Influences of sodium and glycosaminoglycans on skin oedema and the potential for ulceration: a finite-element approach

Venous ulcers are chronic transcutaneous wounds common in the lower legs. They are resistant to healing and have a 78% chance of recurrence within 2 years. It is commonly accepted that venous ulcers are caused by the insufficiency of the calf muscle pump, leading to blood pooling in the lower legs, resulting in inflammation, skin oedema, tissue necrosis and eventually skin ulceration. However, the detailed physiological events by which inflammation contributes to wound formation are poorly understood. We therefore sought to develop a model that simulated the inflammation, using it to determine the internal stresses and pressure on the skin that contribute to venous ulcer formation. A three-layer finite-element skin model (epidermis, dermis and hypodermis) was developed to explore the roles in wound formation of two inflammation identifiers: glycosaminoglycans (GAG) and sodium. A series of parametric studies showed that increased GAG and sodium content led to oedema and increased tissue stresses of 1.5 MPa, which was within the reported range of skin tissue ultimate tensile stress (0.1–40 MPa). These results suggested that both the oedema and increased fluid pressure could reach a threshold for tissue damage and eventual ulcer formation. The models presented here provide insights to the pathological events associated with venous insufficiency, including inflammation, oedema and skin ulceration.


Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s) Please see attached file "Comments on Pan et al.pdf" for details (Appendix A).
Decision letter (RSOS-182076.R0)

28-Mar-2019
Dear Dr Bush, The editors assigned to your paper ("INFLUENCES OF SODIUM AND GLYCOSAMINOGLYCANS ON SKIN EDEMA AND THE POTENTIAL FOR ULCERATION: A FINITE ELEMENT APPROACH") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published. All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Overall: 1. The manuscript is poorly structured and reads like a BS or MS thesis, not a journal paper. 2. The manuscript is often in passive voice. Use active voice where possible.
Specifically (P = page, l = line): P2-l41: Why is there a two-orders-of-magnitude range in the reported ultimate tensile stress of skin? P6-Fig1: Why does it say "More Swelling"? There is no swelling earlier in the flow chart. P6-l27: "a computational model for the skin is required" This is not true. This is the approach that the authors selected, but it's not the only possibility. P7-l18: Why use a three-layer model? There are 2-5 layer models available in the literature. How does the choice of model affect the results and conclusions? P7-l25: How is the geometry of the inclusion determined and justified? Could this be determined by imaging approaches? P7-l37-40: "Boundary conditions were applied to all surfaces except the top surface. Zero displacement was used as the constraint for all surfaces (except the top)." Are these surfaces fixed in all dofs? If so, this is likely far, far too stiff. These should only be fixed normal to the plane. P8-Fig3: This is mislabeled as Figure 1. Was a mesh sensitivity analysis performed? P12-l3-8: What is the justification for this approach? Why not use a design of experiments approach based on the physiological ranges, or something similar? P12-l16-21: How is this paper relevant to the current work? P12-l32-39: Are these values reasonable? P13-Eq6: This is a biphasic implementation in FEBio. What are the models and elements used? P14-l6: Maximum tensile/compressive stress is usually referred to as the first/third principal stress. P14-l21: Why characterize the results using the Von Mises stress? What is the physiological meaning of this stress measure when comparing the results to the ultimate tensile stress? P15-l43: The results at the selected ROIs seems likely to derive from dependence of the mesh and may not be real. P17-Fig7: The selection of sigma_xx, sigma_yy, and sigma_zz is not meaningful, these measures are arbitrary as the depend on the choice of coordinate system. P23-l8: "which was at the lower end of the reported UTS range is likely to be more representative of these patients in comparison to the higher values reported" What is the justification for this statement? P25-Fig12: Don't repeat the original figure. Isn't most of (b) inferable by intuition?
Reviewer: 3 Comments to the Author(s) This manuscript addresses the role of GAGs and sodium content on skin edema and increased tissue stresses as a potential mechanism for tissue damage and ulceration. This is a well-designed basic science study and it is easy to read. The findings are interesting but perhaps not unexpected, considering the observations from previous studies on other biological tissues. I believe the paper still does add to the limited body of data regarding edema and potential mechanisms of skin ulceration. Below are some specific comments. Page 5, line 18: Did these studies report how much sodium content increased in the inflamed tissue? If so, please include the reported values in parentheses. For example, a previous study reported a 3% increase in sodium content of the skin in women with lipedema (Crescenzi, 2018).
Page 7: Please specify the width of the layers and report the number of elements in the models. Did you use any constraints to connect the top layer to the underlying layer? Did you run a mesh sensitivity analysis to ensure that the mesh density was adequate for the simulations?
Page 14, lines 40-43: Please include a quantitative comparison of the changes in the maximum stress with an increase in FCD.
Pages 15-16: I suggest authors to move this paragraph to the methods section. This paragraph does not present any results.
Page 17: Please comment on the trends in stresses (i.e., nonlinear or linear) with an increase in GAGs FCD.
Page 21: Can you report the equation for the best-fit line to provide a functional relationship between fluid pressure change and external bath osmolarity?
Page 25: The updated schematic for the physiological pathway for venous ulcer formation shows an increase in permeability due to tissue swelling. Please elaborate on the schematic and support the claims with some experimental evidence from your work and previous studies.
Page 26: The physiological osmolarity for normal skin was reported to be ~280 mOsm/L. Would you expect to observe tissue shrinking or swelling if tissue sections were immersed in a hypotonic solution (i.e., 50 and 100 mOsm/L solutions)? Please elaborate on the initial configuration and its effect on the results presented in this study.

