Pressure Force in the Upper Ankle Joint

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Manuscript: “Pressure force in the upper ankle joint”
Decision: Minor revision

This manuscript addresses the pressure force in the upper ankle joint during body tilting, and develops a model to calculate joint pressure under varying body postures. The authors use a flat bar model to simulate muscle and gravitational forces, and then apply these to a human example to predict joint pressure force during forward and backward body tilt. The paper aims to offer a better understanding of how body tilt influences the pressure force at the ankle joint, which is critical for sports biomechanics and rehabilitation.

However, there are several Minor methodological issues, incorrect unit usage, and assumptions that need correction before publication. The authors also need to improve clarity in some sections and ensure statistical validity to better support their conclusions.

Concerns:
The manuscript reports forces in “kG” (kilograms) instead of Newtons (N), and moments in kG·m instead of N·m. This introduces confusion, as the kG unit is typically used for force in everyday contexts (kgf), while in physics and biomechanics, force should be reported in Newtons.

The authors assume constant muscle moment arms (rTRI and rTA) for the entire tilt range, stating these values as anatomically constant. However, these moment arms are known to vary with ankle angle and subtalar posture, which is an important factor in determining joint forces. Either justify the constant moment arm assumption with cited anatomical studies showing that these values are relatively stable across tilting ranges, or perform a sensitivity analysis across a reasonable range of moment arms (±25–50%) and show how the results change.

While the authors provide results based on the flat bar model, there is no external validation of the model's predictions with real-world data. The reported joint pressure forces (e.g., 5.23 times body weight) are plausible, but they lack validation from actual instrumented ankle joint data or comparison with literature.

The introduction and the abstract refer to the study as involving both static and dynamic situations, but the model only accounts for quasi-static body tilting in the sagittal plane (without considering dynamic effects or inertial forces).

The paper claims that the joint pressure force vector always passes through the upper ankle joint axis regardless of tilt. While this is true for the idealized hinge model, the human ankle joint is more complex, with non-ideal contact patch and moments during motion.

A light proofread is recommended to fix minor grammatical errors (e.g., "backwads" → "backwards," "constans" → "constants") and ensure subject-verb agreement throughout the text.

While figures are helpful, some captions need to be more self-contained. For example, Table 1 could be simplified, and Figure 1 could be clarified to better explain the anatomical model. Additionally, the units and symbols should be consistent throughout.

Ensure that symbols like CoG1, CoG2, and rTRI are clearly defined on first use and are consistent across the manuscript.

Author Response

Review 1

We are very grateful for your thoughtful review of our work and all your suggestions. We have made every effort to improve our manuscript based on the reviewer's recommendations. Detailed references are provided below.

This manuscript addresses the pressure force in the upper ankle joint during body tilting, and develops a model to calculate joint pressure under varying body postures. The authors use a flat bar model to simulate muscle and gravitational forces, and then apply these to a human example to predict joint pressure force during forward and backward body tilt. The paper aims to offer a better understanding of how body tilt influences the pressure force at the ankle joint, which is critical for sports biomechanics and rehabilitation.

However, there are several Minor methodological issues, incorrect unit usage, and assumptions that need correction before publication. The authors also need to improve clarity in some sections and ensure statistical validity to better support their conclusions.

 

Concerns:

Comment 1:

The manuscript reports forces in “kG” (kilograms) instead of Newtons (N), and moments in kG·m instead of N·m. This introduces confusion, as the kG unit is typically used for force in everyday contexts (kgf), while in physics and biomechanics, force should be reported in Newtons.

Answer 1:

As suggested by the reviewer, we have added N and Nm in addition to the kG and kGm converters.

Comment 2:

The authors assume constant muscle moment arms (rTRI and rTA) for the entire tilt range, stating these values as anatomically constant. However, these moment arms are known to vary with ankle angle and subtalar posture, which is an important factor in determining joint forces. Either justify the constant moment arm assumption with cited anatomical studies showing that these values are relatively stable across tilting ranges, or perform a sensitivity analysis across a reasonable range of moment arms (±25–50%) and show how the results change.

