Crouch Gait Analysis and Visualization Based on Gait Forward and Inverse Kinematics

Round 1

Reviewer 1 Report

This paper focuses on analyzing and visualizing crouch gait which has important practical engineering significance. The research idea of the paper is clear and the derivation is correct. Simulation results demonstrate the effectiveness of the proposed method.

However, there are still some problems which the author should explain clearly in the paper.

1.      The meaning and importance of researching work about crouch gait should be mentioned in the abstract.

In the last sentence of the abstract (line12), the expression is not clear. It is suggested that the last two sentences should be combined into one sentence.

2.      As the paper mentioned in line 106, homogeneous transformation and Denavit- Hartenberg (DH) can be used to model the human model, so the advantages of quaternion-based solutions compared with other methods should be presented in the Introduction part.

3.      During crouching gait cycle, the position of pelvis(Σ0) keeps changing in vertical direction. Is it reasonable to set the position of pelvis as a global fixed frame?（line126）

4.      In 2.1.3, three method which calculating triangle gait workspace areas are introduced. The author should explain the function of introducing these three areas, and why these areas can be used as metric for evaluation the unnormal gait.

5.      The range of the total number of samples N is not given. (line154)

6.      In formula 20-22, the second should be .

7.      In the calculation formula 26, the problem that the gait data of left and right legs may be different is not considered. If this difference is taken into account, is it better to use the average or one-sided data? If the average value is used, what’s error of using the average value in different exercise states?

8.      Fig. 8 shows the experimental results, but does not give the number of sampling points in the paper.

9.      It is suggested a block diagram of calculation process using marked points ( in 3.1)is given in the paper, this will make the context of the article clearerly.

10.   In Table 1, six values are put forward as evaluation criteria, but some of these six values have little difference in different states. Which value best reflects the difference in different states? Is the index quantity enough for an experiment done in one cycle?

11.   What state does SWING in Figure 14 represent? Unclear description.

12.   This article doesn't make it clear in what form the visualization function is realized.

13.   In the conclusion, In the aspect of evaluation index, it quantitatively points out what problems have been solved and what functions have been realized.

Author Response

=========================================================

Rebuttal Letter

• Manuscript Crouch Gait Analysis and Visualization based on Gait Forward and
• Inverse Kinematics
• ID: applsci-1941749
• Submitted to: Applied Sciences/MDPI (Section: Applied Biosciences and Bioengineering, “Biomechanics and Human Motion Analysis”)
• Corresponding Author: Omar Arturo Domínguez-Ramírez
• Email: omar@uaeh.edu.mx

=========================================================

 

==============   Associate Editor   ==============

 

(I) Please revise your manuscript according to the referees’ comments and upload the revised file within 5 days.

(II) Please use the version of your manuscript found at the above link for your revisions.

(III) Please check that all references are relevant to the contents of the manuscript.

(IV) Any revisions made to the manuscript should be marked up using the “Track Changes” function if you are using MS Word/LaTeX, such that changes can be easily viewed by the editors and reviewers.

(V) Please provide a short cover letter detailing your changes for the editors’ and referees’ approval.

 

Response:

 

We authors do dearly acknowledge your disposition, time and effort in handling our paper. In accordance to your decision, and your instructions, we are formatting the revised manuscript as well as addressing Reviewers' queries and concerns, answering all questions and recommendations.

 

We do hope that our revised manuscript meets the expected quality to be considered for possible publication in this journal.

 

 

------     Reviewer 1     ------

General Assessment: This paper focuses on analyzing and visualizing crouch gait which has important practical engineering significance. The research idea of the paper is clear and the derivation is correct. Simulation results demonstrate the effectiveness of the proposed method.

However, there are still some problems which the author should explain clearly in the paper.

Answer:

We appreciate your time and effort to provide this assessment and this review. We have done our most effort to comply to your queries and comments, hope we have produced the appropriate answer to clarify all issues. Thanks for your detailed account.

In addition to the suggested adjustments to address your comments, a review and correction of grammar and typography was made for the entire paper. Also, the ORCID of all authors have been completed.

Comment 1:  The meaning and importance of researching work about crouch gait should be mentioned in the abstract. In the last sentence of the abstract (line12), the expression is not clear. It is suggested that the last two sentences should be combined into one sentence.

