rτkq ,', '( 3 )', 'where r and q are strictly positive free parameters .', 'As a result of this relationship , states with smaller time constants decay faster but are more rapidly updated [5 , 28] .', 'Using averaged data of 21 subjects in actual adaptation to Tasks 1 and 2 ( see details in Materials and Methods ) , the best-fitted parameters of the proposed model were r = 0 . 0333 and q = 0 . 201 .', 'The model fit is shown in Fig 2A , and the 30 states of Task 1 used in the fit are shown in Fig 2B .', 'The overall fit to the averaged data was excellent ( root mean squared error = 4 . 96° , R2 = 0 . 981 ) .', 'In addition , the fit to individual subjects’ data was satisfactory overall , although the fit was only modest for some subjects ( mean ± SEM across subjects: R2 = 0 . 832 ± 0 . 189 ) .', 'We thus used the regressors calculated from the averaged adaptation data for the subsequent fMRI analysis .', 'Because the multiple memory states are highly correlated with each other , especially for larger time constants ( for instance , the correlation coefficient between the state with τ21 = 2 . 2 h and the state with τ30 = 92 . 6 h was 0 . 994 ) , we first entered the states as single regressors in independent univariate analyses of blood-oxygen-level dependent ( BOLD ) signal ( see Materials and Methods ) .', 'Overall , this univariate model-based regression analysis revealed distinct patterns of regions for states with increasing time constants ( Fig 3A ) .', 'The faster states ( τk , ranging from 2 . 0 to 4 . 6 s; k = 1 , 2 , and 3 ) correlated mainly with activity in large regions in the frontal and parietal cortices and with activity in regions in the posterior-lateral cerebellum ( see below ) .', 'By contrast , the states with intermediate time constants ( τk , ranging from 2 . 1 to 87 . 9 min; k = 11 , … , 20 ) correlated with activity in a restricted area in the right anterior region of the inferior parietal lobe ( aIPL , indicated by a blue circle in Fig 3A ) , which is the most anterior of the intraparietal sulcus .', 'Note that the aIPL activity was prominently found in the right hemisphere , contralateral to the left hand used to perform the task but that weak activity was found in the left hemisphere when the threshold was lowered ( see Discussion ) .', 'The slower states ( τk , ranging from 2 . 2 to 92 . 6 h: k = 21 , … , 30 ) primarily correlated with activity in the anterior-medial cerebellum ( see below ) .', 'Supplementary videos show the patterns of correlated regions in both hemispheres for all time constants and corresponding regressors ( S1 and S2 Videos ) .', 'These patterns for each time constant were similar in both the 40° and the −40° condition .', 'Table 1 summarizes prominent clusters for the small ( k = 1 ) , middle ( k = 16 ) , and large ( k = 30 ) time constants for Task 1 .', 'Significant clusters were found to be related to the fastest state ( k = 1 ) in the parietal , frontal , and cerebellar regions when thresholded at p < 0 . 05 corrected for multiple comparisons ( family-wise error rate [FWER] ) throughout the brain at cluster level .', 'Activity related to the middle state ( k = 16 ) was significant in the aIPL ( p < 0 . 05 ) when we applied small volume correction for the superior and inferior lobules , in line with previous studies reporting parietal contribution to visuomotor adaptation [9 , 15] .', 'Activity related to the slowest state ( k = 30 ) was significant in the left and right cerebellum at p < 0 . 05 corrected for the entire brain at cluster level .', 'Fig 3B shows regional difference in the cerebellum between the fast ( k = 1 ) and the slow ( k = 30 ) states .', 'Regions related to the fast state ( blue ) distribute in the posterior-lateral parts of the cerebellar cortex .', 'These parts are mainly in the left and right crus 1 ( see Table 1 ) , which is connected with the prefrontal-parietal networks [29] .', 'Note that activity was found in crus 1 not only for the fastest ( k = 1 ) but also for relatively fast ( k = 2 , … , 7 ) states ( S1 Fig ) .', 'By contrast , regions related to the slow state ( red ) distribute in the anterior-medial parts ( mainly lobule 6 and partly lobule 8 ) , which are connected with cerebral sensorimotor networks [30] .', 'Results from the univariate regression analysis with the 30-state model provided highly redundant but rich information on possible brain regions related to formation of multiple motor memories .', 'For comparison , we checked if the standard two-state model [1 , 28] could explain our behavioral data and brain activity ( see Materials and Methods ) .', 'We found that the two-state model was a subset of the 30-state model .', 'That is , the time constants of the fast process and the slow process in the two-state model were respectively 47 . 9 s and 1 . 