Answer 2:

It is assumed that the muscle force arms are generally constant (with minor exceptions for some muscles, but these changes are minor). The force arm of the triceps calf muscle is constant at 4 cm, a feature of human anatomy. During tilting, the muscle force changes, but the arm remains stationary. The arm that changes during tilting is the gravity arm (arm of the force acting from the center of gravity). Movement at the ankle joint is a result of the interplay of torques. On the one hand, there is the gravitational moment (variable arm, constant force), and on the other, the muscular moment (constant arm, variable force).

Comment 3:

While the authors provide results based on the flat bar model, there is no external validation of the model's predictions with real-world data. The reported joint pressure forces (e.g., 5.23 times body weight) are plausible, but they lack validation from actual instrumented ankle joint data or comparison with literature.

Answer 3:

Indeed, we do not have measurements of the pressure force at the ankle joint. We calculated it based on indirect measurements, i.e., the weight of the entire human body and the weight of a human body without feet. For simplicity, we assume that the human body behaves like a rigid object when leaning forward. By making this assumption, we extrapolate the proportions of the results obtained in the flat bar experiment to the human body.

Our result is undoubtedly an approximation. With our study, we wanted to emphasize that we need to consider joint movement and gravity differently than before. We were also concerned that the lack of experimental evidence in humans might diminish the value of our work until we found publications stating that increased ankle joint stability in dorsiflexion allows it to withstand pressure forces of up to 450% of body weight

[Stauffer, R.N.; Chao, E.Y.; Brewster, R.C. Force and Motion Analysis of the Normal, Diseased, and Prosthetic Ankle Joint. Clin. Orthop. Relat. Res. 1977, 189–196.]

[Procter, P.; Paul, J.P. Ankle Joint Biomechanics. J. Biomech. 1982, 15, 627–634, doi:10.1016/0021-9290(82)90017-3.]

or

During running, the compression forces in the upper ankle joint can exceed even 13 times the body weight.

[Burdett, R.G. Forces Predicted at the Ankle during Running. Med. Sci. Sports Exerc. 1982, 14, 308–316, doi:10.1249/00005768-198204000-00010.]

The research results in the above-mentioned works show that our thinking is heading in the right direction.  Additional experimental studies will undoubtedly be needed to demonstrate the actual pressure force in the ankle joint.

Comment 4:

The introduction and the abstract refer to the study as involving both static and dynamic situations, but the model only accounts for quasi-static body tilting in the sagittal plane (without considering dynamic effects or inertial forces).

Answer 4:

Indeed, the model studies primarily concern static situations, although we also demonstrate how gravitational and muscular forces interact during body tilt, which is important for considerations of human body dynamics.

For clarity, we have used the wording suggested by the reviewer, i.e., instead of dynamic --> quasi-dynamic.

Comment 5:

The paper claims that the joint pressure force vector always passes through the upper ankle joint axis regardless of tilt. While this is true for the idealized hinge model, the human ankle joint is more complex, with non-ideal contact patch and moments during motion.

Answer 5:

The reviewer is correct that the contact plane is more than just an axis. However, in the biomechanics of the upper ankle joint, an approximation is used for purely theoretical purposes. We followed this approach and, in the description of our approach, we indicate that, to simplify description and interpretation, we assume that the force is applied to the upper ankle joint axis. We noted this in the description of the methods.

Comment 5:

A light proofread is recommended to fix minor grammatical errors (e.g., "backwads" → "backwards," "constans" → "constants") and ensure subject-verb agreement throughout the text.

Answer 5:

The text has been corrected according to the reviewer's suggestion.

Comment 6:

While figures are helpful, some captions need to be more self-contained. For example, Table 1 could be simplified, and Figure 1 could be clarified to better explain the anatomical model. Additionally, the units and symbols should be consistent throughout.

Answer 6:

We have clarified the description of the first figure. We have added unit conversions to Table 1, i.e., kG and kGm to N and Nm.

We typically use the units kG and kGm in our research, but we understand that biophysicists and biomechanics specialists, especially when performing computer simulations, prefer to have values ​​expressed in N or Nm.