Answer:

We agree to mention the meaning and importance of the study of crouching gait, so the beginning and the end of the abstract were rewritten considering the suggestion made in line 12.

Some other writing corrections in the abstract have been made.

Modification introduced in revised manuscript:

(lines 1-3) Crouch gait is one of the most common gait abnormalities and it is usually caused by cerebral palsy. There are few works related to the crouch gait kinematics modeling, crouch gait  analysis, and visualization in both workspace and joint space.

 

(lines 11-13) Ultimately, forward and inverse kinematic methods could be applied in rehabilitation settings for the diagnosis and treatment of diseases derived from crouch gaits or other types of gait abnormalities.

Comment 2:  As the paper mentioned in line 106, homogeneous transformation and Denavit- Hartenberg (DH) can be used to model the human model, so the advantages of quaternion-based solutions compared with other methods should be presented in the Introduction part.

Answer:

The introductory paragraph of the section (Quaternions algebra for rotations) now is presented in the Introduction part in (lines 50-55).

Modification introduced in revised manuscript:

(lines 50-55) In addition, quaternions have been used to perform ori-

entations and rotations of objects in a 3D space [30], in areas such as computer graphics, multirotor tracking, control approaches, and also for kinematics and dynamics of rigid bodies [31]. The most used methods in robot kinematics are homogeneous transformation and Denavit-Hartenberg (DH). However, the free representation and gimbal lock avoiding of quaternions have allowed them to be used optimally for this purpose [32].

 

 

Comment 3:  During crouching gait cycle, the position of pelvis (Σ0) keeps changing in vertical direction. Is it reasonable to set the position of pelvis as a global fixed frame?（line 126）

Answer:

The assessment is correct, in a crouched gait the position changes with respect to the ground or to the reference system the reference frame of the pelvis. Therefore, in the model proposed in this work, it is valid by maintaining the axis of the pelvis as the global framework of the 8 DoF system after having considered the offset in the y-axis. Under this consideration, this precision is made in the description of the paper, considering the pelvis frame not as a fixed, but only as the global frame. (lines 131-138)

Figure. Difference between the y-position of the pelvis frame (Σ0) of normal and mild crouch gait.

Modification introduced in revised manuscript:

(lines 131-138) Using a quaternionic representation for solving the forward kinematics of position of the joint references. The home position of the frames of each reference could be represented as follows: pelvic Σ0 = 0 + 0i + 0j + 0k (global frame), right hip Σ1R = 0 + 0i + 0j + L1Rk, right knee Σ2R = 0 + 0i − L2Rj + 0k, right ankle Σ3R = 0 + 0i − L3Rj + 0k, right toe Σ4R = 0 + L4Ri − 0j + 0k, left hip Σ1L = 0 + 0i + 0j − L1Lk, left knee Σ2L = 0 + 0i − L2L j + 0k, left ankle Σ3L = 0 + 0i − L3L j + 0k and left toe Σ4L = 0 + L4Li − 0j + 0k. We assume, that the offset of the position of the pelvis frame in the (y − axis), due to the anthropometric values and gait abnormalities is given. That is, Σ0 is the global frame to model any gait using the DoF kinematic chain.

Comment 4:  In 2.1.3, three method which calculating triangle gait workspace areas are introduced. The author should explain the function of introducing these three areas, and why these areas can be used as metric for evaluation the unnormal gait.

Answer:

The Cartesian position in the workspace of the joint frame references of both lower limbs (knees, ankles and toes) change depending on whether it is a normal gait or an abnormal gait (mild or severe crouch gaits). The area of the triangle formed by both references and the global frame can be used as a performance metric. That is, the degree of abnormality with respect to the normal gait pattern is seen in the decrease in the value of the area. These 3 areas allow a global analysis for each of these or as a whole globally for the entire kinematic chain. This approach can be very useful in the diagnosis or the rehabilitation stage. (lines 158-165)

This metric in gait analysis has not been used with this approach before.

