{"paper_id":"c698998e-6fbb-43b0-bfdd-6439a56bd0ce","body_text":"Across-speaker ar,culatory reconstruc,on from \nsensorimotor cortex  for generalizable  brain-computer \ninterfaces  \n \nRuoling Wu1, Julia Berezutskaya1, Zachary V. Freudenburg1, Nick F. Ramsey1,2 \n \n1 University Medical Center Utrecht Brain Center, Utrecht, The Netherlands \n2 Donders InsHtute for Brain, CogniHon and Behavior, Radboud University, Nijmegen, The \nNetherlands \n \nE-mail: nick.rams ey@ru.nl \n \nAbstract \nObjec&ve: Speech brain-computer interface s (BCIs) can restore speech features like arHculatory \nmovements from brain acHvity. However, for individuals with vocal tract paralysis, lack of arHculatory \nmovements can pose a challenge for speech BCI development. To address this challenge, our study \naims at extracHng generalizable arHculatory features from a group of naHve Dutch speakers and \nreconstrucHng these features from brain data of a separate group of able-bodied individuals. Approach: \nWe applied a tensor component analysis (TCA) model to extract generalisable arHculatory features \nfrom a publicly available arHculatory movement  dataset. To reconstruct arHculatory features from the \nbrain, we analyzed data of three able-bodied parHcipants P1, P2 and P3  with high-density \nelectrocorHcography (HD-ECoG) electrode arrays implanted  over the sensorimotor cortex. For each \nparHcipant, a separate TCA model was applied to extract neural features. A gradient boosHng \nregression model was used to reconstruct arHculatory features from neural features. ReconstrucHon \nperformance was measured as Pearson’s correlaHon coefficient (PCC) between the reconstructed and \nthe generalizable arHculatory features. Results:  The extracted arHculatory features showed even \ncontribuHons across parHcipants, indicaHng that these features captured generalizable arHculatory \nkinemaHc pa\\erns . By using these features, we were able to reconstruct arHculatory features from \nbrain data. PCC between the reconstructed and original arHculatory features were significantly above \nchance for all three parHcipants, with mean PCCs of 0.80, 0.75 and 0.76 for P1, P2 and P3 respecHvely. \nSignificance: With the rapid development of speech BCI, our research demonstrates that speech -\nrelated arHculatory features can be restored from HD-ECoG signal using generalizable arHculatory \nfeatures derived from able -bodied individuals. With the potenHal to reconstruct audio or speech -\nrelated facial movements from the re constructed arHculatory features, our framework may provide a \nnew way for developing speech BCIs for people unable to produce mouth movements . \n \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nIntroduc)on \nTo produce speech, our brain coordinates the movement of vocal tract muscles , referred to as speech \narHculators: lips, jaw, tongue, and larynx (Browman & Goldstein, 1992; CharHer  et al., 2018; Silva et \nal., 2024) . Due to motor impairments  caused by medical condiHons such as  amyotrophic lateral \nsclerosis (ALS)  or brain stem  stroke, some people may lose the ability to control their vocal tract \nmuscles to produce speech. The loss of speech can lead to barriers in social li fe and substanHally \nimpact  life quality (Walshe & Miller, 2011).  \n \nBrain-computer interface s (BCIs) may be able to help these people by restoring their communicaHon \nability. This can be done, for example, by converHng neural signals from brain areas involved in speech \nproducHon to text on computer display or synthesized speech as has been shown in several individuals \n(Silva et al., 2024). However, it is unclear how generalizable these BCIs are across people. Also, these \nBCIs require a lot of data to train the decoding model. Most speech BCIs use signal from the ventral \nsensorimotor cortex (vSMC), where arHculatory kinemaHcs informaHon is strongly encoded (CharHer \net al., 2018; Mugler et al., 2018). Therefore, reconstrucHng the intermediate arHculatory movement  \nfeatures is a logical approach for speech BCIs. Recent BCI applicaHons have demonstrated successful \nspeech synthesis from  arHculatory features reconstructed from limited neural signals (Anumanchipalli  \net al., 2019; Metzger et al., 2023). Accurate reconstrucHon of vocal tract and facial movement has also \nled to a successful implementaHon of a digital facial avatar that a person with motor impairment c ould \nuse for enhancing communicaHon and self -expression (Metzger et al., 2023). So far, research has been \nfocusing on connecHng brain signals to arHculaHon in the same individuals who retain their ability to \ncontrol their vocal tract muscles to some extent. However, people who suffer from severe vocal tract \nparalysis may completely lose the ability to control vocal tract muscles and cannot produce any speech-\nmovement or sound  (Duffy, 2012). For these people, no arHculatory or acousHc data are available to \ntrain BCI decoding models . \n \nFor individuals unable to produce any speech movements, transfer learning could provide a soluHon \nfor developing arHculaHon-based speech-BCIs. Transfer learning applies knowledge learned from one \ndataset to a different but related dataset (Jayaram et al., 2016; Weiss et al., 2016). In the context of \nspeech-BCIs, transfer learning can be used to extract arHculatory features shared across healthy \nindividuals and then map  them  onto the brain acHvity of individuals with vocal tract paralysis. \n \nTwo key research quesHons underlie the integraHon of speech-BCIs with transfer learning: (1) given \nindividual variaHon in vocal tract anatomy, is it possible to extract generalizable arHculatory features \nacross healthy parHcipants? (2) is it possible to reconstruct generalizable arHculatory features from  \nbrain acHvity of a different group of individuals?  \n \nTo address these quesHons, we developed a novel BCI framework that extracts generalizable \narHculatory features across healthy parHcipants and reconstructs them  from brain data collected from \na separate group of parHcipants without using their own arHculatory movement data. We use d a \ntensor component analysis (TCA) model to extract generalizable arHculatory features (Kolda & Bader, \n2009; Williams  et al., 2018). We then used a gradient boosHng regression model to reconstruct the \narHculatory features from high-density ECoG (HD-ECoG) data of three different parHcipants, unseen \nby the TCA model. We show that the arHculatory features can be reconstructed from HD-ECoG with a \nsignificant Pearson’s correlaHon with the original arHculatory features , which demonstrates the \npossibility of cross-parHcipants arHculatory-brain mappings . Our result highlights the potenHal of the \nnovel framework for developing generalizable BCI models that could facilitate speech reconstrucHon \nin people with vocal tract paralysis. \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nMaterials and Methods \nElectromagne,c ar,culography (EMA) dataset \nWe used arHculatory movement s recorded during  word producHon  from a publicly available \nElectromagne-c Ar-culography (EMA) dataset (Wieling et al., 2016). The EMA data was collected \nby a portable 16-channel device (WAVE, Northern Digital InC.) at a sampling rate of 100 Hz  during a \nword producHon experiment. A total of 21 speakers of the Low-Saxon Dutch dialect and 19 speakers \nof the Central Dutch dialect parHcipated in the word producHon experiment.  During the experiment, \nparHcipants performed two tasks. Task I was a picture naming task, in which parHcipants were \npresented with 70 pictures of objects sequenHally and were instructed to nam e the objects out loud \nin their dialect. Task II was a consonant-vowel-consonant ( CVC) sequences reading task, in which  \nparHcipants were presented with 27 CVC sequences on screen sequenHally and were instructed to \nread them out loud in the standard Dutch dialect (Figure 1a). Therefore, the sHmuli included 97 Dutch \nwords in total (70 object names and 27 CVC sequences). SHmuli in both tasks were repeated twice in \nrandom order. For both tasks seven EMA sensors were a\\ached to jaw, lower lip (LL), right corner of \nthe lip (right lip, RL), upper lip (UL), tongue Hp (TT), tongue body (TB) and tongue dorsal (TD) posiHons, \nto track movements  of the corresponding arHculator along three dimensions: up-down, anterior-\nposterior and lem-right direcHons (Figure 2). PosiHons in the lem-right direcHon were excluded from all \nanalyses because speech movement are typically symmetrical and provide li\\le extra informaHon. We \nconfirmed  this with an analysis of variance a long each direcHon, where scores for the lem -right \ndirecHon for tongue was very low (Table S1). The Hmestamps with pronunciaHon onset and offset of \neach word were included in the dataset.  \n \n \nFigure 1. Experimental paradigms of EMA and HD -ECoG data collec>on. a. During task I of the EMA data \ncollec8on, par8cipants were presented with pictures of objects (70 in total) and were instructed to name them. \nDuring task II, par8cipants were asked to read consonant -vowel-consonant (CVC) sequences (27 in total) \npresented on screen. Every picture/ CVC sequence was repeated twice in random order. This figure was adapted \nfrom images provided by Prof. Dr. Wieling, used with permission from the author. b. During the HD-ECoG data \ncollec8on, par8cipants were presented with words from the same set of 70 object names and 27 CVC sequences \n(97 Dutch words in total) used in the EMA experiment. Unlike the EMA experiment, all words were presented in \ntextual form. The task trial dura8on was 2 seconds for P1 and P2, and 1.8 seconds for P3. The dura8on of inter-\ntrial-interval was 1.2 sec onds for P1 and P2, and 1.8 sec onds for P3.  Dutch words shown in the \nfigure: bal (ball), bijl (axe), taak (task), paak (CVC leXer sequence, not a real Dutch word), tor(beetle). \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \nFigure 2. SagiAal view of loca>ons of EMA sensors.  Each sensor loca8on is marked with a sphere, and the \ncorresponding label is shown. There was one EMA sensor placed per loca8on: jaw, lower lip, right lip, upper lip, \ntongue 8p, tongue body  and tongue dorsal loca8ons to track movements of each corresponding ar8culator in \nthree direc8ons anterior-posterior (X-axis), up-down (Y-axis), and le[-right (Z-axis) direc8ons.   \nIn our study, we only included data collected from parHcipants speaking the Central Dutch dialect , \ngiven its greater similarity with the standard Dutch compared to the Low -Saxon Dutch dialect , as \nevidenced by a shorter Levenshtein distance (Heeringa, 2004). To ensure a consistent number of trials \nand comparable arHculator movement amplitude , we addiHonally excluded data from  two Central \nDutch parHcipants with missing trials , eight parHcipants with interrupted trials and one parHcipant \nwith excepHonally large mouth movements  (large amplitude  of EMA signal s beyond the range of \nmean±2.5*std ). EMA data from eight remaining  parHcipants (U1 to U8) were included in our analyses. \nHD-ECoG dataset \nPar$cipants \nThree male parHcipants (P1, P2, P3, age 31, 26, and 40, respecHvely) were admi\\ed to the University \nMedical Centre Utrecht for diagnosHcs and treatment of medicaHon-resistant epilepsy or brain tumour. \nTwo parHcipants (P1 and P2) underwent clinical ECoG implantaHon for epilepsy diagnosHc procedures \nand one parHcipant (P3) underwent electrode implantaHon during awake tumour  resecHon surgery. \nAll parHcipants provided wri\\en informed consent for implantaHon of a high -density ECoG grid for \nresearch purposes. The protocols were approved by the Medical Ethical Commi\\ee of the University \nMedical Cent re Utrecht in accordance with the DeclaraHon of Helsinki (20 24). All parHcipants  \nconsented to use of an high-density (HD) ECoG grid over the somatosensory cortex, which for P1 and \nP2 was implanted in addiHon to standard clinical grids with low density configuraHon. Here, we only \nfocused on the HD-ECoG grids. