Numerical Simulation of Enhancement of Superficial Tumor Laser Hyperthermia with Silicon Nanoparticles

Round 1

Reviewer 1 Report

The manuscript ID photonics-1470370 mainly presents a numerical analysis devoted to photoenergy transfer effects assisted by silicon nanoparticles with potential influence in laser tumor hyperthemia treatments. Here are some comments to the authors:

1. Usually Gaussian beams are employed in photo-thermal treatments, does this consideration is addressed in this study? Please comment how would be the changes in the numerical results for Gaussian and plane waves.
2. Several citations presented in collective form within the introduction section cannot be justified. It is suggested to edit the information with individual expressions for the proper citations that guarantee the current panoramic scenario in the topic of research.
3. A modification in the band gap can be expected by a modification in the size of the silicon nanoparticles. Changes in the absorption coefficient can be neglected in the calculations presented for the different cases explored? Please argue.
4. How is considered the possible agglomeration of the nanoparticles during the incidence of the laser energy in the samples?
5. Nanoscale thermal transfer has been described by different models. You can see for instance:

https://doi.org/10.1016/j.physrep.2019.12.001

Please justify how was selected the equation for describing the nanoscale thermal transfer.

6. Is there an influence of the polarization over the photo-thermal phenomena in the samples studied? Please argue taking into account the anisotropy factor.
7. Thermo-optic effects could be responsible for a change in the refractive index exhibited by silicon nanoparticles. You can see for instance: https://doi.org/10.1364/OE.16.018390. Can it be an advantage to use continuous-wave (CW) sources instead of pulsed light in nanomedical laser treatments? Pulsed light usually present advantages emerging from ultrafast optical nonlinearities and/or other nanoscale mechanisms assisting the laser energy transfer. Please discuss within the text.
8. The results must be confronted with updated publications to see the importance of the main findings.
9. How was selected the wavelength employed for this study?
10. Several references could be updated and better selected.

Author Response

We thank the reviewer for his substantial comments on our manuscript.

We have improved the manuscript text in accordance with the comments.

 

Comment 1: Usually Gaussian beams are employed in photo-thermal treatments, does this consideration is addressed in this study? Please comment how would be the changes in the numerical results for Gaussian and plane waves.

 Response 1: Thank you for this comment. In our preliminary studies we compared illumination with the Gaussian laser beam and uniform intensity distribution and found that at equal intensities the heating of the tumor periphery by a Gaussian beam is lower as compared to the uniform distribution, with the opposite effect in the center of the tumor, which may induce incomplete tumor response in practice. To discuss the choice of the beam configuration we added the following text to the manuscript (lines 168 – 177):

Although Gaussian laser beams were reported to be employed for cancer theranostics  (e.g., [53]),  uniform irradiation of the tumor has some advantages. Our preliminary simulations of tumor hyperthermia with Gaussian laser beam demonstrated lower heating of the tumor edges than in the case of homogeneous beam due to a significant intensity decrease at the beam periphery. Moreover, applying a homogeneous beam seems to be more practical since positioning a laser spot at the skin surface needs smaller precision. Therefore, in simulation we consider a circular laser irradiation area of the radius r with uniform intensity distribution and the laser beam axis coinciding with the axial symmetry axis of the tumor. Such intensity distribution can be achieved with the help of laser radiation homogenisers (see, e.g., [54]).

 

Comment 2: Several citations presented in collective form within the introduction section cannot be justified. It is suggested to edit the information with individual expressions for the proper citations that guarantee the current panoramic scenario in the topic of research.

 Response 2:

In order to fulfil the reviewer requirement we have extended the introduction section and introduced individual expressions describing the main ideas of the cited papers.

Lines 59-66:

One of the most popular objects for therapeutic applications are gold-based nanostructures, which were shown to be efficient  both in experiments [14-16] and in numerical simulations [16–18]. Owing to plasmon resonance properties, these structures were demonstrated to provide a pronounced contrast in both optical scattering and absorption even at relatively low concentrations [19–21]. To simulate laser heating of the tissues with embedded gold NPs the Monte Carlo technique [16,17] is often employed providing good agreement of calculated temperature distributions and experimental results for nanorods  [16] and core-shell [17] gold nanostructures.

Lines 98-102:

High-energy grinding of porous silicon films in water by a planetary mill was demonstrated to result in formation of SiNPs with diameters of 2 to 5 nm agglomerated into big particles of sizes ranging from 40 to 300 nm [33]. SiNPs of diameter less than 220 nm were reported to be formed with the help of fracturing porous silicon by ultrasonication in water [37] and ethanol [38] followed by membrane filtration.

Lines 86-93:

SiNPs were additionally found to be promising as thermal coupling agents for hyperthermia [37–39]. In vitro experiments on a cell culture exposed to near-infrared laser irradiation demonstrated significant reduction of tumor cell viability in presence of SiNPs [37]. Experiments in vivo demonstrated that porous silicon in combination with laser irradiation allows for selective destruction of cancer cells without damaging surrounding healthy cells [38]. Numerical simulations of laser tumor hyperthermia [39] demonstrated the increase of maximum tumor temperature by 4^oC due to SiNPs presence in the tumor site.

 

Comment 3: A modification in the band gap can be expected by a modification in the size of the silicon nanoparticles. Changes in the absorption coefficient can be neglected in the calculations presented for the different cases explored? Please argue.

 Response 3:

Thank you for your comment. Indeed, the nanoparticle size restrictions can result in broadening band gap and variation of optical parameters (the so-called quantum confinement). However,  these effects are detected for silicon nanoparticles of diameter 5 nm and less. Since we consider nanoparticles of diameter above 8 nm, we can expect no quantum confinement and employ in our simulation optical parameters of bulk silicon. To discuss this fact we added to the paper following text  (lines 226 – 234):

Given that the considered SiNP size exceeds 8 nm, whereas quantum-confinement effects in silicon resulting in variations of  band gap  and optical parameters could be detected for SiNP diameter below 5 nm [64] to calculate the SiNP optical parameters we used refractive index n_NP = 3.8823 and extinction coefficient k_NP = 0.0196 for crystalline silicon [65]. Relative variations of these values with temperature increase up to 10°С for bulk silicon are 10^-3 and 10^-5, respectively [66, 67], and, hence, thermooptical effect on the SiNPs embedded into the tumor is expected to be negligible. Refractive index for tumor tissue at the wavelength of 633 nm is assumed to be equal to n_tum = 1.4 [56,68,69]. Optical properties of skin layers and tumor tissue are presented in Table 1.

 

Comment 4: How is considered the possible agglomeration of the nanoparticles during the incidence of the laser energy in the samples?

 Response 4:

We aimed at a slight temperature increase as a result of the laser treatment, no SiNP agglomeration is possible in these circumstances. We added the following phrase to the text (lines 242 – 243):

We expect that during laser hyperthermia the tissue temperature does not significantly exceed 42°C, therefore SiNP agglomeration would not occur.

 

Comment 5: Nanoscale thermal transfer has been described by different models. You can see for instance:

https://doi.org/10.1016/j.physrep.2019.12.001

Please justify how was selected the equation for describing the nanoscale thermal transfer.

 Response 5:

Thank you for your comment.  Let us mention that the prevailing way to find temperature distribution during hyperthermia is solving the bioheat transfer equation. We discussed it in following  paragraph added  into Introduction section (lines 299– 314):

The standard way to obtain temperature distribution within the tissues during hyperthermia procedure is solving bioheat transfer equation, which was initially proposed by Pennes in the following form [78,79]

See formula (9) in the attached file

where T is the biotissue temperature,  is the biotissue density, C_p is the biotissue heat capacity at a constant pressure; k is the thermal conductivity, Q_met is the speed of metabolic heat generation the per unit volume, Q_ext is the external source power density, which in our case is a result of the laser radiation absorption, and Q_perf is power density of the heat loss caused by perfusion (blood transfer through capillaries and extracellular spaces in tissue [80]).  Despite great progress achieved during more than 70 years since its first proposal and various improvements and refinements of the equation (see, e.g., [81,82,83]), the Pennes equation is, nevertheless, applicable for the stationary case of continuous-wave irradiation of the biotissue [81] :

See formula (10) in the attached file

We solved Equation (10) using a finite-difference approach taking obtained absorption maps simulated by the Monte Carlo approach as  the external source power density.

The other part of your remark is connected with thermal parameters of the biotissues with embedded silicon nanoparticles. We added following discussion of this topic into section  2.4. (lines 323 –329):

Generally, thermal parameters of the nanoparticles can differ from ones for bulk material due to variation of phonon spectrum and well-developed surface [89]. However, previously we have shown that Raman spectra of the employed SiNPs coincide with the spectrum for crystalline silicon [34], volume fraction of the SiNPs does not exceed 0.003, and SiNP heating is expected to be at several degrees. Based on this, we consider no variations of thermal parameters both for the SiNPs and for the tumor with embedded SiNPs. 

