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Article
Peer-Review Record

Studying the Degree of Tooth Enamel Mineralization through Raman Spectroscopy in Various Spectral Ranges

by Diana V. Prikule 1, Vladimir I. Kukushkin 2,*, Aleksandr V. Mitronin 1 and Vladislav F. Prikuls 3
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Biophysica 2021, 1(3), 269-278; https://doi.org/10.3390/biophysica1030020
Submission received: 14 April 2021 / Revised: 21 May 2021 / Accepted: 20 June 2021 / Published: 28 June 2021

Round 1

Reviewer 1 Report

Diana V. Prikule et al. present the comparison of different ex situ and in situ Raman instruments for the measurement of apatite in tooth enamel. The article represents a useful instrument comparison, which in contrast to other studies comprises both, ex situ Raman microspectroscopy and in situ Raman sensor approaches and demonstrates that the in situ/in vivo approach can deliver similar information as the destructive ex situ measurements. The article in several parts lacks correct use of scientific terminology and precise description of the actual results. For the latter reason, for example, the abstract promises measurements and results, which are not contained in the following text.

 

For these reasons, I see that the results are worth being published, but their description needs major revisions.

 

Abstract:

As a chemist I stumble over the wording “teeth enamel of different functional groups”, because to me functional groups means something very different. Please check if functional units would be the more appropriate terminology.

This sentence: “Calibration curves have been constructed showing correlations between the amplitude-spectral characteristics of the optical response of tooth enamel on the border between the cutting edge of the tooth and the cervical region and the values of its thickness, the degree of crystallinity, obtained with the usage of comparison methods - electron microscopy and computed tomography.” promises to the reader that a calibration curve showing Raman intensity (y axis) vs. thickness (x axis) was determined and perhaps even another one with the values vs. crystallinity. Further to these graphs the reader expects the article to contain the determination of thickness and degree of crystallinity by CT and SEM. But all this is not the case. Wrong use of the term calibration curve is repeated also in the main text. I come back to this below.

The degree of crystallinity is not mentioned at all in the Results section. Thus, it should be avoided in the abstract. For Raman spectroscopists, crystallinity is related to Raman band widths. Compare: MDPI Heritage 2019, 2, 1662-1683.

Thus, the abstract needs to be thoroughly rephrased.

I like this wording: “The proposed methods can be considered as potential quantitative methods for express diagnostics of the state of tooth enamel in vivo.” much more. Potential quantitative describes the results of this study very well and exactly as they are, and they are worth being published without any overdone interpretation and wrong exaggeration.

 

Introduction:

Page 2, line 57: I wonder why a sum formula of apatite with doubled stoichiometric factors is used here. It is correct, indeed, but commonly the smallest possible integer numbers are used, resulting in Ca5(PO4)3(OH).

The authors mention “optical spectroscopy” methods, which can comprise several methods. If you specifically mean Raman and IR, I find “vibrational spectroscopy” more appropriate.

Experimental details of cited studies do not have to be mentioned in the Introduction, as they can be looked up in the original paper, so for example mentioning a “demineralising solution” is enough here, and the ingredients can be found in the original paper. This helps to shorten the Introduction.

 

Materials and methods:

I appreciate that the spectral resolutions of all spectrographs are mentioned, but there are two important parameters missing. Together with the laser wavelengths, the laser powers must be mentioned (I come back to this below). Also, for being able to judge the power density, either the spot sizes or the numerical apertures of the focusing lenses (enabling calculation of the spot size) should be given in this section.

 

Results

Scanning Raman microscopy. Plotting the calibration curve.

Here I come back to the so-called calibration curve. In Figure 1, the spectral intensities are plotted as function of measurement point numbers, and a linear regression between these two parameters does not make sense. It would make sense, if the arbitrary measurement point numbers would be calculated into distances, leading to a quantitative scale in mm with 1.5-mm steps. If Ref. [24] found a linear decrease of thickness over distance, a linear regression function makes sense. Unfortunately, I am unable to check Ref. [24] because I am unable to find it, and the given reference is a bit confusing with the author Yanushevich. О. О. and a list of authors Yanushevich. О. О. in the same line and leaving unclear to me if this is an article, book, thesis…? Thus, I have to trust the authors that this is correct. In the paragraph where Ref. [24] is cited, my comment on the sentence “This calibration curve allows you to perform an accurate quantitative express analysis to determine the thickness of the tooth enamel.” is: “No, it does not!”. For this aim, I would need a calibration curve of intensity vs. thickness! Unfortunately, there is only a curve of intensity vs. distance! As there are no comparative thickness measurements, it is incorrect to speak of a calibration curve, and indeed you cannot (!) determine the thickness of tooth enamel. Nevertheless, these results are worth being published, but they should be correctly interpreted. Here, the result is a good agreement between the linear trends of thickness (from reference data [24]) and Raman intensity. Thus, the intensity of the most prominent Raman mode of hydroxyapatite can be considered a measure for enamel thickness.

