Reports © 2019 The Reviewers; Decision Letters © 2019 The Reviewers and Editors; 
Responses © 2019 The Reviewers, Editors and Authors. Published by the Royal Society under the 
terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, 
which permits unrestricted use, provided the original author and source are credited 
Review History 
RSPB-2019-1961.R0 (Original submission) 
Review form: Reviewer 1 
Recommendation 
Accept with minor revision (please list in comments) 
Scientific importance: Is the manuscript an original and important contribution to its field? 
Excellent 
General interest: Is the paper of sufficient general interest? 
Excellent 
Quality of the paper: Is the overall quality of the paper suitable? 
Excellent 
Is the length of the paper justified? 
Yes 
The force–length and force–velocity potential of the human 
soleus muscle is related to the energetic cost of running 
Sebastian Bohm, Falk Mersmann, Alessandro Santuz and Adamantios Arampatzis 
Article citation details 
Proc. R. Soc. B 286: 20192560. 
http://dx.doi.org/10.1098/rspb.2019.2560 
Review timeline 
Original submission: 
23 August 2019 
1st revised submission: 
5 November 2019 
2nd revised submission: 
26 November 2019 
Final acceptance:  
26 November 2019 
Note: Reports are unedited and appear as 
submitted by the referee. The review history 
appears in chronological order. 
2 
Should the paper be seen by a specialist statistical reviewer? 
No 
Do you have any concerns about statistical analyses in this paper? If so, please specify them 
explicitly in your report. 
No 
It is a condition of publication that authors make their supporting data, code and materials 
available - either as supplementary material or hosted in an external repository. Please rate, if 
applicable, the supporting data on the following criteria. 
 
Is it accessible? 
 
N/A 
 
Is it clear? 
 
N/A 
 
Is it adequate? 
 
N/A 
Do you have any ethical concerns with this paper? 
No 
Comments to the Author 
This study tests the fascicle length and shortening velocity (imaged using ultrasound) of the 
soleus during running at a moderate speed in 19 participants. The force-length properties are also 
measured in a series of isometric contractions on a dynamometer, and the force-velocity 
properties of the muscle are estimated from the literature. The soleus fascicles are assessed by 
how close they are to optimal length (force length potential) and how slow they shorten (force 
velocity potential), and these are compared to the actual cost of running as measured using 
expired gas analysis from these same participants. It is shown that the fascicles have a high but 
constant force length potential, and a high force velocity potential: this force velocity potential 
varies between participants and was related to the running economy. The fascicle velocity was 
further related (via multi-regression analysis) to the tendon gearing, Achilles tendon moment 
arm, belly gearing and ROM in these participants. 
This is an interesting and timely question, and it is posed well. A thorough set of experimental 
data are collected for the analysis, and the data appear to have been collected very well. The data 
show convincing relations and support the hypothesis. The paper is written clearly, and the 
figures are appropriate. 
Major comments: 
1. Choice of maximum shortening velocity. The major finding is that the running economy is
sensitive to the force-velocity potential: the absolute values of these depend on the Vmax and 
curvature of the force-velocity relation. It is not clear where the value of Vmax = 11.72 s-1 comes 
from. I have followed the cited papers back through several layers of citations, and cannot find 
definitive justification for these values beyond a statement that Vmax is typically 10-12 s-1 for 
modelling studies: this in itself does not justify the value.  
Note that actual measurements of Vmax in humans are rare. Reports of Vmax of 2 and 6 s-1 have 
been made for isolated bundles of slow and fast human muscle fibres, respectively (Faulkner et 
al. 1986), and it has been argued that these values could be less than 8 s-1 and greater than 14 s-1, 
respectively (Epstein & Herzog 1998) from intact human experiments. Higher values are used for 
musculoskeletal simulations in part to overcome the tendency of simulations to under-predict 
muscle forces, but this is not a scientific justification for inflating these values. 
3 
This submitted manuscript would benefit from a clearer description and rationale for the force-
velocity parameters chosen. However, I note (as also discussed on line 370) that the actual choice 
of value has little effect on the conclusions in the study. 
2. Multiple regression. The variables used in the multiple regression all pertain to the length
change of the soleus muscle fascicles. However, fascicle velocity is a function of change in length 
and the time taken for this change. Thus, the time taken for the muscle shortening should be 
considered. Was this constant across participants? Was this considered for the multiple regression 
(and removed later because it had no effect – this would be a good approach but should be 
reported)? 
3. Experimental details. Additional details should be presented in the Methods section for how
the EMG magnitude is quantified, and how fascicles are identified in the ultrasound images. 
Minor comment. 
1. State in the text whether errors are standard deviations or standard errors of the mean.
Review form: Reviewer 2 (Natalie Holt) 
Recommendation 
Major revision is needed (please make suggestions in comments) 
Scientific importance: Is the manuscript an original and important contribution to its field? 
Acceptable 
General interest: Is the paper of sufficient general interest? 
Acceptable 
Quality of the paper: Is the overall quality of the paper suitable? 
Good 
Is the length of the paper justified? 
Yes 
Should the paper be seen by a specialist statistical reviewer? 
No 
Do you have any concerns about statistical analyses in this paper? If so, please specify them 
explicitly in your report. 
No 
It is a condition of publication that authors make their supporting data, code and materials 
available - either as supplementary material or hosted in an external repository. Please rate, if 
applicable, the supporting data on the following criteria. 
 
Is it accessible? 
 
N/A 
 
Is it clear? 
 
N/A 
 
Is it adequate? 
 
N/A 
4 
Do you have any ethical concerns with this paper? 
No 
Comments to the Author 
See attached file. (See Appendix A) 
Decision letter (RSPB-2019-1961.R0) 
23-Sep-2019 
Dear Dr Bohm: 
I am writing to inform you that your manuscript RSPB-2019-1961 entitled "The force-length and 
force-velocity potential of the human soleus muscle is related to the energetic cost of running" 
has, in its current form, been rejected for publication in Proceedings B. 
This action has been taken on the advice of referees, who have recommended that substantial 
revisions are necessary. With this in mind we would be happy to consider a resubmission, 
provided the comments of the referees are fully addressed.  However please note that this is not a 
provisional acceptance. While both reviewers see value to the study, both have concerns about 
some of the assumptions and other aspects of the methods/interpretation. They and the 
Associate Editor need to be won over more if this study is to be accepted. 
The resubmission will be treated as a new manuscript.  However, we will approach the same 
reviewers if they are available and it is deemed appropriate to do so by the Editor. Please note 
that resubmissions must be submitted within six months of the date of this email. In exceptional 
circumstances, extensions may be possible if agreed with the Editorial Office. Manuscripts 
submitted after this date will be automatically rejected. 
Please find below the comments made by the referees, not including confidential reports to the 
Editor, which I hope you will find useful. If you do choose to resubmit your manuscript, please 
upload the following: 
1) A ‘response to referees’ document including details of how you have responded to the
comments, and the adjustments you have made. 
2) A clean copy of the manuscript and one with 'tracked changes' indicating your 'response to
referees' comments document. 
3) Line numbers in your main document.
To upload a resubmitted manuscript, log into http://mc.manuscriptcentral.com/prsb and enter 
your Author Centre, where you will find your manuscript title listed under "Manuscripts with 
Decisions." Under "Actions," click on "Create a Resubmission." Please be sure to indicate in your 
cover letter that it is a resubmission, and supply the previous reference number. 
In your revision process, please take a second look at how open your science is; our policy is that 
all data involved with the study should be made openly accessible-- see: 
https://royalsociety.org/journals/ethics-policies/data-sharing-mining/  
 
 
5 
Insufficient sharing of data can delay or even cause rejection of a paper.  
 
Sincerely, 
Professor John Hutchinson, Editor 
mailto: proceedingsb@royalsociety.org 
 
 
Associate Editor 
Board Member: 1 
Comments to Author: 
Associate Editor: Douglas L Altshuler 
 
The authors have performed an integrative study of muscle physiology and energetics during 
running. The authors and I agree that the methods are sound and creative, and the results are 
clear and interesting. One of the referees expressed some concern that the study may be too 
narrow in scope for the general science audience of ProcB. I would encourage the authors to 
revise their manuscript, and it would be helpful to see how this concern about breadth could be 
addressed. 
 
 
Reviewer(s)' Comments to Author: 
 
Referee: 1 
 
Comments to the Author(s) 
This study tests the fascicle length and shortening velocity (imaged using ultrasound) of the 
soleus during running at a moderate speed in 19 participants. The force-length properties are also 
measured in a series of isometric contractions on a dynamometer, and the force-velocity 
properties of the muscle are estimated from the literature. The soleus fascicles are assessed by 
how close they are to optimal length (force length potential) and how slow they shorten (force 
velocity potential), and these are compared to the actual cost of running as measured using 
expired gas analysis from these same participants. It is shown that the fascicles have a high but 
constant force length potential, and a high force velocity potential: this force velocity potential 
varies between participants and was related to the running economy. The fascicle velocity was 
further related (via multi-regression analysis) to the tendon gearing, Achilles tendon moment 
arm, belly gearing and ROM in these participants. 
This is an interesting and timely question, and it is posed well. A thorough set of experimental 
data are collected for the analysis, and the data appear to have been collected very well. The data 
show convincing relations and support the hypothesis. The paper is written clearly, and the 
figures are appropriate. 
 
Major comments: 
1. Choice of maximum shortening velocity. The major finding is that the running economy is 
sensitive to the force-velocity potential: the absolute values of these depend on the Vmax and 
curvature of the force-velocity relation. It is not clear where the value of Vmax = 11.72 s-1 comes 
from. I have followed the cited papers back through several layers of citations, and cannot find 
definitive justification for these values beyond a statement that Vmax is typically 10-12 s-1 for 
modelling studies: this in itself does not justify the value.  
Note that actual measurements of Vmax in humans are rare. Reports of Vmax of 2 and 6 s-1 have 
been made for isolated bundles of slow and fast human muscle fibres, respectively (Faulkner et 
al. 1986), and it has been argued that these values could be less than 8 s-1 and greater than 14 s-1, 
respectively (Epstein & Herzog 1998) from intact human experiments. Higher values are used for 
6 
musculoskeletal simulations in part to overcome the tendency of simulations to under-predict 
muscle forces, but this is not a scientific justification for inflating these values. 
This submitted manuscript would benefit from a clearer description and rationale for the force-
velocity parameters chosen. However, I note (as also discussed on line 370) that the actual choice 
of value has little effect on the conclusions in the study. 
2. Multiple regression. The variables used in the multiple regression all pertain to the length
change of the soleus muscle fascicles. However, fascicle velocity is a function of change in length 
and the time taken for this change. Thus, the time taken for the muscle shortening should be 
considered. Was this constant across participants? Was this considered for the multiple regression 
(and removed later because it had no effect – this would be a good approach but should be 
reported)? 
3. Experimental details. Additional details should be presented in the Methods section for how
the EMG magnitude is quantified, and how fascicles are identified in the ultrasound images. 
Minor comment. 
1. State in the text whether errors are standard deviations or standard errors of the mean.
Referee: 2 
Comments to the Author(s) 
See attached file 
Author's Response to Decision Letter for (RSPB-2019-1961.R0) 
See Appendix B. 
RSPB-2019-2560.R0 
Review form: Reviewer 1 
Recommendation 
Accept with minor revision (please list in comments) 
Scientific importance: Is the manuscript an original and important contribution to its field? 
Excellent 
General interest: Is the paper of sufficient general interest? 
Excellent 
Quality of the paper: Is the overall quality of the paper suitable? 
Excellent 
Is the length of the paper justified? 
Yes 
7 
Should the paper be seen by a specialist statistical reviewer? 
No 
Do you have any concerns about statistical analyses in this paper? If so, please specify them 
explicitly in your report. 
No 
It is a condition of publication that authors make their supporting data, code and materials 
available - either as supplementary material or hosted in an external repository. Please rate, if 
applicable, the supporting data on the following criteria. 
 