Is the language acceptable? Yes
Is it clear how to access all supporting data? Not Applicable

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation? Accept as is
Comments to the Author(s) It appears that you have addressed reviewers comments/questions. A final manuscript review is necessary to make sure word tense is consistent, ie, at times I notice a flip from past to present which is incorrect; also, verify that ALL references to figures match with text, eg, page 16, I think you should be referring to figure 6, not 5.

Review form: Reviewer 3
Is the manuscript scientifically sound in its present form? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
The authors have satisfactorily responded to all my questions and made the necessary changes to the manuscript. I advise the authors to proofread the manuscript before publication. This paper still has some grammar issues, which need to be addressed.
For example, on page 28 -line 23, it should be "only the role of GAGs and sodium was studied...".

Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
Thank you for the care you took in addressing my concerns.

23-May-2019
Dear Dr Bush: On behalf of the Editors, I am pleased to inform you that your Manuscript RSOS-182076.R1 entitled "INFLUENCES OF SODIUM AND GLYCOSAMINOGLYCANS ON SKIN EDEMA AND THE POTENTIAL FOR ULCERATION: A FINITE ELEMENT APPROACH" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referee suggestions. Please find the referees' comments at the end of this email.
The reviewers and Subject Editor have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.
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• Data accessibility It is a condition of publication that all supporting data are made available either as supplementary information or preferably in a suitable permanent repository. The data accessibility section should state where the article's supporting data can be accessed. This section should also include details, where possible of where to access other relevant research materials such as statistical tools, protocols, software etc can be accessed. If the data has been deposited in an external repository this section should list the database, accession number and link to the DOI for all data from the article that has been made publicly available. Data sets that have been deposited in an external repository and have a DOI should also be appropriately cited in the manuscript and included in the reference list.
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• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
• Acknowledgements Please acknowledge anyone who contributed to the study but did not meet the authorship criteria.
• Funding statement Please list the source of funding for each author.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) The authors have satisfactorily responded to all my questions and made the necessary changes to the manuscript. I advise the authors to proofread the manuscript before publication. This paper still has some grammar issues, which need to be addressed.
For example, on page 28 -line 23, it should be "only the role of GAGs and sodium was studied...".
Reviewer: 1 Comments to the Author(s) It appears that you have addressed reviewers comments/questions. A final manuscript review is necessary to make sure word tense is consistent, ie, at times I notice a flip from past to present which is incorrect; also, verify that ALL references to figures match with text, eg, page 16, I think you should be referring to figure 6, not 5. You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org and openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight schedule, if comments are not received, your paper may experience a delay in publication.
Author's Response to Decision Letter for (RSOS-182076.R1) Comments on Pan et al., Influences of sodium and glycosaminoglycans on skin edema and the potential for ulceration: a finite element approach The hypothesis and associated physiological mechanisms are well-described. Separating out the physiological impact of GAGs and osmolarity is interesting. However, the problem statement is unclear and requires clarification and reorganization in section 2.