Perhaps, it must be also discussed that the Raman intensity depends on the “amount” of hydroxyapatite and thus here, might depend on both thickness and density of enamel. As the authors are much more experts of enamel than I am, I leave it to the authors to decide if this is a significant issue here.

Furthermore, the text says that the Raman intensity of hydroxyapatite is calculated “minus the background intensity of the Raman scattering of the tooth cement”. Do you mean the fluorescence background? There are also “50 Raman measurements at various points” averaged and “50 Raman maps” (in the figure caption) mentioned, which are a bit difficult to understand. Am I right that 50 Raman line scans (indeed, these would be 1-dimensional Raman maps), slightly offset, were performed? That case, I would call them line scans, because the term is easier to understand.

 

Choosing the optimal Raman system

Here, the different Raman lasers/spectrometers are compared. With the strong fluorescence background, it is a bit surprising, that the 532-nm spectrum was considered to be the best, but indeed, the extraordinary intensity is convincing. Nevertheless, if other authors should be able reproduce the results (and in science this must be the case) with other instruments, it is absolutely necessary to mention the different laser powers of the used Raman devices. Thus, here I come back to this point mentioned above. It is very likely that the green laser has a much higher power than the red, NIR lasers. Even if this is the reason, I understand why green is best here, but the reader should be able to fully understand this issue.

Furthermore, I do not understand why 24,000 counts per second are mentioned in the text for 532, when Figure 2A looks more like 14,000 counts per second as the signal-background difference value.

 

Conclusions:

Again, the authors should much more carefully state that the technique has the “potential” to measure enamel thickness, but there is no “calibration curve” so far for quantification. By the way, even though it is not possible to directly use the literature values from a different study to construct such calibration curve by correlation with the Raman intensities from the present manuscript, but it would be very helpful for readers not having detailed knowledge on the structure of tooth enamel to mention some of the numbers from Ref [24] of enamel thickness of the different parts of teeth. With this, the manuscript would come closer to the promised thickness determination, but terms like “calibration curve” or “quantitative thickness determination” should be avoided or declared as outlook.

I like this sentence: “It should be noted that in contrast to the surface probing by laser radiation of the visible range of the body soft tissues(the penetration depth of laser radiation with a wavelength of 532 nm in the tissues is about 500 microns [26]), in the case of interaction of laser radiation with hard tissues of the teeth, the penetration depth is about 1 cm [27].” because it answers a question that came to me when reading this manuscript. The authors demonstrate that they know about the significant issue of penetration depth being a function of laser wavelength. Unfortunately, the value given for hard tissue in Ref. [27] refers to a wavelength of 780 nm, thus is comparing apples and oranges. Please find another citation delivering the depth for 532 nm.

Author Response

Many thanks to the reviewer for comments and recommendations.

Question /Comment: As a chemist I stumble over the wording “teeth enamel of different functional groups”, because to me functional groups means something very different. Please check if functional units would be the more appropriate terminology.

Answer: Yes, outside of dental practice it really would be possible to specify functional groups as units. However, in medicine, in particular in dentistry, there is a concept of the functional groups of teeth such as incisors, canines, premolars and molars. This name refers to the specific functional characteristics that are inherent in these particular teeth.

Question /Comment: The degree of crystallinity is not mentioned at all in the Results section. Thus, it should be avoided in the abstract. For Raman spectroscopists, crystallinity is related to Raman band widths. Compare: MDPI Heritage 2019, 2, 1662-1683.

Answer: Weagree with the comment of the reviewer. Degree of crystallinity / amorphousness is determined by the half-width of Raman peaks. This research is planned in the future, so in the text of the article we removed the mention of this and added the corresponding text to the "Conclusion" part.