5', 'h . These are very close to two time constants of the 30-state model , k = 9 ( 55 . 2 s ) and k = 21 ( 2 . 22 h ) , with correlation coefficients of the states between the two models being respectively 0 . 993 and 0 . 991 .', 'Brain activity identified by the two-state model was essentially the same as that found by the states of k = 9 and k = 21 in the 30-state model ( S2 Fig ) .', 'A possible concern with these univariate regression analyses is that the high-pass filtering with 128 s cut-off frequency , which is used in preprocessing to remove low-frequency noise due to scanner drift , could filter out the lower-frequency components in the cerebellum .', 'An analysis of the frequency components of high-pass filtered BOLD signals using Fast Fourier Transform ( FFT ) shows that the frequency components in the cerebellum remained large enough to be correlated with the regressors with the slower time constants ( see S3 Fig ) .', 'A second possible concern with this analysis is that the identified activity is not related to memory states , but to errors .', 'This is an especially valid concern for the faster states , because the memory states of the fast components correlate with the errors used for updating adaptation , with high values at the initial stages and low values at the late stages of adaptation .', 'In our regression analysis of memory states , we included parametric regressors associated with error as those of no interest ,', 'i . e .', ', as nuisance regressors for the decreasing effects of error-related activity on the estimation of memory-related activity .', 'We verified that these error-associated nuisance regressors appropriately explained away the error in the regression analyses for the faster states ( see S2 Text and S4 Fig ) .', 'The T-map shown in Fig 3 is redundant because of highly correlated regressors .', 'We thus applied the sparse SVD to the T-value profiles of voxels as function of time constants to extract principal components ( see Materials and Methods for details ) .', 'All the voxels that survived the voxel-level threshold p < 0 . 001 for at least one time constant in the initial exploratory regression analysis were included in this sparse SVD analysis .', 'The SVD analysis decomposed the data matrix into the following three matrices: eigenvariates , eigenvalues , and eigenimages .', 'For both Tasks 1 and 2 , a sparse SVD model with four components was selected via the model selection method of Bayesian Information Criterion ( BIC ) [31] .', 'The contributions of these four components to the variance in the matrix of T-values were ( 54 . 26% , 38 . 94% , 6 . 32% , 0 . 47% ) and ( 51 . 38% , 39 . 72% , 8 . 35% , 0 . 55% ) for Tasks 1 and 2 , respectively .', 'The first and second eigenvariates correspond to the fast states ( the second eigenvariate has notably large values for small time constants that rapidly approach zero around 2 min ) , while the third and fourth eigenvariates represent the slow and middle states , respectively ( Fig 4A and 4B ) .', 'Because a similar pattern was observed in corresponding eigenimages for Tasks 1 and 2 ( see S5 Fig and S1 and S2 Videos ) , their overlap is presented in Fig 4C after each image was thresholded so that the top 10% of voxels with the highest values are included in the image .', 'The first component is located mainly around the junction between the supplementary motor area and superior frontal gyrus ( SMA/SFG ) , and in medial occipitoparietal regions ( MOP ) .', 'The second is located mainly in the posterior region of the intraparietal sulcus ( pIPS ) and partly in the posterior cerebellum ( pCBL: crura 1 and 2 ) .', 'The third is mainly in the anterior-medial part of the cerebellum ( a-mCBL: lobules 6 and 8 ) , and the right temporoparietal junction ( TPJ ) .', 'The fourth is in the anterior part of the intraparietal sulcus ( aIPS ) , which includes the aIPL region for the middle component ( e . g . , k = 16 ) , the middle temporal and inferior temporal gyri ( M/ITG ) , and the inferior frontal gyrus ( IFG ) .', 'More detailed quantification of eigenimages for Tasks 1 and 2 are provided in S2–S9 Tables .', 'We then verified whether a reduced model with four states derived from the SVD analysis , instead of the full model with 30 states , could account for the behavioral adaption .', 'From the eigenvariates of the T-map ( Fig 4A and 4B ) , we constructed a reduced four-state model consisting of "eigenstates , " each of which was estimated as a linear combination of the 30 regressors weighted by the corresponding eigenvalues .', 'The variance explained by the four-state model was as high as the original 30-state model ( mean squared error = 4 . 96° , R2 = 0 . 