Author Response
The following is the authors’ response to the original reviews.
eLife assessment
The study by O'Reilly and Delis provides a valuable data-driven framework for extracting task-related muscle synergies in a step towards the understanding and practical use of synergies in real scenarios (e.g., evaluation of patients in a clinical environment). The approach is incomplete since the authors did not compare their method with classical physiologically grounded approaches for assessing muscle synergies. In this sense, the comparisons with classical approaches would clarify if physiological assemblies were preserved and were not altered to incorporate task space variables. Despite limitations, the proposed framework would interest motor control and neural engineering researchers.
We thank the editors for the positive assessment of our work and appreciate their constructive feedback. In our revised manuscript, we believe we have sufficiently addressed the identified limitations by a) comparing our approach to existing physiologically-based methods, providing thorough comparisons of their respective outputs, b) applying it to a dataset of post-stroke participants to demonstrate that it can identify physiologically-interpretable markers of motor recovery and c) providing examples to demonstrate how readers can interpret the novel perspective introduced.
Reviewer #1 (Public Review):
The proposed study provides an innovative framework for the identification of muscle synergies taking into account their task relevance. State-of-the-art techniques for extracting muscle interactions use unsupervised machine-learning algorithms applied to the envelopes of the electromyographic signals without taking into account the information related to the task being performed. In this work, the authors suggest including the task parameters in extracting muscle synergies using a network information framework previously proposed. This allows the identification of muscle interactions that are relevant, irrelevant, or redundant to the parameters of the task executed.
The proposed framework is a powerful tool to understand and identify muscle interactions for specific task parameters and it may be used to improve man-machine interfaces for the control of prostheses and robotic exoskeletons.
With respect to the network information framework recently published, this work added an important part to estimate the relevance of specific muscle interactions to the parameters of the task executed. However, the authors should better explain what is the added value of this contribution with respect to the previous one, also in terms of computational methods.
We thank the reviewer for their constructive comments. We have adjusted the introduction section of the manuscript to better explain the added value of this framework over previous work. Specifically, we draw the reviewer’s attention to the following updated section of the introduction:
“In [11], we considered, key limitations among current approaches to muscle synergy analysis in extracting functionally relevant and interpretable patterns of muscle activity [12]. We proposed a combinatorial approach based on information- and network-theory and dimensionality reduction (the network-information framework (NIF)) that significantly improved the generalisability of the extraction process by, among others, removing restrictive model assumptions (e.g. linearity, same mixing coefficients) and the reliance on variance-accounted-for (VAF) metrics [12]. By determining the pairwise mutual information between muscles, this innovation paved the way for the appropriate mapping of muscular interactions to the task space. To elaborate on the significance of this development, the extraction of motor patterns in isolation of the task space comes at the expense of both functional and physiological relevance [12,13]. Furthermore, effective methods for mapping large-scale physiological dynamics to behaviour is a current gap across the neurosciences [14]. Thus, here we build on this work by, for the first time, directly including task space parameters during muscle synergy extraction. In doing so, we address these current research gaps, progressing muscle synergy research and successful engineering applications in a fruitful direction [12,15,16]. This enables us, in a novel way, to dissect the concept of the muscle synergy and therefore quantify interactions between muscle activations with shared or complementary functional roles.
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In general, the method proposed relies on several hyperparameters and cost functions that have been optimized for the specific datasets. A sensitivity analysis should be performed, varying these parameters and reporting the performance of the framework.
We thank the reviewer for this comment which enabled us to clarify a potential misunderstanding. Our proposed framework does not require setting or varying hyperparameters to optimise cost functions.
For model-rank specification, a modularity maximising cost-function is used which determines what partitioning of the networks results in maximal modularity. We have offered two alternative approaches using this cost-function which consistently converge on the same solution. To further ensure the representativeness of this solution, we also offer a consensus-based approach where we apply these alternative approaches to individual participant or task data, then group the collective partitions together and re-apply the approaches. One of these approaches (Equation 2.2) requires two hyperparameters, γ and ω, which adjust the intra- and inter- network layer resolutions. As stated in the manuscript, we set both of these parameters to 1, thus nullifying their presence in the cost-function and aligning our work with the classical notion of modularity. Across the two alternative approaches to model-rank specification, the solution is unique and data-driven and has a demonstratable generalisability across datasets.