The major flaw is that the theoretical formulation is not included. The manuscript should explicitly lay out the (1) governing equations and (2) mathematical description of the boundary conditions. It's very difficult to understand the foundation of the numerical simulation without it, particularly since some of the terminology is confusing (discussed below). All of the theory should be laid out before diving into material parameters and design of the parametric study. The discussion in section 2.4 provides a useful differentiation between the physiological effects caused by Na and GAGs; however it would be better placed within the theoretical formulation, either at the end of section 2.1 or as a stand-alone section before the current section 2.2.
The computational domain is well-described by  4)). However, matching them to the physiological analogs which are being modeled is not so obvious from Figs 3 and 4 and the text. This is exacerbated by the fact that some of the terminology is confusing. The term "GAGs inclusion" is not terribly helpful since GAGs are molecules and have a characteristic distribution throughout the domain. Perhaps using "GAGs-induced inclusion" or simply "inclusion" would be an option that better describes the spatial nature of what you are describing.
The authors distinguish between the "external bath" and "interstitial fluid", but it's unclear where these fluid domains exist. Fig 4 attempts to define the external bath in relation to the computational domain, but, at least for me, it muddies the waters further. The external bath looks like a 2-dimensional plane behind the 3D skin block as though it exists at the back face of the block in contact with all 3 layers of skin and extends beyond the domain of the epidermis. I don't think that this is the intent. A better visual and written description that describes where these fluid domains reside in relation to the skin block is needed, as well as how the fluid in the skin block, the external bath, and the interstitial space can interact. The text describes how water from the external bath can be drawn "across the membrane" into the interstitial space around p5, line 35, but it doesn't describe what the membrane is. Also, the spatial link between the skin block and the veins is needed since the veins are the ultimate source of the excess fluid in the skin block. A description of the theoretical formulation might have helped to infer the relationships, but I think that you are going to lose your readers unless this is explicitly laid out.
In Fig 5, do these images represent a steady-state solution or are they snapshots at a particular time?
The discussion of results on p 23 is quite good and provides some quantitative estimates of threshold values of their parameters that are associated with pathological changes.
A discussion of grid resolution should be included to confirm that the numerical domain is sufficiently resolved and is essential for establishing credibility. This can be either a brief discussion in the manuscript or a more rigorous description in supplemental material. Grid resolution is particularly important when a new model does not include any validation against experiment and/or other numerical simulations. This may be because there is currently nothing in the literature against which to validate. In the limitations section, the authors describe the need for experimental data to bound a couple of their parameters. Are there other data that would help to validate your model?
The authors chose to use a volume fraction within the range reported in the literature. Do the authors think that the solution is sensitive to volume fraction?
Minor issues: P2 li 41. Sentence beginning "Thus suggesting" makes this a sentence fragment. Suggest using "This suggests" P4 last sentence before section 1.1: the verbs have mixed tense.
In section 1.1, 1 st paragraph, the description of wound angiogenesis appears the second time that the term is used. It would be better to include "(formation of new blood vessels)" the first time that the term is used.
In Figs 8 and 11, it's hard to see the edges of the boxes with dotted fill. Suggest that you use a solid color or include a bounding box around the dotted region. In the legend, should GAGs be "GAGs inclusion" for consistency? Also, there is a typo in "Surrounding tissue".
In Fig 9 title, there is an extra "the" before "defined". P11 li 46, typo: largest magnitude of swelling
Thank you for taking the time to read our manuscript and the positive feedback. Overall: 1.

Reviewer
The manuscript is poorly structured and reads like a BS or MS thesis, not a journal paper.