 

Comment 6: Is there an influence of the polarization over the photo-thermal phenomena in the samples studied? Please argue taking into account the anisotropy factor.

 Response 6:

In our studies the anisotropy factor g is the mean cosine of a scattering angle in biotissue. The laser beam is considered to be randomly polarized and the considered effects do not depend on radiation polarization, since our SiNPs are spherical and skin tissue does not have anisotropic properties. The anisotropy here means non-uniform distribution of the probability of a photon to scatter at a particular angle and is not related to the dependence of refractive index on the direction of beam propagation.

In the entire text “anisotropy factor” was replaced by “scattering anisotropy factor”.

 

Comment 7: Thermo-optic effects could be responsible for a change in the refractive index exhibited by silicon nanoparticles. You can see for instance: https://doi.org/10.1364/OE.16.018390. Can it be an advantage to use continuous-wave (CW) sources instead of pulsed light in nanomedical laser treatments? Pulsed light usually present advantages emerging from ultrafast optical nonlinearities and/or other nanoscale mechanisms assisting the laser energy transfer. Please discuss within the text.

 Response 7:

At employed laser radiation intensities and achieved temperatures the thermooptical effects are extremely small. To discuss the thermoopical effect in the SiNP for the case of hyperthermia process we have added the following text (lines 230 – 234):

Relative variations of these values with temperature increase up to 10°С for bulk silicon are 10^-3 and 10^-5, respectively [66, 67], and, hence, thermooptical effect on the SiNPs embedded into the tumor is expected to be negligible. Refractive index for tumor tissue at the wavelength of 633 nm is assumed to be equal to n_tum = 1.4 [56,68,69]. Optical properties of skin layers and tumor tissue are presented in Table 1.

The reasons for choice of cw radiation are briefly discussed in the added text (lines 126 – 133):

The choice of cw laser radiation for hyperthermia is determined by limits of laser radiation intensity for safe laser treatment of biotissues (below 200 mW/cm²  [50]), especially for healthy tissues surrounding the tumor. Employing pulsed irradiation has no advantages due to decrease of safety energy density limits with shortening pulse duration [50,51]. Although silicon possesses significant cubic nonlinear susceptibility responsible for the light self-action [52], simple estimations demonstrate that for laser pulse energy of order of safety threshold [51] relative variation of absorption for bulk silicon is of order of 10^-4.

 

Comment 8: The results must be confronted with updated publications to see the importance of the main findings.

 Response 8:

In order to fulfil the reviewer requirement we have added the following text at the end of Discussion section (lines 543 – 546):

Since no experimental results are available to assess the validity of the calculations performed, we analysed similar simulations studies. Refs. [37,38,43] report on numerical simulation of heating water suspensions of SiNPs, however, such studies do not account for the effect of surrounding biotissues both in light transport and heat transfer problems.

 

Comment 9: How was selected the wavelength employed for this study?

 Response 9:

The choice of wavelength of 633 nm is based on our previous results. We briefly discuss it in Sec. 2.1 (lines 181 – 184).

Our previous study [39] has compared the application of the wavelengths of 633 and 800 nm for nanoparticles-mediated tumor hyperthermia. It was shown that at equal intensities the wavelength of 633 nm provides higher local heating, which determined the choice of this wavelength for this study.

Comment 10: Several references could be updated and better selected.

Response 10: In order to fulfill the reviewer requirement we revised the reference list.  Added references are listed below;

 

1. Zhou, J.; Cao, Z.; Panwar, N.; Hu, R.; Wang, X.; Qu, J.; Tjin, S.C.; Xu, G.; Yong, K.-T. Functionalized Gold Nanorods for Nanomedicine: Past, Present and Future. Chem. Rev. 2017, 352, 15–66, DOI:10.1016/j.ccr.2017.08.020.
2. Liu, A.; Wang, G.; Wang, F.; Zhang, Y. Gold Nanostructures with Near-Infrared Plasmonic Resonance: Synthesis and Surface Functionalization. Chem. Rev. 2017, 336, 28–42, DOI:10.1016/j.ccr.2016.12.019.
3. Simakin, A.V.; Baimler, I.V.; Smirnova, V.V.; Uvarov, O.V.; Kozlov, V.A.; Gudkov, S.V. Evolution of the Size Distribution of Gold Nanoparticles under Laser Irradiation. Wave Phen. 2021, 29, 102–107, DOI:10.3103/S1541308X21020126.
4. Simakin, A.V.; Astashev, M.E.; Baimler, I.V.; Uvarov, O.V.; Voronov, V.V.; Vedunova, M.V.; Sevost’yanov, M.A.; Belosludtsev, K.N.; Gudkov, S.V. The Effect of Gold Nanoparticle Concentration and Laser Fluence on the Laser-Induced Water Decomposition. Phys. Chem. B 2019, 123, 1869–1880, DOI:10.1021/acs.jpcb.8b11087.
5. Al-Kattan, A.; Nirwan, V.; Popov, A.; Ryabchikov, Y.; Tselikov, G.; Sentis, M.; Fahmi, A.; Kabashin, A. Recent Advances in Laser-Ablative Synthesis of Bare Au and Si Nanoparticles and Assessment of Their Prospects for Tissue Engineering Applications. IJMS 2018, 19, 1563, DOI:3390/ijms19061563.
6. Braguer, D.; Correard, F.; Maximova, K.; Villard, C.; Roy, M.; Al-Kattan, A.; Sentis, M.; Gingras, M.; Kabashin, A.; Esteve, M.-A. Gold Nanoparticles Prepared by Laser Ablation in Aqueous Biocompatible Solutions: Assessment of Safety and Biological Identity for Nanomedicine Applications. IJN 2014, 5415, DOI:2147/IJN.S65817.
7. Kuzmin, P.G.; Shafeev, G.A.; Bukin, V.V.; Garnov, S.V.; Farcau, C.; Carles, R.; Warot-Fontrose, B.; Guieu, V.; Viau, G. Silicon Nanoparticles Produced by Femtosecond Laser Ablation in Ethanol: Size Control, Structural Characterization, and Optical Properties. Phys. Chem. C 2010, 114, 15266–15273, DOI:10.1021/jp102174y.
8. Jean, M.; Schulmeister, K. Laser-Induced Injury of the Skin: Validation of a Computer Model to Predict Thresholds. Opt. Express 2021, 12, 2586, DOI:10.1364/BOE.422618.
9. Bristow, A.D.; Rotenberg, N.; van Driel, H.M. Two-Photon Absorption and Kerr Coefficients of Silicon for 850–2200nm. Phys. Lett. 2007, 90, 191104, DOI:10.1063/1.2737359.
10. Tunç, M.; Çamdali, Ü.; Parmaksizoğlu, C.; Çikrikçi, S. The Bio‐heat Transfer Equation and Its Applications in Hyperthermia Treatments. Engineering Computations 2006, 23, 451–463, DOI:1108/02644400610661190.
11. Wang, X.; Qi, H.; Yang, X.; Xu, H. Analysis of the Time-Space Fractional Bioheat Transfer Equation for Biological Tissues during Laser Irradiation. International Journal of Heat and Mass Transfer 2021, 177, 121555, DOI:1016/j.ijheatmasstransfer.2021.121555.
12. Liu, K.-C.; Chen, T.-M. Comparative Study of Heat Transfer and Thermal Damage Assessment Models for Hyperthermia Treatment. Journal of Thermal Biology 2021, 98, 102907, DOI:1016/j.jtherbio.2021.102907.
13. Santos, O.; Cancino-Bernardi, J.; Pincela Lins, P.M.; Sampaio, D.; Pavan, T.; Zucolotto, V. Near-Infrared Photoactive Theragnostic Gold Nanoflowers for Photoacoustic Imaging and Hyperthermia. ACS Appl. Bio Mater. 2021, 4, 6780–6790, DOI:1021/acsabm.1c00519.
14. Gongalsky, M.B.; Osminkina, L.A.; Pereira, A.; Manankov, A.A.; Fedorenko, A.A.; Vasiliev, A.N.; Solovyev, V.V.; Kudryavtsev, A.A.; Sentis, M.; Kabashin, A.V.; et al. Laser-Synthesized Oxide-Passivated Bright Si Quantum Dots for Bioimaging. Rep. 2016, 6, 24732, DOI:10.1038/srep24732.
15. Barbagiovanni, E.G.; Lockwood, D.J.; Simpson, P.J.; Goncharova, L.V. Quantum Confinement in Si and Ge Nanostructures. Journal of Applied Physics 2012, 111, 034307, DOI:1063/1.3680884.
16. Jellison, G.E.; Modine, F.A. Optical absorption of silicon between 1.6 and 4.7 eV at elevated temperatures, Phys. Lett., 1982, 41, 2, 180-182, DOI: 10.1063/1.93454
17. Jellison, G.E.; Burke, H.H. The temperature dependence of the refractive index of silicon at elevated temperatures at severed laser wavelengths, Appl. Phys., 1986, 60, 2, 841-843, DOI: 10.1063/1.337386
18. Priester, M.I.; Curto, S.; van Rhoon, G.C.; ten Hagen, T.L.M. External Basic Hyperthermia Devices for Preclinical Studies in Small Animals. Cancers, 2021, 13, 4628. DOI: 10.3390/cancers13184628

 

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript of O.I. Sokolovskaya et al. entitled as “Numerical simulation of enhancement of superficial tumor laser hyperthermia with silicon nanoparticles” is devoted to biomedical applications (such as tumor destruction due to laser-induced hyperthermia) of silicon nanoparticles formed by laser ablation of silicon nanowires in different liquid media. The research shows the importance of the presence of laser-activated nanoagents and their properties for the hyperthermia of tumors as well as the selective heating of tumor areas. The manuscript is logically organized and well written. The obtained theoretical data are of interests for interdisciplinary community developing anti-cancer agents and strategies and falls into criteria of “Photonics” journal. After clarification of some point the manuscript can be accepted for the publication.