Comment 7:

Ensure that symbols like CoG1, CoG2, and rTRI are clearly defined on first use and are consistent across the manuscript.

Answer 7:

In the methods section, these abbreviations are expanded and explained.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript addresses ankle joint loading through a mechanical model and a flat-bar experiment. The topic is relevant, but several major issues must be addressed:

- Introduction & References: The background is limited and relies heavily on self-citations. Please expand on recent independent studies (2020–2024) on in-vivo joint pressure, EMG-assisted gait, and computational ankle models. Clearly state the research gap and novelty.

- Units & Consistency: Forces are reported in “kG,” which is ambiguous. Convert all forces to SI units (N, m). Provide at least one worked example of the conversion (Appendix).

- Methods: Important details are missing (number of trials, calibration of the dynamometer, angle measurement method/accuracy). These must be added to ensure reproducibility.

- Equations: Equations (5–14) lack units. Please present them dimensionally consistent, with SI units, and include step-by-step sample calculations in an Appendix.

- Results & Presentation: Table 1 should use SI units, fewer decimals, and include variability (SD). Captions should be self-contained, stating units and sample size.

- Plausibility: Very high force values (e.g., FJ ≈ 4750 N) should be compared with published physiological data, or clarified as theoretical extrapolations.

- Discussion/Conclusions: Clinical implications are overstated. Please add a Limitations section (including static assumptions, simplified geometry, and lack of validation).

- Language: English is understandable but needs revision for clarity, grammar, and style.

Author Response

Reviewer 2

We are very grateful for your thoughtful review of our work and all your suggestions. We have made every effort to improve our manuscript based on the reviewer's recommendations. Detailed references are provided below.

This manuscript addresses ankle joint loading through a mechanical model and a flat-bar experiment. The topic is relevant, but several major issues must be addressed:

Comment 1:

- Introduction & References: The background is limited and relies heavily on self-citations. Please expand on recent independent studies (2020–2024) on in-vivo joint pressure, EMG-assisted gait, and computational ankle models. Clearly state the research gap and novelty.

Answer 1:

We cite our earlier studies in the manuscript because it is necessary to explain the steps taken in the current manuscript. We believe this is justified. It allows us to avoid extensive descriptions of experimental studies that would otherwise have been included in the current manuscript.

 

As suggested by the reviewer, two citations from the last two years have been included in the manuscript regarding: In Vivo Analysis of Ankle Joint Kinematics and  An EMG-Based GRU Model for Estimating Foot Pressure.

Ruan, Y.; Wang, S.; Zhang, N.; Jiang, Z.; Mei, N.; Li, P.; Ren, L.; Qian, Z.; Chang, F. In Vivo Analysis of Ankle Joint Kinematics and Ligament Deformation of Chronic Ankle Instability Patients during Level Walking. Front. Bioeng. Biotechnol. 2024, 12, 1441005, doi:10.3389/fbioe.2024.1441005.

Gunaratne, P.N.; Lee, Y.J.; Kim, Y.J.; Lee, Y.J.; Lee, Y.J. An EMG-Based GRU Model for Estimating Foot Pressure to Assist Ankle Joint Rehabilitation. Sensors 2025, 24, 6666, doi:10.3390/s24206666.

Comment 2:

- Units & Consistency: Forces are reported in “kG,” which is ambiguous. Convert all forces to SI units (N, m). Provide at least one worked example of the conversion (Appendix).

Answer 2:

We converted all values from kG to N and kGm to Nm. Both in the examples and in the summary table (Table 1).

Comment 3:

- Methods: Important details are missing (number of trials, calibration of the dynamometer, angle measurement method/accuracy). These must be added to ensure reproducibility.

Answer 3:

• We add the text to de method section as follow:” The Ruhhy® electronic dynamometer was calibrated using certified standard weights across its measurement range. The device was first zeroed, then incremental loads were applied to verify and adjust readings. Accuracy was confirmed with independent reference weights”.
• We calculated the deflection angle based on the mathematical formula knowing the value of the arm of gravity and the height of the point of gravity. This is described in methods section 2.4. Measurements of the gravity arm and the distance from the axis of rotation to the center of gravity for the analog model were performed three times, and then the average was taken. This information has been added to the methods section.
• For the human, we calculated the gravity arm based on the deflection angle from the model study and the CoG2 cocalization. For the human, these were purely mathematical calculations, requiring no repetition.

