Age-Related Modifications of Muscle Synergies and Their Temporal Activations for Overground Walking

Healthy ageing modifies neuromuscular control of human overground walking. Previous studies found that ageing changes gait biomechanics, but whether there is concurrent ageing-related modulation of neuromuscular control remains unclear. We analyzed gait kinematics and electromyographic signals (EMGs; 14 lower-limb and trunk muscles) collected at three speeds during overground walking in 11 healthy young adults (mean age of 23.4 years) and 11 healthy elderlies (67.2 years). Neuromuscular control was characterized by extracting muscle synergies from EMGs and the synergies of both groups were ${k}$ -means-clustered. The synergies of the two groups were grossly similar, but we observed numerous cluster- and muscle-specific differences between the age groups. At the population level, some hip-motion-related synergy clusters were more frequently identified in elderlies while others, more frequent in young adults. Such differences in synergy prevalence between the age groups are consistent with the finding that elderlies had a larger hip flexion range. For the synergies shared between both groups, the elderlies had higher inter-subject variability of the temporal activations than young adults. To further explore what synergy characteristics may be related to this inter-subject variability, we found that the inter-subject variance of temporal activations correlated negatively with the sparseness of the synergies in elderlies but not young adults during slow walking. Overall, our results suggest that as humans age, not only are the muscle synergies for walking fine-tuned in structure, but their temporal activation patterns are also more heterogeneous across individuals, possibly reflecting individual differences in prior sensorimotor experience or ageing-related changes in limb neuro-musculoskeletal properties.

explore what synergy characteristics may be related to 23 this inter-subject variability, we found that the inter-subject 24 variance of temporal activations correlated negatively with 25 the sparseness of the synergies in elderlies but not young 26 adults during slow walking. Overall, our results suggest 27 that as humans age, not only are the muscle synergies 28 for walking fine-tuned in structure, but their temporal 29 activation patterns are also more heterogeneous across 30 individuals, possibly reflecting individual differences in 31 prior sensorimotor experience or ageing-related changes 32 in limb neuro-musculoskeletal properties. 33 Index Terms-Muscle synergy, ageing, gait, electromyo- 34 graphic signals (EMGs), motor variability. 35 I. INTRODUCTION 36 D URING ageing, gait characteristics may gradually 37 change as a result of age-related changes in the neuro- 38 musculoskeletal system, including reduced muscle strength, 39 decreased joint power, and deteriorated sensorimotor func- 40 tions [1], [2]. Such changes in gait may increase the risk of 41 injury or even reduce mobility [3], [4]. Some past sensorimo-42 tor experience or any history of neuromuscular impairment 43 may also lead to the expression of different learned and 44 compensatory patterns in the person's gait. For instance, 45 when compared with healthy elderlies, disabled elderlies have 46 significantly higher mid-stance hip mechanical energy expen-47 diture related to compensatory gait strategies [5]. Presumably, 48 these altered gait patterns, be they related to age-dependent 49 changes in biomechanics, prior learning, or past injuries, are 50 accompanied by alterations in the neuromuscular gait control 51 strategy implemented by the central nervous system [6]. 52 How is the neural control of gait adjusted during ageing to 53 ensure efficient dynamic motor control as the vast number 54 of internal and external variables fluctuate over the years? 55 Answering this question would necessitate a thorough, mecha-56 nistic understanding of how the immensely variable locomotor 57 muscle patterns are constructed by the motor system. One 58 way to study the neural implementation of gait control is 59 to reduce the observed high-dimensional motor patterns into 60 a low-dimensional set of motor modules representable as 61 muscle synergies [7], [8]. When a muscle synergy is recruited, 62 multiple muscles are activated as specific spinal premotor 63 interneurons [9], [10]  the activation patterns of specific synergies also change. These 124 modifications of muscle synergies may originate from both 125 age-dependent changes in gait biomechanics and the varied 126 sensorimotor experience of the subjects through the years.
The distribution of the dimensionality of the muscle synergy sets (i.e., the number of synergies) for both groups at the three speeds.
where SST is the sum squared total, D i j is the EMG data of 218 the i th muscle at the j th time point, m D i is the average EMG 219 value of the i th muscle, and SSE is the sum squared error.