Question /Comment: I like this wording: “The proposed methods can be considered as potential quantitative methods for express diagnostics of the state of tooth enamel in vivo. ” much more. Potential quantitative describes the results of this study very well and exactly as they are, and they are worth being published without any overdone interpretation and wrong exaggeration.

Answer: Thanks for the recommendation. In the new version of the article, we used the following wording.

Question /Comment: Page 2, line 57: I wonder why a sum formula of apatite with doubled stoichiometric factors is used here. It is correct, indeed, but commonly the smallest possible integer numbers are used, resulting in Ca5(PO4)3(OH).

Answer: In dentistry, it is customary to denote the formula of hydroxyapatite with doubled stoichiometric factors.

Question /Comment: The authors mention “optical spectroscopy” methods, which can comprise several methods. If you specifically mean Raman and IR, I find “vibrational spectroscopy” more appropriate.

Answer: Yes, in this context, the term “vibrational spectroscopy”is more appropriate.                            

Question /Comment: Experimental details of cited studies do not have to be mentioned in the Introduction, as they can be looked up in the original paper, so for example mentioning a “demineralising solution” is enough here, and the ingredients can be found in the original paper. This helps to shorten the Introduction.

Answer: Thanks for the recommendation. We have removed unnecessary descriptions from the text.

Question /Comment: I appreciate that the spectral resolutions of all spectrographs are mentioned, but there are two important parameters missing. Together with the laser wavelengths, the laser powers must be mentioned (I come back to this below). Also, for being able to judge the power density, either the spot sizes or the numerical apertures of the focusing lenses (enabling calculation of the spot size) should be given in this section.

Answer: For the “EnSpectr R532” spectrometer, the laser radiation power was 25 mW, for the “EnSpectr R785” spectrometer - 180 mW, for the “EnSpectr R1064” spectrometer - 250 mW. The beam diameter for each of the above-mentioned spectrometers was 3 µm. For the "PHOTON-BIO 532" light guide spectrometer, the laser radiation power was 20 mW, the diameter of the exciting light guide fiber was 200 μm, and the angular aperture was 0. 22 rad.

Question /Comment: Here I come back to the so-called calibration curve. In Figure 1, the spectral intensities are plotted as function of measurement point numbers, and a linear regression between these two parameters does not make sense. It would make sense, if the arbitrary measurement point numbers would be calculated into distances, leading to a quantitative scale in mm with 1. 5-mm steps. If Ref. [24] found a linear decrease of thickness over distance, a linear regression function makes sense. Unfortunately, I am unable to check Ref. [24] because I am unable to find it, and the given reference is a bit confusing with the author Yanushevich. О. О. and a list of authors Yanushevich. О. О. in the same line and leaving unclear to me if this is an article, book, thesis…? Thus, I have to trust the authors that this is correct. In the paragraph where Ref. [24] is cited, my comment on the sentence “This calibration curve allows you to perform an accurate quantitative express analysis to determine the thickness of the tooth enamel. ” is: “No, it does not!”. For this aim, I would need a calibration curve of intensity vs. thickness! Unfortunately, there is only a curve of intensity vs. distance! As there are no comparative thickness measurements, it is incorrect to speak of a calibration curve, and indeed you cannot (!) determine the thickness of tooth enamel. Nevertheless, these results are worth being published, but they should be correctly interpreted. Here, the result is a good agreement between the linear trends of thickness (from reference data [24]) and Raman intensity. Thus, the intensity of the most prominent Raman mode of hydroxyapatite can be considered a measure for the enamel thickness.

Answer: We rearranged Figure 1 and plotted a quantitative scale in mm along the x-axis, where the first point (х=0) corresponds to the cutting edge of the examined tooth. Ref [24] is a book, we have included a table from this book in the text of our article. This table shows the values of the enamel thickness averaged over all teeth (a total of 65 teeth removed for medical reasons) in different anatomical areas of teeth of different groups (incisors, canines, premolars and molars) of the upper and lower jaws. In the study [24], all teeth were intact according to preliminary clinical and radiological studies and represented the entire morphological range. Yes, you are right, we have observed correlations between changes in the enamel thickness (according to [24]) and the intensity of Raman scattering. Therefore, indeed, the intensity of Raman scattering of enamel can be considered a measure of its thickness. In the article we made a more accurate wording and removed the term "calibration curve".

