Rapid Assessment of Relative Hemolysis Amidst Input Uncertainties in Laminar Flow

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall Assessment

The research explores whether relative hemolysis predictions can be reliably made despite uncertainties in the absoute values predicted by the power-law hemolysis model. It specifically assesses how uncertainties in upstream velocity profiles, blood viscosity models, hemolysis coefficients, and stres exposure times influence the predictive accuracy of Eulerian and Lagrangian frameworks.   The topic is highly relevant to biomedical engineering, especially in blood-contacting medical device design. The study fills a gap by systematically analyzing the robustness of relative hemolysis predictions amid multiple input uncertainties. Focusing on relative rather than absolute predictions is innovative and practically significant for early prototype evaluation.   Compared to existing literature, this work is distinguished by its comprehensive multi-parameter investigation, covering various shear stresses, strain rates, viscosity models, and hemolysis coefficients. The comparison between Eulerian and Lagrangian models under controlled conditions offers valuable insights for computational hemolysis assessment in design processes.   The methodology is thorough and clearly described. The authors effectively combine computational fluid dynamics with hemolysis models, systematically varying key parameters. Including a brief sensitivity analysis in the main text could help readers quickly identify which parameters most influence relative predictions.   The conclusions align with the evidence. They show that relative hemolysis trends are mostly independent of hemolysis power law coefficients but are sensitive to accurate wall shear stress estimation in developing flows, directly addressing the main research question.   The references are current and relevant, properly contextualizing the work within the existing literature.   Tables and figures are well-organized and labeled. Illustrations effectively compare modeling approaches and parameter sets. Adding brief interpetive statements to figure captions could improve understanding.   Overall, this is a well-structured, technically sound, and clearly written manuscript that makes a meaningful contribution to computational hemolysis modeling.

To further strengthen the work, it would be helpful to include a more explicit discussion of certain limitations and boundary conditions. This would not only improve transparency but also help readers better understand the scope of applicability of the results.

Recommendation: Accept with major revisions.

Suggested Revisions:

1. Limitations – Please add a short, dedicated paragraph in the Discussion section addressing the limitations of the models used.
2. Physiological relevance – Briefly explain the physiological relevance of the model parameters (e.g., applied shear stress levels).
3. In vivo extrapolation – Provide a concise explanation of how these findings might be extrapolated to in vivo conditions.

Author Response

We thank all the reviewers for their time and their valuable suggestions. We have taken all their comments seriously and have made modifications to the manuscript. We believe these changes have significantly enhanced the quality of the manuscript without altering our original conclusions and findings.

Reviewer I:

Recommendation: Accept with major revisions.

Suggested Revisions:

1. Limitations – Please add a short, dedicated paragraph in the Discussion section addressing the limitations of the models used.

Response:

Thank you for your time and we appreciate your suggestion. The following sentences and references were added at Lines 488 – 503 of the revised manuscript.

While two geometries with fully developed flow and developing flow conditions were assessed in this study, the extension of the proposed methodology for relative hemolysis assessments in more complicated and clinically relevant device geometries such as blood pumps and heart valves needs to be undertaken. Such geometries may have localized fluid recirculation zones where cell shear stress exposure times may not be accurately represented by the steady-state, fully developed flow Lagrangian framework proposed in this study [22]. Second, the assumption of a fully-developed flow in the Lagrangian framework inherently assumes that the shear stress are maximum at the wall. However, there may be scenarios where hemolysis maybe induced by flow or small scale eddies. In such turbulent scenarios, the modeling of the effective shear stresses experienced by the RBCs is critical and could be undertaken by using the computed energy dissipation terms for instance [23]. Hemolysis occurs as a result of a cascade of processes involving platelet margination, adhesion, aggregation and cohesion that may not be adequately represented by simplistic power law models/coefficients that were generated using shear devices. Therefore, more mechanistic models of hemolysis where cell deformation occurs also need to be considered where the power-law model may not be applicable [24].    

 

22. Taskin, M. E., Fraser, K. H., Zhang, T., Wu, C., Griffith, B. P. and Wu, Z. J., 2012. Evaluation of Eulerian and Lagrangian models for hemolysis estimation. ASAIO journal 58 (4) pp. 363-372.
23. Wu, P., Gao, Q. and Hsu, P.L., 2019. On the representation of effective stress for computing hemolysis. Biomechanics and modeling in mechanobiology, 18(3), pp.665-679.
24. Fogelson, A.L. and Neeves, K.B., 2015. Fluid mechanics of blood clot formation. Annual review of fluid mechanics, 47(1), pp.377-403.

 

2. Physiological relevance – Briefly explain the physiological relevance of the model parameters (e.g., applied shear stress levels).

Response:

Thank you for your time and we appreciate this suggestion. The following sentences and references were added at Lines 482 – 487 of the revised manuscript.

Although only laminar flow conditions were explored in this study, the range of wall shear stresses investigated in this study (1- 600 Pa, cf. Table 3) are within the ranges found in many anatomical regions and device geometries including pumps, heart valves and coronary arteries and stents [21]. Furthermore, the study indicated that a significant amount of the blood volume within these devices do not experience shear stress greater than 50 Pa [21].