Is it accessible? 
 
N/A 
 
Is it clear? 
 
N/A 
 
Is it adequate? 
 
N/A 
Do you have any ethical concerns with this paper? 
No 
Comments to the Author 
The authors have addressed all my previous concerns in a careful manner. 
There remains one further comment that they may choose to consider for the manuscript, and it 
still concerns the choice of Vmax. I appreciate the further analysis that the authors have 
attempted, to provide a value of Vmax for the Soleus. However, it should be noted that the 
running velocity of 2.5 m/s is not all that fast, and indeed the EMG averages less than 50%. As 
such, it is likely that the fastest muscle fibres will not have been recruited, and hence the 
weighted mean taken for Vmax may thus be an overestimate. Coupled to this, with more than 
half of the muscle inactive, the actual Vmax may be less than its constituent fibres (for additional 
reasons: Holt et al. Proc Roy Soc B 2014). If the Vmax for the Soleus were less than the estimated 
6.77 L/s for this experimental situation, then it is likely that the actual spread of Force-velocity 
potentials would be larger than shown in Fig. 3. It is thus worth considering that you have 
actually resulted with a conservative evaluation of the importance of the force-velocity potential. 
Review form: Reviewer 2 (Natalie Holt) 
Recommendation 
Accept with minor revision (please list in comments) 
Scientific importance: Is the manuscript an original and important contribution to its field? 
Good 
General interest: Is the paper of sufficient general interest? 
Good 
8 
Quality of the paper: Is the overall quality of the paper suitable? 
Good 
Is the length of the paper justified? 
Yes 
Should the paper be seen by a specialist statistical reviewer? 
No 
Do you have any concerns about statistical analyses in this paper? If so, please specify them 
explicitly in your report. 
No 
It is a condition of publication that authors make their supporting data, code and materials 
available - either as supplementary material or hosted in an external repository. Please rate, if 
applicable, the supporting data on the following criteria. 
 
Is it accessible? 
 
N/A 
 
Is it clear? 
 
N/A 
 
Is it adequate? 
 
N/A 
Do you have any ethical concerns with this paper? 
No 
Comments to the Author 
See attached file. (See Appendix C) 
Decision letter (RSPB-2019-2560.R0) 
20-Nov-2019 
Dear Dr Bohm 
I am pleased to inform you that your manuscript RSPB-2019-2560 entitled "The force-length and 
force-velocity potential of the human soleus muscle is related to the energetic cost of running" has 
been accepted for publication in Proceedings B. Congratulations!! 
The referee(s) have recommended publication, but also suggest some minor revisions to your 
manuscript. Therefore, I invite you to respond to the referee(s)' comments and revise your 
manuscript. Because the schedule for publication is very tight, it is a condition of publication that 
you submit the revised version of your manuscript within 7 days. If you do not think you will be 
able to meet this date please let us know. 
To revise your manuscript, log into https://mc.manuscriptcentral.com/prsb and enter your 
Author Centre, where you will find your manuscript title listed under "Manuscripts with 
 
 
9 
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Sincerely, 
Professor John Hutchinson, Editor 
mailto: proceedingsb@royalsociety.org 
 
Associate Editor 
Board Member 
Comments to Author: 
Associate Editor: Doug Altshuler 
 
The authors have done a good job addressing the reviewer concerns. A few issues remain, and I 
agree with the reviewers that consideration of these final points would further strengthen the 
manuscript. 
 
 
Reviewer(s)' Comments to Author: 
Referee: 2 
 
Comments to the Author(s).  
See attached file 
 
 
Referee: 1 
 
Comments to the Author(s).  
The authors have addressed all my previous concerns in a careful manner. 
 
There remains one further comment that they may choose to consider for the manuscript, and it 
still concerns the choice of Vmax. I appreciate the further analysis that the authors have 
attempted, to provide a value of Vmax for the Soleus. However, it should be noted that the 
running velocity of 2.5 m/s is not all that fast, and indeed the EMG averages less than 50%. As 
such, it is likely that the fastest muscle fibres will not have been recruited, and hence the 
weighted mean taken for Vmax may thus be an overestimate. Coupled to this, with more than 
half of the muscle inactive, the actual Vmax may be less than its constituent fibres (for additional 
reasons: Holt et al. Proc Roy Soc B 2014). If the Vmax for the Soleus were less than the estimated 
6.77 L/s for this experimental situation, then it is likely that the actual spread of Force-velocity 
11 
potentials would be larger than shown in Fig. 3. It is thus worth considering that you have 
actually resulted with a conservative evaluation of the importance of the force-velocity potential. 
Author's Response to Decision Letter for (RSPB-2019-2560.R0) 
See Appendix D. 
Decision letter (RSPB-2019-2560.R1) 
26-Nov-2019 
Dear Dr Bohm 
I am pleased to inform you that your manuscript entitled "The force-length and force-velocity 
potential of the human soleus muscle is related to the energetic cost of running" has been 
accepted for publication in Proceedings B. 
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Thank you for your fine contribution.  On behalf of the Editors of the Proceedings B, we look 
forward to your continued contributions to the Journal. 
 
Sincerely, 
Proceedings B 
mailto: proceedingsb@royalsociety.org 
 
 
 
 
In this study, the authors explore the effect of muscle force-length and force-velocity conditions on the 
energetic cost of running. In addition, they explore the determinants of of muscle fiber length change. I 
find this to be an extensive and well collected data set that uses in vivo determination of force-length 
and force-velocity relationships, and application of these to muscle function during running to address 
these questions. 
There appear to me to be a few major limitations of the study. These should be addressed throughout. 
1)
Organismal energy consumption is measured, but only the length and velocity profile of soleus.
This prevents the authors from drawing the more interesting conclusion that muscle shortening
velocity is a determinant of energy consumption. This is acknowledged and somewhat
addressed in the discussion, but remains a major limitation to the study.
2)
The strict adherence to force-length and force-velocity relationships as defining features of
muscle performance seems somewhat outdated given a wealth of literature showing that these
relationships do not hold under conditions relevant to locomotion (i.e. history dependence,
activation-dependent changes). These advances do not negate this study, however, it would be
a more accurate representation of the field to acknowledge that they exist, and present this
study as a means to investigate the importance of these relationships.
3)
This paper is fundamentally concerned with the effect of contractile conditions on muscle
energy consumption. However, there is very little discussion of why length and velocity might
affect energy consumption beyond required activation, despite a wealth of evidence on this i.e.
how the cost per unit force varies across the force-length relationship in isolated muscle. In
addition, it may be worth considering findings such as the effect of contractile history on cost
(Joumaa et al., 2013), and the complexity of the cost of work (Holt et al., 2104; Curtin et al.,
2019) in a more comprehensive discussion of in vivo muscle energetics.
Specific comments 
Lines 50-51 – The ongoing debating between the cost of force and the cost of work as determinants of 
organismal cost should be acknowledged here. This could then also lead to a more nuanced discussion 
of factors dictating muscle energetics beyond simply level of activation. 
Lines 123-124 and 185-187 – It is relatively unclear to me how the force-velocity relationship was 
determined here. It appears as though force and velocity were determined as fibers shortened against 
the tendon? Can the authors make this clearer, better define where in the contraction force and velocity 
were determined, and comment on how this might affect findings compared to a more standard 
isotonic or isovelocity protocol.  
Line 197-198 – The meaning of this is unclear to me. This description of touchdown and toe-off should 
be reworded for clarification 
The results section is relatively dense. The authors may wish to consider moving some of the findings 
less critical to addressing their question to a table, to improve readability. 
Appendix A
Line 299-300 – The assertion that the triceps surae consumes 40% of the cost during running is crucial to 
the argument of this paper. Yet it is not clear how this value is arrived at from the Fletcher and 
MacIntosh paper cited (the paper seems to give a large range of values for muscle energy consumption 
and not to relate this to organismal cost), and how reliable the output of their simple model is for this 
purpose. Could the authors give a little more detail on this (in the manuscript if of sufficient interest, or 
simply here). It may also be useful to combine this 40% estimate with the relative size of soleus to give a 
better representation of its likely contribution to energy consumption, considering fiber type as soleus is 
likely cheaper than gastrocs (Barclay, 1993). 
Lines 304-309 - The authors make a good case for why small changes in velocity would require an 
increase in activation and therefore cost. This effect should be seen in EMG recordings. It would seem 
that the argument could be strengthened by showing this as it would provide a more causal link 
between the change in muscle level function and organismal level cost. 
Line 344-345 – There seems to be some discrepancy regarding activation in here. The implication seems 
to be that muscle activation is higher in early stance to enable the tendon to be stretched, and then 
recoil to slow shortening velocity in the later part of stance. Yet a central claim of the paper is that cost 
is lower when shortening velocity is lower, due to a lower requirement for activation. It seems like the 
variation in required activation could balance out over the course of a stance phase? Could it be clarified 
as to why the early increase in activation to enable tendon stretch doesn’t seem to be costly in the way 
that the latter reduction is deemed to be cheap? 
Line 345 – typo “were”? 
Line 375 – The study doesn’t seem to show that energy consumption is related to the force-length-
velocity potential, but rather just the force-velocity potential.  
 