Modification introduced in revised manuscript:

(lines 158-165) The Cartesian position in the workspace of the joint frame references

(knees, ankles and toes) of both lower limbs change depending on whether it is a normal gait or an abnormal gait (mild or severe crouch gaits). The area of the triangle formed by both references and the global frame can be used as a performance metric. That is, the degree of abnormality with respect to the normal gait pattern is seen in the decrease in the value of the area. These 3 areas allow a global analysis for each of these or as a whole globally for the entire kinematic chain. This approach can be very useful in the diagnosis or the rehabilitation stage

Comment 5:  The range of the total number of samples N is not given. (line 154)

Answer:

We change the variable “N” by “M” to avoid confusion with the letter (N) from Normal gait (N). The M-value for each gait is defined in the results section (lines 238-241)

Modification introduced in revised manuscript:

(lines 238-241) The number of samples (M) of the normal, mild crouch, and severe crouch gait signals are (51), (119) and,Af (101), respectively. These are the values used in this work to present the results using the gait cycle (%) as the reference.

Comment 6:  In formula 20-22, the second should be L.

Answer:

In equations 20-22, we changed the letter R by  L. (lines 151-152)

 

Modification introduced in revised manuscript:

(lines 151-152)

Comment 7:  In the calculation formula 26, the problem that the gait data of left and right legs may be different is not considered. If this difference is taken into account, is it better to use the average or one-sided data? If the average value is used, what’s error of using the average value in different exercise states?.

Answer:

Generally, gait analysis is done in the joint space and reorted analysis in Cartesian space is done only in the sagittal plane. This implies that a local analysis is done for each of the lower limbs. In this work, the objective of proposing statistical metrics such as the RMS value of the triangular areas, as in equation 26, is to obtain a global evaluation of the performance of the 8DoF kinematic chain based on metrics throughout the drive cycle. As it is known in what percentage of the gait cycle each phase and event occurs, any of the metrics proposed in the Cartesian space and in particular the RMS allow to compare the gait in different stages.

Modification introduced in revised manuscript:

(line 168) Generally, as we mentioned in previous section, gait analysis is done in the joint space and when analysis is developed only in the Cartesian space. This implies that a local analysis is done for each of the lower limbs. In this work, we aim to propose statistical metrics such as the RMS value of the triangular areas, in order to obtain a global evaluationof the performance of the 8 DoF kinematic chain based on metrics during a gait cycle. If the percentage of the gait cycle when each phase and event is evaluated, any of the metrics proposed in the Cartesian space is useful to compare gaits in different stages.

Comment 8:  Fig. 8 shows the experimental results, but does not give the number of sampling points in the paper.

Answer:

We change the variable “N” by “M” to avoid confusion with the letter (N) from Normal gait (N). The M-value for each gait is defined in the results section (lines 238-241)

Modification introduced in revised manuscript:

(lines 238-241) The number of samples (M) of the normal, mild crouch, and severe crouch gait signals are (51), (119) and,Af (101), respectively. These are the values used in this work to present the results using the gait cycle (%) as the reference.

Comment 9:  It is suggested a block diagram of calculation process using marked points ( in 3.1) is given in the paper, this will make the context of the article clearerly.

Answer:

We agree with incorporate a block diagram to give a clear context of the article. We modify the block diagram in figure 1. and describe it (lines 90-94 and 279-282)

Modification introduced in revised manuscript:

(lines 86) Figure 1. Research framework for gait forward and inverse kinematics analysis and visualization.  

 (lines 90-94) After that, the inverse kinematics algorithm is presented, and to assess the approach, in this work, we consider the Cartesian coordinates from the previous step are the inputs in this stage. However, Cartesian coordinates also can be obtained from a motion marker-based system, which includes the image acquisition and processing units (see Figure 1).

(lines 299-301) Using the Cartesian coordinates calculated for each gait sample of normal gait, mild, and severe crouch gaits with the proposed forward kinematics method (see Figure 1) as input on Equations (4-19), the joint angles of the 8 DoF were calculated.

Comment 10:  In Table 1, six values are put forward as evaluation criteria, but some of these six values have little difference in different states. Which value best reflects the difference in different states? Is the index quantity enough for an experiment done in one cycle?

Answer:

In Table 1, seem that some of these six values have little difference between the diferent gaits. However, it is posible it depends for the units (meters), wich implies a little variation in meters in centimeters is significant. Also, we add in the paper a litle discussion to determine which metric reflects best the diference between the gaits (lines 286-291). Therefore, the index quantity is enough for an experiment done in onse cycle, due to the gait signals are quasiperiodic.

