Review Reports

Round  1

Reviewer 1 Report

The methods and the problem for solving are not clearly described in the paper.

1.     This paper claims that the model contains three parts. The blood (fluid), the artery, and the cardiac muscle. However, from the figures, there is no artery wall (thickness), and there is no description about how the artery is connected to the cardiac muscle. Additionally, what is the boundary condition for the cardiac muscle (the outer boundary of the whole block shown in figure 1 or 3)?

2.     It is not clear that the model is two-way coupled or not. It looks like one-way coupled. If it is one-way, the model is too out of date. There are a lot of 3D numerical models for the two-way coupled blood-artery study.

3.     There is no comparison with ether experiment observation or analytical predictions in the paper. The results or proposed model in the paper is less valuable. 

Author Response

Point 1: This paper claims that the model contains three parts. The blood (fluid), the artery, and the cardiac muscle. However, from the figures, there is no artery wall (thickness), and there is no description about how the artery is connected to the cardiac muscle. Additionally, what is the boundary condition for the cardiac muscle (the outer boundary of the whole block shown in figure 1 or 3)?

Response 1: Figure 3b has been added to show clearly the thickness of the artery.

The following sentence has been added. “Figure 3b depicts the radial discretization of the blood aorta. The central part stands for the blood. The artery and its thickness appear clearly in this figure. However, the muscle is considered as having no thickness and only a boundary condition will be applied to represent this surface. Indeed, the muscle is considered a free surface and no external force is applied on it.”

Point 2: It is not clear that the model is two-way coupled or not. It looks like one-way coupled. If it is one-way, the model is too out of date. There are a lot of 3D numerical models for the two-way coupled blood-artery study.

Response 2: The following sentence has been added. “The model used to solve the governing equations is two-way coupled. Actually, any deformation of blood vessel walls has an effect on the fluid flow and inversely [33, 34]”.

Point 3: There is no comparison with ether experiment observation or analytical predictions in the paper. The results or proposed model in the paper is less valuable.

Response 3: The following sentence has been added. “Our results have the same order of magnitude of previous works [31, 35-37]. For instance, Choudhari and Panse obtained a radial deformation ranging from 1.5 to 2.2 µm and a maximal velocity about 0.6 m/s”.

Reviewer 2 Report

This work invaginates the deformation of human aorta due to the blood flow using FEM. The Naiver-Stokes equation is used as governing equation for the calculation of the velocity field and pressure distribution. The Neo-Hookean hyperplastic model is used for the calculation of deformation. This study is useful for the investigation of cardiovascular diseases. The manuscript is well prepared, and results appear sound. The literature review is adequate and informative. However, the following issues should be addressed before it can be accepted for publication.

1. Please check through the manuscript for spelling and grammar mistakes. For example, Line 19 “will be useful for investigate…”, Line 196 “de-pends” and “un-steady”.
2. The investigation is sole based on FEM simulation. How do authors confidently claim the FEM results is correct? Experimental validation on real human aorta or silicon rubber model will be very useful.
3. Since author claimed that the pressure, velocity and deformation can be predicted with given blood flow velocity, the blood flow velocity then can be inversely predicted from given pressure, velocity and deformation. A discussion of inverse analysis and its usefulness as future works is necessary. Please refer to the following literature for more information of inverse analysis (iterative gradient search method).
https://doi.org/10.1007/s00170-018-2508-6; https://doi.org/10.1007/s00170-019-03286-0
4. The font of color bar in figures 4, 6 and 8 is not readable. Please update the figures.

Author Response

Point 1: This work invaginates the deformation of human aorta due to the blood flow using FEM. The Naiver-Stokes equation is used as governing equation for the calculation of the velocity field and pressure distribution. The Neo-Hookean hyperplastic model is used for the calculation of deformation. This study is useful for the investigation of cardiovascular diseases. The manuscript is well prepared, and results appear sound. The literature review is adequate and informative. However, the following issues should be addressed before it can be accepted for publication.

Please check through the manuscript for spelling and grammar mistakes. For example, Line 19 “will be useful for investigate…”, Line 196 “de-pends” and “un-steady”.

Response 1: The spelling and grammar mistakes are corrected.

Point 2: The investigation is sole based on FEM simulation. How do authors confidently claim the FEM results is correct? Experimental validation on real human aorta or silicon rubber model will be very useful

Response 2: This remark is very interesting. We intend to perform the experimental validation in a future work as we mention it in the conclusion.

Point 3: Since author claimed that the pressure, velocity and deformation can be predicted with given blood flow velocity, the blood flow velocity then can be inversely predicted from given pressure, velocity and deformation. A discussion of inverse analysis and its usefulness as future works is necessary. Please refer to the following literature for more information of inverse analysis (iterative gradient search method). https://doi.org/10.1007/s00170-018-2508-6; https://doi.org/10.1007/s00170-019-03286-0

Response 3: The following sentence has been added. “In this study, the pressure, the velocity and the deformation have been predicted with given blood flow velocity. It is interesting, in future work, to analyze the inverse problem. A numerical method such as iterative gradient search method is expected to be useful to perform this analysis [38, 39]”.

Point 4: The font of color bar in figures 4, 6 and 8 is not readable. Please update the figures.

Response 4: The font color bar in figures 4, 6 and 8 are clear in this version.

Round  2

Reviewer 1 Report

The revised paper can be accepted

Reviewer 2 Report

The authors have successfully addressed all raised issues, the reviewer has no further concerns for this paper. It can now be accepted for publication.