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nData acquisi$on \nAll three parHcipants were implanted with a HD-ECoG grid over the sensorimotor cortex  on the lem \nhemisphere (Figure 3) , with different configuraHons (Table 1). \nHD-ECoG signals were recorded at a sampling rate of 2000 Hz for P1 and P3 (Blackrock Microsystems \nLLC, Salt Lake City, USA), and at 2048 Hz for P2 (Micromed, Treviso, Italy). For P1 and P3 , audio \nrecordings were recorded by a microphone connected to the neural recording system during the task. \nFor P2, audio recordings were obtained with a separate microphone installed in the parHcipant’s room. \nAll audio recordings were  recorded at a sampling rate or 30000 Hz. For P1 and P3, the audio was \nrecorded by Blackrock and was automaHcally synchronised with brain data. For P2, the audio was \nrecorded by the PresentaHon® somware (Version 23.0, Neurobehavioral Systems, Inc., Berkeley, CA, \nwww.neurobs.com) on the sHmulus presentaHon computer and was manually synchronised with brain \ndata based on the PresentaHon log. \n \nFigure 3. Loca>ons of high-density (HD)-ECoG grid electrodes. High-density ECoG grids were implanted over the \nsensorimotor cortex on the le[ hemisphere. In P3, the HD grid was partly on top of another small grid blocking \nsignals. These electrodes were removed from all analyses (marked by red crosses). The yellow lines indicate the \nloca8on of the central sulcus. \nTable 1. HD-ECoG configura>ons across par>cipants. \nParHcipant Number of \nelectrodes \nInter-electrode distance \n(IED) Exposed diameter  \nP1 128 3 mm  1 mm  \nP2 32 4 mm  1 mm  \nP3 96 3 mm  1 mm  \n \nExperimental procedures \nPresentaHon® somware (Version 23.0, Neurobehavioral Systems, Inc., Berkeley, CA, www.neurobs.com) \nwas used to run the experiment s for P1 and P2, and PyQT (h\\ps://wiki.python.org/moin/PyQt) was \nused to run the experiment for P3. As in the EMA experiment, all HD-ECoG parHcipants were instructed \nto read out the same  97 Dutch words, including 70  object names from the picture naming task and 27 \nCVC sequences from the CVC sequence reading task. However, unlike the picture naming task in the \nEMA experimen t, all words in the HD-ECoG experiment were presented to parHcipants in textual form \nto avoid visual responses evoked by pictures (Figure 1b). All words were presented in random order \nand each word appeared on the screen twice. The duraHon of word trials and the inter-trial interval \nvaried across parHcipants as P3 performed the task in the operaHng room , where Hme for research \nwas limited . Thus, in P1 and P2 , the duraHon of a word trial was 2 seconds, and the duraHon of an \ninter-trial interval was 1.2 seconds. In P3, both the word trial and the inter-trial interval had a duraHon \nof 1.8 seconds. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nData Analysis \nThe data analysis framework (Figure 4) consists of two pipelines: the EMA analysis pipeline and the \nHD-ECoG analysis pipeline. Each pipeline includes three steps: data preprocessing, tensor construcHon, \nand feature extracHon. From these steps , we obtained arHculatory features extracted from the EMA \ntensor and neural features extracted from the HD -ECoG tensor. We then used these features for the \narHculatory feature reconstrucHon. \n \nFigure 4. The framework for ar>culatory fea ture reconstruc>on from HD-ECoG signals. The le[ panel shows \nthe analysis pipeline of the EMA and the right panel shows the analysis pipeline of the HD-ECoG dataset. \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nEMA data preprocessing and tensor construc$on \nFirst, we idenHfied missing value s in the EMA data for each parHcipant (U1: 1.35%, U2: 1.14%, U3: \n0.16%, U4: 0.41%, U5: 0.71%, U6: 0.35%, U7:  0.42%, U8: 0.51%). Missing values were imputed  using \nlinear interpolaHon available in the Pandas library of Python (h\\ps://pandas.pydata.org). Then, EMA \ndata were smoothed with a 5th -order, 20 Hz low-pass Bu\\erworth filter. Amer that, EMA data in the \nlem-right direcHon (z-axis) were excluded. We then removed  baseline from the remaining EMA data by \nsubtracHng the mean posiHons for each combinaHon of arHculator and direcHon during a separate 10-\nsecond rest period, in which parHcipants were asked to refrain from speaking or swallowing  (Wieling \net al., 2016).  \nAmer preprocessing, we segmented EMA data by using the Hme window from 0 to 1 second around \nthe speech onset for each word trial and obtained a three-dimensional tensor : 100 x 14 x 194, which \ncorresponds to 100 Hme points, 14 combinaHons of arHculators (7) and direcHons (2), and 194 word \ntrials (97 unique words repeated twice)  for each parHcipant. We then concatenated these tensors \nacross parHcipants and obtained a four-dimensional tensor  (8 x 100 x 14 x194). We experimented with \nshiming the Hme window around the speech onset (prior to speech onset) and different window sizes, \nbut the current Hme window contained the most informaHon . \nHD-ECoG data preprocessing, channel selec$on and tensor construc$on \nThe HD-ECoG data analysis pipeline was applied to each HD-ECoG parHcipant’s dataset. First, we \nvisually inspected if there were channels with noisy or flat signals in the data. No channel was removed \nduring this step for any of the parHcipants. We then removed 14 channels in P3 because of they lay on \ntop of another grid and therefore were not recording signals directly from the brain Hssue (Figure 3). \nNext, for each remaining channel, line noise (50Hz and its harmonics) was removed with a notch filter. \nCommon average referencing was then applied to remove common noise and trends , and HD-ECoG \nsignals were downsampled  to 512 Hz. Amer that, for each channel high frequency band (HFB; 60-170 \nHz) signals were extracted in 1 Hz bins using Morlet wavelet decomposiHon and were averaged across \nfrequency bins. HFB signals were then log-transformed