Question /Comment: Perhaps, it must be also discussed that the Raman intensity depends on the “amount” of hydroxyapatite and thus here, might depend on both thickness and density of enamel. As the authors are much more experts of enamel than I am, I leave it to the authors to decide if this is a significant issue here.

Answer: The intensity of the Raman scattering really depends on the "amount" of hydroxyapatite (quantity of substance), which is determined by its thickness and density. However, the contribution from the density (due to possible differences in it between the amorphous and crystalline forms) is minimal and the intensity is mainly determined by the thickness.

Question /Comment: Furthermore, the text says that the Raman intensity of hydroxyapatite is calculated “minus the background intensity of the Raman scattering of the tooth cement”. Do you mean the fluorescence background? There are also “50 Raman measurements at various points” averaged and “50 Raman maps” (in the figure caption) mentioned, which are a bit difficult to understand. Am I right that 50 Raman line scans (indeed, these would be 1-dimensional Raman maps), slightly offset, were performed? That case, I would call them line scans, because the term is easier to understand.

Answer: We made a change in the text; in the new version of the publication, we used the word "dentin" instead of the word "cement". We meant the following: the penetration depth of the laser radiation is greater than the thickness of the enamel. In this regard, we see a contribution to the integral signal of the optical response (Raman scattering) from the enamel and from the dentin. Therefore, at the zero enamel thickness, we see a non-zero Raman response of hydroxyapatite. Subtracting the "background" (the intensity of the Raman scattering of the dentin) we can judge the thickness of the enamel.

The reviewer is right, 50 linear slightly shifting scans were performed along the tooth surface. In the text of the article we clarified this point.

Question /Comment: Furthermore, I do not understand why 24,000 counts per second are mentioned in the text for 532, when Figure 2A looks more like 14,000 counts per second as the signal-background difference value.

Answer: You rightly pointed out a typo - the intensity of the Raman scattering from Figure 2A was 14,000 counts / sec.

Question /Comment: Again, the authors should much more carefully state that the technique has the “potential” to measure the enamel thickness, but there is no “calibration curve” so far for quantification. By the way, even though it is not possible to directly use the literature values from a different study to construct such calibration curve by correlation with the Raman intensities from the present manuscript, but it would be very helpful for readers not having detailed knowledge on the structure of tooth enamel to mention some of the numbers from Ref [24] of the enamel thickness of the different parts of teeth. With this, the manuscript would come closer to the promised thickness determination, but terms like “calibration curve” or “quantitative thickness determination” should be avoided or declared as outlook.

Answer: We have introduced a more accurate wording on "calibration curves". We have included the table from the book [24] in the text of our article.

Question /Comment: I like this sentence: “It should be noted that in contrast to the surface probing by laser radiation of the visible range of the body soft tissues(the penetration depth of laser radiation with a wavelength of 532 nm in the tissues is about 500 microns [26]), in the case of interaction of laser radiation with hard tissues of the teeth, the penetration depth is about 1 cm [27]. ” because it answers a question that came to me when reading this manuscript. The authors demonstrate that they know about the significant issue of penetration depth being a function of laser wavelength. Unfortunately, the value given for hard tissue in Ref. [27] refers to a wavelength of 780 nm, thus is comparing apples and oranges. Please find another citation delivering the depth for 532 nm.

Answer: We have included another link in an article discussing the penetration depth of 532 nm laser radiation into the hard tissues of the teeth.

Reviewer 2 Report

Raman spectroscopy is a technique that gives an early diagnosis of carious lesions which is non-invasive and of crucial importance for public health. However, this study presents no meaningful results or scientific novelty. As stated by the authors, the objective of this study is to “determine of the degree of demineralization of tooth enamel and its thickness by Raman spectroscopy”. However, there are NO results of degree of mineralization or enamel thickness. Therefore, the data listed in Table 1 and Table 2, i.e., in-vitro or in-vivo Raman intensity of different positions on teeth, are making no sense. I do not think these results have been completed and ready for publication. Some more detailed comments are listed below.