Remark 1.

Two types of silicon nanoparticles prepared in different media and having various optical properties are studied. Can authors comment why “the absorption efficiency for wSiNPs almost does not depend on their concentration while for eSiNPs the increase of the concentration provides noticeable rise“? (lines 327-329)

Remark 2.

In the study, authors used the cw laser radiation that can provide additional heating effects during continuous long lasting irradiation especially at higher intensities. Can one expect any irradiation time effects for silicon nanoparticles hyperthermia and what was the irradiation time in this case?

Remark 3.

Can one expect any additional benefits for laser-induced heating by managing irradiation parameters such as pulsed laser irradiation or changing energy profile of a laser spot?

Remark 4.

One could briefly highlight the importance of silicon nanoparticles that can be used in many various applications (lines 66-74) as well as their customization (lines 56-59) to achieve additional benefits in applications.

Remark 5.

The top part of the Figure 2 is poorly visible and in the Figure 3c is not clear a type of silicon nanoparticles (eSiNPs or wSiNPs).

Author Response

We thank the reviewer for his substantial comments on our manuscript.

We have improved the manuscript text in accordance with the comments.

 

Comment 1: Two types of silicon nanoparticles prepared in different media and having various optical properties are studied. Can authors comment why “the absorption efficiency for wSiNPs almost does not depend on their concentration while for eSiNPs the increase of the concentration provides noticeable rise“? (lines 327-329)

 Response 1:

Silicon nanoparticles produced in different liquid media (water, ethanol) differ only by their size distributions. wSiNPs produced in water are characterized by a mean diameter of about 50 nm with noticeable contribution of the fraction with diameters exceeding 100 nm. eSiNPs produced in ethanol are characterized by smaller mean diameter (less than 30 nm) with no particles larger than 80 nm in size.The difference in typical sizes results in considerably larger contribution of wSiNPs to the overall absorption and scattering in the tumor compared to eSiNPs. The “absorption efficiency” parameter is defined as the product of the absorption coefficient over the thickness of the "skin layer" of radiation penetration into the tumor. Larger absorption and scattering reduce the thickness of the "skin layer" in the tumor. So with the increase of concentration the growing absorption will be compensated by the decrease of the penetration depth of light into the tumor. This effect is more pronounced for wSiNPs with larger partial absorption and scattering than for  eSiNPs in the given range of concentrations provided that the latter are characterized by moderate partial absorption and scattering. However, further increase of concentration will lead to the described compensation effect in eSiNPs as well.

In the manuscript a comment will be added that the described effect is demonstrated only for the given range of concentrations:

“In the given range of mass concentrations C_m, the absorption efficiency A almost does not depend on C_m for wSiNPs, while for eSiNPs the increase in concentration provides a noticeable rise of the parameter A“.                

 

Comment 2: In the study, authors used the cw laser radiation that can provide additional heating effects during continuous long lasting irradiation especially at higher intensities. Can one expect any irradiation time effects for silicon nanoparticles hyperthermia and what was the irradiation time in this case?

Response 2:

Irradiation time is discussed in the text  added in Sec. 2.4 (lines 330 – 334)

In our preliminary studies we demonstrated that stationary temperature distribution is achieved in less than 400 s of continuous-wave cw irradiation [39].  It is worth noting that according to the requirements of hyperthermia procedure the  irradiation time in cw regime may take up to 60 minutes [90]. Thus, for therapeutic procedures longer than 400 s employing a stationary bioheat transfer equation is reasonable.

 

Comment 3: Can one expect any additional benefits for laser-induced heating by managing irradiation parameters such as pulsed laser irradiation or changing energy profile of a laser spot?

Response 3:

Our simulations demonstrate that using the beam size exceeding the tumor size is beneficial for arranging uniform transversal temperature distribution due to heat diffusion. The same reason is for choosing a circular-shaped beam rather than a Gaussian-shaped beam. Using pulsed laser radiation would not influence much the rate of biochemical processes destroying the tumor but may result in complex changing the nanoparticles characteristics and in damaging the surrounding healthy tissue.  

We added some text discussing:

• effect of the beam shape (in Sec.2.1) (lines 168 – 177)

Although Gaussian laser beams were reported to be employed for cancer theranostics  (e.g., [53]),  uniform irradiation of the tumor has some advantages. Our preliminary simulations of tumor hyperthermia with Gaussian laser beam demonstrated lower heating of the tumor edges than in the case of homogeneous beam due to a significant intensity decrease at the beam periphery. Moreover, applying a homogeneous beam seems to be more practical since positioning a laser spot at the skin surface needs smaller precision. Therefore, in simulation we consider a circular laser irradiation area of the radius r with uniform intensity distribution and the laser beam axis coinciding with the axial symmetry axis of the tumor. Such intensity distribution can be achieved with the help of laser radiation homogenisers (see, e.g., [54])..

• effect of pulsed laser radiation (in Sec. 1) (lines 126 – 130)

The choice of cw laser radiation for hyperthermia is determined by limits of laser radiation intensity for safe laser treatment of biotissues (below 200 mW/cm² [50]), especially for healthy tissues surrounding the tumor. Employing pulsed irradiation has no benefit due to decrease of safety energy density limits with shortening pulse duration [50,51].

 

Comment 4: One could briefly highlight the importance of silicon nanoparticles that can be used in many various applications (lines 86 – 93) as well as their customization (lines 81-85) to achieve additional benefits in applications.

Response 4:

Thank you for your comment. We revised and extended the text describing why silicon nanoparticles are important and briefly comparing them with such very popular hyperthermia agents as gold nanoparticles (lines 67 – 93):

However, gold nanoparticles may exhibit strong toxicity, which limits their applications [22,23]. Being injected in the organism, gold nanoparticles readily interact with proteins, which finally makes the effect of gold NPs in vivo unpredictable [24]. Additionally, the toxicity is often caused by presence of undesirable impurities due to application of such chemicals as chloroauric acid, cetrimonium bromide, silver nitrate, sodium borohydride, ascorbic acid and others reagents necessary for synthesising the gold nanoparticles [25, 26]. This so-called secondary toxicity can be sufficiently reduced via surface functionalization or by employing the laser ablation technique [27-30].

A possible solution of the toxicity problem consists in employing silicon nanoparticles (SiNPs), which, besides, are less expensive in production as compared to gold nanoparticles. For example, the NPs based on porous silicon were shown to be biocompatible, biodegradable and have no cytotoxicity [31–33]. The SiNPs of moderate concentrations may be easily fully transformed to orthosilicic acid and removed from living organisms with urine [32] without accumulation effects, unlike gold nanoparticles.

Fabricating SiNPs by pulsed laser ablation of silicon nanowires [34] or porous silicon [35] in liquids opens a way to control SiNPs size through selection of buffer liquid (water, ethanol, liquid helium) and pulse duration [36]. Additionally, the wavelength of ablating radiation affects the SiNPs size, as far as scattering and absorption properties of an ablation target depend on it.

 SiNPs were additionally found to be promising as thermal coupling agents for hyperthermia [37–39]. In vitro experiments on a cell culture exposed to near-infrared laser irradiation demonstrated significant reduction of tumor cell viability in presence of SiNPs [37]. Experiments in vivo demonstrated that porous silicon in combination with laser irradiation allows for selective destruction of cancer cells without damaging surrounding healthy cells [38]. Numerical simulations of laser tumor hyperthermia [39] demonstrated 4^oC increase in maximal tumor temperature due to SiNPs presence in tumor site.

.

Comment 5: The top part of the Figure 2 is poorly visible +and in the Figure 3c is not clear a type of silicon nanoparticles (eSiNPs or wSiNPs).

Response 5: You are absolutely correct about Figure 2. We improved its quality.

Figure 3c presents absorption and scattering cross-section for silicon nanoparticles calculated using Mie theory vs their diameter. The difference in optical parameters between eSiNPs and wSiNPs is determined by the difference of nanoparticle size distributions (Figures 3a and 3c) according to sums in formulae (5) and (6) .

