(A) We apply a novel muscle network analysis approach that leverages Co-Information (II) to map muscle pairs (mx, my) to task performance (τ) (O’Reilly & Delis, 2024), thus dissecting the task-relevant information (pink-orange chequerboard intersection) between muscles from task-irrelevant information (yellow intersection shared exclusively by mx and my), and characterising their functional roles as either net functionally-similar (i.e. redundant) or -complementary (i.e. synergistic). (A) II characterises each muscle interaction as either net redundant (negative values) or synergistic (positive values) by contrasting the total mutual information each muscle shares with τ separately (I(mx; τ) + I(my; τ)) against the task information observed when mx and my are combined (I(mx, my; τ)) (Ince et al., 2017; McGill, 1954). (B) An example virtual scenario from the virtual reality treatment where participants interacted with a real manipulandum to perform motor tasks such as placing a cup on a shelf. The correct movement trajectory (yellow line) was illustrated, which participants had to emulate. Task complexity was enhanced by including different objects and barriers, requiring participants to recruit different muscle groups to emulate the trajectory. Before and after the intervention, sEMGs were recorded from 16 muscles: triceps lateralis (1=TL), triceps medialis (2=TM); biceps short-head (3=BS), biceps long-head (4=BL); anterior deltoid (5=AD); lateral deltoid (6=LD); posterior deltoid (7=PD); upper trapezius (8=UT); rhomboid major (9=RM); brachialis (10=BRACH); supinator (11=SU); brachioradialis (12=BR); pronator teres (13=PT); pectoralis major (14=PM); infraspinatus (15=Infra); teres major (16=TEM) on both affected and unaffected sides, while participants performed 10 repetitions of seven standardised motor tasks (see ‘Experimental setup and Data collection’ in Materials and Methods) (Maistrello et al., 2021; Pregnolato et al., 2025). (C) II is quantified between all sEMG pairs to generate functional muscle networks, the modular structure of which is determined across participants and sessions using network community detection (Ahn et al., 2010). (D) The number of functional modules identified serves as the input parameter into a dimensionality reduction algorithm—projective non-negative matrix factorisation (PNMF)—to extract network components and their underlying session- and participant-specific activation coefficients (see ‘Extraction of Redundant and Synergistic Muscle Networks’ in Materials and Methods) (O’Reilly & Delis, 2022; Yang & Oja, 2010). (E) The activation coefficients are input into a novel divisive clustering algorithm to identify patient clusters both within (impairment clusters) and between (treatment response clusters) pre- and post-treatment (see ‘Clustering stroke survivors based on impairment severity and therapeutic responsiveness’ in Materials and Methods) (O’Reilly & Delis, 2025).

(A) Univariate linear regression analyses revealed the recruitment of both S2 and S6 at baseline was significantly associated with lower FMA-UE scores at baseline (β = −174.5±62.5 (p = 0.008), β = −159.7±45.6 (p = 0.001) respectively) and follow-up (β = −172.5±65.4 (p = 0.012), β = −155.1±48.2 (p = 0.003) respectively). No significant relationships were found between recruitment patterns and FMA-UE scores after stroke. The affected- and unaffected-side network components for S2 and S6 are presented below their corresponding statistical results. The relative muscle interaction strength (network edge widths), degree of involvement (node size) and submodular structure (node colour) are also illustrated. (B) The Canberra distance between the recruitment magnitudes at pre- and post-sessions separately for S3 and S4 significantly differentiated treatment responders and non-responders (Responders: 0.2±0.18, Non-Responders: 0.48±0.31 (t = 3.1 (p = 0.004)) (Median±SD)) and PT and VR treatment groups (PT: 0.19±0.18, VR: 0.33±0.26 (t = −2.2 (p = 0.044)) (Median±SD)) respectively. The affected- and unaffected-side network compononents for S3 and S4 is presented below their corresponding statistical results. The relative muscle interaction strength (network edge widths), degree of involvement (node size) and submodular structure (node colour) are also illustrated.

The average magnitudes of clinical assessment defined responders’ redundant and synergistic interactions (A.1-B.1 respectively) and non-responders’ (C.1-D.1 respectively also) for affected- and unaffected-sides at pre- and post-sessions are illustrated as violin plots. Significant decreases and increases (p < 0.05 (*)) from pre-post session were found on the affected-side for redundant and synergistic networks of responders respectively. To the right of the responder and non-responder plots (A.2-B.2 and C.2-D.2 respectively), muscle interactions identified to be significantly stronger at the pre-session (light coloured network edges) or at the post-session (dark coloured network edges) are illustrated for both affected- and unaffected-sides. For illustrative purposes, the 90th percentile of these significantly different muscle interactions are depicted only. Below, a corresponding output where participants were partitioned using RPre-Post (E-F.1-2) and SPre-Post (G-H.1-2). Pre-post differences here accentuated the differences found using the clinical assessment derived partition (A-D.1-2) with more significant decreases and increases in redundant and synergistic interaction strengths respectively (p < 0.001 (***)).

An overview of the patient clusters extracted using the NIF.

The Mean ± Standard deviations for Age and Time from lesion onset are presented along with the number of patients from each treatment type (i.e. physical therapy (PT) or virtual reality (VR)), conventional treatment response classifications (i.e. responders (R) and non-responders (NR) defined by MCID thresholds on the FMA-UE), and the NIF-derived treatment response clusters (i.e. RPre-Post, SPre-Post).