  • Normally, the results acquired from a newly developed technique should be compared with those from standard or traditional techniques. The authors referred the degree of mineralization of tooth enamel and its thickness data to Reference 24, which were acquired by electron microscopy and computer tomography. However, they did not present their own data on the degree of demineralization and enamel thickness, so there is no way to validate the new Raman technique. Moreover, even if authors presented their own data from Raman, the results should not be directed compared with results from other groups, simply because they are NOT the same teeth.
  • Again, the title of the papers states “…degree of tooth enamel demineralization…”. However, there are NO actual data of the degree of tooth enamel demineralization present in any way in this paper.
  • No comparison of health and carious enamels.
  • Punctuations “<<” and “>>” have been used many times in the manuscript. I do not feel it is appropriate.
  • In section 2.3, what is the standard oral hygrines procedure? More detail should be presented.
  • In the second paragraph of Section 2.2 (Line 131), I assume “plaster retainer” is a typo of “plastic container”. If this is the case, use a plastic container and number the extracted teeth are just common sense. There is no need to state in the experimental section.
  • Line 94: “2x2x1 mm” should be “2mmx2mmx1mm” or “2x2x1 mm3

Author Response

Many thanks to the reviewer for comments and recommendations.

Question /Comment: Raman spectroscopy is a technique that gives an early diagnosis of carious lesions which is non-invasive and of crucial importance for public health. However, this study presents no meaningful results or scientific novelty. As stated by the authors, the objective of this study is to “determine the degree of demineralization of tooth enamel and its thickness by Raman spectroscopy”. However, there are NO results of degree of mineralization or enamel thickness. Therefore, the data listed in Table 1 and Table 2, i. e. , in-vitro or in-vivo Raman intensity of different positions on teeth, are making no sense. I do not think these results have been completed and ready for publication. Somemoredetailedcommentsarelistedbelow.

Answer: Currently, no in vivo results have been presented indicating the intensity of Raman radiation depending on the content of hydroxyapatite in the structure of the tooth enamel. We were among the first one who pointed out how the intensity of Raman scattering depends on the thickness and, accordingly, the mineralization of the enamel (since the mineralization of the enamel depends on the amount of hydroxyapatite).

Important results were obtained in the work:

- patterns were found in the behavior of the intensity of Raman scattering at different sites of different teeth. These patterns are fully described by the differences in the thickness of the enamel in the corresponding areas [24];

- laboratory tests (in vitro) and clinical trials (in vivo) of this method were carried out on a large sample of teeth;

- for in vivo use, the optimal version of the spectrometer with a laser radiation wavelength of 532 nm was selected. This choice, without experimental confirmation, initially seemed not obvious.

Question /Comment: Normally, the results acquired from a newly developed technique should be compared with those from standard or traditional techniques. The authors referred the degree of mineralization of tooth enamel and its thickness data to Reference 24, which were acquired by electron microscopy and computer tomography. However, they did not present their own data on the degree of demineralization and enamel thickness, so there is no way to validate the new Raman technique. Moreover, even if authors presented their own data from Raman, the results should not be directed compared with results from other groups, simply because they are NOT the same teeth.

Answer: We have included the table from the book [24] in the text of our article. This table shows the average values of the enamel thickness of all the teeth (65 teeth totally removed for medical reasons) in different anatomical areas of different teeth functionalgroups (incisors, canines, premolars and molars) of the upper and lower jaws. In the study [24] all teeth were intact according to preliminary clinical and radiological studies and represented the entire morphological range. These data can be considered reliable since they were obtained from a large sample of teeth using two alternative methods. We observed accurate correlations between changes in the enamel thickness (according to [24]) and the intensity of Raman scattering. Therefore, indeed, we can consider the intensity of Raman scattering of enamel as a measure of its thickness. In the article, we made a more accurate wording and removed the term "calibration curve".

Question /Comment: Again, the title of the papers states “…degree of tooth enamel demineralization…”. However, there are NO actual data of the degree of tooth enamel demineralization present in any way in this paper.

Answer: Thank you for your note about the technical error in the writing of the article title. Indeed, what was meant was the degree of enamel mineralization, not its demineralization. We studied the degree of mineralization, so we corrected a typo in the title of the article and the article will be titled "Studying the Degree of Tooth Enamel Mineralization Through Raman Spectroscopy in Various Spectral Ranges".

Question /Comment: No comparison of health and carious enamels.

Answer: We did not compare the intensity of Raman scattering of tooth enamel affected by caries with intact enamel. We examined only intact teeth.

