Biomechanics of keratoconus: Two numerical studies

Nicolas Falgayrettes; Etienne Patoor; Franck Cleymand; Yinka Zevering; Jean-Marc Perone

doi:10.1371/journal.pone.0278455

Peer Review History

Original SubmissionJuly 6, 2022
23 Aug 2022 Decision Letter - Antonio Riveiro Rodríguez, Editor PONE-D-22-17387Biomechanics of keratoconus: two numerical studiesPLOS ONE Dear Dr. Perone, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please, notice that more information about the FEM model is required. Include all the relevant information (mesh convergence model, contact model if used,...) Please submit your revised manuscript by Oct 07 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. 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Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: No ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: The paper presents two numerical studies regarding the biomechanics of keratoconus. According to the reviewer’s opinion, the paper is well-structured and clear. The topic is interesting and falls within the aim of the journal. In addition, the results are well-presented and could be helpful to further develop the same topic. Therefore, the paper can be accepted for publication in the current form. Reviewer #2: The study aims to develop a finite element model for the biomechanics analysis of kerataconus disease. They have used two different models and performed parametric analysis based on idealized geometries. They have related the numerical results to clinical observations. The aim of the study is within the scope of the journal but the manuscript needs revision. I have several suggestions before further assessment. Please see my comments below: There is almost no information about the finite element model. What kind of parameters are set in Abaqus? Please share the mesh convergence test results (which might be a figure in the appendix) for finite element analysis. Which parameter was set for comparison? Did you use any contact model in finite element analysis? Please provide more technical details about how you performed these calibrations: "An iterative approach was used to define the material properties in the different corneal layers and 212 sublayers in our healthy cornea model [49,50,62,65]. The final model was calibrated on the basis of 213 a sensitivity analysis to deform under IOP with an apex displacement between 390 and 400 μm 214 [16,30]." "To reproduce a homogenous stress state under IOP alone, we took the mechanical 226 properties of the different layers from the literature [41,49,50,62,65,66] and calibrated the various 227 parameters as indicated in Table 1." Please describe the cases before their usage: "Figure 4 graphically presents the effect of the 30-20-10 button softening (Case 5) on IOP- 260 induced anterior and posterior corneal elevation at the corneal and button apices (orange/yellow and 261 light/dark blue bars, respectively). " Is this correct? Fingertip rubbing stress is given higher than eye rubbing with the knuckle although the vice versa is stated? "This hypothesis was confirmed by analyzing the first principal stress, which represents 372 maximum tensional stress. Relative to the cornea that was subject only to IOP, eye rubbing with the 373 knuckle tripled the maximal first principal stress from 0.0338 MPa (without rubbing) to 0.1230 MPa. 374 Moreover, the stress induced by knuckle rubbing was concentrated in the posterior stroma near 375 Descemet’s membrane (red/orange regions) while the anterior stroma experienced negative stress due 376 to the lamellar compression (dark-blue regions) (Fig. 9a, b, e). Fingertip rubbing associated with less 377 stress intensity (0.627 MPa) but the same stress distribution (Fig. 9c–e)." There seems other zones in the Figure 3?: "It is composed of three concentric zones that describe the 853 button center (dark-pink), middle (red), and periphery (brown). " Can you show the zones in Figure 3 with arrows as well?: "It is composed of three concentric zones that describe the 853 button center (dark-pink), middle (red), and periphery (brown). " Some figures such as Figure 3, 5 or 6 have missing units. Figure 7: What is the displacement unit? Figure 4: What are the meanings of +, ++? Please describe them in the figure caption. Please check the spelling and English language of the whole manuscript. There are many grammatical and spelling mistakes. Figures and Tables: Describe all of the abbreviations used in the figures/tables including supplementary ones in the corresponding caption. There are many abbreviations. So, please add a table of acronyms. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: Yes: Senol Piskin ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. 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Revision 1