2.
The manuscript is often in passive voice. Use active voice where possible.
Thank you, we reviewed and edited the manuscript for structure and voice. Specifically, we modified the abstract, introduction and discussion as well as implemented specific structural revisions requested by the other reviewers. We recognize that the background section is not typical for all types of publications, but because of the limited research conducted on venous ulcers, we thought it was important for the readers to be familiar with the general physiology associated with venous ulcer formation prior to discussing the model and simulation results.
Specifically (P = page, l = line): P2-l41: Why is there a two-orders-of-magnitude range in the reported ultimate tensile stress of skin?
The reviewer is correct. The literature of skin testing indicates a large range in UTS. The authors did not conduct these studies that are referenced therefore we cannot comment on their methods and accuracy. We can, however speak to skin as a biological tissue. It is a well-documented fact that the elasticity of skin changes over time; thus aged skin will be stiffer (lower strain with higher rupture stress) due to this reduction in elasticity than young skin. Additionally, different body regions yield slightly different mechanical behavior (cheek vs. heel) and the skin sample preparation methods also play a role in the outcomes of the testing. Specifically, the 0. Thank you, we can see how this may be confusing. We have removed the word "more" and just left swelling in the box. (Now Figure 2) P6-l27: "a computational model for the skin is required" This is not true. This is the approach that the authors selected, but it's not the only possibility.
Thank you for this comment, this sentence has been rewritten and is also copied here: "In order to validate this pathway and characterize the detailed mechanical changes in the skin tissue, a computational model for the skin was developed." P7-l18: Why use a three-layer model? There are 2-5 layer models available in the literature. How does the choice of model affect the results and conclusions?

The three layers in the model represent the three layers of the skin: epidermis, dermis, and hypodermis. Models with other layers include more layers in the Epidermis (Stratum Corneum) or referring the base layer beneath dermis as subcutaneous fat. The models that use the stratum corneum as an individual layer usually combine the rest of the epidermis with the dermis layer as the epidermis layer itself is extremely thin. The subcutaneous fat is a synonym for hypodermis. Therefore, we believe the three-layer model best represents skin anatomy and material properties. Additionally, all three layers of the skin were bonded together without frictional force between the layers, thus the skin block behaved as a whole and the differences between each layer consisted of the thickness and the material properties (Young's modulus and Poisson's ratio).
P7-l25: How is the geometry of the inclusion determined and justified? Could this be determined by imaging approaches? P7-l37-40: "Boundary conditions were applied to all surfaces except the top surface. Zero displacement was used as the constraint for all surfaces (except the top)." Are these surfaces fixed in all dofs? If so, this is likely far, far too stiff. These should only be fixed normal to the plane.

We do not have any experimental information that would lead us in one direction or another
We did not fix the surfaces in all dofs; we apologize for the confusion. All surfaces were constrained somewhat, except for the top surface that represented the portion of the epidermis in contact with air. We identified constraints that took into account the symmetry of the model about the XZ plane, which was constrained only normally to the surface (see Figure below). We also considered that we are analyzing a small portion of skin, extrapolated from a large semi-infinite in vivo geometry (when compared to the dimensions of our model). This led us to constrain the displacements in both the normal and shear direction in the back, front, and right faces, which are ideally in contact with the rest of the skin. Finally, since we were mostly concerned with investigating the effects of upward swelling (namely toward the surface of the skin), as opposed to downward (which in this case would mean internal swelling) we decided to constrain the bottom surface in every direction.
We have clarified the manuscript as follows (page 9): Boundary conditions were applied to represent the fact that the model is symmetric with respect to the YZ-plane, see Figure 7, and is isolated from a larger skin plane. Namely, we constrained the normal displacement on the plane of symmetry, and normal and shear displacements on the planes in contact with surrounding skin. Because we are interested in upward / outward swelling, the top surface, representing the side of the epidermis in contact with air, was allowed free swelling, while the bottom surface, representing the side of the hypodermis on contact with surrounding tissue, was constrained in every direction.