Comment 4:

- Equations: Equations (5–14) lack units. Please present them dimensionally consistent, with SI units, and include step-by-step sample calculations in an Appendix.

Answer 4:

We've updated the units as suggested. We're not including the detailed conversion in the appendix, as it would be a short, and perhaps rather obvious, note. However, if the reviewer believes it should still be included, we'll certainly include it.

Comment 5

- Results & Presentation: Table 1 should use SI units, fewer decimals, and include variability (SD). Captions should be self-contained, stating units and sample size.

Answer 5:

Measurements of the model's gravity arms were performed three times at each position, from neutral to maximum anterior and posterior excursion. This information has been added to the methods section.

Comment 6:

- Plausibility: Very high force values (e.g., FJ ≈ 4750 N) should be compared with published physiological data, or clarified as theoretical extrapolations.

Answer 6:

The methods section in our manuscript states that the actual model studies were extrapolated to the human body.

We were surprised by the values ​​obtained, but experimental data from other teams seem to confirm that forces significantly exceeding the total body weight during flexion act on the ankle joint. Suffice it to cite publications stating that increased ankle joint stability in dorsiflexion allows it to withstand pressure forces of up to 450% of body weight.

[Stauffer, R.N.; Chao, E.Y.; Brewster, R.C. Force and Motion Analysis of the Normal, Diseased, and Prosthetic Ankle Joint. Clin. Orthop. Relat. Res. 1977, 189–196.]

[Procter, P.; Paul, J.P. Ankle Joint Biomechanics. J. Biomech. 1982, 15, 627–634, doi:10.1016/0021-9290(82)90017-3.]

or

During running, the compression forces in the upper ankle joint can exceed even 13 times the body weight.

[Burdett, R.G. Forces Predicted at the Ankle during Running. Med. Sci. SportsExerc. 1982, 14, 308–316, doi:10.1249/00005768-198204000-00010.]

The research results in the above-mentioned works show that our thinking and our experimets is heading in the right direction. Additional experimental studies will undoubtedly be needed to demonstrate the actual pressure force in human the ankle joint.

Comments 7:

- Discussion/Conclusions: Clinical implications are overstated. Please add a Limitations section (including static assumptions, simplified geometry, and lack of validation).

Answer 7:

Suggested changes regarding clinical implications have been implemented as weel as study limitation section was added.

Comment 8:

- Language: English is understandable but needs revision for clarity, grammar, and style.

Answer 8:

The style of the English language was improved.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

“Best of all, I hope you always report good quality research and enjoy it.”

 

Thank you for the opportunity to review your manuscript. First, I would like to thank you for your interesting reading of your manuscript. This study holds significant academic significance in that it elucidates the pressure force in the upper ankle joint not as a simple weight-dependent mechanism, but as a vectorial sum of body weight and muscle strength, and quantifies this through mathematical modeling. In particular, the specific presentation of load changes (5.23x and 3.57x, respectively) according to anterior and posterior inclinations and the role of muscles will serve as valuable reference material in the fields of clinical rehabilitation, gait analysis, and sports science. Overall, your study offers a novel interpretation of ankle joint pressure dynamics during static standing, and it is of high academic value as it complements aspects overlooked in the existing literature. Finally, I would like to express my sincere appreciation for the thorough experimental approach and theoretical reflection you demonstrated during the writing of this study. I am confident that this paper, if refined and published, will mark a significant milestone in ankle joint biomechanics research.

 

Major Comments:

None.

 

Minor Comments:

 

< Introduction >

(Line 41-44) "In the dynamics of the human body, the analysis of forces acting on the upper ankle joint has long been a focus of attention for biomechanical researchers in medicine and sports. In this context, muscular force, gravity, and pressure force (described by intra-articular pressure) are mentioned, but without specific connections between them.”

• The term "specific connections" is ambiguous. A clearer definition, such as "causal mechanisms" or "quantitative relationships," would enhance academic rigor.