and downsampled to 100  Hz to match the \nsampling rate of EMA . Finally, for each channel, the resulHng HFB signals were baseline-corrected by \nsubtracHng the mean value s of a 10-second rest period before the first word trial. \nThe speech onset moments were detected by Azure speech -to-text service \n(h\\ps://learn.microsom.com/en -us/azure/ai-services/speech-service/fast-transcripHon-\ncreate?tabs=locale-specified) and manually corrected using Praat (Boersma, 2001) . We used the Hme \nwindow from 0.25 sec before to 0.75 sec amer speech  onset to segment conHnuous recordings into \nword trials. The window starHng at 0.25 s before speech onset captured all informaHon of the first \nphoneme in the sensorimotor cortex and has been shown to produce  opHmal decoding results in \nprevious studies (Jiang et al., 2016; Ramsey et al., 2018). The 1 second window length captured the \narHculatory movements of most words (95 percenHle of the distribuHon of word duraHons: 0.69 sec). \nRest trials were composed of 1 second of data starHng amer the end of the preceding word trial. We \nidenHfied channels with significant responses to the task by comparing the mean HFB acHvity between \nspeech and silence using a two-tailed paired t-test. Since most channels showed very significant p-\nvalues (p<0.001), we selected channels with a large effect size (Cohen’s d >0.8, corresponding to a t-\nvalue of 12.44) to ensure only the most robust task-specific acHvaHon were included. The selected \nchannels are referred to as acHve channels in subsequent analysis. \nAmer channel selecHon, we constructed a three-dimensional tensor (100 x the number of selected \nchannels x 194) for each HD-ECoG parHcipant. Unlike the EMA analysis, we did not concatenate the \nHD-ECoG tensors across parHcipants to construct a four-dimensional tensor, as the channel dimension \ndiffered across parHcipants in number, locaHon and electrode spacing (Figure 3 and Table 1). \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nFeature extrac$on \nTensor component analysis \nTensor decomposiHon was applied to extract a set of matrices . Vectors within these matrices  are \nreferred to as components.  Individual component  captures the variability along each dimension. We \nanalyzed the characterisHcs of these components  quanHtaHvely and qualitaHvely. The tensor \ndecomposiHon and characterisHcs analysis are referred to as tensor component analysis (TCA)  \n(Williams  et al., 2018).  \nCANDECOMP/PARAFAC decomposiHon is one of the most commonly used tensor decomposiHon \nmethod s (Kolda & Bader, 2009). An n-dimensional tensor 𝑋 ∈ \t ℝ!!×\t!\"\t×\t⋯\t×\t!#  is decomposed into the \ncombinaHon of R components  and can be approximated by, \n𝑋 ≈ \t ∑ 𝑎% ∘ 𝑏% ∘ 𝑐% ∘ ⋯ ∘ 𝑛%\t&\n%'( , \nwhere ∘ is the outer product , and  𝑎% ∈ 𝑖( , \t𝑏% ∈ 𝑖) , … , 𝑛%\t(𝑟 = 1, ⋯ , 𝑅) are component s, which are \nthe rth columns of the factor m atrices 𝐴, 𝐵, ⋯ 𝑁, respecHvely. Elements  in each factor matrix  are factor \nloadings. \nThe CANDECOMP/PARAFAC decomposiHon procedure is omen opHmized by the alternaHng least \nsquares method . This method  has two steps. The first is to iniHalize factor matrices  randomly or by \ncertain criteria. The second step is t o opHmize one factor matrix at a Hme while keeping the others \nfixed. The opHmizaHon is achieved by minimizing the objecHve funcHon between the original tensor \nand the approximated tensor. For example, when opHmizing factor matri x 𝐴, we have the objecHve \nfuncHon, \n𝐴 ← \t∑(𝑋 − ∑ 𝑎%; ∘ 𝑏% ∘ 𝑐% ∘ ⋯ ∘ 𝑛%\t&\n%'( )*+\t\t\t\t\t\t\t\n,%-.!/  , \nin which  the minimizaHon is a linear -square matrix problem . All factor matrices are opHmized \niteraHvely. When opHmizing each factor matrix, this procedure is iterated unHl the objecHve funcHon \nconverges or the number of iteraHons reaches a pre-set threshold.  \nEMA tensor decomposi&on and ar&culatory feature extrac&on \nWe used the nonnegaHve CANDECOMP/PARAFAC decomposiHon opHmized by hierarchical alternaHng \nleast squares to decompose the EMA tensor. The decomposiHon pipeline was implemented  using the \nPython library tensortools (Williams  et al., 2018).  \nAmer applying the nonnegaHve CANDECOMP/PARAFAC decomposiHon, t he EMA tensor was \ndecomposed into 29 components  and four factor matrices: the  parHcipant factor, Hme  factor, \narHculator-by-direcHon factor and word trial factor.  The decomposiHon process was repeated four \nHmes and resulted in four TCA runs with consistent results across the runs (Figure S3). We then checked \nthe goodness-of-fit by inspecHng the cumulaHve explained variance of all 29 components, which was \n0.89 averaged across four runs (Figure 5a). Adding more components did not substanHally increase the \nexplained variance. To reduce components , we first selected components by the run with the highest \nexplained variance. Since the explained variance of the first component was over 75%, we used the \nmean explained variance from the 2 nd to the 29 th component  as the threshold to determine the \nnumber of components to select. The 10 th component was the last component with an explained \nvariance above this threshold. Therefore, we only retained the first 10 components  (Figure 5b). In the \nnext step, our goal was to select components that generalized across all parHcipants. To measure the \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\ngeneralizability of each component, we calculate the commonality value of each component  in the \nparHcipant factor as following (Hurley & Rickard, 2009; Williams et al., 2018), \ncom(𝑎%) =\t(∑ 𝑎%! ))0\n!'(\n∑ 𝑎%\n! )0\n!'(\n \nIn which 𝑎%  is the r th component in the parHcipant factor matrix  and  𝑎%!  is the i th element in that \ncomponent.  The commonality value reflects how many parHcipants have similar factor loadings, i.e., \nhow many parHcipants contribute similarly to a component.  