P8-Fig3
: This is mislabeled as Figure 1. Was a mesh sensitivity analysis performed?
We apologize for the mislabeling of Figure 3, that has been corrected. The authors did perform a mesh sensitivity analysis. The element numbers was increased from 28896 to 37296 (a 29% increase) to generate a more refined mesh, and the results (displacement and stress) did not show any difference within the 4 decimals output by FEBio. This information has been added to the manuscript (page 9).
P12-l3-8: What is the justification for this approach? Why not use a design of experiments approach based on the physiological ranges, or something similar?

Unfortunately, there are no reported lower or upper limit values for the FCD or osmolarity in the inflamed skin for the patient population likely to develop venous ulcers (i.e., individuals with vascular disease). This work is specifically focused on this population and was used to obtain insights of what physiological events happen from the initial blood pooling to skin edema and finally ulceration. This work was innovative in its aim to quantify how GAGs increased presence and possible pooling could lead to skin tissue breakdown associated with blood pooling and swelling as observed in the venous ulcer population.
P12-l16-21: How is this paper relevant to the current work? P12-l32-39: Are these values reasonable?
The FCD values for normal skin are reported in the literature (Wiig et al., 2000;Wiig et al., 2012 ) we used this as the starting point and then expanded the range. Additionally, one author used an FCD of 150 in her previously published work (Roccabianca et al., 2014;Roccabianca et al., 2014). This is the first work to study the relationship between the GAGs inclusion and skin ulceration. Therefore, we used the normal range and expanded from there since no information regarding the range of the FCD for inflamed skin is present in the literature. P13-Eq6: This is a biphasic implementation in FEBio. What are the models and elements used?
We developed the mesh using the Hypermesh software, and we used hexahedral elements HEX8 (added to page 9). We employed the biphasic theory at equilibrium, which is already implemented in FEBio, namely the Donna Equilibrium Swelling material. This material represents a porous material, with a charged solid matrix, and an external solution environment that contains monovalent ions. To describe the solid matrix, we used a neo-Hookean material model for all layers of skin, but we specified different mechanical parameters for each layer (as described on page 12 in section 2.3.1) This is a must for this material description, since the Donnan equilibrium theory is based on the existence of a solid matrix that "resists" the swelling. We are aware that an isotropic description of skin is an approximation, however not having access to in house directional mechanical information we felt that this approximation was reasonable for the time being. We will in the future consider the possibility of using a more precise description for the solid matrix (for example considering a fiber reinforced material description).
Finally, the material we consider is porous, however this does not represent a biphasic analysis per se, these results are only valid once the fluid equilibrium is reached, namely we are not analyzing what happens in the transient response. We believe this is a reasonable approximation, since we are considering this to be a pathological condition that leads to PUs, as opposed to a transient condition (for example as associated with inflammation due to trauma).
P14-l6: Maximum tensile/compressive stress is usually referred to as the first/third principal stress.
The authors agree with this statement. However, the authors chose the use of tensile/compressive stress as they are more descriptive and these terms are used by clinicians and surgeons while the first/third principal stress is not commonly used outside of engineering. So, to support readability of researchers from an array of backgrounds, we elected to use these terms.
We have added a clarification statement in the manuscript as follows (page 12): Given that the shear stress component is zero in Eq. 11, the maximum tensile/compressive stress could also be referred to as the 1 st and 3 rd principal stresses, respectively. The authors chose to use the term tensile stress throughout the manuscript as it is a more descriptive term.
P14-l21: Why characterize the results using the Von Mises stress? What is the physiological meaning of this stress measure when comparing the results to the ultimate tensile stress?
The Von Mises stress here was reported to visually understand the critical areas where high stress localization was observed. To relate these data to the physiology, further detailed stress analyses were conducted with the principal stresses in the regions that high Von Mises was displayed. We later compared these principal stresses to the ultimate tensile stress (Figures 8 and 11).
P15-l43: The results at the selected ROIs seems likely to derive from dependence of the mesh and may not be real.
The results at the selected ROIs were the averaged value of the elements in the selected regions. The ROI represents the area where localized high stress occurred. As noted in an earlier response, we did conduct a sensitivity analysis. The elements number was increased from 28896 to 37296 (a 29% increase) to generate a more refined mesh, and the results (displacement and stress) did not show any difference within the 4 decimals output by FEBio.