981 ) .', 'Thus , the model reduced from 30 to four states based on the neural activities well explains the behavioral data .', 'The above model-based regression analysis indicated contributions of the parietal and the anterior cerebellar regions to the middle and slow states , respectively .', 'To exclude the possibility that these regression results are due to spurious correlations , we then conducted a decoding analysis to test whether the regional brain activity could be used to classify the two rotations ( 40° and −40° ) .', 'If classification accuracy varies across the three sessions , this would indicate that activity in these regions changes with dynamics similar to the dynamics of medium or slower states .', 'We thus applied a multivoxel pattern analysis ( MVPA ) to parietal regions in which BOLD signals significantly correlated with at least one of the intermediate components ( k = 11 , … , 20 ) , and in cerebellar regions in which signals were significantly correlated with at least one of the slow components ( k = 21 , … , 30 ) ( Fig 5A , see Materials and Methods ) .', 'The MVPA revealed significantly above chance accuracy ( 50% ) in the right aIPL as well as in the cerebellum for all sessions , with averaged accuracy across subjects ranging from 60% to 70% ( Fig 5B ) .', 'This above-chance classification is not surprising because the direction of hand movements changed depending on the rotation types .', 'However , two-way analysis of variance ( ANOVA ) with regions of interest ( ROIs ) and sessions as a within-subject factor revealed a significant interaction between the two factors ( F ( 2 , 40 ) = 3 . 504 , p < 0 . 05 ) .', 'A simple main effect analysis revealed significant increase of accuracy across sessions in the cerebellum ( F ( 2 , 80 ) = 10 . 16 , p < 0 . 001 ) , but no significant difference in the right aIPL ( F ( 2 , 80 ) = 0 . 736 , p = 0 . 482 ) .', 'These results thus indicate that specificity of activity patterns to the task ( 40 or −40° rotations ) increased with sessions in the cerebellum but did not change in the parietal regions .', 'We then verified that the increase in classification accuracy across sessions observed in the cerebellum was unlikely due to behavioral confounds during adaptation ( see S3 Text ) .'], ['We investigated the spatiotemporal neural correlates of motor memory involved in visuomotor adaptation via estimation of the latent memory states derived from a model with multiple states with different time constants .', 'A univariate regression analysis , which correlated the model states with brain activity during the whole adaptation process , first located the neural substrates related to formation of the multiple motor memories .', 'Then , a sparse SVD analysis showed four characteristic networks , associated with a specific profile of correlation with different time constants .', 'Finally , a classification analysis showed that specific activity patterns to the rotation type were acquired in the cerebellum as adaptation proceeded .', 'We organize the following discussion of our results from the faster to the slower time constants .', 'For the first few fastest constants ( 2 s to 4 . 6 s ) , various brain regions were activated , including frontal and parietal lobes , as well as the visual cortex , the temporal cortex , and regions in the posterior part of the cerebellum , specifically in crus 1 .', 'It is known that regions in the crus 1 are connected with prefrontal and parietal cerebral regions according to studies on cerebro-cerebellar connections in monkeys [29] and humans [30] .', 'For slower but still relatively fast time constants up to k = 6 ( 15 . 9 s ) , the widespread activated regions became more localized into the PPC .', 'A possible reason for activation of parietal activity is mental rotation , which has been known to contribute to early adaptation [7 , 32 , 33] and has been consistently localized in the superior parietal regions ( e . g . , [34 , 35] ) .', 'In line with these studies , the subjects in our study who showed larger reaction times tended to perform the task better with lower directional errors ( R2 = 0 . 229 , p = 0 . 028 ) .', 'For intermediate time constants around 16 . 7 min , we found a characteristic region of activation in the right aIPL ( blue circle in Fig 3 ) .', 'This is consistent with a prism-adaptation study [6] finding activity contralateral to the reaching hand in the lateral bank of the intraparietal sulcus , close to the aIPL activity in our study ( note that subjects used the left hand in the current experiment ) .', 'It has been suggested that the left parietal regions are critical for visuomotor rotation , because patients with left parietal damage show a deficit in adaptation [36 , 37] .', 'We also found activity in the left aIPL correlated with intermediate time constants if the threshold is lowered ( p < 0 . 