The identified patient clusters depicted with respect to pre- and post-session FMA-UE scores for RPre (A.1) and SPre (B.1). Boxplots illustrating the differences between the clusters identified in each partition for baseline FMA-UE scores (A.2-B.2), post-session FMA-UE scores (A.3-B.3) and the change in FMA-UE scores from baseline to follow-up (i.e. ΔFMA-UE) (A.4-B.4). * indicates a significant difference of p<0.05 and ** equates to p<0.01. The network components identified as significantly contributing to (C) RPre and (D.1-2) SPre through fractionation (affected-side (lower triangular matrix)) and merging (unaffected-side (upper triangular matrix)). For interpretation, a corresponding network from a representative participant accompanies each significant network component (i.e. P66, P102 and P112). The submodular structure (node colour) and most proportionally significant (i.e. >95th percentile) muscle interactions (network edges) are also illustrated for each network on human body models. (C) Fractionation of R3 explained participants’ affiliation with cluster 1 of RPre (β = −5.84±2.23 (p < 0.01)), classifying 78.6% of participants correctly. (D.1) Fractionation of S3 (β = −34.82±10.9 (p = 0.001)) and (D.2) merging of S2 (β = −16.4±8.6 (p = 0.056)) explained participants affiliation with SPre cluster 1, together classifying 71.4% of participants correctly. The patient clusters for RPost and SPost along with the main network components and associated physiological response patterns underpinning them are presented in the Supplementary Materials Fig.4.

An overview of the divisive clustering algorithm employed (O’Reilly & Delis, 2025).

Kernel matrices were computed from all possible pairwise combinations of functionally-redundant or -synergistic modular activations, generating a multiplex network (C) where each layer represents the similarity between all participant pairings for a given pair of module activations. (A.1) To cluster participants based on motor impairment, this meant computing C using either the pre- or post-session activations separately, (A.2) while for treatment responsiveness this computation was carried out between pre- and post-session modular activations. The dense layers of C (B.1) were empirically sparsified and their modular structure was quantified using a community detection protocol (the node colours represent different network communities) (B.2). (B.3) Co-membership matrices were generated from each layer-specific computation (i.e. entries indicate whether a participant pairing belong to the same cluster or not) which were then subsequently aggregated into a single representative matrix. (B.4) Finally, network community detection was re-applied to this representative matrix to quantify patient clusters.

The seven tasks performed by each participant before and after the clinical intervention including descriptions of starting position and movement involved.

Five redundant network components (R1-R5) were extracted from the post-stroke cohort across pre- and post-sessions for both affected- and unaffected-sides.

The 95th percentile of highest magnitude muscle interactions are illustrated for both sides on human body models along with the relative interaction strengths (edge-widths), relative network importances (node size) and submodular affiliations (node colour). The biomechanical function interpreted from each component accompanies each human body model and is supported by a table detailing the interaction strength of each muscle interaction along with their combined network importance (i.e. the sum of their eigenvector centrality).

Seven synergistic network components (S1-S7) were extracted from the post-stroke cohort across pre- and post-sessions for both affected- and unaffected-sides.

The 95th percentile of highest magnitude muscle interactions are illustrated for both sides on human body models along with the relative interaction strengths (edge-widths), relative network importances (node size) and submodular affiliations (node colour). The biomechanical function interpreted from each component accompanies each human body model and is supported by a table detailing the interaction strength of each muscle interaction along with their combined network importance (i.e. the sum of their eigenvector centrality).

The dichotomous patient clusters derived from functionally-similar (A) and -complementary (B) as scatter plots with respect to post-session FMA-UE scores (1) and as box-plots with respect to pre-session FMA-UE (2), post-session FMA-UE (3) and the change in FMA-UE scores (ΔFMA-UE) (4). No significant differences could be found across (A.2-4) or (B.2-4) (p>0.05).

The identified patient clusters depicted with respect to post-session FMA-UE scores for (A.1) and (C.1). Boxplots illustrating the differences between the clusters identified in each partition for baseline FMA-UE scores (A.2-B.2), follow-up FMA-UE scores (A.3-B.3) and the change in FMA-UE scores from baseline to follow-up (i.e. ΔFMA-UE) (A.4-B.4). No significant differences between patient clusters were found across (A-B.1-4) (p > 0.05). The network components identified as significantly contributing to (C.1-2) and (D.1-2) through fractionation (affected-side (lower triangular matrix)), preservation and merging (both unaffected-side (upper triangular matrix)). For interpretation, a corresponding affected- or unaffected side network from a representative participant accompanies each significant network component (i.e. P66, P67 and P107). The submodular structure (node colour) and most proportionally significant (i.e. >95th percentile) muscle couplings (network edges) are also illustrated for each network on human body models. (C.1) Fractionation of R4 and (C.2) preservation of R1 explained participants’ affiliation with cluster 1 of (β = −2.32±0.99 (p = 0.019), β = −15.2±6.5 (p = 0.018) respectively), classifying 81% of participants correctly. (D.1) Fractionation of S1 (β = 26.7±12.1 (p = 0.027)) and (D.2) merging of S2 (β =27.3±11.8 (p = 0.021)) explained participants affiliation with cluster 2, together classifying 76.2% of participants correctly.