  
 
 
Referee: 1 
Comment:  
This study tests the fascicle length and shortening velocity (imaged using ultrasound) 
of the soleus during running at a moderate speed in 19 participants. The force-length properties are 
also measured in a series of isometric contractions on a dynamometer, and the force-velocity 
properties of the muscle are estimated from the literature. The soleus fascicles are assessed by how 
close they are to optimal length (force length potential) and how slow they shorten (force velocity 
potential), and these are compared to the actual cost of running as measured using expired gas analysis 
from these same participants. It is shown that the fascicles have a high but constant force length 
potential, and a high force velocity potential: this force velocity potential varies between participants 
and was related to the running economy. The fascicle velocity was further related (via multi-regression 
analysis) to the tendon gearing, Achilles tendon moment arm, belly gearing and ROM in these 
participants. 
This is an interesting and timely question, and it is posed well. A thorough set of experimental data are 
collected for the analysis, and the data appear to have been collected very well. The data show 
convincing relations and support the hypothesis. The paper is written clearly, and the figures are 
appropriate. 
Response:  
Thank you for your valuable comments. All changes are underlined in the revised 
version of the manuscript and the references cited in the responses can be found at the end of the 
document. Please note that some parts of the methods are now presented in the electronic 
supplementary material due to length restrictions of the journal. 
Major comments: 
Comment: 
1.
Choice of maximum shortening velocity. The major finding is that the running
economy is sensitive to the force-velocity potential: the absolute values of these depend on the Vmax 
and curvature of the force-velocity relation. It is not clear where the value of Vmax = 11.72 s-1 comes 
from. I have followed the cited papers back through several layers of citations, and cannot find 
definitive justification for these values beyond a statement that Vmax is typically 10-12 s-1 for 
modelling studies: this in itself does not justify the value. Note that actual measurements of Vmax in 
humans are rare. Reports of Vmax of 2 and 6 s-1 have been made for isolated bundles of slow and fast 
human muscle fibres, respectively (Faulkner et al. 1986), and it has been argued that these values could 
be less than 8 s-1 and greater than 14 s-1, respectively (Epstein & Herzog 1998) from intact human 
experiments. Higher values are used for musculoskeletal simulations in part to overcome the tendency 
of simulations to under-predict muscle forces, but this is not a scientific justification for inflating these 
values. This submitted manuscript would benefit from a clearer description and rationale for the force-
velocity parameters chosen. However, I note (as also discussed on line 370) that the actual choice of 
value has little effect on the conclusions in the study. 
Response:  
Thank you for this comment. Indeed, experimental assessed values of Vmax for human 
muscles in vivo are very rare and for the soleus not reported so far to our knowledge. This was the 
reason why we based our calculations on recommendations for modelling approaches [1,2]. When 
extending our sensitivity analysis about the effect of the magnitude of Vmax, on the correlation of the 
Appendix B
force-velocity potential and energetic cost, we found that the correlation remained statistically 
significant (p<0.05) for Vmax values higher than 3.0 LO/s. Therefore, the observed association of force-
velocity potential and energetic cost seems quite strong. Furthermore, we reported a direct correlation 
between the operating velocity and the energetic cost (r = 0.561 p = 0.012). Since this association is 
independent of the choice of Vmax, we can be confident about the general study findings.  
Biological support for the choice of Vmax could be derived indirectly when referring to in vitro studies on 
the human soleus muscle. Luden et al., (2008) showed Vmax values for MHC I type fibers of 0.77 LO/s and 
2.91 LO/s for MHC IIA type fibers measured at 15°C [3]. Considering the temperature coefficient 
provided by Ranatunga et al., (1984) [4] it can be predicted that Vmax would increase to 4.4 LO/s for 
MHC I type fibers and to 16.8 LO/s for MHC IIA type fibers under physiological temperature conditions 
(37 °C). The fiber type distribution in the human soleus muscle can be estimated from literature reports, 
i.e. Johnson et al., 1973: type 1 fibers 87,7%, type 2 fibers (a and b) 12,3% (average of surface and deep 
fiber location) [5]; Larsson and Moss, 1993: type 1 89%, type 2A 11% [6]; Edgerton et al., 1975: slow 
twitch 70%, fast twitch 30% [7]; Luden et al., 2008: 74% MHC I, 20% MHC IIA (norm to 100%) [3]).  Using 
an average of those reported distribution values (type 1: 81%, type 2: 19%), Vmax for soleus under 
physiological temperature can be calculated as 6.77 LO/s. The broad literature basis for the average 
fiber type distribution was also used to update arel to 0.175 (i.e. 0.1+0.4FT, where FT is the fast twitch 
fiber type percentage [8,9]) and accordingly brel to 1.182 (arel * Vmax [10]).  
We addressed the comment of the reviewer and recalculated the respective values (force-velocity 
potential and normalized velocities and their ranges) using the updated Vmax of 6.77 LO/s, arel and brel  
in the revised manuscript. Again, this did not change any of the statistical correlation outcomes.  
 
We added the following information to the revised manuscript (page: 4, line: 155):  
“Furthermore, we assessed the force-velocity relationship of soleus using the classical Hill equation 
[11], the muscle-specific maximum fascicle shortening velocity (Vmax) and constants of arel and brel. Vmax 
was derived from the study of Luden et al. (2008), which showed Vmax values for type 1 fibers of 0.77 
LO/s and 2.91 LO/s for type 2 fibers of the human soleus muscle measured in vitro at 15°C [3]. 
Considering the temperature coefficient [4], Vmax can be predicted as 4.4 LO/s for type 1 fibers and 16.8 
LO/s for type 2 fibers under physiological temperature conditions (37 °C). Using an average fiber type 
distribution (type 1 fibers: 81%, type 2: 19%) of the human soleus muscle reported in literature [3,5–7], 
Vmax can be calculated as 6.77 LO/s. arel was calculated as 0.1+0.4FT, where FT is the fast twitch fiber 
type percentage (see above), which then equals to 0.175 [8,9]. The product of arel and Vmax then gives 
brel as 1.182 [10]. After rearrangement of the Hill equation and extension to the eccentric component, 
the operating velocity normalized to Vmax can be used to calculate the individual force potential 
according to the force-velocity relationship.” 
 
 
Comment:  
2.      Multiple regression. The variables used in the multiple regression all pertain to 
the length change of the soleus muscle fascicles. However, fascicle velocity is a function of change in 
length and the time taken for this change. Thus, the time taken for the muscle shortening should be 
considered. Was this constant across participants? Was this considered for the multiple regression 
(and removed later because it had no effect – this would be a good approach but should be reported)? 
 
Response:  
Thanks for this comment. The time for the muscle shortening (i.e. stance time) showed 
some variability among the participants as to be expected, i.e. mean 304 ms, SD 23.1 ms, maximum 
362 ms, minimum 270 ms. 
With respect to the four variables (tendon gearing, belly gearing, tendon lever arm and ankle angle 
range) and the effect of time, we reasoned that the tendon and belly gearing are ratios between 
velocities, and are thereby independent of time (i.e. tendon gearing: VMTU/VBelly and belly gearing: 
VBelly/VFascicle, where V is the stance phase-averaged velocity). The tendon lever arm is a quantity that is 
also independent from time, while only the ankle angle range is time-depended. We now calculated the 
stance phase-averaged absolute ankle angle velocity and rebuilt the regression model, which is now 
expressed by the updated equation: 
 
𝐹𝑎𝑠𝑖𝑐𝑙𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = −9.788 (𝑡𝑒𝑛𝑑𝑜𝑛 𝑔𝑒𝑎𝑟𝑖𝑛𝑔) + 0.716 (𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚) − 42.097 (𝑏𝑒𝑙𝑙𝑦 𝑔𝑒𝑎𝑟𝑖𝑛𝑔) +
0.209 (𝑚𝑒𝑎𝑛 𝑎𝑛𝑘𝑙𝑒 𝑎𝑛𝑔𝑙𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦) + 51.341  
 
The model remained significant (p < 0.001, R2 = 0.928, adjusted R2 = 0.907) and so did the four 
independent variables (p < 0.001 for tendon gearing, tendon lever arm and belly gearing, and p = 0.002 
for ankle angle velocity). The standardized coefficients changed slightly to -1.006 for tendon gearing, 
0.638 for lever arm, -0.367 for belly gearing and 0.310 for the ankle angle velocity. 
 
We changed this part in the revised manuscript ((page: 6, line: 262; page: 7, line: 315). 
 
 
Comment:  
3.      Experimental details. Additional details should be presented in the Methods 
section for how the EMG magnitude is quantified, and how fascicles are identified in the ultrasound 
images. 
 
Response:  
We amended the information on the EMG assessment during running in the revised 
manuscript as supplementary material (“EMG processing”). Note that the low-pass filter cut-off 
frequency was changed from 6 Hz to 20 Hz. 
“Raw EMG signals (running and MVC) were processed by a fourth-order high-pass Butterworth zero-
phase filter with a 50 Hz cut-off frequency then a full-wave rectification and a low-pass zero-phase filter 
with a 20 Hz cut-off frequency for creating a linear envelope of the signal [12,13].” 
 
We added some more information on the fascicle identification in the revised manuscript as 
supplementary material (“Fascicle length determination from the ultrasound images”):  
“The procedure included an approximation of the deeper and upper aponeurosis by a best linear fit 
through three manually placed and frame-by-frame adjusted marks. By means of the bwtraceboundary 
function of the Matlab Image Processing toolbox the algorithm then identified the shape and 
orientation of image brightness features between both aponeuroses in each frame, which are indicative 
for the hyperechoic perimysial connective tissue parts aligned with the muscle fascicles (fig. 1A). The 
feature identification criteria were set to: minimal length of 23 pixels (i.e. 0.4 cm, from the bottom left 
to the top right), area to length ratio of 8.5, angle between feature and deeper aponeurosis between 
10° and 70° and 80% of the pixels on a line between the start and end point of a feature had to be white 
[14]. Every frame was visually controlled for adequate feature placement and manually corrected if 
necessary. Based on the identified features, a linear averaged reference fascicle was calculated (fig. 
1A). Reliability of the tracking approach was confirmed and reported in two previous studies [14,15].” 
 
 
Minor comment. 
 
Comment:  
1.      State in the text whether errors are standard deviations or standard errors of the 
mean. 
 
Response:  
We added the information that standard deviations are presented in the revised 
manuscript (page: 5, line: 221). 
 
 
 
 
 
Referee: 2 
 
Comment:  
In this study, the authors explore the effect of muscle force-length and force-velocity 
conditions on the energetic cost of running. In addition, they explore the determinants of muscle fiber 
length change. I find this to be an extensive and well collected data set that uses in vivo determination 
of force-length and force-velocity relationships, and application of these to muscle function during 
running to address these questions. There appear to me to be a few major limitations of the study. 
These should be addressed throughout. 
 
Response:  
Thank you for your valuable comments. All changes are underlined in the revised 
version of the manuscript and the references cited in the responses can be found at the end of the 
document. Please note that some parts of the methods are now presented in the electronic 
supplementary material due to length restrictions of the journal. 
 
 
Comment:  
1) Organismal energy consumption is measured, but only the length and velocity 
profile of soleus. This prevents the authors from drawing the more interesting conclusion that muscle 
shortening velocity is a determinant of energy consumption. This is acknowledged and somewhat 
addressed in the discussion, but remains a major limitation to the study. 
 