05 uncorrected ) , but the activity in the right aIPL was more significant than that in the left aIPL .', 'Muhta and colleagues showed the importance of the left parietal region for construction of visuomotor mapping based on online correction of error [36] .', 'In contrast , we only provided terminal feedback after the end of joystick movement , and the role of online correction was relatively small .', 'Thus , although further studies are needed to understand the contradiction in parietal laterality between our study and Mutha et al . ’s , the above difference in error feedback may explain this difference .', 'For slower time constants , the number of correlated voxels in the aIPL decreased , and the number in the anterior-medial cerebellum increased .', 'With time constants longer than 1 h , the main activities were identified in the anterior-medial cerebellum; this result is in line with previous studies [6 , 15 , 18] .', 'Regions related to the slow states distribute in the anterior-medial parts and mainly in lobule 6 .', 'These cerebellar regions are connected with cerebral sensorimotor networks , including the primary motor and sensory cortices , the premotor cortex , and the supplementary motor area [30] .', 'This suggests that the cerebellar slow states directly contribute to sensorimotor control without help from cognitive processes ( prefrontal-parietal functions ) probably corresponding to an “autonomous” stage [38] by constructing internal models [18 , 25 , 39] .', 'A recent study reported that transcranial direct current stimulation ( tDCS ) over the cerebellum induced faster adaptation during training but did not affect retention after training [40] .', 'Because tDCS is likely to affect neural activity in the posterior part of the cerebellum to a greater extent than in the anterior-medial part , our findings of the fast components of motor memory in the posterior part ( Fig 3 and S1 Fig ) are consistent with this previous study .', 'The existence of slow components in lobule 6 is consistent with a study reporting that patients with focal degeneration in this lobule have difficulty in adapting to a visuomotor rotation [41] .', 'In addition , activity related to kinematic errors that drive visuomotor rotation has been found in cerebellar regions , including lobule 6 [20] .', 'The SVD analysis of variability in specificities to timescales over the brain identified four components , two fast , one middle , and one slow , each associated with different brain networks .', 'Three groups of components ( fast , middle , and slow ) are consistent with a recently proposed three-component model of visuomotor adaptation [42] .', 'The first and second SVD components are subset regions of the fastest component delineated by the regression analysis and indicate the existence of two types of fast components: one related to SMA/SFG and MOP , and the other related to posterior IPS and cerebellum .', 'Our previous study [43] indicated that medial parietal regions ( including MOP ) are related to switching of internal models based on contextual cues and that posterior-lateral regions of the IPS are related to switching based on sensorimotor feedback .', 'Analogy of the current results to our previous study suggests that the first SVD component corresponds to association between visual cue ( target color ) and responses for tasks , while the second one corresponds to fast adaptation ( or rearrangement of haptic directions ) based on sensorimotor feedback .', 'The third component confirmed the slow component in the anterior-medial cerebellum .', 'The fourth component in the aIPS completely includes aIPL found for the middle time constant .', 'This component was also found in the IFG and M/ITG .', 'Neurons in the IFG are activated when monkeys [44]and humans [45 , 46] observe goal-directed hand actions and when humans imagine hand actions [47] .', 'The IFG has been suggested to contain sensorimotor memory representation related to hand movement [48] .', 'The M/ITG is known to be involved in visual motion analysis [49] , but specific interpretation of this region in the visuomotor adaptation is unknown , at least to our knowledge .', 'Our decoding analysis indicated that the activity pattern in the cerebellum became more specific to rotation type as adaptation proceeded .', 'A previous study by one of us [25] showed that cerebellar activities correlated with learning to control two different cursors ( rotation and velocity ) were spatially segregated , supporting modular organization of internal models , thus suggesting that overlapped regions represent common properties of learning two tasks .', 'In contrast , the results of the present study show no significant regional difference of activities in either the parietal or the cerebellar regions between visuomotor rotations of 40° and −40° ( S6 Fig ) .', 'We surmise that the overlap arises because the two visuomotor transformations are identical except for the rotation angle .', 'Within this common cerebellar