 

(Line 45-47) “Currently, the professional literature contains many reports on the distribution of pressure in the upper ankle joint in various foot positions [1] [2] [3] [4]. However, there is a lack of theoretical explanation for the observed phenomena.”

• “lack of theoretical explanation” is too general. It would be helpful to clarify which specific theoretical models (e.g., biomechanical load models, musculoskeletal dynamics) are missing.

 

(Line 54-57) “In this context, the foot is like an element of the ground [6] [7] [8] and should not be included in the weight of the rest of the body leaning on the upper ankle joint. Meanwhile, the weight of the foot based on the ground is included in the weight of the leaning body [9] [10] [11], which is an incorrect approach.”

• "Incorrect approach" is a rather assertive and strong expression in academic writing. It is better to revise it to a more neutral and evidence-based expression, such as "methodologically inaccurate" or "conceptually inconsistent."

 

(Line 58-59) “In addition, joint pressure force is commonly tested excluding muscle work, because the tests are conducted on cadavers [1] [3].”

• It's important to point out the limitations of cadaver studies. However, the expression "excluding muscle work" is overly simplistic. → Example: "because cadaveric testing does not account for active muscular contraction."

 

(Line 62-64) “The pressure in the upper ankle joint increases from the heel strike phase and reaches a maximum during the last phase of support.”

• In biomechanics literature, the terms heel strike → stance → toe-off are standard. Replacing "last phase of support" with "terminal stance" is more technical.

 

(Line 80-81) “Thanks to this, the upper ankle joint becomes "closely packed" and therefore as stable as possible [10].”

• "As stable as possible" is somewhat of an exaggeration. → It is more academically appropriate to specify a specific situation, such as "maximally stabilized under dorsiflexion."

 

< Materials and Methods >

(Line 213-215) “Since these two axes are slightly deviated from each other, the concept of one resultant axis of the upper ankle joint is used to simplify the explanation.”

• The explanation is adequate, but "simplify the biomechanical modeling" is more academically appropriate than "simplify the explanation."

 

(Line 238-240) “When an object is in a vertical position, the arm of the force of gravity is zero, and each deflection from the vertical at an angle β generates an arm of the force, and therefore, the gravitational moment.”

• The sentences are overly long and repetitive. → “At vertical alignment, the gravitational arm is zero; any deflection at angle β generates a gravitational moment.”

 

< Results >

(Line 393-397) “Similarly, the values ​​of the gravity force W_TRI calculated from the principle of the equality of torques or from the principle that twice the approach to the axis of rotation doubles the weight at that point, which are W_TRI=5.297 kg (12) and 5.296 kg (W_TRI=2×2.648 because W_CoG2=2.648 kg), respectively, match.”

• The explanation is lengthy and redundant. The point is that “the two calculations are numerically equivalent,” so it would be better to simplify it.

 

(Line 443-444) “In the unloaded foot, the sum of gravity and muscle force does not occur, so there is no observed joint pressure force (Fig. 6A).”

• In actual physiology, resting muscle tone and passive tissue tension exist, so the expression “no observed joint pressure force” is overly definitive.

 

(Line 495-496) “Of all human positions, from leaning forward to backward with balance, the neutral position has the least pressure on the upper ankle joint.”

• This is practically a self-evident conclusion. It would be better to delete this sentence or reinforce it with experimental data, such as "This has also been experimentally confirmed."

 

(Line 611-612) “It has been shown that muscle strength (F_TRI) and joint pressure force (F_J) decrease as one approaches the vertical.”

• This is generally an expected conclusion. What matters here is not simple confirmation, but how well the experimental values ​​match the theoretical model. Presenting the model-experiment agreement (% error) strengthens scientific rigor.

 

< Discussion >

(Line 619-620) “According to some authors, the entire maximum body weight concentrated in the human overall center of gravity in an upright position falls on the talus trochlea.”

• The reliability of the cited reference [17] is weakened by the lack of specific data (whether it is experimental or theoretical). The nature of the source (experimental/theoretical/review) should be clarified.