Response:  
We agree with the reviewers comment that although the soleus contributes to a great 
portion of the overall energetic costs during running [16] other limb muscles are involved that were not 
considered in the present study and this remains a limitation. However, the main energy source 
(positive work) is the ankle joint (41%) while the contribution of the knee and hip joint is comparably 
lower during running [17]. The soleus is the greatest muscle among the main plantar flexors with 
respect to physiological cross-sectional area and volume (soleus: 131 cm² and 477 cm³, gastrocnemius 
medialis: 51 cm² and 285 cm³, gastrocnemius lateralis: 24 cm ² and 146 cm³ [18]), giving this muscle a 
key role. Using a modeling approach, Hamner and Delp (2013) showed that the contribution of soleus 
to the vertical acceleration of the center of mass at the same velocity as in our study (i.e. 2.5 m/s) is 
remarkably higher than those of the other lower limb muscles (7.5x than gastroc., 9.5x than vasti, 24x 
than rect. fem., 9.5x than tib. ant., 12x than glut. max.; visual inspection of fig. 5). For the fore-aft 
acceleration a similar superior contribution of soleus was shown (3x higher than gastroc. and 8.8x 
higher than hamstrings [19]). The propulsive function of soleus during running is achieved by active 
shortening. Active shortening reduces the force-velocity potential as discussed extensively in the 
present manuscript. Consequently, a greater active muscle volume is required to achieve the required 
mechanical energy gain.  
In contrast, the quadriceps muscle group, the main contributor during early stance, decelerating and 
supporting body mass [19,20], features more economical fascicle dynamics. Recently we showed that 
the fascicles of the vastus lateralis muscle, as a representative of the quadriceps muscle group operates 
with a high force-length (i.e. 0.91) and force-velocity potential (i.e. 0.97) during the stance phase of 
running. Operating at high force potentials reduces the energetic cost of this energetically expensive 
(due to its long fascicle length) muscle by reducing active muscle volume. This may indicate that the 
mechanical energy by muscular work required for steady state running is generated by muscles that 
are metabolically less expensive, likely to compensate for the reduction of the force-velocity potential.  
  
We discussed the reviewers comment as a limitation in the revised manuscript (page: 8, line: 360):  
“Although the soleus likely contributes to a great portion of the overall energetic costs during running, 
other limb muscles that were not considered in the present study are involved. However, the main 
energy source (positive work) is the ankle joint (41%) [17] and the soleus is the greatest muscle among 
the main plantar flexors with respect to physiological cross-sectional area (soleus 63%, gastroc. med. 
25%, gastroc. lat. 12%) and volume (53%, 31% and 16% [18]). The key role of soleus is further supported 
by the modeling study of Hamner and Delp (2013), which showed that the soleus is by far the biggest 
contributor to the vertical acceleration and fore-aft acceleration of the center of mass [19]. This 
function is achieved by active shortening, which reduces the force-velocity potential and consequently 
requires a greater active muscle volume. In contrast, the quadriceps muscle group, the main contributor 
during early stance, decelerating and transferring body mass [19,20], features more economical 
fascicle dynamics. Recently we showed that the fascicles of the vastus lateralis muscle as a 
representative of the quadriceps muscle group operates with a high force-length (i.e. 0.91) and force-
velocity potential (i.e. 0.97) during the stance phase of running. Operating at high force potentials 
minimizes the cost of this muscle, which is energetically expensive due to its long fascicle length (i.e. LO 
= 94 mm [15]), by reducing active muscle volume. This may indicate that the mechanical energy by 
muscular work required for steady state running is generated by muscles that are metabolically less 
expensive, likely to compensate for the reduction of the force-velocity potential.” 
 
 
Comment:  
2) The strict adherence to force-length and force-velocity relationships as defining 
features of muscle performance seems somewhat outdated given a wealth of literature showing that 
these relationships do not hold under conditions relevant to locomotion (i.e. history dependence, 
activation-dependent changes). These advances do not negate this study, however, it would be a more 
accurate representation of the field to acknowledge that they exist, and present this study as a means 
to investigate the importance of these relationships. 
 
Response:   
 
 
First note – History dependence: 
We agree with the reviewers comment that the phenomenon of history dependence of force production 
after active muscle lengthening or shortening may be present for the soleus during running and may 
affect the force production [21–23]. In the present study, the soleus fascicles shortened continuously 
during running when activated, which would indicate a condition of force depression. Force depression 
has been shown to increase with increasing shortening magnitude [24], with decreasing shortening 
velocity [25] and with increasing activation levels [26]. Since the soleus shortening magnitude was 
notable (25.9 ± 7.8 %LO), the shortening velocity moderate (0.118 ± 0.039 Vmax) and the activation 
submaximal (average during stance phase: 0.32 ± 0.19 EMGmax; maximum activation: 0.52 ± 0.18 
EMGmax), an effect of force depression on the force production can theoretically be expected. Yet, the 
force-length and force-velocity relationships remain the basic mechanisms for muscle force production. 
Interestingly, force depression is likely to be reduced due to the tendon and belly gearing mechanisms 
because those reduce the shortening magnitude and activation. The observed main finding of a 
correlation of the operating velocity and force-velocity potential with the energetic cost, however, does 
not neglect the presence of force depression but indicates that shortening velocity and consequently 
the force-velocity potential has a direct effect on the muscle energetics.  
 
We added the following sentences in the introduction and discussion of the revised version of the 
manuscript (page: 2, line: 59; page: 7, line: 307):   
 
“Besides the operating length and velocity as the main determinants, the history dependence of force 
generation [23], i.e. increased force after active muscle lengthening [27] and decreased force after 
active shortening [22,25], may additionally influence the force potential.” 
 
“Furthermore, we showed that the soleus shortened continuously during the stance phase of running, 
which reflects a condition for force depression. Since a depression of force was shown to be 
accompanied by a decrease in the ATPase activity [28], force depression would have little or no effect 
on the energetic cost itself.” 
 
 
Second note – Shift in optimal length: 
Furthermore, it is correct that we assessed the force-length curve during maximal isometric 
contractions at different ankle joint angles and, using this relationship, we calculated the force-length 
potential of the soleus muscle during running at submaximal activation. There is evidence from early 
[29] and more recent [30,31] in vitro studies that the force-length curve depends on muscle activation, 
i.e. optimum length increases with submaximal activation. However, a recent study by Fontana and 
Herzog (2016) on the human vastus lateralis muscle showed that this holds not necessarily true for in 
vivo assessments [32]. In contrast to the in vitro studies, a rightward shift of optimal length was not 
observed when force was normalized to the maximum EMG signal (i.e. optimal length remained 
constant at different levels of activation). The authors suggested that the disagreement of the in vitro 
and in vivo studies might be an artefact related to the in vitro testing setup (e.g. non-physiological 
stimulation frequency range or calcium concentrations). Therefore, we can argue that mapping the 
submaximal fascicle operating length onto the force-length curve in the present in vivo study should 
not affect the findings. 
 
We added the following information in the discussion part of revised manuscript as follows (page: 9, 
line: 385):  
“Furthermore, we assessed the force-length curve during maximal isometric contractions and used it 
to calculate the force-length potential of the soleus muscle during running at submaximal activation. 
There is evidence from in vitro studies that the force-length curve depends on muscle activation [29–
31]. However, in a recent in vivo study by Fontana and Herzog (2016) on the human vastus lateralis 
muscle, a rightward shift of optimal length with submaximal activation was not observed when force 
was normalized to the maximum EMG signal [32]. The authors suggested that the shift in optimal 
length phenomenon might be related to the in vitro testing setup (e.g. non-physiological stimulation 
frequency range or Ca2+concentrations). Therefore, we can argue that mapping the submaximal fascicle 
operating length onto the force-length curve in the present in vivo study should not affect the findings.” 
 
 
Comment:  
3) This paper is fundamentally concerned with the effect of contractile conditions on 
muscle energy consumption. However, there is very little discussion of why length and velocity might 
affect energy consumption beyond required activation, despite a wealth of evidence on this i.e. how 
the cost per unit force varies across the force-length relationship in isolated muscle. In addition, it may 
be worth considering findings such as the effect of contractile history on cost (Joumaa et al., 2013), 
and the complexity of the cost of work (Holt et al., 2104; Curtin et al., 2019) in a more comprehensive 
discussion of in vivo muscle energetics. 
 
Response:  
 
 
First note - Variation of cost per unit force across the force-length relationship: 
We agree with the reviewer that the energy turnover can differ across the force-length relationship in 
isolated animal muscle fibers tested in vitro [33]. During isometric contractions at sarcomere length 
shorter than optimal length, the force output is reduced but  the ATPase rate seems not to greatly differ 
from the rate at optimal length, indicating a comparably higher cost of contraction at shorter length 
[34,35]. However, this effect seems to be more pronounced at very short lengths, which might not be 
covered during regular in vivo movements like locomotion, i.e. soleus operating range (0.75-1.01 LO).   
 
We added the following information in the revised version of the manuscript as follows (page: 7, line: 
300):  “Besides the favorable high force-length potential for economical force production, operating 
close to optimal length may additionally preserved from relatively higher energetic cost that can arise 
when contracting at shorter length. In vitro evidence showed that although force is reduced at shorter 
sarcomere length, the ATPase rate seems not to differ from the rate at optimal length, indicating 
comparably higher cost of contraction at shorter length [34,35]. However, this effect seems more 
pronounced at very short lengths, a portion of the force-length curve that is likely not covered by the 
soleus during running (operating range 0.75-1.01 LO).” 
 
 
Second note - Effect of contractile history on cost: 
We added the following paragraph to the discussion part of the revised manuscript (page: 7, line: 307):  
“Furthermore, we showed that the soleus shortened continuously during the stance phase of running, 
which reflects a condition for force depression. Since a depression of force was shown to be 
accompanied by a decrease in the ATPase activity [28], force depression would have little or no effect 
on the energetic cost itself.” 
 
 
Third note - complexity of the cost of work: 
Thanks for this comment. We agree with the reviewer on the ongoing debate on the cost of force and 
the cost of work. From our perspective, when a muscle contracts, force is generated and this consumes 
metabolic energy independently of the contraction type (i.e. isometric, eccentric, concentric). During 
concentric contractions (active shortening) positive mechanical work is generated and during eccentric 
contractions (active lengthening) the work is negative. In stretch-shortening conditions, the net work 
could be zero when positive and negative work cancel each other out. Under isometric contractions, no 
mechanical work is generated by definition, which would again indicate no mechanical energy 
production (Joule), although force is generated and metabolic energy expended. The energy index of 
work in the context of the explanation of metabolic energy, therefore, might not be very appropriate 
(metabolic energy is not zero when work is zero e.g. during isometric contractions). Instead, an index 
of force and metabolic energy might better reflect the organismal cost during locomotion.  
With our study, we cannot provide any new information on this discussion because work and force of 
soleus were not measured during running (which in our opinion is not possible at the moment). 
Therefore, we think that this topic is beyond of the scope of the present study and for this reason we 
would prefer not to go deeper in the discussion of cost of force and work but rather stay close to our 
experimental results.  
 
 
 
Specific comments 
 
Comment:  
Lines 50-51 – The ongoing debating between the cost of force and the cost of work as 
determinants of organismal cost should be acknowledged here. This could then also lead to a more 
nuanced discussion of factors dictating muscle energetics beyond simply level of activation. 
 
Response:  
As responded in more detail to the previous comment, we would not like to refer the 
manuscript to the discussion of cost of work and force because this is beyond the scope of the present 
study. By our study design (force and work not measured) and results we cannot provide any significant 
contribution to the mentioned ongoing discussion.  
 
 
Comment:  
Lines 123-124 and 185-187 – It is relatively unclear to me how the force-velocity 
relationship was determined here. It appears as though force and velocity were determined as fibers 
shortened against the tendon? Can the authors make this clearer, better define where in the 
contraction force and velocity were determined, and comment on how this might affect findings 
compared to a more standard isotonic or isovelocity protocol. 
 