We added the following clarification to the text (lines 217 – 220):

Assuming spherical shapes and high crystallinity of both synthesized wSiNPs and eSiNPs, Mie theory [62] can be employed to calculate scattering cross-section σ_s,i, absorption cross-section σ_a,i (Figure 3c) and anisotropy factor g_i for i-th size fraction of silicon nanocrystals.

Author Response File: Author Response.pdf

Reviewer 3 Report

Review of the manuscript "Numerical simulation of enhancement of superficial tumor laser hyperthermia with silicon nanoparticles" written by Olga I. Sokolovskaya, Ekaterina A. Sergeeva, Leonid. A. Golovan, Pavel K. Kashkarov, Aleksandr V. Khilov, Daria A. Kurakina, Natalia Yu. Orlinskaya, Stanislav V. Zabotnov, Mikhail Yu. Kirillin. A very interesting work on modeling the propagation of visible light in biological tissues is presented. The manuscript is undoubtedly devoted to an urgent and important problem! 

We, on the street named after one of the presidents of the Academy of Sciences and his brother, a geneticist, are always interested in reading works from the street named after the main revolutionary and the avenue named after the first cosmonaut. 

Despite the generally positive assessment of the work, I would like to make a number of suggestions to the authors:
1. Design. You need to put the numbers in ascending order, you cannot put 2,1, for example Khilov2,1.
2. Introduction. Silicon nanoparticles also interact with macromolecules, including proteins and nucleic acids. How much better than gold is a debatable issue. It all depends on the origin. In my experience, gold nanoparticles are usually more stable (zeta potential reaches -50mV, colloids are stable for years), which means they are less prone to all kinds of interactions.
3. Introduction. Mass production of nanoparticles using laser ablation, unfortunately, is not economically viable. Laser ablation is still a tool of labor for "jewelers", not for workers in production. It seems to me that this should be reflected in the text of the manuscript.
4. Conceptually. It seems to me that the authors need to set out in the manuscript the differences between ablation processes in water and ethanol. The fact is that nanoparticles obtained in ethanol almost always contain an admixture of amorphous carbon (ethanol burns in plasma, carbon condenses on seeds). Most of the ablated nanoparticles have traces of carbon on the surface. At my center, for example, with the help of this technology, they recently learned how to obtain graphene on the surface of gold and nickel nanoparticles. In general, authors should at least make it clear to readers that all these processes are not taken into account in the manuscript. And it looks like something strange ...

In general, I recommend the minor revision.

Author Response

We thank the reviewer for his substantial comments related to our manuscript.

We have improved the manuscript text in accordance with the comments.

 

Comment 1: Design. You need to put the numbers in ascending order, you cannot put ²,¹, for example Khilov²,¹.

 Response 1: Thank you for your comment and attentiveness, we have corrected the order of the affiliation numbers.

 

Comment 2: Introduction. Silicon nanoparticles also interact with macromolecules, including proteins and nucleic acids. How much better than gold is a debatable issue. It all depends on the origin. In my experience, gold nanoparticles are usually more stable (zeta potential reaches -50mV, colloids are stable for years), which means they are less prone to all kinds of interactions.

Response 2: You are absolutely correct in pointing out that gold nanoparticles are also promising in biomedicine including tumor hyperthermia. However, it is worth mentioning that many papers report on the toxicity of gold nanoparticles, although they allow achieving higher absorption efficiency as compared to SiNPs. To avoid this problem the gold nanoparticles need additional surface functionalization as one more technological stage. Porous silicon or laser-ablated SiNPs often may be applied as is. About stability we can say the following. On the one hand, excellence stability of the gold nanoparticles provides their use for long time scales, on the other hand, worse stability of the SiNPs does not obstruct their full transformation to orthosilicic acid and remove from living organisms with urine excluding accumulation which often occurs with the gold nanoparticles. And finally, silicon is sufficiently cheaper than gold.

According to your comment, we corrected and added texts about our choice in favor of biodegradable SiNPs:

Lines 67 – 85

However, gold nanoparticles may exhibit strong toxicity, which limits their applications [22,23]. Being injected in the organism, gold nanoparticles readily interact with proteins, which finally makes the effect of gold NPs in vivo unpredictable [24]. Additionally, the toxicity is often caused by the presence of undesirable impurities due to application of such chemicals as chloroauric acid, cetrimonium bromide, silver nitrate, sodium borohydride, ascorbic acid and others reagents necessary for synthesising the gold nanoparticles [25, 26]. This so-called secondary toxicity can  be sufficiently reduced via surface functionalization or by employing the laser ablation technique [27-30].

A possible solution of the toxicity problem consists in employing silicon nanoparticles (SiNPs), which, besides, are less expensive in production as compared to gold NPs. For example, the NPs based on porous silicon were shown to be biocompatible, biodegradable and have no cytotoxicity [31–33]. The SiNPs of moderate concentrations may be easily fully transformed to orthosilicic acid and removed from living organisms with urine [32] without accumulation effects, unlike gold nanoparticles.

Fabricating SiNPs by pulsed laser ablation of silicon nanowires [34] or porous silicon [35] in liquids opens a way to control SiNPs size through selection of buffer liquid (water, ethanol, liquid helium) and pulse duration [36]. Additionally, the wavelength of ablating radiation affects the SiNPs size, as far as scattering and absorption properties of an ablation target depend on it.

Lines 111 – 115

Employing arrays of silicon nanowires (SiNWs) as ablation targets seems to have various advantages for producing the SiNPs for biophotonics applications including satisfactory stability of water- and ethanol-based suspensions with an absolute value of the zeta potential up to 30 mV [44]. Stability can be potentially increased via coating with biocompatible and biodegradable polymers as it has been done for porous silicon [45].

 

Comment 3: Introduction. Mass production of nanoparticles using laser ablation, unfortunately, is not economically viable. Laser ablation is still a tool of labor for "jewelers", not for workers in production. It seems to me that this should be reflected in the text of the manuscript.

Response 3: You are absolutely correct that the reported technique is currently an expensive tool for the production of silicon nanoparticles. However, the considered technique allows to fabricate almost crystalline SiNPs with desirable structural and optical properties. After the proof of the efficiency of the particular SiNPs as hyperthermia enhancing agents, development of a more efficient technique for their production can become the aim of a separate study.  In the presented text we mentioned one of the ways to increase ablation products yield. This approach is being developed in our laboratory now:

Lines 118 – 120

Ablation threshold of SiNWs is up to 8 times lower than in crystalline silicon [34,35] which increases product yield and reduces the estimated production cost.

Additionally, cheapening the technology may be reached via optimization laser ablation by selecting a proper laser source, for example, it may be a more powerful and cheap nanosecond laser instead picosecond and femtosecond laser sources.  We added an appropriate comment to Conclusion:

Lines 566 – 577

As a result, the choice of laser-ablated SiNPs seems promising and suitable for treatment by photohyperthermia. In comparison with gold nanoparticles widely discussed as photohyperthermia agents, the SiNPs give advantages in the price of initial matter and easy biodegradability. However, laser ablation technology still stays relatively expensive to use in practice. The problem may be solved by using silicon targets with a reduced ablation threshold, for example, the discussed in this article SiNWs, as well as by optimization of laser source parameters. In the last case, relatively cheap powerful nanosecond lasers allow fabricating a lot of SiNPs with desirable sizes and properties and may take over more expensive femto- and picosecond lasers, which are often used now. Additionally, it will be necessary to carry out experiments with real biological tissues by the photohyperthermia technique to confirm our calculations.

 

Comment 4: Conceptually. It seems to me that the authors need to set out in the manuscript the differences between ablation processes in water and ethanol. The fact is that nanoparticles obtained in ethanol almost always contain an admixture of amorphous carbon (ethanol burns in plasma, carbon condenses on seeds). Most of the ablated nanoparticles have traces of carbon on the surface. At my center, for example, with the help of this technology, they recently learned how to obtain graphene on the surface of gold and nickel nanoparticles. In general, authors should at least make it clear to readers that all these processes are not taken into account in the manuscript. And it looks like something strange ...

Response 4: You are correct, we need to pay more attention to explain a probable difference between ablation processes in water and ethanol. In our opinion, we need to emphasize specific structural features of exactly SiNPs. We mentioned appropriate results obtained in Prokhorov General Physics Institute of the Russian Academy of Sciences and Lomonosov Moscow State University, and gave brief justification of consideration of crystalline SiNPs in our calculations:

Lines 196 –201

According to previous studies of similar laser-ablated SiNPs, they may have a thin oxide shell [36, 59] as well as a small fraction of amorphous phase [60]. Besides, eSiNPs undergo surface carbonization due to high power laser action to ethanol [36]. However, these effects may be excluded from the following consideration in our calculations due to their negligible contribution to SiNPs optical properties, and pure crystalline silicon particles are considered in the study.