21. Hong, J.K., Gao, L., Singh, J., Goh, T., Ruhoff, A.M., Neto, C. and Waterhouse, A., 2020. Evaluating medical device and material thrombosis under flow: current and emerging technologies. Biomaterials Science, 8(21), pp.5824-5845.
22. In vivo extrapolation – Provide a concise explanation of how these findings might be extrapolated to in vivo conditions.

Response:

Thank you for your time and we appreciate this suggestion. A direct extension of this study to thrombus prediction in-vivo scenarios is challenging due to the transient nature of the process and the complexity of the interactions among the various blood constituents. We anticipate that the initial application of the results from this study would be towards rapid assessments and relative hemolysis predictions in different device design prototypes as highlighted in the following sentences of the revised manuscript: 65-67, 474 - 476.   

Therefore, the following sentences and references were added at Lines 503 – 510 of the revised manuscript.

A direct extension of the results of this study to thrombus prediction in vivo scenarios is challenging. While the complex hydrodynamic interactions between deformable RBCs, ellipsoid platelets and a model thrombus have been simulated and compared against in vivo data from mouse models [25] and significant advances have been made in the modeling of coagulation, platelet deposition and aggregation, and embolization, developing patient-specific models capable of predicting the transient process of thrombus formation and embolism under in vivo conditions remains a challenge [26].

 

25. Wang, W., Diacovo, T.G., Chen, J., Freund, J.B. and King, M.R., 2013. Simulation of platelet, thrombus and erythrocyte hydrodynamic interactions in a 3D arteriole with in vivo comparison. PLoS One, 8(10), p.e76949.
26. Hosseinzadegan, H. and Tafti, D.K., 2017. Modeling thrombus formation and growth. Biotechnology and bioengineering, 114(10), pp.2154-2172.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors:

The manuscript is quite strong in terms of technical rigor, data depth, and methodical presentation, but it definitely would benefit from some revisions before submission, mainly for clarity, conciseness, and flow rather than scientific accuracy.

1. Readability and Conciseness

• The manuscript has very long sentences (sometimes >40 words) with multiple clauses. This makes it harder to follow, especially for readers outside CFD.

• Overuse of parentheses breaks reading flow. Some could be moved to footnotes or rephrased.

• Repetition (e.g., multiple times you mention “absolute hemolysis cannot be predicted accurately but relative values can”).

2. Abstract

• Currently dense and overly technical for an abstract. Example: Instead of listing all parameter ranges (strain rates, stresses, etc.), summarize as “covering a wide range of shear stresses, strain rates, and exposure times.”

3. Introduction

The introduction mixes literature review with your study’s findings. It’s better to:

Explain problem + why it matters.

Summarize prior limitations.

End with your unique approach + objectives.

Some figure references (e.g., Figure 1) come too early before they’re fully introduced.

Language and Formatting

• Some small grammatical errors (e.g., “differences reduce” → “differences decrease”).

Author Response

We thank all the reviewers for their time and their valuable suggestions. We have taken all their comments seriously and have made modifications to the manuscript. We believe these changes have significantly enhanced the quality of the manuscript without altering our original conclusions and findings.

Reviewer II:

The manuscript is quite strong in terms of technical rigor, data depth, and methodical presentation, but it definitely would benefit from some revisions before submission, mainly for clarity, conciseness, and flow rather than scientific accuracy.

1. Readability and Conciseness

• The manuscript has very long sentences (sometimes >40 words) with multiple clauses. This makes it harder to follow, especially for readers outside CFD.
• Overuse of parentheses breaks reading flow. Some could be moved to footnotes or rephrased.
• Repetition (e.g., multiple times you mention “absolute hemolysis cannot be predicted accurately but relative values can”).

Response:

We thank you for your time and encouragement. We have read through manuscript carefully and made edits to improve readability. In particular, we have removed parenthesis from several locations.

2. Abstract

• Currently dense and overly technical for an abstract. Example: Instead of listing all parameter ranges (strain rates, stresses, etc.), summarize as “covering a wide range of shear stresses, strain rates, and exposure times.”

Response:

We thank you for this suggestion. The abstract has been modified as per your suggestion.

3. Introduction

The introduction mixes literature review with your study’s findings. It’s better to:

Explain problem + why it matters.

Summarize prior limitations.

End with your unique approach + objectives.

Some figure references (e.g., Figure 1) come too early before they’re fully introduced.

 

 

Response:

We appreciate you for this suggestion!

We went through the Introduction carefully and made edits where appropriate. We felt it was prudent to bring up the main problem that we are trying to address (i.e., the four different sources of uncertainties) upfront. Hence, we introduced these via Figure 2 in Line 60.

Subsequently, in order to delineate our specific contributions towards addressing the four sources of uncertainties, we elaborate on our specific contributions in Lines 91 – 262 by comparing against previous literature. I hope that you find out approach reasonable.   

Language and Formatting

• Some small grammatical errors (e.g., “differences reduce” → “differences decrease”).

Response:

Thank you! We have now corrected this in Line 365.