Response:  
The force-velocity curve in the present study was not derived from experimentally 
measured force estimates and fascicle velocities. In the first version of the manuscript Vmax was 
calculated based on the soleus muscle-specific constants of arel and brel reported by literature [10] as 
11.75 LO/s. According to a comment from the other reviewer, we now based our choice of Vmax on more 
biological evidence as follows. The in vitro study of Luden et al., (2008) on the human soleus muscle 
reported Vmax values for MHC I type fibers of 0.77 LO/s and 2.91 LO/s for MHC IIA type fibers measured 
at 15°C [3]. Considering the temperature coefficient provided by Ranatunga et al., (1984) [4] it can be 
predicted that Vmax would increase to 4.4 LO/s for MHC I type fibers and to 16.8 LO/s for MHC IIA type 
fibers under physiological temperature conditions (37 °C). The fiber type distribution in the human 
soleus muscle can be estimated from literature reports, i.e. Johnson et al., 1973: type 1 fibers 87,7%, 
type 2 fibers (a and b) 12,3% (average of surface and deep fiber location) [5]; Larsson and Moss, 1993: 
type 1 89%, type 2A 11% [6]; Edgerton et al., 1975: slow twitch 70%, fast twitch 30% [7]; Luden et al., 
2008: 74% MHC I, 20% MHC IIA (norm to 100%) [3]). Using an average of this reported distribution 
values (type 1: 81%, type 2: 19%), Vmax for soleus under physiological temperature can be calculated as 
6.77 LO/s. The broad literature basis for the average fiber type distribution was also used to update arel 
to 0.175 (i.e. 0.1+0.4FT, where FT is the fast twitch fiber type percentage [8,9]) and accordingly brel to 
1.182 (arel * Vmax [10]). We then assessed the force-velocity curve by using the classical Hill formula, (i.e. 
(F+a)(v+b)=(Fmax+a)b), and the muscle-specific values of Vmax, arel and brel. 
We recalculated the respective values (force-velocity potential and normalized velocities and their 
ranges) using the updated Vmax of 6.77 LO/s, arel and brel in the revised manuscript. Note that this 
adjustment in the calculation did not changed any statistical result but only few numerical expressions 
(underlined in the revision). A revised and more detailed description of the calculation of the force-
velocity potential is also now provided in the updated manuscript (see below).  
The reason why we did not measured Vmax experimentally is that precise measurements of Vmax in vivo 
in humans are extremely challenging, technically and methodologically (e.g. restricted high 
dynamometer velocities, limited ultrasound capture frequencies in high velocities, limited range of 
motion to reach maximum force in high velocities, consideration of antagonistic co-contraction, 
mechanical properties of the tendon, history dependence effects).  
 
We added the following information to the revised manuscript (page: 4, line: 155):  
“Furthermore, we assessed the force-velocity relationship of soleus using the classical Hill equation [11] 
and the muscle-specific maximum fascicle shortening velocity (Vmax) and constants of arel and brel. Vmax 
was derived from the study of Luden et al. (2008), which showed Vmax values for type 1 fibers of 0.77 
LO/s and 2.91 LO/s for type 2 fibers of the human soleus muscle measured in vitro at 15°C [3]. 
Considering the temperature coefficient [4], Vmax can be predicted as 4.4 LO/s for type 1 fibers and 16.8 
LO/s for type 2 fibers under physiological temperature conditions (37 °C). Using an average fiber type 
distribution (type 1 fibers: 81%, type 2: 19%) of the human soleus muscle reported in literature [3,5–7], 
Vmax can be calculated as 6.77 LO/s. arel was calculated as 0.1+0.4FT, where FT is the fast twitch fiber 
type percentage (see above), which then equals to 0.175 [8,9]. The product of arel and Vmax then gives 
brel as 1.182 [10]. After rearrangement of the Hill formula and extension to the eccentric component, 
the normalized operating velocity (to Vmax) can be used to calculate the individual force potential 
according to the force-velocity curve.” 
 
 
Comment:  
Line 197-198 – The meaning of this is unclear to me. This description of touchdown 
and toe-off should be reworded for clarification.  
 
Response:  
We changed the description to be more clear as follows (page: 4, line: 175): 
“The touchdown of the foot and toe off were defined by the kinematic data as the first and second peak 
in knee extension, respectively [36,37].“ 
  
 
Comment:  
The results section is relatively dense. The authors may wish to consider moving some 
of the findings less critical to addressing their question to a table, to improve readability. 
 
Response:  
Some of the results are now presented in the table to improve readability.  
 
 
Comment:  
Line 299-300 – The assertion that the triceps surae consumes 40% of the cost during 
running is crucial to the argument of this paper. Yet it is not clear how this value is arrived at from the 
Fletcher and MacIntosh paper cited (the paper seems to give a large range of values for muscle energy 
consumption and not to relate this to organismal cost), and how reliable the output of their simple 
model is for this purpose. Could the authors give a little more detail on this (in the manuscript if of 
sufficient interest, or simply here). It may also be useful to combine this 40% estimate with the relative 
size of soleus to give a better representation of its likely contribution to energy consumption, 
considering fiber type as soleus is likely cheaper than gastrocs (Barclay, 1993). 
 
Response:  
The statement that the triceps surae consumes 40% of the energy during running can 
be derived from the comparison of figure 4 and 5 in the paper of Fletcher and MacIntosh (2015) and is 
numerically presented by the authors themselves in several subsequent published manuscripts (e.g. 
[38,39]). We agree with the reviewer that the presented calculations on muscle energy consumption in 
the aforementioned study may only provide a rough estimate. We also do not persist on the fixed value 
of 40% but rather we would like to understand this value as an indication of the great contribution of 
the triceps surae to the overall energetic cost. Within the triceps surae the gastrocnemius medialis and 
lateralis contribute to the propulsion as well but the physiological cross-sectional area (PCSA) and 
volume of soleus are notably higher (soleus: 131 cm² and 477 cm³, gastrocnemius medialis: 51 cm² and 
285 cm³, gastrocnemius lateralis: 24 cm ² and 146 cm³ [18]).  
Further calculations on the separate contribution of the single muscles of the triceps surae based on 
portions of force are very difficult if even possible because of strong underlying assumptions of the 
calculation. E.g., calculating the soleus muscle force using the PCSA relative to the other triceps muscles 
(gastroc. med and lat.) would premise that the force-potential due to the force length/velocity 
relationship and activation of all triceps surae muscles are equal. This assumption cannot be correct 
because the gastrocnemi are biarticular muscles. For this reason, we would not like to include this 
approach in our manuscript but rather stay on the more direct findings.   
 
We softened our formulation by deleting the 40% in revised manuscript (page: 7, line: 280). 
 
 
Comment:  
Lines 304-309 - The authors make a good case for why small changes in velocity would 
require an increase in activation and therefore cost. This effect should be seen in EMG recordings. It 
would seem that the argument could be strengthened by showing this as it would provide a more 
causal link between the change in muscle level function and organismal level cost. 
 
Response:  
Thanks for this comment. We did not go into any correlation analysis in the study 
because the parameter of surface EMG activation does not reflects active muscle volume adequately.   
However, a significant correlation can be found for the force-length-velocity potential (EMG mean: r = 
-0.504, p = 0.028; EMG max: r = -0.525, p = 0.021; EMG integral: : r = -0.504, p = 0.028). Please note 
that the processing of the EMG signal can affect the correlation coefficients but not the significance 
itself (p < 0.05). Here a 20 Hz low pass filter was used after rectification and preprocessing with a high 
pass filter of 50 Hz.  
Given the mentioned limitation, the observed correlation might provide a cautious indication that a 
decreased EMG activity is associated with a higher force-length-velocity potential of the soleus muscle 
during the stance phase of running and that may affect the metabolic cost.  
 
We added the association between EMG activity and force-length-velocity potential in the revised 
manuscript without an extended interpretation because, as we mentioned before, the active muscle 
volume cannot be assessed accurately from the EMG activity (page: 6, line: 255; page: 7, line: 291).  
 
 
Comment:  
Line 334-335 – There seems to be some discrepancy regarding activation in here. The 
implication seems to be that muscle activation is higher in early stance to enable the tendon to be 
stretched, and then recoil to slow shortening velocity in the later part of stance. Yet a central claim of 
the paper is that cost is lower when shortening velocity is lower, due to a lower requirement for 
activation. It seems like the variation in required activation could balance out over the course of a 
stance phase? Could it be clarified as to why the early increase in activation to enable tendon stretch 
doesn’t seem to be costly in the way that the latter reduction is deemed to be cheap? 
 
Response:  
Thanks for this comment. The rationale of this argumentation is that the observed 
activation pattern can be interpreted as appropriate for a coordinated MTU interaction during the 
running task with respect to economy. We changed the formulation in the respective section as follows 
(page: 7, line: 322): 
“The soleus produces mechanical work/energy for the lift and acceleration of the body throughout the 
entire stance phase. In the first half, where the MTU is elongated, the fascicles actively shorten. This 
means that a part of the mechanical energy of the human body is transferred to the tendon. Also, in 
this setting the muscle fascicles produce work under favorable conditions due to the force-length and 
force-velocity relationships (both potentials in this phase were very high) and save work as strain 
energy in the tendon. In the second half, the tendon strain energy is returned and at the same time the 
fascicles produce work by active shortening at a reduced force-velocity potential (fascicle shortening 
velocity is higher in this phase). The higher shortening velocity is associated with a reduction in the EMG 
activity and an increase in belly gearing. It has been suggested that increased gearing at fast shortening 
velocities and lower forces is a mechanism that allows particularly slower type fascicles to be more 
effective in generating forces [40]. This supports the idea that the observed activation pattern fostered 
an economical MTU interaction during running.”  
 
 
 
Comment:  
Line 345 – typo “were”? 
 
Response: 
We corrected the typo accordingly.  
 
 
 
Comment:  
Line 375 – The study doesn’t seem to show that energy consumption is related to the 
force-length-velocity potential, but rather just the force-velocity potential. 
 
Response:  
The force-length-velocity potential is the product of the force-length and force-velocity 
potential and was inversely associated with the energetic cost like the force-velocity potential. The 
force-length potential was consistently high among the participants and showed no significant 
association to the energetic cost. This indicates that the reason for the association of the force-length-
velocity potential to the energetic cost was caused by the observed correlation of the force-velocity 
potential, i.e. variability in the force-length-velocity potential relied on the variability of the force-
velocity potential that cohered the variability of the energetic cost. However, as we mentioned in the 
discussion, a high force-length potential is also important for economical muscle force generation. 
 