14 Oct 2022 Author Response Point-by-point responses to editor and reviewer comments Responses to the editor Please, notice that more information about the FEM model is required. Include all the relevant information (mesh convergence model, contact model if used,...) Reply: We have provided this information as detailed below in our replies to Reviewer 2. Journal requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf Reply: We have ensured that the paper meets PLOS One style requirements. We also ensured that the figures meet PLOS One requirements by using the PACE tool. 2. Thank you for stating the following in the Acknowledgments Section of your manuscript: "We thank Alessio Gizzi of Università Campus Bio-Medico, Roma, Italy for his invaluable help when developing the simulation. This work is supported by grant n°17CP-1391-C63 to N.F. from Region Grand Est, France." We note that you have provided funding information that is not currently declared in your Funding Statement. However, funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form. Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows: "This work is supported by grant n°17CP-1391-C63 to N.F. from Region Grand Est, France. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript." Please include your amended statements within your cover letter; we will change the online submission form on your behalf. Reply: The funding-related information in the manuscript was removed. We included the amended funding statement in the revised cover letter (Point No. 5). 3. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability. "Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized. Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access. We will update your Data Availability statement to reflect the information you provide in your cover letter. Reply: Everything that is needed to reproduce the simulations in our study (the methods and the normal corneal dimensions and intraocular pressure of an author, which we used to develop the model) is available in the paper. A comment relating to this (Point No. 6) has been added to the cover letter. 4. We note that you have included the phrase “data not shown” in your manuscript. Unfortunately, this does not meet our data sharing requirements. PLOS does not permit references to inaccessible data. We require that authors provide all relevant data within the paper, Supporting Information files, or in an acceptable, public repository. Please add a citation to support this phrase or upload the data that corresponds with these findings to a stable repository (such as Figshare or Dryad) and provide and URLs, DOIs, or accession numbers that may be used to access these data. Or, if the data are not a core part of the research being presented in your study, we ask that you remove the phrase that refers to these data. Reply: We have removed the phrase that refers to these data. 5. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information. Reply: We have added the captions of the Supporting Information to the end of the manuscript. We have also checked to make sure the references are correct. Responses to the Reviewers Reviewer #1: The paper presents two numerical studies regarding the biomechanics of keratoconus. According to the reviewer’s opinion, the paper is well-structured and clear. The topic is interesting and falls within the aim of the journal. In addition, the results are well-presented and could be helpful to further develop the same topic. Therefore, the paper can be accepted for publication in the current form. Reply: We are very grateful for the time you spent on our manuscript, your thoughtful consideration, and your positive decision. Thank you very much! Reviewer #2: The study aims to develop a finite element model for the biomechanics analysis of kerataconus disease. They have used two different models and performed parametric analysis based on idealized geometries. They have related the numerical results to clinical observations. The aim of the study is within the scope of the journal but the manuscript needs revision. I have several suggestions before further assessment. Reply: Thank you very much for your time, your thoughtful and careful review of our manuscript, and your helpful comments. We have addressed all comments to the best of our ability and feel that this has significantly improved the manuscript. Please see my comments below: Q1. There is almost no information about the finite element model. What kind of parameters are set in Abaqus? Q4. Please provide more technical details about how you performed these calibrations: "An iterative approach was used to define the material properties in the different corneal layers and 212 sublayers in our healthy cornea model [49,50,62,65]. The final model was calibrated on the basis of 213 a sensitivity analysis to deform under IOP with an apex displacement between 390 and 400 