A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Round 1

Reviewer 1 Report

The innovative point of the article is not clear. What improvements have the authors made? The structure of the paper needs to be rewritten to meet the basic paper framework. The mdpi template was not used to submit the paper.

Some minor grammar and spelling errors need to be corrected.

Author Response

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Reviewer 2 Report

The authors present an interesting theme used Transcranial

Magnetic Stimulation (TMS) in neurology. The article is well founded from a mathematical and methodological point of view for the presentation of the electromagnetic field propagation concept.

The method is not new in the specialized literature, but the authors' way of presentation brings a plus, especially for the mathematical foundation.

I ask the authors to introduce in chapter 7, a short comparison between the method proposed in the TMS article and the use of ultrasonic sensors instead of coils.

Author Response

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Reviewer 3 Report

There are various models of the coil-brain system of Transcranial Magnetic Stimulation (TMS). The present study undertakes an analysis of the advantages, and disadvantages associated with each formulation used for computing TMS fields in order to serve as a guide for reproduction and future implementation of TMS stimulations.

The introduction is clear with an evident study question. The manuscript is well written.

The analysis is clear, to the point, and in line with the study question.

The discussion is obvious, a logic consequence of the analysis, and ends with a conclusion which answer the study question.

Author Response

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Reviewer 4 Report

The presented review is very well detailed and organized. The impact could be very extensive, since the increase of TMS employment in scientific research for investigating brain dynamics in humans. Therefore, I would recommend addressing very minor issues:

1. The authors provided an extensive and technical analysis of the most used methods and approaches for TMS. In this regard, I would recommend to underline how such methods were selected and why they are the most interesting.

2. In the Conclusion section there is probably a typo: the acronym "TNS" is not defined previously. Probably the authors meant "TMS".

3. In table 3 the font in central column is not easily readable.

Author Response

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Round 2

Reviewer 1 Report

As the authors responded to me, they have not clearly given the main works or contributions in the abstract part and conclusions part in the revised manuscript. Transcranial Magnetic Stimulation is short as TMS. Please check the keywords and revised it. TMS simulation is not the accurate representation. Please check the whole manuscript. Please polish the full text carefully.

Moderate editing of English language required.

Author Response

Reviewer:

Reviewer:  As the authors responded to me, they have not clearly given the main works or contributions in the abstract part and conclusions part in the revised manuscript:

Authors: We agree with the reviewer. The abstract and the conclusions were modified to clarify the contributions of the work ( the modifications are presented in the marked manuscript)

Abstract:

“Since the inception of the Transcranial Magnetic Stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems, and numerical solutions employed in TMS fields simulations, analyzing  the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the Finite Difference and Finite Element Method. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.”

Conclusions:

“The present works present a survey of the most used formulations, Boundary Value Problems and Implementations for the numerical computation of TNS TMS fields. These aspects are analyzed showing theirs limitations and advantages. The deduction of the formulations from the Maxwell equations and the numerical solution of the corresponding BVP are described in detail. Including the deduction of some numerical solutions not found in the consulted literature, such as Finite Difference for Quasi-static magnetic A-j and Darwin models, and Finite Element for Quasi-static magnetic A-j and Darwin models using the Galerkin method, as well as their implementation of boundary conditions applied to TMS fields. The present work aim to serve as guide for reproduction and future implementation of TMS simulations.

Several of the main results deduced from the TMS fields simulations emphasize in the importance of the stimulation parameters. In particular, the coil parameters and arrangement, followed by the precision on the specification of the electrical properties of the tissue and details of the brain geometry model………”

 

Reviewer: Transcranial Magnetic Stimulation is short as TMS. Please check the keywords and revised it. TMS simulation is not the accurate representation.

Authors: We agree with the reviewer,   keywords were corrected according to reviewer comments, as it can be seen in the marked version of the manuscript

Reviewer: Please check the whole manuscript. Please polish the full text carefully. (Moderate editing of English language required.)

Authors: The authors performed and extensive review of the text grammar and spelling. The changes could be seen in the marked version of the manuscript

Author Response File: Author Response.pdf