 
 
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Referee: 2
I appreciate the authors addressing these comments and amending the manuscript accordingly. 
A few final responses to the authors’ responses are made in red below 
Comment:  
In this study, the authors explore the effect of muscle force-length and force-velocity 
conditions on the energetic cost of running. In addition, they explore the determinants of muscle fiber 
length change. I find this to be an extensive and well collected data set that uses in vivo determination 
of force-length and force-velocity relationships, and application of these to muscle function during 
running to address these questions. There appear to me to be a few major limitations of the study. 
These should be addressed throughout. 
Response:  
Thank you for your valuable comments. All changes are underlined in the revised 
version of the manuscript and the references cited in the responses can be found at the end of the 
document. Please note that some parts of the methods are now presented in the electronic 
supplementary material due to length restrictions of the journal. 
Comment: 
1) Organismal energy consumption is measured, but only the length and velocity
profile of soleus. This prevents the authors from drawing the more interesting conclusion that muscle 
shortening velocity is a determinant of energy consumption. This is acknowledged and somewhat 
addressed in the discussion, but remains a major limitation to the study. 
Response:  
We agree with the reviewers comment that although the soleus contributes to a great 
portion of the overall energetic costs during running [16] other limb muscles are involved that were not 
considered in the present study and this remains a limitation. However, the main energy source 
(positive work) is the ankle joint (41%) while the contribution of the knee and hip joint is comparably 
lower during running [17]. The soleus is the greatest muscle among the main plantar flexors with 
respect to physiological cross-sectional area and volume (soleus: 131 cm² and 477 cm³, gastrocnemius 
medialis: 51 cm² and 285 cm³, gastrocnemius lateralis: 24 cm ² and 146 cm³ [18]), giving this muscle a 
key role. Using a modeling approach, Hamner and Delp (2013) showed that the contribution of soleus 
to the vertical acceleration of the center of mass at the same velocity as in our study (i.e. 2.5 m/s) is 
remarkably higher than those of the other lower limb muscles (7.5x than gastroc., 9.5x than vasti, 24x 
than rect. fem., 9.5x than tib. ant., 12x than glut. max.; visual inspection of fig. 5). For the fore-aft 
acceleration a similar superior contribution of soleus was shown (3x higher than gastroc. and 8.8x 
higher than hamstrings [19]). The propulsive function of soleus during running is achieved by active 
shortening. Active shortening reduces the force-velocity potential as discussed extensively in the 
present manuscript. Consequently, a greater active muscle volume is required to achieve the required 
mechanical energy gain.  
In contrast, the quadriceps muscle group, the main contributor during early stance, decelerating and 
supporting body mass [19,20], features more economical fascicle dynamics. Recently we showed that 
the fascicles of the vastus lateralis muscle, as a representative of the quadriceps muscle group operates 
with a high force-length (i.e. 0.91) and force-velocity potential (i.e. 0.97) during the stance phase of 
running. Operating at high force potentials reduces the energetic cost of this energetically expensive 
(due to its long fascicle length) muscle by reducing active muscle volume. This may indicate that the 
Appendix C
mechanical energy by muscular work required for steady state running is generated by muscles that 
are metabolically less expensive, likely to compensate for the reduction of the force-velocity potential.  
  
We discussed the reviewers comment as a limitation in the revised manuscript (page: 8, line: 360):  
“Although the soleus likely contributes to a great portion of the overall energetic costs during running, 
other limb muscles that were not considered in the present study are involved. However, the main 
energy source (positive work) is the ankle joint (41%) [17] and the soleus is the greatest muscle among 
the main plantar flexors with respect to physiological cross-sectional area (soleus 63%, gastroc. med. 
25%, gastroc. lat. 12%) and volume (53%, 31% and 16% [18]). The key role of soleus is further supported 
by the modeling study of Hamner and Delp (2013), which showed that the soleus is by far the biggest 
contributor to the vertical acceleration and fore-aft acceleration of the center of mass [19]. This 
function is achieved by active shortening, which reduces the force-velocity potential and consequently 
requires a greater active muscle volume. In contrast, the quadriceps muscle group, the main contributor 
during early stance, decelerating and transferring body mass [19,20], features more economical 
fascicle dynamics. Recently we showed that the fascicles of the vastus lateralis muscle as a 
representative of the quadriceps muscle group operates with a high force-length (i.e. 0.91) and force-
velocity potential (i.e. 0.97) during the stance phase of running. Operating at high force potentials 
minimizes the cost of this muscle, which is energetically expensive due to its long fascicle length (i.e. LO 
= 94 mm [15]), by reducing active muscle volume. This may indicate that the mechanical energy by 
muscular work required for steady state running is generated by muscles that are metabolically less 
expensive, likely to compensate for the reduction of the force-velocity potential.” 
 
 
 
Comment:  
2) The strict adherence to force-length and force-velocity relationships as defining 
features of muscle performance seems somewhat outdated given a wealth of literature showing that 
these relationships do not hold under conditions relevant to locomotion (i.e. history dependence, 
activation-dependent changes). These advances do not negate this study, however, it would be a more 
accurate representation of the field to acknowledge that they exist, and present this study as a means 
to investigate the importance of these relationships. 
 
Response:   
 
 
First note – History dependence: 
We agree with the reviewers comment that the phenomenon of history dependence of force production 
after active muscle lengthening or shortening may be present for the soleus during running and may 
affect the force production [21–23]. In the present study, the soleus fascicles shortened continuously 
during running when activated, which would indicate a condition of force depression. Force depression 
has been shown to increase with increasing shortening magnitude [24], with decreasing shortening 
velocity [25] and with increasing activation levels [26]. Since the soleus shortening magnitude was 
notable (25.9 ± 7.8 %LO), the shortening velocity moderate (0.118 ± 0.039 Vmax) and the activation 
submaximal (average during stance phase: 0.32 ± 0.19 EMGmax; maximum activation: 0.52 ± 0.18 
EMGmax), an effect of force depression on the force production can theoretically be expected. Yet, the 
force-length and force-velocity relationships remain the basic mechanisms for muscle force production. 
Interestingly, force depression is likely to be reduced due to the tendon and belly gearing mechanisms 
because those reduce the shortening magnitude and activation. The observed main finding of a 
correlation of the operating velocity and force-velocity potential with the energetic cost, however, does 
not neglect the presence of force depression but indicates that shortening velocity and consequently 
the force-velocity potential has a direct effect on the muscle energetics.  
 
We added the following sentences in the introduction and discussion of the revised version of the 
manuscript (page: 2, line: 59; page: 7, line: 307):   
 
“Besides the operating length and velocity as the main determinants, the history dependence of force 
generation [23], i.e. increased force after active muscle lengthening [27] and decreased force after 
active shortening [22,25], may additionally influence the force potential.” 
 
“Furthermore, we showed that the soleus shortened continuously during the stance phase of running, 
which reflects a condition for force depression. Since a depression of force was shown to be 
accompanied by a decrease in the ATPase activity [28], force depression would have little or no effect 
on the energetic cost itself.” 
 
 
Second note – Shift in optimal length: 
Furthermore, it is correct that we assessed the force-length curve during maximal isometric 
contractions at different ankle joint angles and, using this relationship, we calculated the force-length 
potential of the soleus muscle during running at submaximal activation. There is evidence from early 
[29] and more recent [30,31] in vitro studies that the force-length curve depends on muscle activation, 
i.e. optimum length increases with submaximal activation. However, a recent study by Fontana and 
Herzog (2016) on the human vastus lateralis muscle showed that this holds not necessarily true for in 
vivo assessments [32]. In contrast to the in vitro studies, a rightward shift of optimal length was not 
observed when force was normalized to the maximum EMG signal (i.e. optimal length remained 
constant at different levels of activation). The authors suggested that the disagreement of the in vitro 
and in vivo studies might be an artefact related to the in vitro testing setup (e.g. non-physiological 
stimulation frequency range or calcium concentrations). Therefore, we can argue that mapping the 
submaximal fascicle operating length onto the force-length curve in the present in vivo study should 
not affect the findings. 
 
We added the following information in the discussion part of revised manuscript as follows (page: 9, 
line: 385):  
“Furthermore, we assessed the force-length curve during maximal isometric contractions and used it 
to calculate the force-length potential of the soleus muscle during running at submaximal activation. 
There is evidence from in vitro studies that the force-length curve depends on muscle activation [29–
31]. However, in a recent in vivo study by Fontana and Herzog (2016) on the human vastus lateralis 
muscle, a rightward shift of optimal length with submaximal activation was not observed when force 
was normalized to the maximum EMG signal [32]. The authors suggested that the shift in optimal 
length phenomenon might be related to the in vitro testing setup (e.g. non-physiological stimulation 
frequency range or Ca2+concentrations). Therefore, we can argue that mapping the submaximal fascicle 
operating length onto the force-length curve in the present in vivo study should not affect the findings.” 
 
I find the rationale of this Herzog and Fontana paper quite difficult to follow, particular with regards 
to how they cite other studies. They attempt to distinguish between activation and force which, while 
may have some bearing on the mechanism responsible, does nothing to counter the finding that shifts 
in optimum length not predicted by the sliding filament theory occur with changing contractile 
conditions. For the purposes of this argument, what I take from this study is that if you change muscle 
force production, optimum length shifts (Fig. 3 Herzog and Fontana 2016). This is in line with other in 
vivo studies of this phenomenon (Ichinose et al., 1997; Kwah et al 2013), and makes it less obvious that 
this potential effect should be ignored in the present paper.  
 
This does not change the arguments of this paper, and I leave this to the authors discretion, but it is 
my feeling that it would be a stronger paper if it shifted its focus from the conviction that force-length 
and force-velocity potential of the muscle dictates in vivo performance (if this were true, Hill-type 
muscle models would do a better job (Lee et al., 2013; Dick et al., 2017)) to an argument that multiple 
factors influence muscle mechanical and energetic performance under dynamic conditions, and that 
this paper seeks to understand to what extent force-velocity effects dictate energetic performance. 
It’s a subtle shift that would require minor rewording throughout, but it’s my feeling that this would 
much better reflect that state of the field.  
 
Reference to the Herzog and Fontana paper is made again in the discussion, the authors may wish to 
consider how well it supports their argument and the contradictory findings of other in vivo papers. 
 
Comment:  
3) This paper is fundamentally concerned with the effect of contractile conditions on 
muscle energy consumption. However, there is very little discussion of why length and velocity might 
affect energy consumption beyond required activation, despite a wealth of evidence on this i.e. how 
the cost per unit force varies across the force-length relationship in isolated muscle. In addition, it may 
be worth considering findings such as the effect of contractile history on cost (Joumaa et al., 2013), 
and the complexity of the cost of work (Holt et al., 2104; Curtin et al., 2019) in a more comprehensive 
discussion of in vivo muscle energetics. 
 
Response:  
 
 
First note - Variation of cost per unit force across the force-length relationship: 
We agree with the reviewer that the energy turnover can differ across the force-length relationship in 
isolated animal muscle fibers tested in vitro [33]. During isometric contractions at sarcomere length 
shorter than optimal length, the force output is reduced but  the ATPase rate seems not to greatly differ 
from the rate at optimal length, indicating a comparably higher cost of contraction at shorter length 
[34,35]. However, this effect seems to be more pronounced at very short lengths, which might not be 
covered during regular in vivo movements like locomotion, i.e. soleus operating range (0.75-1.01 LO).   
 
We added the following information in the revised version of the manuscript as follows (page: 7, line: 
300):  “Besides the favorable high force-length potential for economical force production, operating 
close to optimal length may additionally preserved from relatively higher energetic cost that can arise 
when contracting at shorter length. In vitro evidence showed that although force is reduced at shorter 
sarcomere length, the ATPase rate seems not to differ from the rate at optimal length, indicating 
comparably higher cost of contraction at shorter length [34,35]. However, this effect seems more 
pronounced at very short lengths, a portion of the force-length curve that is likely not covered by the 
soleus during running (operating range 0.75-1.01 LO).” 
 