 

(Line 624-626) “According to our findings, this is not the case, as the researchers cited above claim, that the upper ankle joint is loaded only by the body's weight and relieved when the body is tilted."

• While presenting counterarguments is good, directly presenting quantitative evidence strengthens the argument. Rather than simply contrasting the results, it's better to link them with something like, "Our results (FJ = 484 kg at forward tilt) clearly exceed the body's weight alone."

 

(Line 633-635) “In other scientific reports [2] [10], the authors indicate that the main compressive force on the upper ankle joint during walking is the force generated by the contraction of the triceps calf muscle.”

• The discussion mixes walking and static standing situations, making the comparison ambiguous. To ensure rigor, the differences between the walking phase (stance phase) and this study (static anterior-posterior tilt model) must be distinguished.

 

(Line 657-660) “Generally, tilting the body is not energetically beneficial; therefore, the body strives to limit gravitational moments by bringing the projection of the center of gravity (CoG2) as close as possible to the axis of rotation (minimizing the length of the gravity arm), thereby reducing muscle force.”

• This is an interesting physiological interpretation, but without citing electromyography (EMG) or oxygen consumption studies, it remains speculative. Additional citations are needed.

 

(Line 670-672) “The consequence of this is an increase in joint pressure, which, in extreme situations, repeated many times, can lead to damage to the joint cartilage and degenerative changes.”

• While the clinical implications are well-connected, this study did not prove a direct causal relationship with joint damage. It would be desirable to mitigate this to the extent of “can be associated with.”

 

(Line 672-674) “Too much body weight hurts the upper ankle joint because the increased weight forces the increased work of the triceps and calf muscles, which also increases joint pressure, affecting the risk of degenerative changes in this joint.”

• The expression "hurts" is colloquial. Correcting it to "adversely affects" or "increases mechanical stress on" would be more academic.

 

< Conclusion >

(Line 685-688) “The value of the pressure force in the upper ankle joint is the vector sum of the values ​​of two forces: the weight of the tilting body measured at the level of the proximal insertion of the muscle (the force of gravity at this point) and the force of the muscle applied to that point."

• While appropriate as a key conclusion, it is overly long. Simplifying it to "The ankle joint pressure force is the vector sum of gravitational and muscular forces" would improve readability.

 

(Line 712-715) “The triceps surae muscle force at maximum forward tilt of the body is the highest and is 3.29 times greater than the weight of the tilting part of the body (without feet). When the body is tilted backward and balanced by the tibialis anterior, this ratio is 1.51.”

• This is a very important conclusion. However, rather than reiterating the calculations repeated in the text, a summary that emphasizes the pattern, such as “Forward tilt requires over twice the muscle force compared to backward tilt, highlighting asymmetric loading patterns,” would be preferable.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Reviewer 3

Thank you for the opportunity to review your manuscript. First, I would like to thank you for your interesting reading of your manuscript. This study holds significant academic significance in that it elucidates the pressure force in the upper ankle joint not as a simple weight-dependent mechanism, but as a vectorial sum of body weight and muscle strength, and quantifies this through mathematical modeling. In particular, the specific presentation of load changes (5.23x and 3.57x, respectively) according to anterior and posterior inclinations and the role of muscles will serve as valuable reference material in the fields of clinical rehabilitation, gait analysis, and sports science. Overall, your study offers a novel interpretation of ankle joint pressure dynamics during static standing, and it is of high academic value as it complements aspects overlooked in the existing literature. Finally, I would like to express my sincere appreciation for the thorough experimental approach and theoretical reflection you demonstrated during the writing of this study. I am confident that this paper, if refined and published, will mark a significant milestone in ankle joint biomechanics research.

 Answer 1:

We are very grateful for all the words of appreciation for our achievements described in the manuscript.

Those words were truly needed, as we work hard, and it's rare, very rare, that we meet someone who understands our effort.

Thank you again for your positive feedback on our work. We are equally grateful for all your suggestions and tips regarding our manuscript. We have followed all the suggestions and hope that the current version of the text will be accepted for publication.

 

 

The reviewer was incredibly insightful in his fine-tuning of our text. It is undoubtedly much better in its current form.