Modification introduced in revised manuscript:

(lines 286-291) In table 1, the value that best reflects the difference between the gaits for the six metric values is the arithmetic mean, and closely is the RMS value, being the less significant for this purpose the standard deviation. Then, in a gait data analytics approach is possible to choose in the feature selection stage the most useful metric. In addition, all the results presented in this work are based only on one gait cycle, which is enough for the analysis since the gait cycle could be considered a quasiperiodic signal.

Comment 11:  What state does SWING in Figure 14 represent? Unclear description.

Answer:

The 7 events with the respective elapsed percentage of the gait cycle are initial contact (IC, 0%), opposite toe off (OTO, 12%), heel rise (HR, 30%), opposite initial contact (OIC, 40%), and toe off (TO, 60%) belong the stance phase. While, the feet adjacent (FA, 75%), tibia vertical (TV, 85%), and initial contact (IC, 100%) are associated with the stance phase [2]. (lines 226-230)

We associate figures (14), (15) and (16), with the description of section 2.3. (lines 345-349)

Modification introduced in revised manuscript:

(lines 226-230) The 7 events with the respective elapsed percentage of the gait cycle are initial contact (IC, 0\%), opposite toe off (OTO, 12\%), heel rise (HR, 30\%), opposite initial contact (OIC, 40\%), and toe off (TO, 60\%) belong the stance phase. While, the feet adjacent (FA, 75\%), tibia vertical (TV, 85\%), and initial contact (IC, 100\%) are associated with the stance phase  [2]

(lines 345-349) Once the joint angles have been calculated using the inverse kinematics method proposed in this work, the angles are used as input for the 3D gait animation unit of the research framework presented in section 2.3. Figures (15 - 17), show a comparative of the stance and swing phases (7 events) of a gait cycle for normal, mild, and severe crouch gaits.

Comment 12:  This article doesn't make it clear in what form the visualization function is realized.

Answer:

(line 209) We add a block diagram a rewrite section (2.3. Virtual gait visualization) to clarify the visualization function.

(lines 215-226) Also we add the description of this block diagram.

Modification introduced in revised manuscript:

Figure 8. 3D Virtual gait visualization framework. (line 209)

(lines 215-226) The starting point of the visualization framework is the creation or modeling of the 3D- CAD human skeleton model. In this work we use an open-access skeletal model [48]. Then, access and orientation of the model are required, the referred orientation may be based on the model shown in Figure 2. The data input of the keyframes control is the joint angles obtained on the inverse kinematic method, which are stored as the joint angles dataset. However, due to the data features and for accessing in an automatic way through script, a data editing and scripting process is required. Subsequently, the 3D gait animation for gait visualization is programmed through a timeline that contains the number of samples of each gait. The timeline of the gait animation is controlled by the keyframes. Finally, a visual comparison between the three gaits over the three anatomical planes taking as reference the 7 events of the gait cycle is carried out to compare the 7 events for each plane and each gear a manual selection of the snapshot corresponding to each percentage of the cycle.

Comment 13:  In the conclusion, In the aspect of evaluation index, it quantitatively points out what problems have been solved and what functions have been realized.

Answer: We rewrite the conclusions section to highlith and clrify important aspects as the evaluation. (lines 386-411)

Modification introduced in revised manuscript:

(lines 386-411) In this paper, gait forward and inverse kinematics framework to model the gait during walking, for analysis and visualization purposes were presented. Both methods are used to model an 8 DoF kinematic chain representing the lower limbs during the gait cycle. Also, gait workspace and gait anatomical space analysis allow establishing the normal gait ranges as the pattern to assess gait using objective metrics. Also, we presented an extended assessment for mild and severe crouch gaits in both workspace and anatomical using statistical metrics, using the normal gait as a reference. Depending the aim of the analysis, diagnostic or rehabilitation assessment any of these metrics could be used to classify the gaits. The advantages of the forward kinematics method using quaternions algebra proposed are scalable and useful to model kinematic chains increasing the degrees o freedom and avoiding the gimbal lock and mathematical complexity. Reduction in mathematical and computational complexity, as well as the instrumentation required for data acquisition in the workspace, is one of the main advantages of the approach for gait inverse kinematics presented.