 
Second note - Effect of contractile history on cost: 
We added the following paragraph to the discussion part of the revised manuscript (page: 7, line: 307):  
“Furthermore, we showed that the soleus shortened continuously during the stance phase of running, 
which reflects a condition for force depression. Since a depression of force was shown to be 
accompanied by a decrease in the ATPase activity [28], force depression would have little or no effect 
on the energetic cost itself.” 
 
 
Third note - complexity of the cost of work: 
Thanks for this comment. We agree with the reviewer on the ongoing debate on the cost of force and 
the cost of work. From our perspective, when a muscle contracts, force is generated and this consumes 
metabolic energy independently of the contraction type (i.e. isometric, eccentric, concentric). During 
concentric contractions (active shortening) positive mechanical work is generated and during eccentric 
contractions (active lengthening) the work is negative. In stretch-shortening conditions, the net work 
could be zero when positive and negative work cancel each other out. Under isometric contractions, no 
mechanical work is generated by definition, which would again indicate no mechanical energy 
production (Joule), although force is generated and metabolic energy expended. The energy index of 
work in the context of the explanation of metabolic energy, therefore, might not be very appropriate 
(metabolic energy is not zero when work is zero e.g. during isometric contractions). Instead, an index 
of force and metabolic energy might better reflect the organismal cost during locomotion.  
With our study, we cannot provide any new information on this discussion because work and force of 
soleus were not measured during running (which in our opinion is not possible at the moment). 
Therefore, we think that this topic is beyond of the scope of the present study and for this reason we 
would prefer not to go deeper in the discussion of cost of force and work but rather stay close to our 
experimental results.  
 
This cost of work argument could entirely be thought of as cost of muscle fiber shortening argument. 
Which is obviously very pertinent to this paper. It is my opinion that this paper would be strengthened 
by greater discussion of this complexity and what the data presented here do to advance our 
understanding -i.e. cheap work (shortening) may be possible in some cases (Holt et al., 2014; Curtin et 
al., 2019), but in this case, more rapid active muscle shortening does seem to incur energetic costs. 
But again, I leave this to the authors discretion. 
 
Specific comments 
 
Comment:  
Lines 50-51 – The ongoing debating between the cost of force and the cost of work as 
determinants of organismal cost should be acknowledged here. This could then also lead to a more 
nuanced discussion of factors dictating muscle energetics beyond simply level of activation. 
 
Response:  
As responded in more detail to the previous comment, we would not like to refer the 
manuscript to the discussion of cost of work and force because this is beyond the scope of the present 
study. By our study design (force and work not measured) and results we cannot provide any significant 
contribution to the mentioned ongoing discussion.  
 
 
Comment:  
Lines 123-124 and 185-187 – It is relatively unclear to me how the force-velocity 
relationship was determined here. It appears as though force and velocity were determined as fibers 
shortened against the tendon? Can the authors make this clearer, better define where in the 
contraction force and velocity were determined, and comment on how this might affect findings 
compared to a more standard isotonic or isovelocity protocol. 
 
Response:  
The force-velocity curve in the present study was not derived from experimentally 
measured force estimates and fascicle velocities. In the first version of the manuscript Vmax was 
calculated based on the soleus muscle-specific constants of arel and brel reported by literature [10] as 
11.75 LO/s. According to a comment from the other reviewer, we now based our choice of Vmax on more 
biological evidence as follows. The in vitro study of Luden et al., (2008) on the human soleus muscle 
reported Vmax values for MHC I type fibers of 0.77 LO/s and 2.91 LO/s for MHC IIA type fibers measured 
at 15°C [3]. Considering the temperature coefficient provided by Ranatunga et al., (1984) [4] it can be 
predicted that Vmax would increase to 4.4 LO/s for MHC I type fibers and to 16.8 LO/s for MHC IIA type 
fibers under physiological temperature conditions (37 °C). The fiber type distribution in the human 
soleus muscle can be estimated from literature reports, i.e. Johnson et al., 1973: type 1 fibers 87,7%, 
type 2 fibers (a and b) 12,3% (average of surface and deep fiber location) [5]; Larsson and Moss, 1993: 
type 1 89%, type 2A 11% [6]; Edgerton et al., 1975: slow twitch 70%, fast twitch 30% [7]; Luden et al., 
2008: 74% MHC I, 20% MHC IIA (norm to 100%) [3]). Using an average of this reported distribution 
values (type 1: 81%, type 2: 19%), Vmax for soleus under physiological temperature can be calculated as 
6.77 LO/s. The broad literature basis for the average fiber type distribution was also used to update arel 
to 0.175 (i.e. 0.1+0.4FT, where FT is the fast twitch fiber type percentage [8,9]) and accordingly brel to 
1.182 (arel * Vmax [10]). We then assessed the force-velocity curve by using the classical Hill formula, (i.e. 
(F+a)(v+b)=(Fmax+a)b), and the muscle-specific values of Vmax, arel and brel. 
We recalculated the respective values (force-velocity potential and normalized velocities and their 
ranges) using the updated Vmax of 6.77 LO/s, arel and brel in the revised manuscript. Note that this 
adjustment in the calculation did not changed any statistical result but only few numerical expressions 
(underlined in the revision). A revised and more detailed description of the calculation of the force-
velocity potential is also now provided in the updated manuscript (see below).  
The reason why we did not measured Vmax experimentally is that precise measurements of Vmax in vivo 
in humans are extremely challenging, technically and methodologically (e.g. restricted high 
dynamometer velocities, limited ultrasound capture frequencies in high velocities, limited range of 
motion to reach maximum force in high velocities, consideration of antagonistic co-contraction, 
mechanical properties of the tendon, history dependence effects).  
 
We added the following information to the revised manuscript (page: 4, line: 155):  
“Furthermore, we assessed the force-velocity relationship of soleus using the classical Hill equation [11] 
and the muscle-specific maximum fascicle shortening velocity (Vmax) and constants of arel and brel. Vmax 
was derived from the study of Luden et al. (2008), which showed Vmax values for type 1 fibers of 0.77 
LO/s and 2.91 LO/s for type 2 fibers of the human soleus muscle measured in vitro at 15°C [3]. 
Considering the temperature coefficient [4], Vmax can be predicted as 4.4 LO/s for type 1 fibers and 16.8 
LO/s for type 2 fibers under physiological temperature conditions (37 °C). Using an average fiber type 
distribution (type 1 fibers: 81%, type 2: 19%) of the human soleus muscle reported in literature [3,5–7], 
Vmax can be calculated as 6.77 LO/s. arel was calculated as 0.1+0.4FT, where FT is the fast twitch fiber 
type percentage (see above), which then equals to 0.175 [8,9]. The product of arel and Vmax then gives 
brel as 1.182 [10]. After rearrangement of the Hill formula and extension to the eccentric component, 
the normalized operating velocity (to Vmax) can be used to calculate the individual force potential 
according to the force-velocity curve.” 
 
Line 104-103 – it therefore seems misleading to say ‘as a function of their experimentally assessed 
force-velocity relationships’ 
Line 126-127 – similar issue in that this seems to suggest experimental measurements of force-velocity 
relationships in this study 
 
Comment:  
Line 197-198 – The meaning of this is unclear to me. This description of touchdown 
and toe-off should be reworded for clarification.  
 
Response:  
We changed the description to be more clear as follows (page: 4, line: 175): 
“The touchdown of the foot and toe off were defined by the kinematic data as the first and second peak 
in knee extension, respectively [36,37].“ 
  
 
Comment:  
The results section is relatively dense. The authors may wish to consider moving some 
of the findings less critical to addressing their question to a table, to improve readability. 
 
Response:  
Some of the results are now presented in the table to improve readability.  
 
 
Comment:  
Line 299-300 – The assertion that the triceps surae consumes 40% of the cost during 
running is crucial to the argument of this paper. Yet it is not clear how this value is arrived at from the 
Fletcher and MacIntosh paper cited (the paper seems to give a large range of values for muscle energy 
consumption and not to relate this to organismal cost), and how reliable the output of their simple 
model is for this purpose. Could the authors give a little more detail on this (in the manuscript if of 
sufficient interest, or simply here). It may also be useful to combine this 40% estimate with the relative 
size of soleus to give a better representation of its likely contribution to energy consumption, 
considering fiber type as soleus is likely cheaper than gastrocs (Barclay, 1993). 
 
Response:  
The statement that the triceps surae consumes 40% of the energy during running can 
be derived from the comparison of figure 4 and 5 in the paper of Fletcher and MacIntosh (2015) and is 
numerically presented by the authors themselves in several subsequent published manuscripts (e.g. 
[38,39]). We agree with the reviewer that the presented calculations on muscle energy consumption in 
the aforementioned study may only provide a rough estimate. We also do not persist on the fixed value 
of 40% but rather we would like to understand this value as an indication of the great contribution of 
the triceps surae to the overall energetic cost. Within the triceps surae the gastrocnemius medialis and 
lateralis contribute to the propulsion as well but the physiological cross-sectional area (PCSA) and 
volume of soleus are notably higher (soleus: 131 cm² and 477 cm³, gastrocnemius medialis: 51 cm² and 
285 cm³, gastrocnemius lateralis: 24 cm ² and 146 cm³ [18]).  
Further calculations on the separate contribution of the single muscles of the triceps surae based on 
portions of force are very difficult if even possible because of strong underlying assumptions of the 
calculation. E.g., calculating the soleus muscle force using the PCSA relative to the other triceps muscles 
(gastroc. med and lat.) would premise that the force-potential due to the force length/velocity 
relationship and activation of all triceps surae muscles are equal. This assumption cannot be correct 
because the gastrocnemi are biarticular muscles. For this reason, we would not like to include this 
approach in our manuscript but rather stay on the more direct findings.   
 
We softened our formulation by deleting the 40% in revised manuscript (page: 7, line: 280). 
 
 
Comment:  
Lines 304-309 - The authors make a good case for why small changes in velocity would 
require an increase in activation and therefore cost. This effect should be seen in EMG recordings. It 
would seem that the argument could be strengthened by showing this as it would provide a more 
causal link between the change in muscle level function and organismal level cost. 
 
Response:  
Thanks for this comment. We did not go into any correlation analysis in the study 
because the parameter of surface EMG activation does not reflects active muscle volume adequately.   
However, a significant correlation can be found for the force-length-velocity potential (EMG mean: r = 
-0.504, p = 0.028; EMG max: r = -0.525, p = 0.021; EMG integral: : r = -0.504, p = 0.028). Please note 
that the processing of the EMG signal can affect the correlation coefficients but not the significance 
itself (p < 0.05). Here a 20 Hz low pass filter was used after rectification and preprocessing with a high 
pass filter of 50 Hz.  
Given the mentioned limitation, the observed correlation might provide a cautious indication that a 
decreased EMG activity is associated with a higher force-length-velocity potential of the soleus muscle 
during the stance phase of running and that may affect the metabolic cost.  
 