 

Major Comments:

None.

 

Minor Comments 1:

< Introduction >

(Line 41-44) "In the dynamics of the human body, the analysis of forces acting on the upper ankle joint has long been a focus of attention for biomechanical researchers in medicine and sports. In this context, muscular force, gravity, and pressure force (described by intra-articular pressure) are mentioned, but without specific connections between them.”

• The term "specific connections" is ambiguous. A clearer definition, such as "causal mechanisms" or "quantitative relationships," would enhance academic rigor.

 

(Line 45-47) “Currently, the professional literature contains many reports on the distribution of pressure in the upper ankle joint in various foot positions [1] [2] [3] [4]. However, there is a lack of theoretical explanation for the observed phenomena.”

• “lack of theoretical explanation” is too general. It would be helpful to clarify which specific theoretical models (e.g., biomechanical load models, musculoskeletal dynamics) are missing.

 

(Line 54-57) “In this context, the foot is like an element of the ground [6] [7] [8] and should not be included in the weight of the rest of the body leaning on the upper ankle joint. Meanwhile, the weight of the foot based on the ground is included in the weight of the leaning body [9] [10] [11], which is an incorrect approach.”

• "Incorrect approach" is a rather assertive and strong expression in academic writing. It is better to revise it to a more neutral and evidence-based expression, such as "methodologically inaccurate" or "conceptually inconsistent."

 

(Line 58-59) “In addition, joint pressure force is commonly tested excluding muscle work, because the tests are conducted on cadavers [1] [3].”

• It's important to point out the limitations of cadaver studies. However, the expression "excluding muscle work" is overly simplistic. → Example: "because cadaveric testing does not account for active muscular contraction."

 

(Line 62-64) “The pressure in the upper ankle joint increases from the heel strike phase and reaches a maximum during the last phase of support.”

• In biomechanics literature, the terms heel strike → stance → toe-off are standard. Replacing "last phase of support" with "terminal stance" is more technical.

 

(Line 80-81) “Thanks to this, the upper ankle joint becomes "closely packed" and therefore as stable as possible [10].”

• "As stable as possible" is somewhat of an exaggeration. → It is more academically appropriate to specify a specific situation, such as "maximally stabilized under dorsiflexion."

 

< Materials and Methods >

(Line 213-215) “Since these two axes are slightly deviated from each other, the concept of one resultant axis of the upper ankle joint is used to simplify the explanation.”

• The explanation is adequate, but "simplify the biomechanical modeling" is more academically appropriate than "simplify the explanation."

 

(Line 238-240) “When an object is in a vertical position, the arm of the force of gravity is zero, and each deflection from the vertical at an angle β generates an arm of the force, and therefore, the gravitational moment.”

• The sentences are overly long and repetitive. → “At vertical alignment, the gravitational arm is zero; any deflection at angle β generates a gravitational moment.”

 

< Results >

(Line 393-397) “Similarly, the values ​​of the gravity force W_TRI calculated from the principle of the equality of torques or from the principle that twice the approach to the axis of rotation doubles the weight at that point, which are W_TRI=5.297 kg (12) and 5.296 kg (W_TRI=2×2.648 because W_CoG2=2.648 kg), respectively, match.”

• The explanation is lengthy and redundant. The point is that “the two calculations are numerically equivalent,” so it would be better to simplify it.

 

(Line 443-444) “In the unloaded foot, the sum of gravity and muscle force does not occur, so there is no observed joint pressure force (Fig. 6A).”

• In actual physiology, resting muscle tone and passive tissue tension exist, so the expression “no observed joint pressure force” is overly definitive.

 

(Line 495-496) “Of all human positions, from leaning forward to backward with balance, the neutral position has the least pressure on the upper ankle joint.”

• This is practically a self-evident conclusion. It would be better to delete this sentence or reinforce it with experimental data, such as "This has also been experimentally confirmed."

 

(Line 611-612) “It has been shown that muscle strength (F_TRI) and joint pressure force (F_J) decrease as one approaches the vertical.”

