Asymptotic Solution for Skin Heating by an Electromagnetic Beam at an Incident Angle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a theoretical analysis of the thermal effects on skin tissue within millimeter-wave electromagnetic waves at various incident angles. Its primary contribution lies in the development of an asymptotic solution for the temperature distribution in the skin, taking into account the impact of incident angle on heating patterns. However, similar studies have been widely reported in the literatures, and the current work offers limited novelty.

Several suggestions are list bellow:

First, the absence of experimental validation significantly limits the practical relevance and scientific impact of the work.

Second, the study relies on several simplifying assumptions, such as uniform skin properties, negligible lateral heat conduction, and a semi-infinite tissue domain. A more critical discussion of these assumptions and their influence on the results is needed.

Third, the manuscript would benefit from a more thorough comparison with existing literature. 

In conclusion, the manuscript does not currently meet the standards for publication in this journal. In its present form, I recommend rejection. Alternatively, the authors may consider submitting their work to a more suitable venue, such as the Journal of Directed Energy, where the topic may be more closely aligned with the journal’s scope and target readership.

Author Response

Comment1 :

The paper presents a theoretical analysis of the thermal effects on skin tissue within millimeter-wave electromagnetic waves at various incident angles. Its primary contribution lies in the development of an asymptotic solution for the temperature distribution in the skin, taking into account the impact of incident angle on heating patterns. However, similar studies have been widely reported in the literatures, and the current work offers limited novelty.

Response:

To our knowledge, there is no other studies on the thermal effect of an electromagnetic beam at an arbitrary incident angle. 

Comment 2:

First, the absence of experimental validation significantly limits the practical relevance and scientific impact of the work.

Second, the study relies on several simplifying assumptions, such as uniform skin properties, negligible lateral heat conduction, and a semi-infinite tissue domain. A more critical discussion of these assumptions and their influence on the results is needed.

Third, the manuscript would benefit from a more thorough comparison with existing literature. 

In conclusion, the manuscript does not currently meet the standards for publication in this journal. In its present form, I recommend rejection. Alternatively, the authors may consider submitting their work to a more suitable venue, such as the Journal of Directed Energy, where the topic may be more closely aligned with the journal’s scope and target readership.

Response:

This manuscript is a mathematical study of thermal effect of electromagnetic beam at an arbitrary incident angle. We did make some simplifications (like the uniform skin material properties  to make the analytical solution tractable. The benefit of having an analytical solution is that we can have a better understanding of various physical parameters on the thermal heating. Other simplifications are well justified when introduced. negligible lateral heat conduction is justified because the lateral length scale is much larger than the penetration depth.  The semi-infinite domain is justified because the penetration depth of 95GHz is only 0.16mm. Any tissue significantly thick than that can be approximately treated as semi-infinite. We have revised the manuscript to clarify these points.

We agree that "Journal of Directed Energy" would also be a suitable journal for this manuscript. 

 

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript entitled “Asymptotic Solution for Skin Heating by an Electromagnetic Beam at an Incident Angle” is well written and adequately structured. In the first section of the paper, the problem addressed by the study is briefly explained. In my opinion, this section should be expanded with a more detailed explanation of the problem (focusing solely on its physical aspects). Additionally, it is necessary to include a review of previous research, either within this section or as a separate section of the manuscript. In the second and third section, a mathematical model is presented for skin temperature when exposed to an incident beam. In the fourth section of the paper, the scaling properties are presented. In the final section of the paper, concluding remarks are presented.

Although the paper is very interesting, I believe it should include a calculation example and a comparison with the classical approach.

Author Response

Comment: 

The manuscript entitled “Asymptotic Solution for Skin Heating by an Electromagnetic Beam at an Incident Angle” is well written and adequately structured. In the first section of the paper, the problem addressed by the study is briefly explained. In my opinion, this section should be expanded with a more detailed explanation of the problem (focusing solely on its physical aspects). Additionally, it is necessary to include a review of previous research, either within this section or as a separate section of the manuscript. In the second and third section, a mathematical model is presented for skin temperature when exposed to an incident beam. In the fourth section of the paper, the scaling properties are presented. In the final section of the paper, concluding remarks are presented.

Although the paper is very interesting, I believe it should include a calculation example and a comparison with the classical approach.

Response:

The main objective of this mathematical study is to investigate the effect of incident angle on thermal effect of electromagnetic wave. The analytical solution obtained demonstrates the effect. The background of this study is the Active Denial System. Drawing an example from that will unnecessarily complicate this theoretical study. 

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

The introduction does not contain any references to previous studies and models. The authors should introduce the referenced studies and models, and others, highlighting the novelty of the presented models.

Concerning the paper structure, a discussion section should be included before the conclusions, where the authors discuss the precision of the developed model, highlighting possible weaknesses and challenges that should be considered in future developments.

This paper could be improved by comparing the correctness of the developed analytical models models with experimental measurements of MMW beam depth in skin tissue and local skin volume temperature increase.

It seems that there is no expression for calculating the skin absorption coefficient (mu) from the beam frequency. If not, a method for such calculation should be included.

Expression (16) should be enlarged to avoid the superposition of “power absorbed” with “per volume”.