We added the association between EMG activity and force-length-velocity potential in the revised 
manuscript without an extended interpretation because, as we mentioned before, the active muscle 
volume cannot be assessed accurately from the EMG activity (page: 6, line: 255; page: 7, line: 291).  
 
 
Comment:  
Line 334-335 – There seems to be some discrepancy regarding activation in here. The 
implication seems to be that muscle activation is higher in early stance to enable the tendon to be 
stretched, and then recoil to slow shortening velocity in the later part of stance. Yet a central claim of 
the paper is that cost is lower when shortening velocity is lower, due to a lower requirement for 
activation. It seems like the variation in required activation could balance out over the course of a 
stance phase? Could it be clarified as to why the early increase in activation to enable tendon stretch 
doesn’t seem to be costly in the way that the latter reduction is deemed to be cheap? 
 
Response:  
Thanks for this comment. The rationale of this argumentation is that the observed 
activation pattern can be interpreted as appropriate for a coordinated MTU interaction during the 
running task with respect to economy. We changed the formulation in the respective section as follows 
(page: 7, line: 322): 
“The soleus produces mechanical work/energy for the lift and acceleration of the body throughout the 
entire stance phase. In the first half, where the MTU is elongated, the fascicles actively shorten. This 
means that a part of the mechanical energy of the human body is transferred to the tendon. Also, in 
this setting the muscle fascicles produce work under favorable conditions due to the force-length and 
force-velocity relationships (both potentials in this phase were very high) and save work as strain 
energy in the tendon. In the second half, the tendon strain energy is returned and at the same time the 
fascicles produce work by active shortening at a reduced force-velocity potential (fascicle shortening 
velocity is higher in this phase). The higher shortening velocity is associated with a reduction in the EMG 
activity and an increase in belly gearing. It has been suggested that increased gearing at fast shortening 
velocities and lower forces is a mechanism that allows particularly slower type fascicles to be more 
effective in generating forces [40]. This supports the idea that the observed activation pattern fostered 
an economical MTU interaction during running.”  
 
 
 
Comment:  
Line 345 – typo “were”? 
 
Response: 
We corrected the typo accordingly.  
 
 
 
Comment:  
Line 375 – The study doesn’t seem to show that energy consumption is related to the 
force-length-velocity potential, but rather just the force-velocity potential. 
 
Response:  
The force-length-velocity potential is the product of the force-length and force-velocity 
potential and was inversely associated with the energetic cost like the force-velocity potential. The 
force-length potential was consistently high among the participants and showed no significant 
association to the energetic cost. This indicates that the reason for the association of the force-length-
velocity potential to the energetic cost was caused by the observed correlation of the force-velocity 
potential, i.e. variability in the force-length-velocity potential relied on the variability of the force-
velocity potential that cohered the variability of the energetic cost. However, as we mentioned in the 
discussion, a high force-length potential is also important for economical muscle force generation. 
 
 
 
 
Response to referees 
Response to referee 1 
Comment: 
The authors have addressed all my previous concerns in a careful manner. 
Response:  
Once again thank you for your valuable review.  
Comment: 
There  remains  one  further  comment  that  they  may  choose  to  consider  for  the 
manuscript, and it still concerns the choice of Vmax. I appreciate the further analysis that the authors 
have attempted, to provide a value of Vmax for the Soleus. However, it should be noted that the 
running velocity of 2.5 m/s is not all that fast, and indeed the EMG averages less than 50%. As such, it 
is likely that the fastest muscle fibres will not have been recruited, and hence the weighted mean taken 
for Vmax may thus be an overestimate. Coupled to this, with more than half of the muscle inactive, 
the actual Vmax may be less than its constituent fibres (for additional reasons: Holt et al. Proc Roy Soc 
B  2014).  If  the  Vmax  for  the  Soleus  were  less  than  the  estimated  6.77  L/s  for  this  experimental 
situation, then it is likely that the actual spread of Force‐velocity potentials would be larger than shown 
in Fig. 3. It is thus worth considering that you have actually resulted with a conservative evaluation of 
the importance of the force‐velocity potential. 
Response:  
Thank you for this comment. We agree with the opinion of the reviewer that Vmax during 
submaximal  running  in  vivo  might  be  influenced  by  factors  not  considered  in  our  calculation  (e.g. 
selective slow fiber type recruitment, muscle resistance to shortening). Referring to the results of Holt 
et al. (2014), Vmax could be in deed lower. We now acknowledge this aspect in the respective paragraph 
of the revised manuscript (see below, page: 8, line: 378). We also added the aspect of more economical 
selective slow fiber type recruitment for submaximal slow contractions as during running to a more 
comprehensive paragraph in the discussion section of the revised manuscript (see response to reviewer 
2, page: 9, line: 399). 
“To assess the force‐velocity potential we used a biologically funded value of Vmax, based on in vitro 
studies human soleus, i.e. 6.77 L0 s−1 (279.0 ± 34.9 mm s−1). However, during submaximal running in 
vivo the lower activation level and selective slow fiber type recruitment may affect the actual force‐
velocity potential of the soleus muscle.  
Response to referee 2 
General:  
Once again thank you for your valuable review. 
Comment:  
I find the rationale of this Herzog and Fontana paper quite difficult to follow, particular 
with regards to how they cite other studies. They attempt to distinguish between activation and force 
which, while may have some bearing on the mechanism responsible, does nothing to counter the 
Appendix D
finding that shifts in optimum length not predicted by the sliding filament theory occur with changing 
contractile conditions. For the purposes of this argument, what I take from this study is that if you 
change muscle force production, optimum length shifts (Fig. 3 Herzog and Fontana 2016). This is in line 
with other in vivo studies of this phenomenon (Ichinose et al., 1997; Kwah et al 2013), and makes it 
less obvious that this potential effect should be ignored in the present paper.  
This does not change the arguments of this paper, and I leave this to the authors discretion, but it is 
my feeling that it would be a stronger paper if it shifted its focus from the conviction that force‐length 
and force‐velocity potential of the muscle dictates in vivo performance (if this were true, Hill‐type 
muscle models would do a better job (Lee et al., 2013; Dick et al., 2017)) to an argument that multiple 
factors influence muscle mechanical and energetic performance under dynamic conditions, and that 
this paper seeks to understand to what extent force‐velocity effects dictate energetic performance. 
It’s a subtle shift that would require minor rewording throughout, but it’s my feeling that this would 
much better reflect that state of the field. Reference to the Herzog and Fontana paper is made again 
in the discussion, the authors may wish to consider how well it supports their argument and the 
contradictory findings of other in vivo papers. 
 
 
Response:  
 
 
First note: Fontana and Herzog (2016) paper and lack of shift in optimal length 
As described by Fontana  and Herzog  (2016) – and  we agree on that – the  shift in optimal length 
reported in the former human in vivo study of Ichinose et al., (1997) is constrained by the experimental 
setup because the authors controlled the torque (i.e. used a percentage of the maximum force) and not 
the muscle activation in each of the assessed knee joint angles. Due to the force‐depended elongation 
of tendon and aponeurosis, the result of a shift in optimal fascicle length is to be expected and the 
conclusion of a shift in optimal length is misleading. The experimental constrain from the Ichinose et 
al., (1997) study was overcome in the Fontana and Herzog (2016) study by referring the fascicle length 
to activation level, leading to the lack of shift in optimal length.  
 
We added the following text in the revised manuscript (page: 9, line: 395):  
 
“The discrepancy of the in vitro and in vivo evidence clearly warrants future investigation to elucidate 
the shifting length phenomenon in the context of in vivo submaximal locomotion. Given the current 
human in vivo evidence [1], we can argue that mapping the submaximal fascicle operating length onto 
the force‐length curve in the present in vivo study should not affect the findings.” 
 
 
Second note: Complexity of energetic cost and muscle contraction 
We  agree  with  the  opinion  of  the  reviewer  that  multiple  factors  may  affect  energetic  cost  during 
submaximal  human  running  and  further  that  simple  models  not  reflect  the  complexity  of  muscle 
mechanical  and  energetic  performance  under  dynamic  conditions  appropriately.  To  address  the 
reviewers general comment we added the following paragraph to the limitations section of the revised 
manuscript (page: 9, line: 400): 
 
“In the present study we focused on the understanding of the contribution of the force‐length and force‐
velocity potential to the energetic cost of running and we showed that the force‐velocity potential is 
inversely related to the energetic cost, explaining about one third of its variance. We argue that an 
increase of active muscle volume due to the decreased force‐velocity potential would increase the 
energetic  cost  of  running.  However,  it  must  be  acknowledged  that  the  energetic  cost  of  muscle 
contraction is complex and multifactorial. Independent of active muscle volume, in higher shortening 
velocities the rate of cross‐bridges cycling is increased and as a consequence the consumed energy. In 
our study, shortening velocities of the soleus muscle were in average 0.118 Vmax throughout the stance 
phase, a range where the rate of ATP hydrolysis shows a steep increase [2]. Furthermore, in submaximal 
intensity contractions as during our investigated running velocity selective slow fiber type activation 
might decrease the energetic cost by reducing the contribution of energetically more expensive fast 
twitch fibers.” 
 
 
Comment:  
This  cost  of  work  argument  could  entirely  be  thought  of  as  cost  of  muscle  fiber 
shortening argument. Which is obviously very pertinent to this paper. It is my opinion that this paper 
would be strengthened by greater discussion of this complexity and what the data presented here do 
to advance our understanding ‐i.e. cheap work (shortening) may be possible in some cases (Holt et al., 
2014; Curtin et al., 2019), but in this case, more rapid active muscle shortening does seem to incur 
energetic costs. But again, I leave this to the authors discretion. 
 
Response:  
Thanks for this comment. We added the aforementioned paragraph to the manuscript 
to provide a broader discussion of this topic.   
 
 
Comment:  
Line  104‐103  –  it  therefore  seems  misleading  to  say  ‘as  a  function  of  their 
experimentally assessed force‐velocity relationships’. Line 126‐127 – similar issue in that this seems to 
suggest experimental measurements of force‐velocity relationships in this study. 
 
Response:  
To avoid any confusion we reworded the sentences as follows: 
 
“In the present study, we investigated the operating length and velocity of the soleus muscle fascicles 
(i.e. bundles of fibers) during running as a function of the experimentally determined force‐length and 
assessed  force‐velocity  relationships  (i.e.  force‐length  and  force‐velocity  potential)  and  their 
association to the energetic cost of running. “ 
 
“The derived optimal fascicle length for force production was further used to calculate the force‐velocity 
relationship of the soleus fascicles.” 
 
 
 
References 
1.  Fontana H de B, Herzog W. 2016 Vastus lateralis maximum force‐generating potential occurs at optimal fascicle length 
regardless of activation level. Eur. J. Appl. Physiol. 116, 1267–1277. (doi:10.1007/s00421‐016‐3381‐3) 
2.  Barclay CJ. 2015 Energetics of contraction. Compr. Physiol. 5, 961–995. (doi:10.1002/cphy.c140038) 
 
 
 
 
 

The force-length-velocity potential of the human soleus muscle is related to the energetic cost of running.
Bohm, Sebastian,Mersmann, Falk,Santuz, Alessandro,Arampatzis, Adamantios