The only other cost-function present in the framework is during dimensionality reduction, which is a standard loss function used across the muscle synergy analysis literature. Thus, the approach is essentially parameter-free and we now have mentioned this more explicitly in the manuscript:
“To empirically determine the number of components to extract in a parameter-free way, we then concatenated these adjacency matrices into a multiplex network and employed network community-detection protocols to identify modules across spatial and temporal scales (fig.3(D)) [29–32,44].”
“In its generalised multilayer form, the Q-statistic is given an additional term to consider couplings between layers l and r with intra- and inter-layer resolution parameters γ and ω (Equation 2.2). Here, μ is the total edge weight across the network and γ and ω were set to 1 in the current study for classical modularity [30], thus removing the need for any hyperparameter tuning.”
It is not clear how the well-known phenomenon of cross-talk during the recording of electromyographic muscle activity may affect the performance of the proposed technique and how it may bias the overall outcomes of the framework.
Indeed artifacts such as crosstalk are a standard issue across the EMG literature and may impact the performance of subsequent analyses where prevalent in the dataset. Crosstalk is expected to be present irrespective of the task and so should not affect redundant and synergistic muscle representations, however it could be present in the task-irrelevant muscle interactions extracted. Due to the prominence of long-range functional connections with the task-irrelevant representations extracted, we suggest that such artifacts are unlikely to have played a prominent role in the extracted patterns. Nonetheless, we have recognised this possibility with the following updated sentence in the Discussion section:
“Although distinguishing task-irrelevant muscle couplings may capture artifacts such as EMG crosstalk, our results convey several physiological objectives of muscles including gross motor functions [65], the maintenance of internal joint mechanics and reciprocal inhibition of contralateral limbs [20,50].”
Reviewer #2 (Public Review):
This paper is an attempt to extend or augment muscle synergy and motor primitive ideas with task measures. The authors idea is to use information metrics (mutual information, co-information) in 'synergy' creation including task information directly. My reading of the paper is that the framework proposed radically moves from attempts to be analytic in terms of physiology and compositionality with physiological bases, instead into more descriptive ML frameworks that may not support physiological work easily.
We thank the reviewer for taking the time to provide a thorough commentary on this manuscript. An overall aim in developing this framework is to build on other recent developments in providing a more fine-grained functional architecture underlying movement control [1,2]. It is a requirement for the successful communication and introduction of this toolbox to the field to provide readers with an understanding of how to use the framework and an intuition on how to interpret the results. Thus, we agree with the reviewer that functional interpretations are of crucial use.
We also agree with the reviewer that maintaining a physiological underpinning is a desirable direction for the field and should not be made secondary to functional descriptions. In our updated version of this manuscript, we have therefore included direct comparisons with the gold-standard in the field for muscle synergy extraction, namely non-negative matrix factorisation based muscle synergy extraction (see ‘Building on current approaches to muscle synergy analysis’ and fig.5-6 of revised manuscript) [3,4]. In these comparison, we show how our framework goes beyond this current approach in terms of functional insight while still maintaining physiological relevance. Indeed, in the revised manuscript we also include a fourth dataset comprising post-stroke participants and healthy controls (Fig.6). We demonstrate, through a simple example application to this dataset, how our proposed framework can produce more predictive representations of motor impairment than the gold-standard approach. The representations we identified were discriminative of motor impairment measured via the Fugl-Meyer assessment using just one trial per participant. This improves considerably upon the sensitivity of the current approach to altered motor patterns which have predominantly required many trials and participants to gain significance [5,6]. Thus, the patterns we extract are a more comprehensive representation of the actual underlying physiological state of the participants.
This approach is very different from the notions of physiological compositional elements as muscle synergies and motor primitives, and to me seems to really be striving to identify task relevant coordinative couplings. This is a meta problem for more classical analyses. Classical analyses seek compositional elements stable across tasks. These elements may then be explored in causal experiments and generative simulations of coupling and control strategies. The present work does not convince me that the joint 'meta' analysis proposed with task information added is not unmoored from physiology and causal modeling in some important ways. It also neglects publications and methods that might be inconvenient to the new framework.
We would be very interested in receiving the reviewer’s suggestions of existing approaches that we have not incorporated here and would be happy to discuss these in the revised manuscript.
Information based separation has been used in muscle synergy analyses using infomax ICA, which is information not variance based at core. Though linear mixing of sources is assumed, minimized mutual information is the basis.