Author Response File: Author Response.pdf

Reviewer 4 Report

There are some weaknesses through the manuscript which need improvement. Therefore, the submitted manuscript cannot be accepted for publication in this form, but it has a chance of acceptance after a major revision. My comments and suggestions are as follows:

1- Abstract gives information on the main feature of the performed study, but a couple of sentences on the background of the study must be added.

2- Authors must clarify necessity of the performed research. Objectives of the study must be clearly mentioned in introduction.

3- The literature study must be enriched. In this respect, authors must read and refer to the following papers: (a) https://doi.org/10.1007/s40094-016-0217-9 (b) https://doi.org/10.1016/j.jpowsour.2015.12.112

4- It would be nice, if authors could add illustrate Fig. 2 in a high quality. In addition, curves in Fig. 3 must be presented in a more scientific way, e.g., error bar, etc.

5- The main reference of each formula must be cited. Moreover, each parameters in equations must be introduced. Please double check this issue.

6- Standard deviation is the presented curves must be discussed. In addition, error in calculation must be considered and discussed.

7- In its language layer, the manuscript should be considered for English language editing. There are sentences which have to be rewritten.

8- The conclusion must be more than just a summary of the manuscript. List of references must be updated based on the proposed papers. Please provide all changes by red color in the revised version.

 

 

 

Author Response

We thank the reviewer for his substantial comments on our manuscript.

We have improved the manuscript text in accordance with the comments.

 

Comment 1: Abstract gives information on the main feature of the performed study, but a couple of sentences on the background of the study must be added.

Response 1: We fully accept your comment. We began our Abstract with the following sentences (lines 18 – 20):

Biodegradable and low-toxic silicon nanoparticles (SiNPs) have potential in different biomedical applications. Previous experimental studies revealed efficiency of some types of SiNPs  in tumor hyperthermia. To analyse the feasibility of employing SiNPs produced by laser ablation of silicon nanowire arrays in water and ethanol as agents for laser tumor hyperthermia, we numerically simulated effects of heating a millimeter-size nodal basal-cell carcinoma with embedded nanoparticles by continuous-wave laser radiation at 633 nm.

 

Comment 2: Authors must clarify necessity of the performed research. Objectives of the study must be clearly mentioned in introduction.

Response 2:

The Introduction section of the manuscript contains the formulation of the objective of the study and a description of the way how the objective is achieved in the following form (lines 122 – 140):

In this work, we aimed at estimating the potential of SiNPs fabricated by laser ablation of the SiNW arrays in water and ethanol as thermal coupling agents for hyperthermia. We performed a numerical simulation of heating a millimeter-sized nodular basal cell carcinoma (nBCC), which is the most common form of human skin cancer, located in human facial skin tissue [49], by means of a continuous-wave (cw) laser irradiation. The choice of cw laser radiation for hyperthermia is determined by limits of laser radiation intensity for safe laser treatment of biotissues (below 200 mW/cm²  [50]), especially for healthy tissues surrounding the tumor. Employing pulsed irradiation has no advantages due to decrease of safety energy density limits with shortening pulse duration [50,51]. Although silicon possesses significant cubic nonlinear susceptibility responsible for the light self-action [52], simple estimations demonstrate that for laser pulse energy of order of safety threshold [51] relative variation of absorption for bulk silicon is of order of 10^-4.

 We considered two configurations of the beam: (1) beam width corresponds to tumor transversal size to avoid excessive surrounding tumor heating, and (2) beam width exceeds it to ensure tumor heating at transversal boundaries. The considered beam power range was 60-200 mW. A systematic analysis of the effect of SiNPs concentration and beam configuration of hyperthermia performance was conducted. Optimal irradiation parameters providing hyperthermia of the entire tumor without significant overheating of surrounding healthy tissues were found.

 

Comment 3: The literature study must be enriched. In this respect, authors must read and refer to the following papers: (a) https://doi.org/10.1007/s40094-016-0217-9 (b) https://doi.org/10.1016/j.jpowsour.2015.12.112

Response 3: We have carefully read the papers proposed by the reviewer, however, we regret to confess that we failed to find any relevance of the proposed papers with our study. The first paper considers a theoretical solution for analysis of nonlinear vibration of a single carbon nanotube with a fluid within it. The second paper describes the development of an electrode for solar cells using TiO₂ nanoparticles. We could hardly imaging, in which context should these papers be cited in the manuscript, and what is the rationale of including them to the reference list, since many papers on Si nanoparticles or tumor hyperthermia are not cited in the manuscript, as in view of modern development of the field it is impossible to cite every paper somehow related to the study, while only the most close ones are usually chosen. We have to mention that we have extended the number of the cited papers with works closely related to the study.

 Added references are listed below;

 

1. Zhou, J.; Cao, Z.; Panwar, N.; Hu, R.; Wang, X.; Qu, J.; Tjin, S.C.; Xu, G.; Yong, K.-T. Functionalized Gold Nanorods for Nanomedicine: Past, Present and Future. Coord. Chem. Rev. 2017, 352, 15–66, DOI:10.1016/j.ccr.2017.08.020.
2. Liu, A.; Wang, G.; Wang, F.; Zhang, Y. Gold Nanostructures with Near-Infrared Plasmonic Resonance: Synthesis and Surface Functionalization. Coord. Chem. Rev. 2017, 336, 28–42, DOI:10.1016/j.ccr.2016.12.019.
3. Simakin, A.V.; Baimler, I.V.; Smirnova, V.V.; Uvarov, O.V.; Kozlov, V.A.; Gudkov, S.V. Evolution of the Size Distribution of Gold Nanoparticles under Laser Irradiation. Phys. Wave Phen. 2021, 29, 102–107, DOI:10.3103/S1541308X21020126.
4. Simakin, A.V.; Astashev, M.E.; Baimler, I.V.; Uvarov, O.V.; Voronov, V.V.; Vedunova, M.V.; Sevost’yanov, M.A.; Belosludtsev, K.N.; Gudkov, S.V. The Effect of Gold Nanoparticle Concentration and Laser Fluence on the Laser-Induced Water Decomposition. J. Phys. Chem. B 2019, 123, 1869–1880, DOI:10.1021/acs.jpcb.8b11087.
5. Al-Kattan, A.; Nirwan, V.; Popov, A.; Ryabchikov, Y.; Tselikov, G.; Sentis, M.; Fahmi, A.; Kabashin, A. Recent Advances in Laser-Ablative Synthesis of Bare Au and Si Nanoparticles and Assessment of Their Prospects for Tissue Engineering Applications. IJMS 2018, 19, 1563, DOI:10.3390/ijms19061563.
6. Braguer, D.; Correard, F.; Maximova, K.; Villard, C.; Roy, M.; Al-Kattan, A.; Sentis, M.; Gingras, M.; Kabashin, A.; Esteve, M.-A. Gold Nanoparticles Prepared by Laser Ablation in Aqueous Biocompatible Solutions: Assessment of Safety and Biological Identity for Nanomedicine Applications. IJN 2014, 5415, DOI:10.2147/IJN.S65817.
7. Kuzmin, P.G.; Shafeev, G.A.; Bukin, V.V.; Garnov, S.V.; Farcau, C.; Carles, R.; Warot-Fontrose, B.; Guieu, V.; Viau, G. Silicon Nanoparticles Produced by Femtosecond Laser Ablation in Ethanol: Size Control, Structural Characterization, and Optical Properties. J. Phys. Chem. C 2010, 114, 15266–15273, DOI:10.1021/jp102174y.
8. Jean, M.; Schulmeister, K. Laser-Induced Injury of the Skin: Validation of a Computer Model to Predict Thresholds. Biomed. Opt. Express 2021, 12, 2586, DOI:10.1364/BOE.422618.
9. Bristow, A.D.; Rotenberg, N.; van Driel, H.M. Two-Photon Absorption and Kerr Coefficients of Silicon for 850–2200nm. Appl. Phys. Lett. 2007, 90, 191104, DOI:10.1063/1.2737359.
10. Tunç, M.; Çamdali, Ü.; Parmaksizoğlu, C.; Çikrikçi, S. The Bio‐heat Transfer Equation and Its Applications in Hyperthermia Treatments. Engineering Computations 2006, 23, 451–463, DOI:10.1108/02644400610661190.
11. Wang, X.; Qi, H.; Yang, X.; Xu, H. Analysis of the Time-Space Fractional Bioheat Transfer Equation for Biological Tissues during Laser Irradiation. International Journal of Heat and Mass Transfer 2021, 177, 121555, DOI:10.1016/j.ijheatmasstransfer.2021.121555.
12. Liu, K.-C.; Chen, T.-M. Comparative Study of Heat Transfer and Thermal Damage Assessment Models for Hyperthermia Treatment. Journal of Thermal Biology 2021, 98, 102907, DOI:10.1016/j.jtherbio.2021.102907.
13. Santos, O.; Cancino-Bernardi, J.; Pincela Lins, P.M.; Sampaio, D.; Pavan, T.; Zucolotto, V. Near-Infrared Photoactive Theragnostic Gold Nanoflowers for Photoacoustic Imaging and Hyperthermia. ACS Appl. Bio Mater. 2021, 4, 6780–6790, DOI:10.1021/acsabm.1c00519.
14. Gongalsky, M.B.; Osminkina, L.A.; Pereira, A.; Manankov, A.A.; Fedorenko, A.A.; Vasiliev, A.N.; Solovyev, V.V.; Kudryavtsev, A.A.; Sentis, M.; Kabashin, A.V.; et al. Laser-Synthesized Oxide-Passivated Bright Si Quantum Dots for Bioimaging. Sci. Rep. 2016, 6, 24732, DOI:10.1038/srep24732.
15. Barbagiovanni, E.G.; Lockwood, D.J.; Simpson, P.J.; Goncharova, L.V. Quantum Confinement in Si and Ge Nanostructures. Journal of Applied Physics 2012, 111, 034307, DOI:10.1063/1.3680884.
16. Jellison, G.E.;  Modine, F.A. Optical absorption of silicon between 1.6 and 4.7 eV at elevated temperatures, Appl. Phys. Lett., 1982, 41, 2, 180-182, DOI: 10.1063/1.93454
17. Jellison, G.E.;  Burke, H.H. The temperature dependence of the refractive index of silicon at elevated temperatures at severed laser wavelengths, J. Appl. Phys., 1986, 60, 2, 841-843, DOI: 10.1063/1.337386
18. Priester, M.I.; Curto, S.; van Rhoon, G.C.; ten Hagen, T.L.M. External Basic Hyperthermia Devices for Preclinical Studies in Small Animals. Cancers, 2021, 13, 4628. DOI: 10.3390/cancers13184628