P17-Fig7:
The selection of sigma_xx, sigma_yy, and sigma_zz is not meaningful, these measures are arbitrary as the depend on the choice of coordinate system.
To keep the description of results consistent for all ROIs, we chose to use the global reference system and refer to sigma_xx, sigma_yy, and sigma_zz during analysis. The coordinate system was displayed in Figure 6. At different regions of interest, the stress direction is different. Such as Sigma_yy is perpendicular at the right and left sides and parallel to the top.
P23-l8: "which was at the lower end of the reported UTS range is likely to be more representative of these patients in comparison to the higher values reported" What is the justification for this statement?
The lower UTS ranges were derived from samples that came from 5~9 month porcine skin (Gallagher et al., 2012); porcine has been shown to be the closest to human skin material properties and have long been used as an alternative for excised human skin tissue (Groves at al., 2013;Ankersen et al., 1999). In consideration of the formation of venous ulcers, patients who develop these ulcers have compromised vascular systems and are experiencing inflammation and edema in their lower leg, causing decreased skin extensibility (Pierard et al., 2014). With edema, the skin is weakened and unable to sustain pressure and stress (Bansal et al., 2005) The references for this statement are: [  Dermatol 2005;44:805-10. doi:10.1111/j.1365-4632.2005x. This manuscript addresses the role of GAGs and sodium content on skin edema and increased tissue stresses as a potential mechanism for tissue damage and ulceration. This is a well-designed basic science study and it is easy to read. The findings are interesting but perhaps not unexpected, considering the observations from previous studies on other biological tissues. I believe the paper still does add to the limited body of data regarding edema and potential mechanisms of skin ulceration. Below are some specific comments.
Thank you for the comment. Indeed, we agree and believe this work provides insights to the physiological events that are not possible to observe.
Page 2, lines 41-46: This is not a full sentence.
The sentence has been rewritten and also copied here: The results suggested that both the edema and increased fluid pressure could reach a point of tissue damage and eventual ulcer formation.  (Odland et al. 2004;Hargens et al. 1989;Wiese 1993) and ulcer formation (Hargens et al. 1989;McGee et al. 2009 Thank you for suggesting this new reference, we have also included in our manuscript.
Thank you, this has been corrected.
Page 7: Please specify the width of the layers and report the number of elements in the models. Did you use any constraints to connect the top layer to the underlying layer? Did you run a mesh sensitivity analysis to ensure that the mesh density was adequate for the simulations?
Thank you for these questions. We have added this information to the manuscript (page 9). The width and depth of each layer is 5mm x 5mm. The total number of the elements is 28896. In these simulations, the layers were considered to be perfectly bonded with one another. We did perform a mesh sensitivity study where the elements number was increased from 28896 to 37296 (a 29% increase) to generate a more refined mesh, and the results (displacement and stress) did not show any difference within the 4 decimals output by FEBio Page 14, lines 40-43: Please include a quantitative comparison of the changes in the maximum stress with an increase in FCD.
A detailed stress analysis with quantitative comparisons between changes in FCD and changes in maximum principal stress are available in Figure 8. The Von Mises stress was used in Figure 6 to provide a visual perspective of where the localized high stresses occurred, here we only showed the trend of increased stress with increased FCD.
The following was added to the text (page 19): The highest stress was 400 times more when the FCD was 30 times higher than the normal value. When the GAGs inclusion FCD was at 150 mEq/L, the same value reported being used by Roccabianca et al.,[37], the maximum elastic stress was 30 times higher than that at normal FCD value.
Pages 15-16: I suggest authors to move this paragraph to the methods section. This paragraph does not present any results.
Thank you for the suggestion. The reason why this paragraph was initially positioned here was because without the preliminary observation of the high stress localization, it was not possible to predetermine the Regions of Interest (ROIs). We have edited the manuscript and these statements have been moved to the methods section.
Page 17: Please comment on the trends in stresses (i.e., nonlinear or linear) with an increase in GAGs FCD.