We agree with the reviewer that ICA relies on information measures, however it does not incorporate task-space information. The novelty of our approach lies in the characterisation of muscle interactions with respect to the task at hand. If the reviewer could provide references to this statement, we would be able to consider this further.
Physiological causal testing of synergy ideas is neglected in the literature reviews in the paper. Although these are in animal work, the clear connection of muscle synergy choices and analyses to physiology is important and needs to be managed in the new methods proposed. Is any correspondence assumed? Possible?
We agree with τhe reviewer that this a crucial element of muscle synergy research and will aim to address it in our future work. However, we would like to point out that the current manuscript is a “tools and resources” article aiming to introduce a new framework. In our revised manuscript, we have incorporated an application of the framework to a dataset from post-stroke patients to demonstrate the use of the framework in clinical settings to identify biomarkers and use them to make predictions of motor recovery (see Fig.6 of updated manuscript).
Questions and concerns with the framework as an overall tool:
First, muscle based motor information sources have influences on different time scales in the task mechanics. Analyses of synergies in the methods proposed will be very much dependent on the number and quality of task variables included and how these are managed. Standardizing and comparing among labs, tasks sets and instrumentation differences is not well enough considered as a problem in this new proposed method toolset, at least in my reading. Will replication, and testing across groups ever be truly feasible in this framework?
We agree with the reviewer that this important point can be a limitation of the applicability of the framework. For this reason, we chose a “holistic” approach, applying the framework to several datasets collected in different settings, and selecting different kinds of task variables to extract muscle networks from. Crucially, we used a leave-one-task-out and leave-one-participant-out cross validation procedure to specifically address this point. Our results showed that the extracted couplings are robust irrespective of the task variable and/or participant excluded and this lends credit to the generalisability of the framework.
Muscle based motor information sources have influences on different time scales in the task mechanics. Kinematic analyses, dynamic analyses and force plate analyses of the same task may provide task variables that alter the results in the proposed framework it seems.
As we have mentioned above, here we used all the above types of task variables together to illustrate the range of measures that can be included in the proposed framework and showed that the outputs are robust to the exclusion of any task/participant. This point is especially evident for dataset 3 results, where high levels of generalisability were found despite the inclusion of kinematic, dynamic and IMU data (see Table 1. of original submission and updated manuscript). We believe that this is an advantage of the approach as it allows researchers to apply the method to different kinds of measurements they may have collected and gain insights into the relationships of muscle couplings with kinematic/dynamic/force parameters. This will also enable scientists to attribute different functional roles to the identified couplings and it is something we plan to do in future applications of the framework.
Second, there is a sampling problem in all synergy analyses. We cannot record all muscles or all task parameters. Examining synergies across multiple tasks seeks 'stationary' compositionality. Including task specific elements may or may not reinforce or give increased coordinative precision to the stationary compositionality.
We fully agree that this is a limitation of all synergy analyses and aimed to consider this study a step in the direction of addressing this limitation by providing the research community with a toolbox that can be used to quantify muscle couplings that can have different levels of task specificity.
To me the new methods proposed seem partly orthogonal to the ideas of stable compositionality. The 'synergies' obtained will likely differ, and are more likely to be coordinative control groupings of recurrent task and muscle motifs (based on instrumentation) which may or may not relate to core compositionality in physiology. Is there any expectation that the framework should relate to core compositionality and physiology. This is not clear in the paper as written.
In our new analysis, we have compared the proposed approach to existing physiologically-based methodologies and showed that the new framework can capture several salient physiological features of movement that the current NMF-based approach cannot. For example, as we have moved away from optimising variance accounted for metrics, our framework can identify subtle muscle couplings that have important functional roles. These subtle couplings are often not captured in current muscle synergy analysis as, against physiological relevance, higher amplitude muscles often take prominence. Further, by directly including task parameters during extraction, we can determine the muscles that have a functional role concerning the included task parameter rather than inferring this relationship indirectly using knowledge about the task executed. In our updated manuscript, by applying the framework to post-stroke participants (see Fig.6), we were also able to demonstrate that the extracted couplings are associated with functional parameters of motor recovery and have a clear link with the physiological state of individual participants.
It would be useful to explore the approach with a range of neuromechanical models and controllers and simulated data to explore the issues I am raising and convince readers that this analysis framework adds clarity rather than dissolving the generalizability and interpretability of analyses in terms of underlying causal mechanisms.