 

 

Comment 4: It would be nice, if authors could add illustrate Fig. 2 in a high quality. In addition, curves in Fig. 3 must be presented in a more scientific way, e.g., error bar, etc. 

Response 4: You are absolutely correct about Figure 2. We improved its quality.

Additionally, we added necessary error bars to Figures 3а,b. The errors were estimated using the number of SiNPs which are considered at plotting each histogram. The relative error for the wSiNP size distribution (Figures 3а) equals 6.0 %, for the eSiNP size distribution (Figures 3b) equals 10.4 %. These values are mentioned in the text (lines 247 – 248).

Errors in Figure 3c are not applicable because the curves for scattering and absorption are calculated using Mie theory for the specific values of the SiNP diameter. They are theoretical curves, not experimental.

 

Comment 5: The main reference of each formula must be cited. Moreover, each parameters in equations must be introduced. Please double check this issue.

Response 5:

In order to fulfill the reviewer requirement we revised the references and appearance order for formulas and employed parameters and made the following corrections:

in Sec. 2.4 (lines 299 – 322):

The standard way to obtain temperature distribution within the tissues during hyperthermia procedure is solving bioheat transfer equation, which was initially proposed by Pennes in the following form [78, 79]:

See formula (9) in the attached file

where  is the biotissue temperature,  is the biotissue density,  is the biotissue heat capacity at a constant pressure; k is the thermal conductivity,  is the speed of metabolic heat generation the per unit volume,  is the external source power density, which in our case is a result of the laser radiation absorption, and  is power density of the heat loss caused by perfusion (blood transfer through capillaries and extracellular spaces in tissue [80]). Despite great progress achieved during more than 70 years since its first proposal and various improvements and refinements of the equation (see, e.g., [81,82,83]), the Pennes equation is, nevertheless, applicable for the stationary case of continuous-wave irradiation of the biotissue [81] :

See formula (10) in the attached file

We solved Equation (10) using a finite-difference approach taking obtained absorption maps as  the external source power density. In its stationary form the Pennes equation (9) does not depend on biotissue density and heat capacity:

See formula (11) in the attached file

Here k is the thermal conductivity coefficient, Q_met = 420 W/cm³ is the volumetric rate of metabolic heat generation [84], and the final term of Equation (11) describes the perfusion heat loss power density, with  ρ_bl = 1060 kg/m³, C_bl = 3770 J/(kg∙К) [85,86], T_bl, = 37.2˚С [87, 88], ω_bl (Table 3) being the blood density, heat capacity, temperature and perfusion coefficient (transfer of blood through capillaries and extracellular spaces [55]), respectively.

in Sec. 2.2 (lines 221 – 226)

Due to small SiNP volume fraction, which does not exceed 0.003 for the maximal SiNP concentration,  scattering (see the attached file) and absorption (see the attached file) coefficients of the tumor with the embedded SiNPs can be found by adding scattering and absorption coefficient of all nanoparticles ( and , respectively) to scattering (see the attached file) and absorption (see the attached file) coefficients of the tumor without SiNPs, respectively [19]:

See formulas (5) and (6) in the attached file

The relation between scattering anisotropy factor  for the tumor with the SiNPs, scattering anisotropy factor  of the tumor without SiNPs, and scattering anisotropy factor  of  i-th SiNP fraction is given by expression [19]:

See formula (7) in the attached file

and effective attenuation coefficient of diffusive light (see the attached file) for the SiNPs with embedded SiNPs [63] is:

See formula (7) in the attached file

 

Comment 6: Standard deviation is the presented curves must be discussed. In addition, error in calculation must be considered and discussed

Response 6: We absolutely agree with you. We added the following comment:

 Lines 246 – 250

The errors for μ_а,  μ_s  and g of tumor with SiNPs originate  from the error of size distribution measurement that were estimated as  6.0% and 10.4% for wSiNPs and eSiNPs respectively. This yields an estimated error 2% in scattering and absorption characteristics evaluated by Mie formulas, which caused no relevant change in obtained results.

 

Comment 7: In its language layer, the manuscript should be considered for English language editing. There are sentences which have to be rewritten.

Response 7: The English language has been substantially revised through the entire manuscript.

 

Comment 8: The conclusion must be more than just a summary of the manuscript. List of references must be updated based on the proposed papers. Please provide all changes by red color in the revised version.

Response 8: You are absolutely correct, the presented Conclusion seemed as unfinished. We added the following text to it (lines 566 – 577):

As a result, the choice of laser-ablated SiNPs seems promising and suitable for treatment by photohyperthermia. In comparison with gold nanoparticles widely discussed as photohyperthermia agents, the SiNPs give advantages in the price of initial matter and easy biodegradability. However, laser ablation technology still stays relatively expensive to use in practice. The problem may be solved by using silicon targets with a reduced ablation threshold, for example, the discussed in this article SiNWs, as well as by optimization of laser source parameters. In the last case, relatively cheap powerful nanosecond lasers allow fabricating a lot of SiNPs with desirable sizes and properties and may take over more expensive femto- and picosecond lasers, which are often used now. Additionally, it will be necessary to carry out experiments with real biological tissues by the photohyperthermia technique to confirm our calculations.

List of references was updated. The list of added references is presented below:

 