Question /Comment: Punctuations “<<” and “>>” have been used many times in the manuscript. I do not feel it is appropriate.

Answer: We have removed the extra signs

Question /Comment: In section 2. 3, what is the standard oral hygrines procedure? More detail should be presented.

Answer: Under the term standard oral hygiene procedure, dentists mean the standard principle of brushing teeth according to G. N. Pakhomov [Fattal R., Risovannaya, O., Melekhov S., Popkov V., Domenyuk D. Comparative evaluation of the major groups of manual tooth brushes efficiency and their effect on the oral cavity hygienic status. Archiv Euromedica. 2019. Vol. 9. P. 156; Kuzmina E. Preventive dentistry: text book/ E. M. Kuzmina, O. O. Yanushevich. – Moscow: Practical medicine, 2017, P. 34-36], which is basically consistent with the Leonardo method. Cleaning starts with maxillary molars located on the right side, then move to the front teeth, and then finish on the left molars. On the lower jaw, the left molars are first cleaned, then the anterior teeth and then the right molars. The vestibular and oral surfaces are cleaned with sweeping movements from gum to tooth, the brush head is at an angle of 45 ° to the gum. The occlusal surface is cleaned by reciprocating movements. Cleaning is finished by a  circular motion adjusted to the teeth segments.

Question /Comment: In the second paragraph of Section 2. 2 (Line 131), I assume “plaster retainer” is a typo of “plastic container”. If this is the case, use a plastic container and number the extracted teeth are just common sense. There is no need to state in the experimental section.

Answer: ISO class III plaster was used to fix the extracted teeth in it. We did not use plastic.

Question /Comment: Line 94: “2x2x1 mm” should be “2mmx2mmx1mm” or “2x2x1 mm3”

Answer: done.

Round 2

Reviewer 1 Report

I appreciate that the authors have considered all my comments and beyond have substantially improved the manuscript. There is only the following part of the abstract that I have to criticise:

“Correlations between the amplitude-spectral characteristics of the optical response of tooth enamel on the border between the cutting edge of the tooth and the cervical region and the values of its thickness obtained using comparison methods - electron microscopy and computed tomography.”

This does not sound like a complete sentence to me and it still imposes that a calibration function directly between intensity and thickness was obtained. Furthermore, it misleads readers to search for your own electron microscopy and computed tomography results. I propose to use a modified version of this (somehow shortly summarising this relatively long sentence):

“The obtained dependence of the Raman scattering intensity on the distance from the incisal edge (Fig.1) is in good agreement with the literature data [24], where two independent methods (computer tomography (Tab.1) and electron microscopy (Tab.2)) were used to determine the enamel thickness values”

which I found in the Results section.

Author Response

Thank you for your comment! We have made corrections to the text of the article.

Reviewer 2 Report

Thanks to the authors' efforts, the revised manuscript has been improved significantly. However, despite the significant importance of Raman technique in the detection of early caries, this manuscript still lacks in-depth study. I do not think it is appropriate to just "borrow" two whole tables from Ref.24 (Tables 1&2 in the revised version). I am not sure whether the authors acquired copyright permission from the publisher of Ref.24. Ref. 24. I still believe the authors should do their own measurements. The tooth specimens used by the authors and those in Ref. 24 are different. Therefore, these numbers of enamel thickness will be slightly different.

More importantly, neither did the authors provide any data of enamel thickness from their own Raman experiments. So what is the point to cite the whole two tables from Ref. 24?

Author Response

Thank you for your comments! We have received permission to use Ref [24].

  1. We are talking about the correlations between the behaviours of the average values (obtained from a large-sample analisys) of Raman scattering intensities and the average values of the enamel thickness (also obtained from a large-sample analysis). As the sample is large and the inaccuracy is insignificant both for our study and for the reference [24] we can compare the behavior of these dependencies and be sure that this method can be considered quantitativein the future.
  2. Moreover, we have shown what wavelength the spectrometer should have to make such a study possible and optimal.
  3. The method to determine the thickness of the enamel is extremely important regardless of the caries assessment because it reveals the need to examine the thickness of the enamel for further effective diagnosis, prophylaxis and teeth treatment.

Round 3

Reviewer 2 Report

The new version has been improved from the original submission. I suggest it can be accepted in the current form.

 

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