If all parHcipants have similar factor \nloadings, the commonality of this component equals the number of parHcipants. In contrast, if only \none parHcipant has a non-zero factor loading, the commonality of this component equals 1, indicaHng \nthat only that parHcipant contributes to this component . We permuted elements across components \n1000 Hmes to simulate the distribuHon of commonality (Figure 5c). Figure 5d shows examples of a \ncomponent with high commonality and a component  with low commonality. We used the mean \ncommonality (4.57) as the threshold, as this value indicates that more than half of eight parHcipants \ncontributed equally to the component . Using a h igher threshold yields too few features and could \ncompromise reconstrucHon performance. By using this threshold, six components with commonality \nabove it were selected for further analyses.  \nWe refer to selected components in these factor matrices as features. Specifically, in our \nreconstrucHon analysis, we refer to features from the word trial factor as the arHculatory features. \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nFigure 5. Tensor component selec>on in the EMA dataset . a. Cumula8ve explained variance of all 29 tensor \ncomponents averaged across 4 runs. b. Explained variance per component (star8ng from component 2 since \ncomponent 1 explained approximately 80% explained variance) averaged across 4 runs. The mean explained \nvariance was indicated by the red line and used as the threshold for component pre-selec8on. Component 10th \nis the last component with an explained variance above  the threshold . c. The simulated distribu8on of \ncommonality obtained by permu8ng factor loadings across the 29 components. The red doXed line indicates the \nmean commonality of the simulated distribu8on. d. Examples of a component with high commonality and a \ncomponent with low commonality, which was 7.93 and 3.03, respec8vely \nHD-ECoG tensor decomposi&on and neural feature extrac&on \nAs in the arHculatory feature extracHon, we extracted features from the HD-ECoG tensors by using the \nnonnegaHve CANDECOMP/PARAFAC decomposiHon opHmized by hierarchical alternaHng least squares. \nThe HD-ECoG tensor s were decomposed into 10, 14, and 17 components for P1, P2, and P3, \nrespecHvely, corresponding to 80% explained variance. We chose 80% explained variance as the cut-\noff point for model fiyng because adding more components did not increase the explained variance \nsubstanHally. \nTo select reproducible features across repeHHons, we used Pearson’s correlaHon coefficient (PCC) \nbetween word trial factor loadings to select components . Since HD-ECoG tensor decomposiHon yield \nless components than EMA tensor, only one-step component selecHon is needed . First, we shuffled \nword trial loadings across components 1000 Hmes and calculated PCC between repeHHons for all \ncomponents . Figure 6 shows the distribuHon of PCC of word trial factors between repeHHons for each \nHD-ECoG parHcipant. We calculated the 95th percenHle of the distribuHon and used it to select \ncomponents with PCC above this threshold from the word trial factor as neural features. This resulted \nin 7, 6, and 6 components for parHcipants P1, P2, and P3, respecHvely. The mean PCC of extracted \ncomponents  between repeHHons was 0.59 for P1, 0.30 for P2 and 0.49 for P3.   \nAs in the EMA analysis, we combined vectors from the selected components to create a factor matrix  \nfor each dimension of the HD-ECoG tensor. We obtained three factor matrices: the channel factor, the \nHme factor, and the word factor, which captured spaHal, temporal, and kinemaHc variaHons across \nwords in neural acHvity, respecHvely. We also refer to components from these factor matrices as \nfeatures. In our reconstrucHon analysis, features from the word trial factor matrix are referred to as \nthe neural features. \n \nFigure 6. Selec-on of neural features in the HD-ECoG data. The panels show the distribuHons of PCC \nof word factors between word repeHHons across all components over 1000 shuffles for HD-ECoG \nparHcipants P1, P2, and P3, respecHvely. The significance threshold (α=0.05) (indicated by the green \ndo\\ed line, which represents the 95th percenHle of the distribuHon) of each distribuHon was 0.33, 0.17, \nand 0.31 for parHcipant P1, P2 and P3, respecHvely. We selected components with a PCC above these \nthresholds. \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nGeneralisable ar,culatory feature reconstruc,on from neural features \nTo capture the complex relaHonships between neural data and arHculatory data, we used the gradient \nboosHng regression model to reconstruct the generalisable arHculatory features from the neural \nfeatures (Friedman, 2001; 2002; HasHe, 2009) . This model was chosen for its robust performance  on \nsmall datasets so that overfiyng can be avoided . ReconstrucHon performance was evaluated by the \nPCC between the reconstructed and original arHculatory features and was cross-validated across all \nwords using the leave-one-word-out scheme . We used the permutaHon test to determine the \nsignificance of reported PCC values by shuffling word labels of all trials 1000 Hmes. PermutaHon was \nperformed on data of repeHHon 1 and repeHHon 2 separately. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nResults \nHD-ECoG channel selec,on \nFor P1, P2, and P3, respecHvely, 19.5% (25/128), 75% (24/32) and 25.6% (21/82) of HD-ECoG channels \nshowed very strong HFB increases during word trials. These channels were referred to as acHve \nchannels (Figure 7). \n \nFigure 7. T-value maps comparing high-frequency band (HFB) responses during speech periods and silence \nperiods. The channel colour represents t-values, as shown in the colormap. The threshold for t-values is 12.44, \ncorresponding to a large effect size (Cohen’s d>0.8). Only channels with a t-value above the threshold were \ncolor-coded to highlight the most robust task-specific ac8va8on. In P3, the greyed-out channels were lay on top \nof another grid. The grey line indicates the loca8on of the central sulcus.  