• This is generally an expected conclusion. What matters here is not simple confirmation, but how well the experimental values ​​match the theoretical model. Presenting the model-experiment agreement (% error) strengthens scientific rigor.

 

< Discussion >

(Line 619-620) “According to some authors, the entire maximum body weight concentrated in the human overall center of gravity in an upright position falls on the talus trochlea.”

• The reliability of the cited reference [17] is weakened by the lack of specific data (whether it is experimental or theoretical). The nature of the source (experimental/theoretical/review) should be clarified.

 

(Line 624-626) “According to our findings, this is not the case, as the researchers cited above claim, that the upper ankle joint is loaded only by the body's weight and relieved when the body is tilted."

• While presenting counterarguments is good, directly presenting quantitative evidence strengthens the argument. Rather than simply contrasting the results, it's better to link them with something like, "Our results (FJ = 484 kg at forward tilt) clearly exceed the body's weight alone."

 

(Line 633-635) “In other scientific reports [2] [10], the authors indicate that the main compressive force on the upper ankle joint during walking is the force generated by the contraction of the triceps calf muscle.”

• The discussion mixes walking and static standing situations, making the comparison ambiguous. To ensure rigor, the differences between the walking phase (stance phase) and this study (static anterior-posterior tilt model) must be distinguished.

 

(Line 657-660) “Generally, tilting the body is not energetically beneficial; therefore, the body strives to limit gravitational moments by bringing the projection of the center of gravity (CoG2) as close as possible to the axis of rotation (minimizing the length of the gravity arm), thereby reducing muscle force.”

• This is an interesting physiological interpretation, but without citing electromyography (EMG) or oxygen consumption studies, it remains speculative. Additional citations are needed.

 

(Line 670-672) “The consequence of this is an increase in joint pressure, which, in extreme situations, repeated many times, can lead to damage to the joint cartilage and degenerative changes.”

• While the clinical implications are well-connected, this study did not prove a direct causal relationship with joint damage. It would be desirable to mitigate this to the extent of “can be associated with.”

 

(Line 672-674) “Too much body weight hurts the upper ankle joint because the increased weight forces the increased work of the triceps and calf muscles, which also increases joint pressure, affecting the risk of degenerative changes in this joint.”

• The expression "hurts" is colloquial. Correcting it to "adversely affects" or "increases mechanical stress on" would be more academic.

 

< Conclusion >

(Line 685-688) “The value of the pressure force in the upper ankle joint is the vector sum of the values ​​of two forces: the weight of the tilting body measured at the level of the proximal insertion of the muscle (the force of gravity at this point) and the force of the muscle applied to that point."

• While appropriate as a key conclusion, it is overly long. Simplifying it to "The ankle joint pressure force is the vector sum of gravitational and muscular forces" would improve readability.

 

(Line 712-715) “The triceps surae muscle force at maximum forward tilt of the body is the highest and is 3.29 times greater than the weight of the tilting part of the body (without feet). When the body is tilted backward and balanced by the tibialis anterior, this ratio is 1.51.”

• This is a very important conclusion. However, rather than reiterating the calculations repeated in the text, a summary that emphasises the pattern, such as “Forward tilt requires over twice the muscle force compared to backward tilt, highlighting asymmetric loading patterns,” would be preferable.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The revised manuscript has been significantly improved. The authors have adequately addressed all major comments, including updates to references, unit consistency, methodological details, and the addition of a clear Limitations section.

Only a minor issue remains:
- please include standard deviation (SD) values in Table 1 to reflect measurement variability.
- Overall, the paper is well revised and can be accepted after minor correction.

Comments on the Quality of English Language

 The text is clear and readable, with only minor grammatical or stylistic issues remaining. A brief final proofreading is recommended before publication.

Author Response

Reviewer 2 – round 2

 

Comment 1

Only a minor issue remains:

- please include standard deviation (SD) values in Table 1 to reflect measurement variability.

- Overall, the paper is well revised and can be accepted after minor correction.

 

Answer 1

Measurements of the model's gravity arms were performed three times at each position, from neutral to maximum anterior and posterior excursion. These standard deviations are included in Table 1.

 

Author Response File: Author Response.pdf