I propose to change the title of section (3.2) from “Asymptotic Solution of (19)” to “Asymptotic Solution for the rate of skin temperature increase”.

The conclusion section seems to be very narrative. References for Figures should not be included in the conclusion. Please summarize more, shortening the conclusion, focusing, and pointing out the novelty of the model and the main achievements compared to previous models.

Author Response

Comment 1:

The introduction does not contain any references to previous studies and models. The authors should introduce the referenced studies and models, and others, highlighting the novelty of the presented models.

Concerning the paper structure, a discussion section should be included before the conclusions, where the authors discuss the precision of the developed model, highlighting possible weaknesses and challenges that should be considered in future developments.

Response:

To our knowledge, there is no other studies on the thermal effect of an electromagnetic beam at an arbitrary incident angle. In the revised manuscript, we added a discussion on the limitation of our current solution and future developments. 

Comment 2:

This paper could be improved by comparing the correctness of the developed analytical models models with experimental measurements of MMW beam depth in skin tissue and local skin volume temperature increase.

It seems that there is no expression for calculating the skin absorption coefficient (mu) from the beam frequency. If not, a method for such calculation should be included.

Expression (16) should be enlarged to avoid the superposition of “power absorbed” with “per volume”.

I propose to change the title of section (3.2) from “Asymptotic Solution of (19)” to “Asymptotic Solution for the rate of skin temperature increase”.

We changed the title of section (3.2) to "Asymptotic Solution of the skin temperature"

The conclusion section seems to be very narrative. References for Figures should not be included in the conclusion. Please summarize more, shortening the conclusion, focusing, and pointing out the novelty of the model and the main achievements compared to previous models.

Response: 

Most measurements of thermal effects of MMW human exposures are not public domain data. In addition, we are not aware of experiments of MMW exposures in which the incident angle is controlled and recorded. Also skin internal temperature and activated skin volume are not directly measurable in experiments. 

The skin absorption coefficient (\mu) as a function of frequency is solved in our current thermal model. \mu for skin for 95GHz is known in literature and is used in our model. Solving for \mu is a study of Maxwell equation for electromagnetic wave propagation. 

In the revised manuscript, we revised the conclusion section to make it stand-alone as much as possible. 

Reviewer 4 Report

Comments and Suggestions for Authors

After a short introduction, the governing equations for beam propagation within the skin (z positive axes) and outside are precised, using three types of configurations for the beam, considering the power density over this intersection as a function of (x, y) that follows a general 2D Gaussian distribution. Figure 2 is well done.

Power Density Projected onto the Skin Surface

Skin Temperature Evolution is computed using conservation of energy equation, with boundary conditions. Temperature equation with boundary conditions depends on the ratio of depth scale to lateral scale, and the problem is written with dimensionless variables. The asymptotic solution is studied according to this ratio. The paper continues with the study of scaling properties. Conclusions end the paper.

 

I recommend publication of the paper.

 

Please write eq. (16) in a readable manner.

Author Response

Comment: 

After a short introduction, the governing equations for beam propagation within the skin (z positive axes) and outside are precised, using three types of configurations for the beam, considering the power density over this intersection as a function of (x, y) that follows a general 2D Gaussian distribution. Figure 2 is well done.

Power Density Projected onto the Skin Surface

Skin Temperature Evolution is computed using conservation of energy equation, with boundary conditions. Temperature equation with boundary conditions depends on the ratio of depth scale to lateral scale, and the problem is written with dimensionless variables. The asymptotic solution is studied according to this ratio. The paper continues with the study of scaling properties. Conclusions end the paper.

I recommend publication of the paper.

Please write eq. (16) in a readable manner.

Response:

In the revised manuscript, we updated equation (16).

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Although the author has made the relevant revisions, I still believe that an experimental validation is necessary to demonstrate the correctness of the theoretical work. Otherwise, the contribution to the academic community remains limited.

Author Response

Comment:

Although the author has made the relevant revisions, I still believe that an experimental validation is necessary to demonstrate the correctness of the theoretical work. Otherwise, the contribution to the academic community remains limited.

Response:

We agree with the reviewer on that the ultimate validation of any theoretical work is an experimental validation. However, in the electromagnetic heating of skin tissue, the practical difficulties are i) the power density arriving at the skin surface and is absorbed into skin is not directly measurable, and ii) the skin internal temperature is not directly measurable in experiments. A direct experimental validation is not immediately practical. In addition, so far there is no experimental work in which the incident angle is controlled and varied intentionally. The current value of our mathematical analysis is to make theoretical predictions that hopefully will motivate future experimental investigations. In the revised manuscript, we clarified this. 

Reviewer 3 Report

Comments and Suggestions for Authors

In the introduction detail what the differences in the studies from references [1] to [8], instead of just posting these eigth references without differenciating them.

Please reduce the size of the conclusion and include a discussion section before the conclusion.

The paper should conform to the MDPI format.

 

Author Response

Comment:

In the introduction detail what the differences in the studies from references [1] to [8], instead of just posting these eigth references without differenciating them.

Please reduce the size of the conclusion and include a discussion section before the conclusion.

The paper should conform to the MDPI format.

Response:

In the revised manuscript, we expanded the text around the references in introduction. 

We added a discussion section and shortened the conclusion section.