220
To prevent the extracted synergy set from respresenting 221 a suboptimal local minimum on the error surface, at each 222 number of synergies, NNMF was run 20 times, each time with 223 different initial parameters which were uniformly distributed 224 between 0 and the maximum EMG amplitude. The run with 225 the highest R 2 was selected for further analyses. For both 226 the younger and older groups, the numbers of synergies thus 227 selected ranged from five to eight (Fig. 2).

D. Clustering Muscle Synergies 229
To characterize the muscle synergy patterns of both groups, 230 the synergies of all subjects in both groups were k-means 231 clustered together using Matlab. We verified that analogous 232 results were obtained when the synergies of the two groups 233 were separately clustered. The algorithm was initialized with 234 random cluster centroids. The number of clusters was deter-235 mined as the smallest number that yielded a local maximum 236 of average silhouette value (across 1 to 14 clusters). Each 237 run of the k-means algorithm was repeated 100 times to 238 ensure robustness in our determination of the number of 239 clusters. To quantify the between-group synergy similarity at 240 the population level, the scalar product (SP) between every pair 241 of synergy vectors from both groups was calculated in each 242 cluster; the SP of synergy pairs within the younger and older 243 groups were also calculated as baselines. The scalar product 244 ranges from 0 to 1, with 1 indicating two identical vectors and 245 0 indicating two vectors with no correlation.

E. Variability of Synergies' Temporal Activations 247
The variability of synergies' activation coefficients across 248 subjects in each group was evaluated after the muscle syner-249 gies shared by both age groups were extracted. In this way, 250 we ensured that the temporal activations from the two groups 251 being compared were coefficients for the exact same set of 252 basis vectors. Pre-processed EMGs of all subjects of all three 253 speeds in both groups were concatenated into a single EMG 254 matrix, which was then factorized using NNMF. The minimum 255 number of synergies that yielded an EMG-reconstruction R 2 of 256 80% was selected as the number of synergies for this analysis. 257 After extracting the shared synergies, the temporal acti-258 vation of each synergy was segmented into individual gait 259 cycles using the timings of heel strike and toe off for each 260 subject [27], with each cycle time-normalized and resampled 261 Fig. 3. Cluster analysis of muscle synergies during overground walking at three self-selected speeds for both age groups. 10, 9 and 9 clusters were identified for fast, normal and slow speed, respectively. Despite between-group differences in some specific muscle components (marked with * , p < 0.05; ANOVA) and an additional 10th cluster involving RF (CSRF, CS standing for cluster of synergy) in fast speed, all the nine clusters have grossly similar synergies between the two age groups. For every synergy, we applied statistical parametric mapping 280 (SPM) to further compare the temporal activations (averaged 281 across subjects) between the subject groups. The SPM is a 282 topological methodology for detecting field changes in smooth 283 n-dimensional continuous signals. It detects the regions of 284 interest of the continuous signals [29] by applying statistical 285 tests, such as subtraction, correlation, regression, t-test, and 286 ANOVA. The SPM is frequently used in the statistical analysis 287 of neuroimaging voxel data for functional mapping and func-288 tional connectivity investigations [30]. Here, we employed the 289 SPM in a fashion analogous to that used in neuroimaging to 290 identify the temporal intervals of the temporal activations with 291 significant between-group differences ( p < 0.05). We began by verifying that there was no significant differ-296 ence between the body-height normalized walking speed of the 297 two age groups at all three self-selected speeds (Fig. 1). Thus, 298 any between-group differences in synergies or kinematics 299 should more likely originate from ageing effects rather than 300 walking. For all walking speeds, the synergies of both groups 305 could be grouped into 9-10 clusters, with 1 cluster involving 306 muscle RF specific to fast walking (Fig. 3). Within individual 307 clusters, between-group differences were speed-, cluster-, and 308 muscle-specific (e.g., ExtO in cluster 9, slow speed; TA and 309 ExtO in cluster 4, fast speed; and AL in cluster 4, normal 310 speed) (Fig. 3). For all walking speeds and each cluster, 311 we compared the similarity of young-versus-old synergy pairs 312 against baseline similarity from within-young and within-old 313 synergy pairs (Fig. 4). The young-versus-old similarity was 314 significantly lower than both baselines in 3 clusters for fast 315 speed, 1 cluster for normal speed, and none in slow speed, 316 thus further supporting the result that there were speed-specific 317 between-group differences in some of the synergy clusters.

