Dear Dr. Reimann,

Thank you very much for submitting your manuscript "The condition for dynamic stability in humans walking with feedback control" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers were generally enthusiastic about the approach of combining biomechanics and neural control within a single model to analyze the stability of walking. However, the reviewers expressed a range of concerns that should be addressed. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

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Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Thomas Serre

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: This manuscript investigates an inverted pendulum model of walking with neural feedback control in the form of the stepping strategy. The concept is quite simple (and elegant) by combining two established methods – simple inverted pendulum models and foot placement control based on mid-stance. The description and development of the model were thorough and easy to follow. Although some theorems were unsurprising for those familiar with the models, the authors gave clear explanations for those that might be less familiar. The control gains and cadence finding is also very interesting and relevant to open questions in the field as well. The comparisons with human data as presented, however, left me unconvinced about the validity of the model in comparison to human behavior. Yet, the authors did an extensive job of outlining the utility and deficiencies of the model which was much appreciated.

1. Experimental data comparisons: Previous data was used to evaluate (very qualitatively) whether the model could predict human behavior. While I believe the human comparisons are probably necessary, they currently weaken the paper in my view. In Figure 5A, there is considerable scatter in the lower cadence data. While the shift in bd was later explained, the wider scatter in bp was not. In addition, comparing the model against human data at more than two cadences would be beneficial. A quantitative method of comparisons would also lend more strength to the arguments. I do not doubt the validity and usefulness of the model, but barring gathering more data, I would almost be more interested more broadly in the model’s predictions, not just with respect to cadence.

2. One notable feature missing from this model is collisional losses. As also noted in Lines 311-312, the model has no method of dissipating energy which can build up. A nice explanation was provided in the Discussion, but the argument for why the effect of collision is small is unconvincing. Although push-off can make up for this energy loss, collisional losses have a substantial effect on system dynamics. Impacts might also be another reason for the difference between the current model and the Bauby and Kuo model, rather than model complexity.

3. The sections on energy loss, effective leg length, and ankle roll were informative in outlining why model predictions might be wrong. It was also interesting that low bd could be explained by the lack of ankle roll. However, the effect of the other two missing items seemed to be treated more dismissively. On a similar note to the prior concern and without going outside the scope of the paper, could the authors give some indication whether a constant leg length is expected to have a large or small effect on model predictions? Otherwise, it currently reads that the ankle roll was already decided to have the largest effect based on the author’ past work, which might be true, but minimizing the other two items still requires more support to be convincing to readers.

4. Figure 5 – the caption notes that the human data in Figure 5BC is the same as from Figure 5A. Both are from a previous experiment where individuals walked at a set cadence dictated by a metronome. If so, why are there variations in the human cadences for Figure BC?

5. What was the approximate speed range at these two cadences? Were they comparable between human data and model? And among the studies discussed in "How is the model useful"?

6. Line 503 states that humans vary cadence "in direct proportion" to speed. However, there is also an established power law that links speed and step length (and cadence) by [1] (see also [2]), resulting in a more curvilinear relationship.

Minor comments:

If cadence is to be the primary focus, it should be noted, perhaps in the last paragraph of Introduction.

Line 190 – how were the initial conditions chosen "exactly right"?

Line 572 – Typo ")although"

[1] D. W. Grieve, "Gait patterns and the speed of walking," Biomed. Eng., vol. 3, pp. 119–122, 1968.

[2] S. H. Collins and A. D. Kuo, "Two independent contributions to step variability during over-ground human walking," PLoS ONE, vol. 8, no. 8, p. e73597, 2013.

Reviewer #2: Manuscript Number: PCOMPBIOL-D-23-00629

The condition for dynamic stability in humans walking with feedback control

SUMMARY OF WORK:

This manuscript addresses the very important topic of stability during human walking developing a simple model that incorporates both (bio)mechanics and neural control and then employing it to make predictions about the contribution of center of mass state feedback to dynamic balance at slow vs faster walking speeds. These predictions are tested using data from relevant human walking experiments in a laboratory setting.

First the authors clearly present mathematical descriptions of both the mechanical system (i.e., a two-legged, 2DOF (fore-aft + medio-lateral) passive inverted pendulum (Eqs. 1, 2)) and control system (i.e., a proportional-derivative feedback control law that maps center of mass (CoM) state at midstance to an updated contact point of the foot on the ground relative to the CoM (Eqs. 3,4) and show output of walking simulations driven by the model (Fig. 1).

Next, the authors mathematically define periodic orbits and their stability to changes in control gains (Figs.2, 3) culminating in the key result describing the range of feedback control parameters that yield stable walking for a fixed step time (Fig. 4).

Then, the authors test their model’s prediction that slower walking (i.e., longer step time) should require higher feedback control gains against model-fits from human walking experiments at different walking speeds. The simple model does a reasonable job at predicting what humans do (Fig. 5).

Finally, the authors provide a comprehensive critique of their own model by addressing many, if not all, of the key limitations and how they might influence predictions about stability during real human walking (e.g., contribution of ankle roll to modulate CoP (Fig. 6). In doing so, the authors demonstrate how their model is ‘wrong, and useful’- a welcome approach that is all too commonly lost in the literature in favor of presenting more complicated models with ‘cleaner’ results, often at the expense of deeper understanding of the system.