region , as well as in the PPC , the MVPA discriminated the representation of the opposing rotations with higher decoding accuracy than chance level .', 'As mentioned earlier , this result is not surprising because the direction of hand movements changed depending on the rotational types and could contribute to successful decoding .', 'Importantly , however , we observed significant increase of the decoding accuracy across sessions in the cerebellar regions related to the slow states ( lobules 6 and 8 ) , but not in the parietal regions related to middle states .', 'The increase in classification accuracy in the cerebellum , especially from the second to the third session , does not appear to be due to changes in performance , because we could not identify significant difference in performance between the second and third sessions .', 'While the primary motor cortex ( M1 ) has been involved in the late stage of adaptation in previous studies [8 , 40 , 50 , 51] , we found no significantly correlated activities in M1 .', 'In addition , in a recent study [51] , we found that MVPA could classify opposite rotational types ( 90° or −90° ) from activity patterns in sensorimotor cortex including M1 , suggesting separate representation for dual visuomotor adaptation .', 'However , the classification was based on fMRI activity measured after intensive training on a continuous tracking task for more than 3 d and a total of 160 min .', 'Therefore , M1 may be correlated with even slower timescales beyond the range of our study , inducing structural changes [8] , although further studies would be necessary to confirm this correlation .', 'Unlike conventional fMRI regression analysis , model-based fMRI regression analysis allows the study of the underlying latent variables generating the behavior in motor adaptation .', 'In previous neuroimaging studies of motor adaptation , the observable behavioral variables of interest were used to define contrasts or regressors for analysis of brain activity .', 'However , the multiple motor memories and related activity that drive the behavior are internal to the subject undergoing adaptation and thus cannot be measured directly ( although they can , in theory , be manipulated by experimental conditions such as task schedules , e . g . , [52] ) .', 'Here , as in a number of reinforcement learning studies ( e . g . , [53] for review ) , we circumvented this difficulty by first estimating internal memory states via computational modeling and then by using these internal variables in the regression analysis to detect neural representations related to formation of motor memories at multiple timescales .', 'Note that we carefully designed our regression models by including possible confounding variables , notably type of task , hand movement , error , and reaction time in each trial .', 'However , when confounding variables are correlated with memory states , such as errors with fast memory states , regression cannot completely dissociate activity related to these confounding variables from activity directly related to memory itself .', 'In addition , our regression models did not include additional behavioral and physical quantities that may correlate with memory states in the model and that may or may not be related to formation of multiple memories , such as attention , eye movements , and repetition of the task .', 'Thus , our results revealed the neural substrates related to formation of the multiple memories at multiple time scales , but not necessarily the neural substrates of multiple memories at multiple time scales per se .', 'Experiments in which nuisance parameters ( such as error ) are varied while adaptation is constant would allow the effects of these confounds to be dissociated .', 'Recent studies have suggested that motor adaptation is a multifaceted process .', 'In particular , behavior during adaptation is not only updated by error-based learning mechanisms , as we have assumed with our model , but also presumably updated by reward-based and use-dependent mechanisms [54–56] .', 'Each of these processes likely operates at multiple time constants as well .', 'In addition , explicit and implicit aspects of motor adaptation have been recently shown to have fast and slow dynamics , respectively [57] .', 'Thus , although the interpretation of what “memory states” represent varies between adaptation studies , our experiment of the neural correlates related to formation of motor memories at multiple time scales is , we believe , highly relevant .', 'Note , however , that our study does not provide a clear picture of the connectivity and spatial arrangements of the multiple neural representations involved .', 'In particular , in line with a previous study supporting a parallel architecture of motor memories over a serial architecture [2] , we have assumed a parallel architecture in our model in which all memories were updated by a common error signal ( see Eq 2 ) .', 'Our results , however , cannot provide evidence for such parallel architecture .', 'To further clarify the actual neural mechanism , model-based fMRI regression can be complemented by functional connectivity analysis [58] or causal and interfering manipulation of neural function via transcranial magnetic stimulation ( TMS ) or tDCS [59–62] .'], ['Twenty-one right-handed and neurologically healthy volunteers participated in the study ( 20–50 y old , mean age of 27 . 