We appreciate this question. Using the left ROI as an example, we plotted the stresses against GAGs FCD, it can be seen that the stresses had a nonlinear increase with GAGs FCD. We have included a statement of this trend in our discussion (page 26). This statement is also below: "The maximum stress exhibited a nonlinear increase with the increase of the GAGs inclusion FCD." Page 21: Can you report the equation for the best-fit line to provide a functional relationship between fluid pressure change and external bath osmolarity?
Thank you for the comment. In order to find the best-fit trend line, the logarithm transform was performed and the fluid pressure change can be expressed with a polynomial fit of the log osmolarity values. The equations and R 2 values are reported in the figures below: Page 25: The updated schematic for the physiological pathway for venous ulcer formation shows an increase in permeability due to tissue swelling. Please elaborate on the schematic and support the claims with some experimental evidence from your work and previous studies.
Thank you for this comment. Permeability by definition is the ability of the membrane wall to allow fluids to pass. When tissue is swollen, the pressure difference between the two sides of the membrane is increased, pushing the fluid transport through the membrane. Therefore, we have indicated permeability occurs in association with increased edema. We have included text in the manuscript noting this relationship (page 27). Additionally, several researchers have also discussed the relationship between edema and increased permeability [1-3]: [1] Guo, Xiaomei, Yoram Lanir, and Ghassan S Kassab. 2007 We have added the following to the manuscript (page 27): We observed that when GAGs and sodium were increased, as reflected by the inflammatory process within the tissue, they caused an increase in deformation and higher fluid pressure, thus promoting more fluid transport across the membrane (i.e. increased permeability), resulting in skin edema.
Page 26: The physiological osmolarity for normal skin was reported to be ~280 mOsm/L. Would you expect to observe tissue shrinking or swelling if tissue sections were immersed in a hypotonic solution (i.e., 50 and 100 mOsm/L solutions)? Please elaborate on the initial configuration and its effect on the results presented in this study.
When the tissue is immersed in a hypotonic solution, which means the external bath has a lower sodium (Na+) concentration compared to inside the tissue, more water will be drawn from the external bath into the tissue due to the pressure/concentration difference. Therefore, when the tissue is in the hypotonic solution, it will swell. Here is a schematic presentation of this swelling process. Since two reviewers asked questions about this point, we have added this figure to the manuscript (Figure 1).
However, the problem statement is unclear and requires clarification and reorganization in section 2.The major flaw is that the theoretical formulation is not included. The manuscript should explicitly lay out the (1) governing equations and (2) mathematical description of the boundary conditions. It's very difficult to understand the foundation of the numerical simulation without it, particularly since some of the terminology is confusing (discussed below). All of the theory should be laid out before diving into material parameters and design of the parametric study. The discussion in section 2.4 provides a useful differentiation between the physiological effects caused by Na and GAGs; however it would be better placed within the theoretical formulation, either at the end of section 2.1 or as a stand-alone section before the current section 2.2.
Thank you for the suggestions. Based on Reviewer 4's comments, we have reorganized Section 2 significantly. As requested, the theoretical formulation has been moved earlier in the manuscript. The fluid flux at the final stage of the equilibrium will be zero as the fluid transfer reach the balance. The symmetric boundaries have the displacement constraints as follows: The computational domain is well-described by Fig 3 (mistakenly labeled Fig 1 -also the color scheme in Fig 1(c) and (d) should match the other images of the domain (Fig 1(a)  and (b) and Fig 4)). However, matching them to the physiological analogs which are being modeled is not so obvious from Figs 3 and 4 and the text.
Thank you, this has been corrected. Figure 3 (a)~(d) and Figure 4 (now Figures 4 & 5) were obtained from the same model. Figure 4 (a) was displayed as a transparent image for the left half and the wireframe image displayed for the right half. We presented in this format because we thought it was easier to see the symmetry and the three layers could be easily seen and identified.