Bio-Mechanical and Bio-Rheological Aspects of Sickle Red Cells in Microcirculation: A Mathematical Modelling Approach
Round 1
Reviewer 1 Report
In the paper the authors investigate the fluid flow of a RBC through narrow blood vessels, considering a varying cell compliance. The authors thus conclude that the blood discharge in capillary decreases with decrease in cell compliance. Moreover, they claim that the findings of the paper justify the flow properties of sickle blood in microcirculation.
Sickle cell is a blood disease inherited from both parents. Normal red blood cells are very flexible and have a discoid shape. The flexibility and shape allow it to move freely through the small blood vessels. In people with sickle cell disease, the RBCs acquire a crescent or sickle shape and also lose flexibility. Abnormal cells adhere to the inside of the capillaries, blocking the flow of blood.
The paper is original and the problem addressed is interesting. However, it cannot be published in the present state as it is practically unreadable. It needs deep and major revisions.
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Section 2 need to be erased and rewritten from scratch.
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How do the authors distinguish a normal RBC from a sickle-like one? Shape and deformability are the parameters. It is well known that the curvature of a sickle RBC is significantly larger than that of a normal RBC. This fact needs to be clarified in the article. In fig. 3 they show that the fluid velocity was not significantly affected by the change in the value of k’. Why? This aspect must be clarified otherwise the article cannot be published. In my opinion this is due to an error in the model as the authors consider that the inlet RBC has the usual biconcave shape. Not the case for a sickle RBC.
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If α is the radial compliances of the tube why the authors consider a uniform tube radius?
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The link between b (beta) and the cell deformability is totally unclear. This aspect must be clarified otherwise the article cannot be published. There are tons of articles that analyze the RBCs deformations, linking them to the visco-elastic properties of the membrane as well as to the elastic characteristics of the cytoskeleton. How do the authors model the deformability of the RBC with a single parameter? If this aspect is not clarified in all details, the paper cannot be published.
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How do the authors obtain formula (3)? An appeal to readers trust is certainly not sufficient. I want to see the rationale which justifies formula (3) otherwise the paper cannot be accepted.
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The figures as they are proposed are illegible. All figures must be erased and redone from scratch. For each figure the authors must clearly report all the data they used.
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The way of writing formulas (6), (13) and (17) is awful.
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The authors repeatedly state that their results are in agreement with the results of other papers. These statements are right and proper when the paper contains figures or tables in which one's data are compared with those of the articles referred to. There is neither a comparison table nor a comparison figure in this paper. So, either the authors insert figures and comparison tables or they eliminate all the claims in which they “compare” their data to the ones of other articles.
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The bibliography is not complete and needs to be updated.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript addresses the relevant problem of characterizing blood rheology in presence pf pathologies that perturb the red blood cell bio-mechanical properties. The particular case of sickle cell disease is addressed.
Under some restrictive hypotheses, the authors propose a lubrication model to study the interactions between the red blood cells and the vascular wall, separated by a thin layer of plasma. The approach provides an interesting compromise between the insight it can bring on the problem and the its applicability, as it allows for semi-analytical solutions.
Overall i believe this interesting manuscript that should be considered for publication on Fluids, provided that the following shortcomings are thoroughly addressed by the authors:
1) the physical assumptions at the basis of the model are poorly illustrated. Fore example, Figure 1 just gives a vague sketch of what physical phenomena are addressed by the model. More importantly, the authors should stress the main physical assumptions and limitations of the lubrication model. What range of Reynolds number can the model address? that range of red blood cell densities (basically the hematocrit) can be studied by the model? can the model address changes in the particle configuration/orientation?
2) In the results and discussion the authors basically perform a simple sensitivity analysis of some model outputs with respect to some input quantities. However, the authors should more clearly illustrate the distinction between inputs and outputs of the model.
3) the results and discussion is presented as a crude list of results with subsequent comments. What is the overall strategy? what is the central questions that the authors would like to prove? The whole section should be revisited trying to clarify these aspects.
overall I recommend major revision, following the above suggestions, before the manuscript is re-considered for publication.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have addressed most of my comments, but the bibliography is still uncomplete. I suggest the authors to add these very recent papers: Chebbi R. Journal of Biological Physics 2015; Chebbi R., Journal of Biological Physics 2018, Farina A., Rosso F., Fasano A., Journal of Biological Physics 2021, Farina A., Fasano A., Rosso F., Mathematical Models for Some Aspects of Blood Microcirculation, Symmetry 2021, 13,1020, and the book Fasano A., Sequeira A., Hemomath: The Mathematics of Blood, Springer 2017.
Reviewer 2 Report
The authors have addressed appropriately my concerns, the manuscript is now acceptable for publication.