μm 214 [16,30]." "To reproduce a homogenous stress state under IOP alone, we took the mechanical 226 properties of the different layers from the literature [41,49,50,62,65,66] and calibrated the various 227 parameters as indicated in Table 1." Q2. Please share the mesh convergence test results (which might be a figure in the appendix) for finite element analysis. Which parameter was set for comparison? Reply: We apologize for the lack of methodological detail. We have placed Comments Q1, Q4, and Q2 together so that we can explain our modeling approach more cohesively. The parameters we used are shown in Table 1. Of particular interest are µ (ground substance stiffness) and k1 (collagen fiber stiffness), which we varied in Numerical Study #1 (Analyses 1–3) to assess the effect of softening specific regions of the cornea on corneal elevation and thinning. Another important parameter is kappa, which describes the dispersion of fibers around a mean direction and changes in the different parts of the stroma. In Analysis 4 of Numerical Study #1, we increased kappa in the middle and/or posterior stroma to disperse the fibers, and then examined the effect on corneal elevation. Our normal cornea model was constructed as follows: First, we examined the literature for material models that are often used in corneal biomechanics. This showed that the HGO model is often employed to describe the stroma. As indicated in the Introduction, this material model describes the strain-hardening hyperelasticity and anisotropy of soft tissue that contains several families of fibers with defined direction and dispersion that are embedded within an isotropic matrix. Moreover, the Yeoh hyperelastic model has been used to describe the sclera because it describes the strain-hardening behaviour of soft biological tissues that have an isotropic fiber distribution. Similar literature researches led us to adopt the Neo-Hookean hyperelastic model to describe the behavior of the epithelium, Descemet membrane, and endothelium, while an isotropic formulation of the HGO law was used to describe the behavior of Bowman’s membrane. The material parameters of these models are all shown in Table 1. Second, we assigned material orientations to the collagen fibers in the stroma to mimic the collagen architecture revealed by the X-ray studies of Meek et al. [ref 6 in our paper]. These studies showed that the collagen fibers in the posterior stroma of the cornea follow a distinct orthogonal pattern (one set of fibers each is oriented in the nasal-temporal and superior-inferior directions) and, as they approach the limbus, they start to curve, eventually forming a stiff reinforcing annular ring of fibers around the edge of the cornea in the posterior stroma (see Figure 2b). This approach has been used in many other studies on corneal mechanics (e.g. refs 16, 45–48, 50, 58). Third, we cut the stroma into several parts so that we could assign isotropic fiber dispersion in the anterior stroma and completely anisotropic fiber dispersion in the posterior stroma, with a transition zone in between (Fig. 2a). Others have achieved a similar gradient of fiber dispersion with complex mathematical calculations (e.g. refs 5, 7, 16, 39–41). We chose to take this cutting approach so that we could alter µ, k1, and kappa in specific parts of the corneal stroma. Fourth, because the different dispersion, orientation, and fiber stiffness of the stromal parts impose different “absolute” stiffnesses, we proportionally tuned the HGO parameters µ and k_1 so that the stress distribution throughout the full thickness of the corneal stroma was homogeneous when the corneal model was submitted to normal IOP: this homogeneity is displayed in Fig. 5b. To achieve this homogeneity, we conducted an inflation test on a monolayer corneal geometry with the material properties found in the literature for a cornea with fully anisotropic properties (no dispersion) to calculate a reference value of apex vertical displacement. We then tuned the stiffness parameters of layers with different dispersion so that we would achieve the same vertical displacement the monolayer geometry. Fifth, we meshed the finite element model with 10-node quadratic tetrahedron elements (C3D10) and combined the material properties described above with the stroma-partitioned geometry (Fig. 2a). We applied boundary conditions of IOP and null displacements on the scleral border as shown in S2 Fig. All these operations were conducted on the in vivo IOP-deformed geometry recreated from the ophthalmological measurements of one of the authors. S2 Fig. Internal pressure and encastre boundary condition defined in the model. Sixth, to find the stress-free reference geometry of the cornea with these particular boundary conditions and material properties, we ran an inverse procedure working on the corneal geometry (nodes coordinates). The stop criterion was reached when the deformed reference geometry matched the in vivo IOP-deformed geometry that had been recreated from the ophthalmological measurements. Thus, the final model on which we ran the parametric analyses consisted of the defined material properties assigned to the partitioned stroma and the boundary conditions of loading pressure and null displacements applied to this reference geometry. During this process, the solution was always computed with an implicit scheme in static analysis. Seventh, we conducted a mesh convergence study using two variables that play key roles when the cornea is subjected to IOP, namely, vertical apex displacement and stress in the central anterior stroma. When we doubled the number of tetrahedral elements at each iteration, the results reached convergence with a mesh of ≥40,000 elements. Given that we had to run a complete parametric analysis with numerous simulations, we therefore used 40,000 elements during the study, since this gave the best balance between precision and speed of calculation (S3 Fig.). S3 Fig. Mesh convergence study. To address Q1, Q4, and Q2, we revised the Methods section by: 1. Taking information regarding the computer modeling from Supporting Information and adding it to the Methods. 2. Completely rewriting the Methods to make the points above (lines 158–291). 3. Adding new references that show the use of the HGO, Yeoh, and Neo-Hookean models to describe the corneal layers (e.g. ref 64). 4. Adding supplementary figures demonstrating our approach (new S2 Fig and new S3 Fig). Q3. Did you use any contact model in finite element analysis? Reply: The same corneal model with fiber reinforcement described above was used in Abacus to simulate contact of the finger with the eyelid over the cornea. For this, we defined a contact pair with the finger as the master surface and the cornea as the slave surface in a surface-based contact model. The tangential behavior between this contact pair was set to be frictionless, meaning that when nodes are in contact they slide on each other without inducing shear forces. This is justified by the presence of the eyelid sliding between the finger and the cornea during eye rubbing. Since we did not want any penetration between this contact pair, we defined normal behavior as a "hard" contact pressure-overclosure formulation in Abaqus. As a constraint enforcement method for hard contact, we started with a direct method, which avoided approximations such as those in penalty or augmented Lagrangian constraint enforcement. Since our simulation converged with this method, we did not have to resort to other methods. To address this point, we added a new section to the Methods (lines 292–303). Q5. Please describe the cases before their usage: "Figure 4 graphically presents the effect of the 30-20-10 button softening (Case 5) on IOP- 260 induced anterior and posterior corneal elevation at the corneal and button apices (orange/yellow and 261 light/dark blue bars, respectively). " Reply: To address this comment, we changed the text as follows: “Fig 4 graphically summarizes the effect of the 30-20-10 button softening and our subsequent explorations (i.e. different levels of softening or softening in specific corneal layers, see Analyses 1–3 below) on IOP-induced anterior and posterior corneal elevation at the corneal and button apices (orange/yellow and light/dark blue bars, respectively). The healthy (unsoftened) cornea is designated Case 1 while the 30-20-10 button softening condition is denoted Case 5.” (lines 320–324) Q6. Is this correct? Fingertip rubbing stress is given higher than eye rubbing with the knuckle although the vice versa is stated? "This hypothesis was confirmed by analyzing the first principal stress, which represents 372 maximum tensional stress. Relative to the cornea that was subject only to IOP, eye rubbing with the 373 knuckle tripled the maximal first principal stress from 0.0338 MPa (without rubbing) to 0.1230 MPa. 374 Moreover, the stress induced by knuckle rubbing was concentrated in the posterior stroma near 375 Descemet’s membrane (red/orange regions) while the anterior stroma experienced negative stress due 376 to the lamellar compression (dark-blue regions) (Fig. 9a, b, e). Fingertip rubbing associated with less 377 stress intensity (0.627 MPa) but the same stress distribution (Fig. 9c–e)." Reply: Thank you very much for picking this up: there was a missing zero (0.627 Mpa should have been 0.0627 Mpa, i.e. double the maximal first principal stress without any rubbing). We put the missing zero in the text. (line 440) Q7. There seems other zones in the Figure 3?: "It is composed of three concentric zones that describe the 853 button center (dark-pink), middle (red), and periphery (brown). " Can you show the zones in Figure 3 with arrows as well?: Reply: Yes, we did not describe this figure sufficiently. Briefly, Figure 3 depicts the creation of a bullseye-like inferocentral button on the corneal geometry shown in Figure 2a. This means that the yellow, blue, and green zones shown in Figure 2a are also shown in Figure 3. Figure 3 also depicts the internal concentric zones of the button (pink, red, and brown). To make this clearer and Figures 2 and 3 more harmonious, we rewrote the Fig 3 legend (lines 921–941) and modified the Fig 2 legend (lines 911–919). As suggested, we also added arrows and labels to Fig 3b to make the figure clearer. Q8. Some figures such as Figure 3, 5 or 6 have missing units. Reply: The missing unit is mm (displacement) or Mpa (strain) in all cases. This is now made clear in the legends to Fig 3 (line 922), Fig 5 (line 963–964), Fig 9 (line 999), and Fig 10 (line 1012). Q9. Figure 7: What is the displacement unit? Reply: The displacement is given as µm in the y-axis title and was added to the Figure 7 legend (line 989). Q10. Figure 4: What are the meanings of +, ++? Please describe them in the figure caption. Reply: We added explanations to the Fig 4 legend as follows: “In Cases 4 and 5, button softening was respectively doubled (to 20, 13.3, and 6.7, respectively; + indicates moderately increased softening relative to Case 3) and tripled (to 30, 20, and 10, respectively; ++ indicates greatly increased softening relative to Case 3). In Cases 6–10, the indicated button layer(s) were softened by dividing their μ and k1 values in the button center, middle, and periphery by 30, 20, and 10, respectively (++ indicates all layers were softened to the same degree).” (lines 955–961) Q11. Please check the spelling and English language of the whole manuscript. There are many grammatical and spelling mistakes. Reply: One of us (YZ) is a medical writer with 25 years experience. She agrees that there were quite a few errors and has read through the manuscript very carefully to correct them. Thank you very much! Q12. Figures and Tables: Describe all of the abbreviations used in the figures/tables including supplementary ones in the corresponding caption. Reply: We made sure all abbreviations are spelled out in the figure legends, including the supplementary figures. Q13. There are many abbreviations. So, please add a table of acronyms. Reply: A table of acronyms was added (line 24). ________________________________________ Attachments Attachment Submitted filename: Response to reviewers.docx https://doi.org/10.1371/journal.pone.0278455.r002
6 Nov 2022 Decision Letter - Antonio Riveiro Rodríguez, Editor PONE-D-22-17387R1Biomechanics of keratoconus: two numerical studiesPLOS ONE Dear Dr. Perone, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please, address the minor comments provided by Reviewer 2. Please submit your revised manuscript by Dec 21 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. 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Revision 2
10 Nov 2022 Author Response Point-by-point responses to editor and reviewer comments (second) Responses to the editor Please, address the minor comments provided by Reviewer 2. Reply: We have addressed the minor comments provided by Reviewer 2 by adapting Fig. 4 (we replaced the + signs with asterisks). The revised Figure was checked by PACE. Journal requirements: Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Reply: Our reference list has been checked and is now correct: we removed one duplicate reference (refs 61 and 69 were the same) and corrected 11 refs. There were no retracted papers. Responses to the Reviewers Reply: We thank the reviewers again for their time and for helping us improve our manuscript. Rev 2: '++' symbol has already been used for the "greatly increased softening" in the figure caption. So another symbol such as '+++' can be used here: "++ indicates all layers were softened 961 to the same degree" Reply: We decided to use two asterisks and have made the appropriate change to Figure 4 and the Figure 4 legend (Line 960). ________________________________________ Attachments Attachment Submitted filename: Response to reviewers (second).docx https://doi.org/10.1371/journal.pone.0278455.r004
17 Nov 2022 Decision Letter - Antonio Riveiro Rodríguez, Editor Biomechanics of keratoconus: two numerical studies PONE-D-22-17387R2 Dear Dr. Perone, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Antonio Riveiro Rodríguez, PhD Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0278455.r005
Formally Accepted
23 Dec 2022 Acceptance Letter - Antonio Riveiro Rodríguez, Editor PONE-D-22-17387R2 Biomechanics of keratoconus: two numerical studies Dear Dr. Perone: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Antonio Riveiro Rodríguez Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0278455.r006

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