1. Zhou, J.; Cao, Z.; Panwar, N.; Hu, R.; Wang, X.; Qu, J.; Tjin, S.C.; Xu, G.; Yong, K.-T. Functionalized Gold Nanorods for Nanomedicine: Past, Present and Future. Coord. Chem. Rev. 2017, 352, 15–66, DOI:10.1016/j.ccr.2017.08.020.
2. Liu, A.; Wang, G.; Wang, F.; Zhang, Y. Gold Nanostructures with Near-Infrared Plasmonic Resonance: Synthesis and Surface Functionalization. Coord. Chem. Rev. 2017, 336, 28–42, DOI:10.1016/j.ccr.2016.12.019.
3. Simakin, A.V.; Baimler, I.V.; Smirnova, V.V.; Uvarov, O.V.; Kozlov, V.A.; Gudkov, S.V. Evolution of the Size Distribution of Gold Nanoparticles under Laser Irradiation. Phys. Wave Phen. 2021, 29, 102–107, doi:10.3103/S1541308X21020126.
4. Simakin, A.V.; Astashev, M.E.; Baimler, I.V.; Uvarov, O.V.; Voronov, V.V.; Vedunova, M.V.; Sevost’yanov, M.A.; Belosludtsev, K.N.; Gudkov, S.V. The Effect of Gold Nanoparticle Concentration and Laser Fluence on the Laser-Induced Water Decomposition. J. Phys. Chem. B 2019, 123, 1869–1880, doi:10.1021/acs.jpcb.8b11087.
5. Al-Kattan, A.; Nirwan, V.; Popov, A.; Ryabchikov, Y.; Tselikov, G.; Sentis, M.; Fahmi, A.; Kabashin, A. Recent Advances in Laser-Ablative Synthesis of Bare Au and Si Nanoparticles and Assessment of Their Prospects for Tissue Engineering Applications. IJMS 2018, 19, 1563, doi:10.3390/ijms19061563.
6. Braguer, D.; Correard, F.; Maximova, K.; Villard, C.; Roy, M.; Al-Kattan, A.; Sentis, M.; Gingras, M.; Kabashin, A.; Esteve, M.-A. Gold Nanoparticles Prepared by Laser Ablation in Aqueous Biocompatible Solutions: Assessment of Safety and Biological Identity for Nanomedicine Applications. IJN 2014, 5415, doi:10.2147/IJN.S65817.
7. Kuzmin, P.G.; Shafeev, G.A.; Bukin, V.V.; Garnov, S.V.; Farcau, C.; Carles, R.; Warot-Fontrose, B.; Guieu, V.; Viau, G. Silicon Nanoparticles Produced by Femtosecond Laser Ablation in Ethanol: Size Control, Structural Characterization, and Optical Properties. J. Phys. Chem. C 2010, 114, 15266–15273, doi:10.1021/jp102174y.
8. Jean, M.; Schulmeister, K. Laser-Induced Injury of the Skin: Validation of a Computer Model to Predict Thresholds. Biomed. Opt. Express 2021, 12, 2586, DOI:10.1364/BOE.422618.
9. Bristow, A.D.; Rotenberg, N.; van Driel, H.M. Two-Photon Absorption and Kerr Coefficients of Silicon for 850–2200nm. Appl. Phys. Lett. 2007, 90, 191104, DOI:10.1063/1.2737359.
10. Tunç, M.; Çamdali, Ü.; Parmaksizoğlu, C.; Çikrikçi, S. The Bio‐heat Transfer Equation and Its Applications in Hyperthermia Treatments. Engineering Computations 2006, 23, 451–463, DOI:10.1108/02644400610661190.
11. Banerjee, A.; Ogale, A.A.; Das, C.; Mitra, K.; Subramanian, C. Temperature Distribution in Different Materials Due to Short Pulse Laser Irradiation. Heat Transfer Engineering 2005, 26, 41–49, doi:10.1080/01457630591003754.
12. Wang, X.; Qi, H.; Yang, X.; Xu, H. Analysis of the Time-Space Fractional Bioheat Transfer Equation for Biological Tissues during Laser Irradiation. International Journal of Heat and Mass Transfer 2021, 177, 121555, doi:10.1016/j.ijheatmasstransfer.2021.121555.
13. Liu, K.-C.; Chen, T.-M. Comparative Study of Heat Transfer and Thermal Damage Assessment Models for Hyperthermia Treatment. Journal of Thermal Biology 2021, 98, 102907, doi:10.1016/j.jtherbio.2021.102907.
14. Santos, O.; Cancino-Bernardi, J.; Pincela Lins, P.M.; Sampaio, D.; Pavan, T.; Zucolotto, V. Near-Infrared Photoactive Theragnostic Gold Nanoflowers for Photoacoustic Imaging and Hyperthermia. ACS Appl. Bio Mater. 2021, 4, 6780–6790, doi:10.1021/acsabm.1c00519.
15. Gongalsky, M.B.; Osminkina, L.A.; Pereira, A.; Manankov, A.A.; Fedorenko, A.A.; Vasiliev, A.N.; Solovyev, V.V.; Kudryavtsev, A.A.; Sentis, M.; Kabashin, A.V.; et al. Laser-Synthesized Oxide-Passivated Bright Si Quantum Dots for Bioimaging. Sci Rep 2016, 6, 24732, doi:10.1038/srep24732.
16. Barbagiovanni, E.G.; Lockwood, D.J.; Simpson, P.J.; Goncharova, L.V. Quantum Confinement in Si and Ge Nanostructures. Journal of Applied Physics 2012, 111, 034307, doi:10.1063/1.3680884.
17. Jellison, G.E.;  Modine, F.A. Optical absorption of silicon between 1.6 and 4.7 eV at elevated temperatures, Appl. Phys. Lett., 1982, 41, 2, 180-182, DOI: 10.1063/1.93454
18. Jellison, G.E.;  Burke, H.H. The temperature dependence of the refractive index of silicon at elevated temperatures at severed laser wavelengths, J. Appl. Phys., 1986, 60, 2, 841-843, DOI: 10.1063/1.337386
19. Priester, M.I.; Curto, S.; van Rhoon, G.C.; ten Hagen, T.L.M. External Basic Hyperthermia Devices for Preclinical Studies in Small Animals. Cancers, 2021, 13, 4628. https://doi.org/10.3390/cancers13184628

 

We provided all our principal changes by red colour in the text.

Round 2

Reviewer 1 Report

Some of the most important issues raised in the first review stage were partially addressed:

**Typically, a Gaussian beam is provided by a laser system in laser treatments. No evidence of this practical consideration was numerically presented in this numerical study.

**Evidence of the estimation of the temperature in this report that guarantees absence of agglomeration or change of size of nanoparticles induced by adsorption was analyzed.

**A citation to validate that skin tissues does not present anistropic optical properties and an induced thermo-optical effect that can be negligible or significant for different laser irradiances like those used in laser treatments is missing.

***The results must be confronted with updated publications to see the importance of the main findings. No necessarily the use of the same material or the same laser system.

Author Response

We thank the reviewer for his substantial comments on our manuscript.

We have improved the manuscript text in accordance with the comments.

 

Comment 1: Typically, a Gaussian beam is provided by a laser system in laser treatments. No evidence of this practical consideration was numerically presented in this numerical study.

 Response 1:

We additionally discussed the choice of the circular flat intensity distribution for laser hyperthermia simulation  in Sec. 2.1. Geometry and optical parameters of the model . We also provided references for the papers where non-Gaussian laser beams were used in experiments.

(Lines 170 – 179)

We considered cw laser irradiation with the circular homogeneous intensity distribution; radius of the circle is r, and the laser beam axis coincides with the axial symmetry axis of the tumor; laser radiation is assumed to be non-polarized. This beam shape is typical for hyperthermia carried out by light-emitting diodes [53] or lasers generating in multimode regime [54]. In these cases, circular homogeneous intensity distribution can be achieved with the help of laser radiation homogenizers enabling spatially flat-top laser spot of non-polarized laser radiation (see, e.g., [55]). Applying a homogeneous beam seems to be more practical due to more homogeneous transversal distribution of the intensity as compared to alternatively employed Gaussian beams.

 

To meet the referee’s remark we added to the text a new section 3.2.3. Comparison of flat beam and Gaussian beam irradiation. In this section, we discussed the difference between cases of tumor irradiation by circular flat laser beam and Gaussian beam. We added the results of numerical simulation for the latter case, which demonstrate no advantages of Gaussian beam over circular uniform beam, moreover, the former case was found to result in underheating the tumor periphery in comparison with circular uniform beam at equal laser power.

(Lines 545 – 601):

Gaussian beam is a widely used alternative to flat intensity distribution in tissue irradiation configuration. Inhomogeneity of intensity distribution is considered as a drawback in laser hyperthermia due to possible hot spots in the target area [92]. Comparison of these two irradiation regimes evidences longer time necessary for cancer cell necrosis in the latter case [99]. Nevertheless, Gaussian laser beams are often employed for cancer theranostics (e.g., [100]). To compare effects for both cases we carried out simulations for the Gaussian laser beam with the same parameters as were employed for the flat beam.

In these simulations, the laser beam axis coincides with the axis of the tumor. Incident laser radiation power depends on x аnd y coordinates as:

See formula (16) in the attached file.

where r is the beam radius at 1/e level,  is the total laser power. In Monte Carlo simulations, to obtain Gaussian beam intensity distribution Box – Muller transform [101] was employed. The obtained cross-sections q(x, y = 0, z) of the normalized volumetric density of absorbed energy is presented in Figure 9.

See Figure 9 in the attached file.

Figure 9. Cross-section x, y = 0 of normalized volumetric density of absorbed energy q(x, y, z) for Gaussian beam radius of 4 mm: in absence of SiNPs in nBCC (a); BCC with eSiNPs (b) and wSiNPs (c) at SINP mass concentration of 5 mg/mL.

As one can see, qualitatively, the absorption distribution for Gaussian beam does not differ significantly (cf. Figures 5a, 5d, and 5e and Figures 9a, 9b, and 9c) from one for the flat beam except from the region outside the tumor. Embedding in tumor eSiNPs with smaller absorption results in heating the entire tumor, whereas in the case of wSiNP the rear tumor part is underheated. Detailed calculations of the temperature distribution inside the tissue (Figure 10) evidence that at equal power Gaussian laser beam enables heating up to lower temperature than the flat one: the tumor is not completely heated up to 42 °C at P₀ = 110 mW and r = 2.5 mm (precisely of the tumor diameter) (cf. Figure 10a, 10b, and Figure 6) and precisely up to 42 °C at P₀ = 165 mW and r = 4 mm (cf. Figure 10c, 10d, and Figure 7, note that the beam radius for uniform circular beam is larger than that for the Gaussian beam, which indicates even less tumor heating efficiency in the latter case). The reasons of this effect are obvious: (i) more than 37% of the laser radiation is absorbed outside the tumor if the beam radius exceeds the tumor radius, and (ii) due to strongly non-uniform heat rate the heat flux is more prominent than in the case of uniform intensity distribution. Thus, carried out simulation of the hyperthermia by Gaussian beam evidences that circular flat laser beam has certain advantages over the Gaussian one.