The authors need to better frame their work in relation to causal analyses if they are claiming links to muscle synergies analyses and claim extension/refinement. Alternatively, these may not be linked, and instead parallel approaches exploring different hypotheses and goals using different organizational data descriptors.
To address the reviewers concerns here, we have included in the updated manuscript a toy example simulating situations in which pairs of muscles would have a redundant or synergistic functional relationship (see Fig.2). This simulation gives clear intuition on situations where two muscles (e.g. an antagonist-agonist pair) may share functionally similar or complementary information about task direction (left vs right). In particular, within the main text describing this figure, we state how current NMF based approaches consider muscles functionally equivalent when they share similar magnitude activations, whereas our framework captures muscles with identical task information. Thus, our work is an extension of current approaches towards understanding causal mechanisms. The suggestion to use neuromechanical models is valuable, however we consider it beyond the scope of this work. This “Tools and Resources” paper is aimed at introducing the computational framework for the analysis of large-scale muscle couplings in task space. Our future work will use this framework to address unanswered questions in the field and we hope that it will be helpful for other scientists in testing their hypotheses.
To me this appears a data science tool that may not help any reductionist efforts and leads into less interpretable descriptions of motor control. Not invalid, but sufficiently different that common term use muddies the water.
We believe that the novel evidence we provided both on simulated and real data have contributed to a better interpretability of the approach outcomes. Specifically, we have introduced examples showing the functional roles of the different types of interactions as well as the predictive power of the outputs. Concerning the use of the term synergy, we have provided a clear description throughout the manuscript regarding the interpretation of synergy vs redundancy in the novel perspective we propose. For example in the discussion section:
“ We thus sought to provide greater nuance to the notion of ‘working together’ by defining motor redundancy and synergy in information-theoretic terms [6,56]. In our framework, redundancy and synergy are terms describing functionally similar and complementary motor signals respectively, introducing a new perspective that is conceptually distinct from the traditional view of muscle synergies as a solution to the motor redundancy problem [3,6,7]. In this new definition of muscle interactions in the task space, a group of muscles can ‘work together’ either synergistically or redundantly towards the same task. In doing so, the perspective instantiated by our approach provides novel coverage to the partitioning of task-relevant and -irrelevant variability implemented by the motor system along with an improved specificity regarding the functional roles of muscle couplings [20–22]. Our framework emphasises not only the role of functionally redundant muscle couplings that result from the underlying degeneracy of the motor system, but also of complementary, synergistic dependencies that are important for communication and integration across specialised neural circuitry [57,58]. Thus, the present study aligns the muscle synergy concept with the current mechanistic understanding of the nervous system whilst offering an analytical approach amenable to the continued advances in large-scale data capture [14,59].”
Reviewer #3 (Public Review):
In this study, the authors developed and tested a novel framework for extracting muscle synergies. The approach aims at removing some limitations and constrains typical of previous approaches used in the field. In particular, the authors propose a mathematical formulation that removes constrains of linearity and couple the synergies to their motor outcome, supporting the concept of functional synergies and distinguishing the task-related performance related to each synergy. While some concepts behind this work were already introduced in recent work in the field, the methodology provided here encapsulates all these features in an original formulation providing a step forward with respect to the currently available algorithms. The authors also successfully demonstrated the applicability of their method to previously available datasets of multi-joint movements.
Preliminary results positively support the scientific soundness of the presented approach and its potential. The added values of the method should be documented more in future work to understand how the presented formulation relates to previous approaches and what novel insights can be achieved in practical scenarios and confirm/exploit the potential of the theoretical findings.
Strengths:
This work proposes a novel framework that addresses physiologically non-verified hypothesis of standard muscle synergy methods: it removes restrictive model assumptions (e.g. linearity, same mixing coefficients) and the reliance on variance-accounted-for (VAF) metrics.
The method is solid and achieves the prescribed objectives at a computational level and in preliminary laboratory data.
A toolbox is available for testing the methods on a larger scale.
The paper is well written and shows a high level of innovation, original content and analysis
Weaknesses:
Task performance variables could be specified in more quantitative definition in future work (e.g.: articular angles rather than a generic starting point- end point).
We agree with this point and will incorporate it in future work. Our aim here was to show that the framework would work with any task variable and that scientists can use it to identify the relevance of muscle interactions to different types of task parameters.