318
Beyond the muscle-and speed-specific between-group dif-319 ferences noted above, synergies of the two groups were also 320 different in the sense that some clusters comprised more syner-321 gies from one of the age groups. in the older group (65%) (Fig. 5(c)). Note that TFL, GM, 330 and Hams are all related to hip motion, and Hams to knee 331 motion as well. We therefore proceeded to examine the hip-332 and knee-joint kinematics of the two age groups in more detail. To investigate if the between-group differences in muscle 336 synergies noted above may correlate with differences in gait 337 biomechanics, we compared the gait kinematics between the 338 two age groups. Indeed, over a gait cycle, older adults had 339 higher hip flexion angle but lower hip extension angle when 340 compared with younger subjects at all speeds of overground 341 walking (Fig. 6). The peak hip flexion of the older group 342 was significantly higher than that of the younger group at all 343 speeds ( Fig. 7(a)) whereas the peak hip extension of the older, 344 significantly smaller than those of the younger (Fig. 7(b)) 345 ( p < 0.05, ANOVA). On the other hand, knee flexion was 346 not significantly different between two groups. To compare the muscle synergies' temporal activations 350 between the two groups, we enforced the EMGs of both 351 groups to be explained by the same set of synergies (Fig. 8, 352 column 1) so that for each synergy, the activations being 353 compared represented coefficients for the same basis vector. 354 This enforcement is justified given the synergies of the two 355 groups were grossly similar (Fig. 3, 4). As shown in Fig. 8, 356 the average temporal activation coefficients of the two groups 357 were different in amplitude at certain phases of the gait cycle 358 in the synergies involving GM (SGM) and TA (STA) (phases 359 with significant between-group differences are highlighted in 360 grey ( p < 0.05, SPM)). To further contrast the temporal 361 activations of the two groups, we also calculated and compared 362 the across-subject variance of the coefficients at each time 363 point of both groups. For the normal and slow speeds, the inter-364 subject temporal-activation variability of the older adults was 365 significantly higher than that of younger subjects in 6 synergies 366 involving the TA (STA), triceps surae (STRP), quadriceps 367 (SQCP), Hams (SHS), LatDor (SLD), and TFL (STFL), 368 respectively ( p < 0.05, ANOVA) (Fig. 9). To further confirm 369 the validity of this analysis, we compared the variances of both 370 groups after excluding an older-group subject whose speed 371 was an outlier. The results for fast and slow speeds remained 372 the same as before, but the differences in SQCP and SHS at 373 normal speed became insignificant after outlier exclusion.

374
For completeness, we also considered the intra-subject 375 cycle-to-cycle variability of the temporal activations (Fig. 10). 376 The intra-subject temporal-activation variability of the elder-377 lies was statistically higher than that of young adults in SGM 378 at fast speed, STRP and SHS at normal speed, and STA at 379  Similarly, across 404 all gait speeds and across subjects, the across-time variance 405 of the temporal activations of each synergy (Var(C t )) also 406 correlated negatively with the sparseness of the same W in 407 both age groups (Fig. 13) (old, r = −0.78, p 0.05; young, 408 r = −0.79, p 0.05, Pearson's r). For completeness, We also 409 performed additional analyses on finding potential correlations 410 between the sparseness of synergies and their activation peak 411 and average activations, respectively. Our results show that 412 for activation peak, significant correlations were found in both 413 groups at all three speeds, but for average activations, only at 414 the fast speed of the younger group.  Our k-means clustering identified 9 basic locomotor muscle 419 synergies that were utilized by both age groups for over-420 ground walking at different self-selected gait speeds (Fig. 3).

421
At fast speed, one additional synergy (CSRF) was recruited,  [32]. 438 The consistency of the overall compositions of the synergies 439 observed here agrees well with this result, but the small 440 between-group differences noted (Fig. 3) may reflect age-441 related fine-tunings of the synergies structures already reported 442 in the rodents.