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, hemolysis prediction is investigated considering the effects of viscosity models, hemolysis power law coefficients, shear stresses, strain rates and exposure times. A laminar flow assumption is used and computational fluid dynamics analyses are performed for the comparison between various cases. In my opinion, the methodology is well described and the results provided important findings in terms of rapid assessment of relative hemolysis during device design. On the other hand, I have several recommendations for minor revisions to improve the quality of the submitted paper. The recommendations are stated below:

• The content of Figure 2 is well defined, but I think the graphical representation of Figure 2 can be improved (For example, colored boxes can be used, alignment of arrows can be more regular, the writings can be aligned better, the fonts in the figure can be larger, etc.).
• In line 116-117, it is referenced that the pulsatile flow does not have a critical effect on the time-averaged wall shear stresses. Could you provide a numerical comparison from the referenced studies in order to see the level of differences?
• In line 121, the symbol of shear rate does not seem proper (the dot seems towards left).
• The font size in Figure 3 is quite large compared to the text size, the size in the figure can be rearranged for better visual representation.
• In lines 221 and 222, the ksi was used as 0.5, 0.75 and 1.0. However, the ksi value defined in the parenthesis in line 221 shows that the ksi is larger than 1. Is this true? If not, please correct the statement in the parenthesis.
• The font sizes in Figure 4 and Figure 5 can be revised. The fonts in the figure seem quite larger than the text font size.
• In Figures 8, 10, and 11, the typo “Cassan” should be revised.
• In Figure 9, could you provide additional information about the Blood damage II, Blood damage III, and Blood damage IV for better understanding. Are these damage levels correspond to the three different ksi levels given in Figure 4. If so, please explain clearly.

Author Response

We thank all the reviewers for their time and their valuable suggestions. We have taken all their comments seriously and have made modifications to the manuscript. We believe these changes have significantly enhanced the quality of the manuscript without altering our original conclusions and findings.

Reviewer III:

In this paper, hemolysis prediction is investigated considering the effects of viscosity models, hemolysis power law coefficients, shear stresses, strain rates and exposure times. A laminar flow assumption is used and computational fluid dynamics analyses are performed for the comparison between various cases. In my opinion, the methodology is well described and the results provided important findings in terms of rapid assessment of relative hemolysis during device design. On the other hand, I have several recommendations for minor revisions to improve the quality of the submitted paper. The recommendations are stated below:

• The content of Figure 2 is well defined, but I think the graphical representation of Figure 2 can be improved (For example, colored boxes can be used, alignment of arrows can be more regular, the writings can be aligned better, the fonts in the figure can be larger, etc.).

 

Response:

Thank you for this comment! We have now revised Figure 2 as per your suggestion!

 

• In line 116-117, it is referenced that the pulsatile flow does not have a critical effect on the time-averaged wall shear stresses. Could you provide a numerical comparison from the referenced studies in order to see the level of differences?

 

Response:

Thank you for this question! In references [12, 13], the prediction variations resulting from using constant and pulsatile velocity in flow conditions were shown only graphically and were not numerically quantified. This has now been elaborated as follows in Lines 119-122 of the revised manuscript:

While Stiem et al. [12] showed distinct differences between time-averaged axial velocity profiles generated from constant velocity and pulsatile velocity inflow boundary conditions downstream of the throat in the forward flow direction (cf. Figure 1c), these differences did not manifest themselves for derived quantities like shear stresses.

 

• In line 121, the symbol of shear rate does not seem proper (the dot seems towards left).

 

Response:

Thank you for your meticulous observation and for pointing this out! This has now been fixed in Line 125 of the revised manuscript.

 

• The font size in Figure 3 is quite large compared to the text size, the size in the figure can be rearranged for better visual representation.

 

Response:

Thank you! The font size associated with Figure 3 has now been reduced in the revised submission.

 

• In lines 221 and 222, the ksi was used as 0.5, 0.75 and 1.0. However, the ksi value defined in the parenthesis in line 221 shows that the ksi is larger than 1. Is this true? If not, please correct the statement in the parenthesis.

 

Response:

Thank you! Yes, this was a typo which has been corrected in Line 226 of the revised manuscript.

 

• The font sizes in Figure 4 and Figure 5 can be revised. The fonts in the figure seem quite larger than the text font size.

 

Response:

Thank you! The font sizes associated with Figures 4 and 5 have now been reduced in the revised submission.

 

• In Figures 8, 10, and 11, the typo “Cassan” should be revised.

 

Response:

Thank you! This typo has been fixed in the corresponding figures.

 

• In Figure 9, could you provide additional information about the Blood damage II, Blood damage III, and Blood damage IV for better understanding. Are these damage levels correspond to the three different ksi levels given in Figure 4. If so, please explain clearly.

Response:

We apologize for the confusion resulting from using the terms “Blood damage” and “Model” interchangeably in the original manuscript. Towards addressing this, the generic term “Model” in Tables 2 and 3 have been replaced with the term “Blood damage.”

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors of the article have made the necessary updates and clarifications to the text. Therefore, I recommend the manuscript for publication as it is.