3 y , six females ) .', 'Handedness was assessed by a modified version of the Edinburgh Handedness Inventory [63] .', 'Written informed consent was obtained from all subjects in accordance with the Declaration of Helsinki .', 'The experimental protocol received approval from the local ethics committee at the Advanced Telecommunications Research Institute International .', 'We designed a dual-task adaptation experiment with two opposing visuomotor rotations .', 'At the beginning of each trial , a white cross appeared at the center of screen; this cross served both as the fixation point and as the initial cursor position .', 'A round colored target of 0 . 7 cm radius appeared on the top of the screen 8 cm from the center .', 'Subjects were instructed to manipulate an fMRI compatible joystick to move the cursor to the target within 1 . 5 s ( maximum movement time ) ; otherwise , the trial was considered a missed trial , and the data was not analyzed .', 'After the maximum movement time , the cursor appeared in the direction of the joystick movement at 8 cm from the center for 500 ms to provide angular error feedback .', 'To encourage subjects to respond faster , the color of the feedback cursor turned yellow if the subject did not move within 800 ms . ITIs were randomly generated from 4 to 14 s from an exponential distribution , in 2 s increments .', 'For each trial , we calculated the angular error between the targ
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['Recent computational and behavioral studies suggest that motor adaptation results from the update of multiple memories with different timescales .', 'Here , we designed a model-based functional magnetic resonance imaging ( fMRI ) experiment in which subjects adapted to two opposing visuomotor rotations .', 'A computational model of motor adaptation with multiple memories was fitted to the behavioral data to generate time-varying regressors of brain activity .', 'We identified regional specificity to timescales: in particular , the activity in the inferior parietal region and in the anterior-medial cerebellum was associated with memories for intermediate and long timescales , respectively .', 'A sparse singular value decomposition analysis of variability in specificities to timescales over the brain identified four components , two fast , one middle , and one slow , each associated with different brain networks .', 'Finally , a multivariate decoding analysis showed that activity patterns in the anterior-medial cerebellum progressively represented the two rotations .', 'Our results support the existence of brain regions associated with multiple timescales in adaptation and a role of the cerebellum in storing multiple internal models .']
['Motor adaptation , a form of motor learning in which motor commands are modified to compensate for disturbances in the external environment , usually proceeds at a rapid pace initially and is then followed by more gradual adjustments .', 'This suggests that at least two learning processes are involved , but little is known about how many distinct memories the brain actually updates during motor adaptation .', 'In addition , it is unclear whether these putative multiple motor memories reside within a single neural system that encompasses different timescales or in qualitatively distinct neural systems .', 'We addressed these issues using a model-based functional imaging approach in which we first used behavioral data to derive a large number of possible memory “states , ” each with different dynamics , and then correlated these memory states with neural activities .', 'We identified four components: two fast , one intermediate , and one slow , each associated with different brain networks .', 'In particular , areas in the prefrontal and parietal lobes and the posterior part of the cerebellum were associated with formation of memories for short timescales .', 'By contrast , the inferior parietal region and the anterior-medial cerebellum were associated with formation of memories for intermediate and long timescales , respectively .']
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A model-based functional MRI study reveals the existence of brain regions associated with four distinct timescales in motor adaptation.