443
Beyond the small amplitude differences in certain muscle 444 components, the synergies of the younger and older groups 445 were also different in the sense that certain synergy clusters 446 were dominated by synergies from one of the two age groups 447 (Fig. 5). The clusters involving TFL (CSTFL) and Hams 448 (CSHS) included more older-subject synergies at fast and 449 slow speeds, respectively, but another cluster involving GM 450 (CSGM) was dominated by younger-subject synergies at all 451 speeds. We can infer that at the population level, older subjects 452 are more likely to utilize CSTFL and CSHS than younger 453 subjects, while younger adults are more likely to use CSGM 454 Fig. 10. The within-subject variance of temporal activations across gait cycles ( * p < 0.05, * * p < 0.01, ANOVA). The instances with the younger group showing higher intra-subject C-variance are marked with pink stars.  the synergy-encoding networks being constantly adjusted by 464 sensory and descending signals [34] throughout the lifetime. 465 Interestingly, the age-specific synergy clusters are related 466 to muscles TFL, GM, and Hams which are hip flexor, hip 467 extensor, and knee flexor, respectively. From this observation, 468 we can infer the potential of the Hams to compensate GM for 469 weak hip extension during gait. This inference agrees with the 470 previous result that biceps femoris (whose long head is a part 471 of Hams) contributes to stance hip extension in the presence of 472 a weak GM [35]. Also, the prevalence of the TFL synergy in 473 the older group during fast walking may reflect the use of TFL 474 for generating additional hip flexor torque due to weakness of 475 other hip flexors (e.g. iliacus and psoas) in older subjects.

B. Origins of Age-Related Muscle Synergy Modifications 477
The identified changes in the muscle synergies may reflect 478 age-related changes in the biomechanical requirements of 479 walking. Certainly, ageing is associated with changes in 480 biomechanical properties [3], [36], [37], which may impose 481 a different set of biomechanical constraints to functional 482 gait [12], thus necessitating muscle synergy modifications [38]. 483 In our findings, at all speeds, the older subjects had larger 484 ranges of hip flexion but smaller ranges of hip extension 485 (Fig. 7). Previously, Judge et al. found that elderlies tended to 486 use more hip flexor power to compensate for the insufficient 487 ankle plantarflexor power to ensure gait performance [3], [4]. 488 The between-group difference in the frequencies of use of the 489 hip-related muscle synergies we report here (Fig. 5)    have been interpreted as neuromotor modules that corre-547 spond to how discrete spinal or cortical premotor networks 548 co-activate the motoneuronal pools of multiple muscles, the 549 temporal activation may reflect the dynamic neural activi-550 ties that drive the recruitment of these networks [32]. The 551 sparseness of the synergy vectors studied here, on the other 552 hand, quantifies the degree of muscle co-activations in each 553 motor module. The synergy with the highest sparseness would 554 involve the activation of only 1 muscle, while the synergy with 555 the lowest sparseness, co-activation of all recorded muscles. 556 Presumably, the synergy's sparseness should reflect the con-557 nectivity between the premotor neurons encoding the synergy 558 and the moto neurons [10].

559
As an attempt to relate properties of the synergy vectors (W) 560 to characteristics of their temporal activations, we correlated 561 W-sparseness with both the inter-and intra-subject variability 562 of C (Fig. 11, 12, 13) and surprisingly found a negative 563 correlation between them. To the best of our knowledge, 564 our finding is the first demonstration that variability of the 565 synergies' drives could be related to the numbers of muscles 566 coordinated by the synergies. Thus, synergies with lower 567 sparseness values (i.e., more muscle components) have more 568 diverse temporal activations, both within and across subjects. 569 We speculate that the premotor networks that coordinate larger 570 numbers of muscles are also susceptible to modulation by 571 feedback signals coming from more muscles, thus giving them 572 greater variability of activations. Such feedback modulation 573 can be underpinned either by intraspinal reflex pathways or 574 long-loop reflex circuits that involve the descending pathways. 575 Indeed, it has been shown that synergy-encoding premotor 576 interneurons are directly contacted by both proprioceptive 577 and descending synaptic terminals [47]. In one of our recent 578 works, we showed that muscle synergies that exhibit higher 579 variability in their activations might play a more important role 580 in driving changes in motor outputs during early motor skill 581 learning [17]. Therefore, our demonstration of the negative 582 correlation between synergy sparseness and activation variabil-583 ity implies that the synergies that are less sparse may play a 584 more critical role in helping the CNS arrive at the appropriate 585 motor outputs during the initial phase of locomotor adaptation 586 or gait retraining. Whether muscle synergies that are less 587 sparse should represent better targets of intervention awaits 588 further study. We do not know the functional implications of 589 this arrangement. Perhaps it reflects how motor-output vari-590 ability is maximized for functional flexibility when the outputs 591 themselves are constrained by the structures of the muscle 592 synergies and the connectivity of the premotor networks.