Label “A” represents the anterior \ndirec8on and label “P” represents the posterior direc8on. \nFeatures extracted from the EMA tensor \nFigure 8 shows the Hme, arHculator-by-direcHon, parHcipant and word trial factors extracted from the \nEMA tensor . The Hme factor shows temporal  profiles of kinemaHc pa\\erns  shared across all \narHculators. The arHculator-by-direcHon factor illustrates the strength of movements per arHculator \nalong different direcHons. Considering both factors together reveals how the kinemaHc pa\\erns evolve \nacross Hme for each arHculator. For example, features 2 and 3 capture the tongue movements along \nthe anterior-posterior direcHon within the first 0.5 seconds amer the speech onset.  Overall, most  \nmovements  occurred within 0.5 sec amer speech onset, which is the mean duraHon of word producHon. \nIn the parHcipant factor, the commonality values of features 1-6 were 7.92, 7.88, 7.39, 7.32, 6.37, and \n4.72, respecHvely, indicaHng that over half of parHcipants contribute similarly to the selected features. \nThis result means  that the extracted features generalize well across parHcipants. The word trial factor \nreflects the spaHotemporal arHculatory features for each word trial. In the word trial factor, the PCC \nbetween repeHHon 1 and 2 were 0.97, 0.93, 0.83, 0.95, 0.62, and 0.49 . PCC values were significant \n(P<0.05) for the first four features. Features 5 and 6 show a lower PCC, as well as lower commonality. \nTaken together, features 5 and 6 may reflect trial-specific arHculatory kinemaHcs pa\\erns. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \nFigure 8. Ar>culatory features extracted from EMA data using TCA. The par>cipant factor of the EMA tensor. \nEach bar represents the contribu8on of each par8cipant to the feature . The ar>culator-by-direc>on factor of \nthe EMA tensor. Each bar shows movements recorded by a sensor along anterior -posterior (x) or up-down (y) \ndirec8on.  We grouped sensors into three groups by ar8culators (lip, jaw, and tongue) and colored them in blue, \ngreen and orange according to the group . The dark colors (dark blue, dark green and dark orange) represent \nmovements along the anterior-posterior (x) direc8on, and the light colors (light blue, light green, and light orange) \nrepresent movements along the up-down (y) direc8on. The >me factor of EMA tensor. The black line indicates \nthe speech onset, and the red line indicates the mean dura8on of spoken wo rds averaged across all trials and \nacross all par8cipants. The word factor of the EMA tensor. We showed the Pearson’s correla8on (r) between \nfactor loadings of repe88ons for all words, as well as the linear regression fiXed line between repe88ons (shown \nas the red line).  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nFeatures extracted from HD-ECoG tensor \nAs in the EMA tensor, each dimension in the HD -ECoG tensor corresponds to one factor.   \nSupplementary Figure S1 show the Hme, channel factor and word factor for P1, P2, and P3. Features \nin the Hme factor show the Hme profiles of basis funcHons that reflect the HFB acHvity shared across \nall acHve channels. In all parHcipants, we idenHfied three types of brain responses by inspecHng the \nHme profiles: early response, mid response and late response. For each parHcipant, the basis funcHon \nreaching its peak amplitude prior to speech onset is marked as the early response; the basis funcHon \nshowing rising acHvity amer speech onset and reaching its peak amplitude before mean speech offse t \nis marked as the mid response; and the basis funcHon reaching its peak amplitude around or amer the \nmean speech offset is marked as the late response  (Figure 9). Features in the channel factor illustrate \nhow the basis funcHons in the Hme factor are weighted for each channel , suggesHng the anatomical \nlocalizaHon of basis funcHons. In P1 and P3, channels with large weights are most located posteriorly, \nwhile in P2, channels with large weights are most located anteriorly. When examining  the anatomical \nlocalizaHon of different types of brain responses, we did not observe a clear disHncHon in P1 and P3. \nHowever, in P2, the early response is evenly located across all acHve channels, while the mid and late \nresponses are more anteriorly located. \nFeatures in the word trial factor reflect the spaHotemporal neural features for each word trial, i.e., the \ncombinaHon of anatomical distribuHon of neural acHvaHon and Hme profiles of brain response . The \nPCC corresponding to early responses appeared to be lower than those corresponding with mid and \nlate responses. \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nFigure 9. Three types of brain responses during the task: early, mid response and late responses. All temporal \nprofiles were min-max normalized to enable direct comparison across par8cipants. The early, mid, late response \nare shown by the blue, orange and green line, respec8vely. We iden8fied the complete set of 8me features for \neach response type . For the early and late response, only one 8me feature  was iden8fied  per par8cipant , \nwhereas for the middle response, two 8me features were iden8fied in P2. The speech onset is shown by the \nblack dashed line, and the mean speech offset by the red dashed line. \nGeneralisable ar,culatory feature reconstruc,on  \nWe reconstructed arHculatory features from neural features by using the gradient boosHng regression \nmodel . Figure 10 demonstrates the reconstrucHon performance averaged across word repeHHons. \nAmong three HD -ECoG parHcipants, P1 achieved the best reconstrucHon performance, with a mean \nPCC of 0.8 0 (p<0.05), while P2 and P3  achieved a mean PCC of 0.75 (p<0.05)  and 0.76 (p<0.05) , \nrespecHvely. \n \n \nFigure 10. Results of a r>culatory feature reconstruc>on from neural features . For each par8cipant, we \ncalculated the real distribu8on of PCC (shown in blue). We also calculated the simulated distribu8on of PCC by \nshuffling word labels of all features 1000 8mes (shown in yellow). The red dashed line denotes the significance \nthreshold (α = 0.05), and the blue dashed line denotes the mean PCC of the real distribu8on.   \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \nDiscussion \nIn our study, by recording brain acHvity from the vSMC using HD-ECoG grids and leveraging a publicly \navailable EMA dataset , we demonstrated a generali zable BCI framework that reconstructed \narHculatory features from three parHcipants without relying on their arHculatory or acousHc data.  For \nindividuals with severe vocal tract paralysis, this generalizable BCI framework , which is independent \nof individual-specific arHculatory or acousHc data, could be a promising way to restore speech from \nbrain acHvity. \nBecause arHculator movements were not measured in the HD-ECoG parHcipants, we used a TCA model \nto extract arHculatory features from a public EMA dataset . We then selected features with high \ncommonality values, indicaHng that these arHculatory features capture arHculatory movement \npa\\erns shared across speakers. Earlier studies also a\\empted  to align arHculatory features across \nspeakers. For example, Bocquelet and colleagues used a linear model to map the arHculatory features \nof individual speakers to the feature space of a reference speaker (Bocquelet et al., 2016). However, \ntheir approach can be biased by the arHculatory characterisHcs of the chosen reference, such as vocal \ntract shape. In contrast, our approach employed commonality to ensure that the selected features \nshowed generalizable arHculatory kinemaHcs across healthy speakers, which is parHcularly \nadvantageous when both acousHc and arHculatory data cannot be obtained from target users . A \nprevious study not having arHculatory movement data available reported good results using an  \nacousHc-to-arHculatory inversion model relying on parHcipants’ own audio data  to generate \narHculatory data for speech BCI development (Anumanchipalli  et al., 2019). However, their approach \nrequires parHcipants to produce intelligible speech, which is not feasible for individuals with severe \nvocal tract paralysis.  \nHaving extracted a set of generalizable arHculatory features across speakers, we next examined the \ninterpretability of the extracted neural features. In all three parHcipant we idenHfied three types of \nbrain responses: early, mid and late. Compared with previous studies, the early and late responses we \nobserved resemble the transient response, which shows increased acHvity around speech onset/offset, \nand the mid response resembles the sustained response , which shows increased acHvity during the \nu\\erance (Conant et al., 2018; Salari et al., 2018). However, we did not observe a clear disHncHon in \nthe anatomical organizaHon among  these responses, while Salari and colleagues found that transient \nresponses were more anteriorly located and the sustained responses were more posteriorly located in \ntheir parHcipants with HD grids  (Salari et al., 2018). One possible explanaHon is the relaHvely small \nnumber of acHve channels in our analysis . Beyond the anatomical  organizaHon of these brain \nresponses, we also considered their possible funcHonal roles: early and late responses may reflect the \narHculator movements at the speech onset/offset, such as mouth opening or closing .  AlternaHvely, \nthe early response may also reflect movement planning  (Salari et al., 2018). For the mid response, it \nmay represent a nonspecific signal for holding the vocal tract configuraHon  (Conant et al., 2018). To \nfurther understand the neural representaHon during word producHon, more HD -ECoG data will be \nneeded. \nTo reconstruct arHculatory features from brain acHvity, we train ed a gradient boosHng regression \nmodel  using word trial factors from both the EMA and HD -ECoG TCA model s. In all three parHcipants, \nthe reconstructed and the original arHculatory features  significantly correlated with each other . \nHowever, the correlaHon coefficients were only slightly above the significance threshold (α = 0.05) , \nindicaHng that the arHculatory features may be similar across words . One possibility is that the \narHculatory features of different words cluster closely in the low-dimensional space . Further studies \nshould include more repeHHons per word and train a word -level classifier to evaluate the  \ndiscriminability of arHculatory features. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nTo the best of our knowledge, this is the first study to extract generalizable arHculatory features from \nhealthy individuals and reconstruct them from  brain acHvity of different individuals. Previous work \nshowed that speakers share a similar state -space of arHculatory features, but only used this to  \nreconstruct voice, demonstraHng the cross-subject arHculatory-acousHc transfer (Anumanchipalli  et \nal., 2019) . Our study extends their work by showing the cross-subject arHculatory-neural transfer, \ndemonstraHng that the generalizable arHculatory features can be reconstructed from brain acHvity, \neven if the two modaliHes are from different individuals. This finding  is also consistent with  prior \nresearch, where authors report structural similarity between the arHculatory features from healthy \nparHcipants and neural features from an individual with paralysis (Wille\\ et al., 2023). Such cross-\nsubject arHculatory-neural transfer is beneficial for speech BCI design: even for individuals with severe \nvocal tract paralysis, it may sHll be possible to reconstruct arHculatory movements by developing \nmodels  using arHculatory data from healthy individuals. \nRecent advances in speech BCIs have shown the possibility of reconstrucHng speech directly from brain \nsignal without relying on intermediate  arHculatory features (Wairagkar et al., 2024; Li\\lejohn et al., \n2025). However, previous research suggests that arHculatory features are more robustly encoded in \nthe vSMC  than acousHcs features, and therefore can be learned faster with limited neural data \n(CharHer et al. , 2018; Conant  et al. , 2018; Anumanchipalli  et al. , 2019) . Thus, incorporaHng \nintermediate arHculatory features may enhance the speech decoding performance (Anumanchipalli  et \nal., 2019) . Apart from audio synthesis, the intermediate arHculatory features can also be used to \nrestore speech-related orofacial movements  (Metzger et al., 2023). .  \nTaken together, our results indicate that our generalizable BCI framework could be a promising  \napproach for restoring the communicaHon for individuals with severe vocal tract paralysis, for whom \narHculatory or acousHc data are not available. However, our current use of EMA data, which only \ncontains 7 sensors a\\ached to the upper vocal tract , restricts the ability to capture complete  vocal \ntract movements.  Using more complete arHculatory features that span the enHre vocal tract space \nmay enable speech synthesis with human-like fidelity (Wu et al., 2023).     \nAnother limitaHon of our study is the vocabulary size. Our restricted vocabulary of 97 Dutch words is \nlikely not enough to capture the full range of arHculatory gestures in natural conversaHon. Expanding \nto larger vocabularies and to sentences will be important for assessing reconstrucHon performance in \nmore realisHc contexts. Finally, the proposed pipeline has only been validated offline. In the future, \nadapHng this framework for online use could enable real-Hme arHculatory-based speech BCIs. \nConclusion \nOverall, we demonstrated that our proposed framework could reconstruct generalizable arHculatory \nfeatures from brain acHvity from a separate group of able-bodied speakers, even when these speakers’ \narHculatory or audio data were not available . Using these generalizable arHculatory features has \npotenHal for developing speech BCIs that can restore full communicaHon  for individuals with severe \nvocal tract paralysis, while reducing the need for a large amount of training data. \nAcknowledgement \nThis work is supported by Dutch Brain Interface IniHaHve (DBI2), project number 024.005.022 of the \nresearch programmed GravitaHon, which is financed by the Dutch Ministry of EducaHon, Culture, and \nScience (OCW) via the Dutch Research Council (NWO). \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. 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It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \nWilliams, A.H., Kim, T.H., Wang, F., Vyas, S., Ryu, S.I., Shenoy, K.V., Schnitzer, M., Kolda, T.G. & \nGanguli, S. (2018) Unsupervised discovery of demixed, low-dimensional neural \ndynamics across mul-ple -mescales through tensor component analysis. Neuron, 98, \n1099-1115. e1098. \n \nWu, P ., Li, T., Lu, Y ., Zhang, Y ., Lian, J., Black, A.W., Goldstein, L., Watanabe, S. & \nAnumanchipalli, G.K. (2023) Deep speech synthesis from MRI-based ar-culatory \nrepresenta-ons. arXiv preprint arXiv:2307.02471. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nSupplementary materials \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \n \nFigure S1 ECoG Components of P1, P2, and P3. From le[ to right in each panel, we showed the channel factor, \nthe 8me factor, and the word factor for par8cipant P1, P2 and P3, respec8vely. In the channel factor, the grey \nlines indicate the loca8on of central sulcus. In the 8me factor, the black dash lines indicate the speech onset and \nthe red dash lines indicate the speech offset averaged across word trials. For components with the flat line, no \nbrain ac8vity was reflected during the corresponding period . In the word factor, the red line s are the linear \nregression fiXed line between feature loadings of repe88on 1 and 2. We also showed the Pearson’s correla8on \n(r) between feature loadings of repe88on 1 and 2 for each selected feature. \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\n \n \nFigure S2 Distribu>on of word produc>on during HD-ECoG data collec>on. We accumulate all word produc8on \ndura8on, which is the interval between speech onset and offset across all word trials for three HD -ECoG \npar8cipants and calculate the distribu8on. \n \n \nFigure S3. Similarity scores between TCA runs with different number of components. For each TCA \nrun (blue dot), a similarity score was calculated across all TCA runs and the run with the lowest \nreconstrucHon error \n \n \n \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint \n\nTable S1. Average variance per ar-culator-by-direc-on across par-cipants . For each arHculator, the \nvariance of movements along each direcHon: anterior -posterior (X), up-down (Y), and lem-right (Z) \nwas calculated and average across parHcipants. \nAr-culator            Direc-on  Anterior-posterior \n(x) \nUp-down \n(Y) \nLej-right \n(Z) \nUL 1.41 1.62 1.52 \nRL 4.27 1.20 4.09 \nLL 6.18 4.38 3.19 \nJAW 2.23 2.55 1.69 \nTD 16.57 8.77 3.96 \nTB 17.22 9.46 3.93 \nTT 18.81 9.52 5.24 \n \nSimilarity score \nThe similarity of two fi\\ed TCA models were calculated based on the angles between latent factors \n(Tomasi & Bro, 2006; Williams  et al., 2018). For two fi\\ed four-factor TCA models  with R components , \n{𝐴, 𝐵, 𝐶, 𝐷} and {𝐴1, 𝐵1\t, 𝐶1, \t𝐷1}, the similarity score is, \n𝑚𝑎𝑥\n𝑤 ∈ \tΩ\t 1\n𝑅 \t G H(1 − I𝜆% − 𝜆2(%)K\nmaxN𝜆%, 𝜆2(%)OP (𝑎5𝑎1 ∙ 𝑏5𝑏1 ∙ 𝑐5𝑐1 ∙ 𝑑5𝑑1)]\n&\n%'(\n, \nwhere Ω denotes all possible permutaHons of all factors , and 𝑤 is a parHcular permutaHon. When \ncalculaHng the similarity score, every Hme one component is selected from each of the four factors, \neach scaled to unit length and 𝜆%\tdenotes the product of these scalings. The similarity score is averaged \nacross all components. Amer enumeraHng all possible permutaHons, the maximal similarity score is \ntaken as the final similarity score between these two TCA models. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted October 8, 2025. ; https://doi.org/10.1101/2025.10.08.680888doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}