The paper does not show a comparison with previous approaches (e.g.: NMF) or recently developed approaches (such as MMF).
We have now illustrated such a comparison on two datasets and explained more how the new framework can dissect the different types of muscle groupings (see ‘Building on current approaches to muscle synergy analysis’ section and Fig.5-6 of revised manuscript).
A discussion of the likely impact of the work on the field, and the utility of the methods and data to the community.
In our revised manuscript, we have introduced 2 new applications of the framework to real data to exemplify its use for a) functional interpretability and b) identification of biomarkers (see ‘Building on current approaches to muscle synergy analysis’ section and Fig.5-6 of revised manuscript). We also point towards its use in movement restoration and augmentation devices and in the clinical setting in the discussion section:
“The separate quantification of these muscle interaction types opens up novel opportunities in the practical application of muscle synergy analysis, as demonstrated in the current study through the identification of a significant predictor of motor impairment post-stroke from single-trials [5,12,65]. For instance, these distinct representations may encapsulate different neural substrates that can be specifically assessed at the muscle-level for the purpose of bodily restoration and augmentation [66]. Uncovering their neural underpinnings is an interesting topic for future research.”
In this work, the effort of the authors aimed at developing the field is clear. It is fundamental to develop novel frameworks for synergy extraction and use them to make them more interpretable and applicable to real scenarios, as well as more adherent to recent findings achieved in motor control and neuroscience that are not reflected in the standard models. At the same time, muscle synergies are being used more and more in research but their impact in practical scenarios is still limited, probably because synergies have rarely been analyzed in a functional context. This paper shows a very in-depth analysis and a novel framework to interpret data that links to the task space from a functional perspective. I also found that the results on the datasets are very well commented but could expand more to show why using this framework is advantageous.
There are some key points for discussion that follow from this paper which can be described more, maybe in future work, and that might contribute to major developments in the field, including:
The understanding of how the separation between relevant (redundant and synergistic) and irrelevant synergies impact on synergy analysis in practical works;
We have now introduced new figures (Fig. 5 and 6) to the revised manuscript, demonstrating simple applications of the framework and providing intuition regarding the outputs. We have also added points to the Discussion commenting on the differences between types of couplings and how they can be interpreted in future works:
“Our framework emphasises not only the role of functionally redundant muscle couplings that result from the underlying degeneracy of the motor system, but also of complementary, synergistic dependencies that are important for communication and integration across specialised neural circuitry [57,58]. Thus, the present study aligns the muscle synergy concept with the current mechanistic understanding of the nervous system whilst offering an analytical approach amenable to the continued advances in large-scale data capture [14,59].”
“Although distinguishing task-irrelevant muscle couplings may capture artifacts such as EMG crosstalk, our results convey several physiological objectives of muscles including gross motor functions [64], the maintenance of internal joint mechanics and reciprocal inhibition of contralateral limbs [19,49]. Thus, task-irrelevant muscle interactions reflect both biomechanical- and task-level constraints that provide a structural foundation for task-specific couplings. The separate quantification of these muscle interaction types opens up novel opportunities in the practical application of muscle synergy analysis, as demonstrated in the current study through the identification of a significant predictor of motor impairment post-stroke from single-trials [5,12,65]. For instance, these distinct representations may encapsulate different neural substrates that can be specifically assessed at the muscle-level for the purpose of bodily restoration and augmentation [66]. Uncovering their neural underpinnings is an interesting topic for future research.”
Interpreting how different synergistic organizations described in this work allows to better describe data from real scenarios (e.g.: motor recovery of patients after neurological diseases);
We have now added an example application of the framework to a dataset of stroke patients (Fig.6) and identified a redundant muscle patterns that are predictive of functional measures.
Discussing in detail how the presented findings compare with standard algorithms such as NMF to determine the added value provided with this approach;
As indicated above, we have now shown such a comparison on two new datasets (see Fig.5-6 of revised manuscript).
Describe how redundant synergies reflect real neural organization and - if their "existence" is confirmed - how they contribute to redesign the concept of muscle synergies and of modular/synergistic control in general.
This is an important point that we have now addressed more in our Discussion by relating redundant muscle couplings to degeneracy in the motor system and synergistic couplings to integrative dynamics by higher-level processes. We have also added a simple simulation illustrating how synergistic and redundant interactions co-exist and represent different contributions to task performance (see Fig.2 of revised manuscript).