See Figure 10 in the attached file.

Figure 10. Temperature distribution in biotissue with SiNPs embedded in the tumor at the mass concentrations of 5 mg/mL upon irradiation by Gaussian laser beam with radius of 2.5 mm and power of 110 mW (a,b), radius of 4 mm and power of 165 mW: (a, c) axial temperature profile at the beam axis T(x=0, y=0, z); (b, d) transversal temperature profile at the depth z = 1 mm corresponding to the tumor center. Red horizontal line indicates the hyperthermia threshold temperature of 42^oC; dashed vertical lines show the tumor edges.

 

Since no experimental results are available to assess the validity of the calculations performed, we analysed similar simulations studies. Refs. [37,38,43] report on numerical simulation of heating water suspensions of SiNPs, however, such studies do not account for the effect of surrounding biotissues both in light transport and heat transfer aspects.

Recently, various inorganic metallic compounds were tested for their effectiveness as thermal coupling agents. In [102] CuFeSe₂ nanosheets with mean hydrodynamic diameter of 200 nm were experimentally shown to be able to heat water to 30^oC within 600 sec. In [103] palladium hydride nanoparticles suspended in water gained additional heating 10^oC during 180 secs at NIR laser power of 154 mW. However, they require sophisticated fabrication technique, while pulsed laser ablation of silicon nanostructures in liquids seems to be a promising scalable technology. As for inert materials studies, gold nanoparticles irradiated with NIR light permit selective tumor hyperthermia at 42−43 °C without side effects to surrounding healthy tissues due to spatial and temporal control of heat generation (selective accumulation and irradiation of heat nanosources) [104]. Nevertheless, silicon demonstrates more prominent biodegradation compared to gold, since silicon presents in living organisms as natural trace compound.

 

Comment 2: Evidence of the estimation of the temperature in this report that guarantees absence of agglomeration or change of size of nanoparticles induced by adsorption was analyzed.

Response 2:

Thank you for your comment. To estimate the possible nanoparticles agglomeration in tumor site with maximal temperature of 48 ^oC reached in conducted numerical experiment, we turned our attention to the stability properties of source SiNPs suspension in water and ethanol. They possess moderate stability with an absolute value of the zeta potential up to 30 mV accordingly our previous experimental work [44 with DOI:10.3390/s20174874]. It means that during tens of hours the discussed silicon nanoparticles don’t agglomerate, and this time is enough to conduct photothermal therapy. Besides, such moderate stability of SiNPs does not obstruct their full transformation to orthosilicic acid and remove from living organisms with urine excluding accumulation nanoparticle in the body, which is typical for the gold nanoparticles. We briefly discussed this in introduction (lines 111-116):

Employing arrays of silicon nanowires (SiNWs) as ablation targets seems to have various advantages for producing the SiNPs for biophotonics applications including satisfactory stability of water- and ethanol-based suspensions with an absolute value of the zeta potential up to 30 mV [44]. This value indicates the typical time scale of spontaneous agglomeration as tens of hours, and the sonification of the SiNPs suspension prior to application allows to exclude the effect of agglomeration in the course of the procedure.

 

In order to consider the effect of the temperature increase on SiNPs agglomeration ability as a result of SiNPs surface melting (sintering), a maximal temperature of 48^oC considered in this study excludes SiNPs agglomeration, since it takes place at temperatures above 1000 К [Schierning, G.; Theissmann, R.; Wiggers, H.; Sudfeld, D.; Ebbers, A.; Franke, D.; Witusiewicz, V.T.; Apel, M. Microcrystalline Silicon Formation by Silicon Nanoparticles. Journal of Applied Physics 2008, 103, 084305, DOI:10.1063/1.2903908].

 

 

Comment 3: A citation to validate that skin tissues does not present anistropic optical properties and an induced thermo-optical effect that can be negligible or significant for different laser irradiances like those used in laser treatments is missing.

Response 3:

We would like to pay attention to the fact that this numerical study is based on biotissue optical characteristics measured employing unpolarized light. Scattering and absorption coefficients and scattering anisotropy factor μ_s, μ_a and g of skin layers and nodular basal cell carcinoma were obtained through integrating sphere measurements combined with the inverse Monte Carlo technique. [57 with DOI:10.1117/1.2398928]. In order to obtain the diffuse reflectance and total transmittance values of skin specimens the light from a halogen lamp was focused onto the sample, which was mounted on the entrance and exit ports of the integrating sphere. Interpretation of all the experimental data obtained in this study was conducted under the assumption of the Henyey-Greenstein scattering phase function. Moreover, laser treatment is usually performed using unpolarised light, especially is beam homogeniziers are used.

We specially mentioned this in line 172 – 173: laser radiation is assumed to be non-polarized

and in lines 239 – 241:

It is worth nothing that all optical parameters values were measured for non-polarized light source [57].

To discuss the possible thermooptical effect that can occur in epidermis with maximal temperature rise of 11 ^oC and subcutaneous fat with temperature rise of 7 ^oC, we referred to the following paper [69 with DOI:10.1038/s41598-020-80254-9] where In vivo absorption coefficients, scattering coefficients, and anisotropy factors of mouse ear were found at three temperatures of 25 °C, 36 °C, and 60 °C. 

For the maximal temperature rise obtained in our simulation setup, from 37 ^oC to 48 ^oC that takes place for epidermis tissue, the increase in absorption and scattering coefficients at considered in this study wavelength of 633 nm due to thermooptical effect is about 0.02 cm^-1K^-1 that is even lower than the accuracy of absorption coefficient measurement employing the technique discussed above. Therefore, in the case of mild hyperthermia that is the subject of present paper the biotissue thermooptical effects are negligible.

We also added the following text in Section 2.2:

Lines 232 – 237:

Thermooptical effects in the biotissue is also extremely small. According to Ref. [69] the value of dm_a/dT for biotissues does not exceed 0.02 cm^-1 K^-1. Considering the typical temperature increase in the treated biotissues and their absorption coefficients (see Tables 1 and 2), the possible relative variation in absorption is estimated to not exceed 7% for tumor with embedded 1 mg/mL of eSiNPs and an order of magnitude smaller for tumor with 7 mg/ml wSiNPs.

 

Comment 4: The results must be confronted with updated publications to see the importance of the main findings. No necessarily the use of the same material or the same laser system.

 Response 4:

 Thank you for your comment. We added the following references and text:

Lines 590 – 601:

Recently, various inorganic metallic compounds were tested for their effectiveness as thermal coupling agents. In [102] CuFeSe₂ nanosheets with mean hydrodynamic diameter of 200 nm were experimentally shown to be able to heat water to 30^oC within 600 sec. In [103] palladium hydride nanoparticles suspended in water gained additional heating 10^oC during 180 secs at NIR laser power of 154 mW. However, they require sophisticated fabrication technique, while pulsed laser ablation of silicon nanostructures in liquids seems to be a promising scalable technology. As for inert materials studies, gold nanoparticles irradiated with NIR light permit selective tumor hyperthermia at 42−43 °C without side effects to surrounding healthy tissues due to spatial and temporal control of heat generation (selective accumulation and irradiation of heat nanosources) [104]. Nevertheless, silicon demonstrates more prominent biodegradation compared to gold, since silicon presents in living organisms as natural trace compound.

 

102. Liu, M.; Radu, D.R.; Selopal, G.S.; Bachu, S.; Lai, C.-Y. Stand-Alone CuFeSe2 (Eskebornite) Nanosheets for Photothermal Cancer Therapy. Nanomaterials 2021, 11, 2008, DOI:3390/nano11082008.
103. Cruz, C.C.R.; da Silva, N.P.; Castilho, A.V.; Favre-Nicolin, V.A.; Cesar, C.L.; Orlande, H.R.B.; Dos Santos, D.S. Synthesis, Characterization and Photothermal Analysis of Nanostructured Hydrides of Pd and PdCeO2. Rep. 2020, 10, 17561, DOI:10.1038/s41598-020-74378-1.
104. Mulens-Arias, V.; Nicolás-Boluda, A.; Pinto, A.; Balfourier, A.; Carn, F.; Silva, A.K.A.; Pocard, M.; Gazeau, F. Tumor-Selective Immune-Active Mild Hyperthermia Associated with Chemotherapy in Colon Peritoneal Metastasis by Photoactivation of Fluorouracil–Gold Nanoparticle Complexes. ACS Nano 2021, 15, 3330–3348, DOI:1021/acsnano.0c10276.

 

All or corrections are highlighted by yellow in the revised article.

Author Response File: Author Response.pdf

Reviewer 4 Report

The paper has been improved and corresponding modifications have been conducted.

Author Response

We are kindly grateful to the reviewer for his attention to our article.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The authors have importantly improved the presentation of their work. It can be considered for publication in present form.