In short, the manuscript presents a ‘first of its kind’ simple neuro+mechanical model that, as the authors would say themselves, is ‘wrong, but incredibly useful’. Their formulation acknowledges, and creatively merges previous mathematical descriptions of the mechanics and (neural) control of walking, with a keen focus on clearly and rigorously defining a set of formal conditions for dynamic stability. A strength is that the model is used to make testable predictions that are directly addressed with relevant human experiments. The interpretation of their results with respect to model limitations is especially strong. In this reviewer’s opinion, this work is truly exciting and stands to have great impact as a ‘go to’ foundation for how scientists, clinicians and engineers define, understand and work to preserve or augment balance in two-legged locomotion systems – not just in humans, but also robots, and humans wearing robots. The manuscript already offers a fine contribution as is, but below I offer a handful of comments that may help to further strengthen the clarity of the presentation and expand the scope of the discussion – two aspects that could increase the impact of the work.

COMMENTS:

1. As stated above, the modeling approach to merge the mechanics and control of walking and application of formal analysis to define stability are both excellent and clearly described in text and using mathematical formulas. What is missing, however, is a clear schematic description of the elements of the model at the front-end of the main text. One potential version of this would show a ‘cartoon’ that defines the inverted pendulum geometry and states and a block diagram that represents the feedback control. Introducing the phase space representation in this schematic with and example of stable and unstable orbits would also help frame the reader’s expectation early.

2. Along the lines of point 1. above, it would be helpful to have a clearer understanding of what the parameter b0 is? Is this akin to a baseline relative pose of the legs on the ground? i.e. a baseline ‘base of support’? A pictorial representation of the system would help clarify this.

3. Linked to point 2. above, in some cases in the presentation of results it is unclear whether both A/P and M/L directions are being addressed (e.g., sensitivity to control parameters b0, bp, bd – Figs. 3, 4, 5). It is suggested to tighten and clarify throughout about whether/when AP vs. ML are being addressed. Perhaps using different subscripts or subplots?

4. Does it matter how the perturbation is applied? For example, is perturbing via a change in initial conditions (Fig. 1) the same as a perturbation from a fixed periodic orbit (Fig. 3)? Is a perturb in position the same as a perturb in velocity? Does the phase and direction of the perturbation matter? If so, how would these issues affect the stability analysis throughout?

5. In reading the manuscript, this reviewer noted many model simplifications that the authors would do well to address (e.g., massless limbs, no joints, no swing leg dynamics, no arms, no angular momentum!; -- no explicit force production of the legs on the ground, no double support period, no collision losses; -- a hyperfocus on midstance state as the discrete control input). But, by the end of the paper, the authors had handled most if not all of these – often pointing to model modifications that could add complexity if/when needed.

One aspect that could use a bit more discussion is how the feedback control law presented in this manuscript would work in the physiological system. What sensory modalities are involved, how are they integrated to give CoM position and velocity? What about integral control? (i.e. the ‘I’ in PID).

6. The authors mention the need for ‘large sets of human data’ to ‘see the typical stability regions in humans’. There is a recent example of this, an open-source data set created by Jennifer Leestma at GaTech that may be useful to cite or even use in future collaborative work.

Biomechanics of locomotion during ground translation perturbations

JK Leestma, PR Golyski, CR Smith, GS Sawicki, A Young

Georgia Institute of Technology

Linking whole-body angular momentum and step placement during perturbed human walking

JK Leestma, PR Golyski, CR Smith, GS Sawicki, AJ Young

Journal of Experimental Biology 226 (6), jeb244760

Reviewer #3: The review is uploaded as an attachment.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No: Yes, for the code. However, not for the human data. Cannot access "foot_placement_ml_by_com_50_CAD.csv" for instance when running the Matlab code.

Reviewer #2: No: The code that runs the walking simulations could be shared.

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: Yes: Gregory S. Sawicki

Reviewer #3: No

Figure Files:

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Attachments

Attachment

Submitted filename: PCOMPBIOL-D-23-00629-review.pdf

Dear Dr. Reimann,

Thank you very much for submitting your manuscript "The condition for dynamic stability in humans walking with feedback control" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. 

The reviewers overall were very satisfied with the responses and revisions, and had only relatively minor comments. Reviewer 3 in particular had a number of remaining issues that require clarification. We would therefore like to invite you to submit a further minor revision which addresses these remaining comments through revisions to the paper and/or responses to the reviewers' comments.

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Thomas Serre

Section Editor

PLOS Computational Biology

***********************

A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact ploscompbiol@plos.org immediately:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have addressed my concerns in their thorough responses. I have a few minor suggestions.

Figure 1 is a very helpful overview, but a more detailed caption might also help the reader to define some of the variables or know broadly what the components mean without searching in the text.

I do not think my comment about data accessibility was relayed to the authors, so I have reiterated it here. The human data is currently inaccessible, e.g., cannot access "foot_placement_ml_by_com_50_CAD.csv" when running the Matlab code.

Reviewer #2: Great job addressing feedback in the revised submission. Looking forward to citing this when it is published.

Nice work.

Reviewer #3: Uploaded as attachment.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No: Yes, for the code. However, not for the human data. Cannot access “foot_placement_ml_by_com_50_CAD.csv” for instance when running the Matlab code.

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: Yes: Gregory S. Sawicki

Reviewer #3: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References:

Review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript.

If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Attachments

Attachment

Submitted filename: PCOMPBIOL-D-23-00629_R1_review.pdf

Dear Dr. Reimann,

We are pleased to inform you that your manuscript 'The condition for dynamic stability in humans walking with feedback control' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Thomas Serre

Section Editor

PLOS Computational Biology

***********************************************************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #3: The authors have adequately addressed my comments and I now believe the paper is suitable for publication.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #3: Yes

**********

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Reviewer #3: No