The graphical comparison using the gait visualization framework for the 7 events of the gait cycle for normal, mild, and severe crouch gaits was carried out. This is an important aspect for improving the interpretation of the specialist and the motivation of the patient. The advantages for modeling and visualization of the approach proposed in this work as a future perspective offer an alternative for the development of a comprehensive exergaming rehabilitation platform. In addition, virtual gait visualization feedback in real-time for any patient and the anthropometry of the subject could be adjusted automatically.

In future work, a 3 DoF experimental platform to emulate and assess the gait cycle for different gaits in the sagittal plane will be developed. In addition, acquiring the Cartesian coordinates for the 8 DoF with a MoCap system investigating real patients will be developed. Ultimately gait recognition framework based on the biomechanical modeling and metrics established will be carried out.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

I think the subject of research on crouching gait is a very interesting and helpful study in the field. In addition, techniques for mathematical modeling, reverse kinematic analysis, and clinical utilization by dividing sections were sufficient to help readers understand.

However, it would be better if an explanation of the process of deriving research results was added. In particular, it is judged that the contents and experimental settings and methods of how many subjects and trials were used to generalize the results should be added.

In addition, it is necessary to explain on what criteria the walking type was classified.

Author Response

=========================================================

Rebuttal Letter

• Manuscript Crouch Gait Analysis and Visualization based on Gait Forward and
• Inverse Kinematics
• ID: applsci-1941749
• Submitted to: Applied Sciences/MDPI (Section: Applied Biosciences and Bioengineering, “Biomechanics and Human Motion Analysis”)
• Corresponding Author: Omar Arturo Domínguez-Ramírez
• Email: omar@uaeh.edu.mx

=========================================================

 

==============   Associate Editor   ==============

 

 

(I) Please revise your manuscript according to the referees’ comments and upload the revised file within 5 days.

(II) Please use the version of your manuscript found at the above link for your revisions.

(III) Please check that all references are relevant to the contents of the manuscript.

(IV) Any revisions made to the manuscript should be marked up using the “Track Changes” function if you are using MS Word/LaTeX, such that changes can be easily viewed by the editors and reviewers.

(V) Please provide a short cover letter detailing your changes for the editors’ and referees’ approval.

 

Response:

 

We authors do dearly acknowledge your disposition, time and effort in handling our paper. In accordance to your decision, and your instructions, we are formatting the revised manuscript as well as addressing Reviewers' queries and concerns, answering all questions and recommendations.

We do hope that our revised manuscript meets the expected quality to be considered for possible publication in this journal.

------     Reviewer 2     ------

I think the subject of research on crouching gait is a very interesting and helpful study in the field. In addition, techniques for mathematical modeling, reverse kinematic analysis, and clinical utilization by dividing sections were sufficient to help readers understand.

However, it would be better if an explanation of the process of deriving research results was added. In particular, it is judged that the contents and experimental settings and methods of how many subjects and trials were used to generalize the results should be added.

In addition, it is necessary to explain on what criteria the walking type was classified.

Answer:

We appreciate your time and effort to provide this assessment and this review. We have done our most effort to comply to your queries and comments, hope we have produced the appropriate answer to clarify all issues. Thanks for your detailed account.

We include in the paper a description to clarity some aspects related with the exerimental design for te presented results and what criteria is used to classify the gaits.

In addition to the suggested adjustments to address your comments, a review and correction of grammar and typography was made for the entire paper. Also, the ORCID of all authors have been completed.

Modification introduced in revised manuscript:

(lines 237-238) This model is well-known and widely used in biomechanical modelling settings, the experimental design to obtain the gait data is presented in [50].

(lines 242- 245) In this work, we aim the numerical validation for the proposed methods for forward and inverse kinematics using the widely used gait data, for this reason we use only a single trial for each gait (normal, mild crouch and severe crouch). But, it is possible to take as an input difference gait trials.

(lines 392 394) Depending the aim of the analysis, diagnostic or rehabilitation assessment any of these metrics could be used to classify the gaits.

.

Author Response File: Author Response.docx