Numerical Simulation of Low-Frequency Magnetic Fields and Gradients for Magnetomechanical Applications
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript entitled "Numerical simulation of low-frequency magnetic fields and 2 gradients for magnetomechanical applications" presents an interesting and valuable contribution to the field and only requires minor refinements before I can recommend it for publication. The authors provide a clear overview of magneto-mechanical (MM) approaches. However, several points would benefit from further detail to improve clarity and usefulness for the reader.
- The manuscript currently refers to three papers used as case studies, but the information provided is too limited. I suggest that the authors expand their descriptions of these studies so that readers do not need to search the original papers to understand the key experimental details. In particular, it would be important to know, whether the reported MM experiments resulted in cancer-cell killing or destruction. Also, what experimental protocols were used in each study.
Since MNP shape has a known influence on MM efficacy, the authors should briefly discuss the nanoparticle shape and any relevant physicochemical characteristics in each study. This information is essential to contextualise the theoretical calculations presented.
These details could be added to the Materials and Methods section (around line 190) and summarised in Table 2 for clarity.
- MM applications have shown convincing results in vitro. Given the authors’ expertise in MM approaches, it would be very valuable if they could discuss potential pathways for developing this technique toward preclinical studies. Even a brief forward-looking perspective would significantly strengthen the impact of the manuscript.
In summary, this is a well-written and relevant manuscript. I recommend its publication following the minor revisions suggested above.
Author Response
R1: The manuscript entitled "Numerical simulation of low-frequency magnetic fields and 2 gradients for magnetomechanical applications" presents an interesting and valuable contribution to the field and only requires minor refinements before I can recommend it for publication. The authors provide a clear overview of magneto-mechanical (MM) approaches. However, several points would benefit from further detail to improve clarity and usefulness for the reader.
- The manuscript currently refers to three papers used as case studies, but the information provided is too limited. I suggest that the authors expand their descriptions of these studies so that readers do not need to search the original papers to understand the key experimental details. In particular, it would be important to know, whether the reported MM experiments resulted in cancer-cell killing or destruction. Also, what experimental protocols were used in each study.
Since MNP shape has a known influence on MM efficacy, the authors should briefly discuss the nanoparticle shape and any relevant physicochemical characteristics in each study. This information is essential to contextualise the theoretical calculations presented.
Author response:
We appreciate the reviewer’s constructive comment. In response, we have expanded the Materials and Methods section and added a dedicated paragraph discussing the nanoparticle shape, magnetic regime, size, and surface physicochemical characteristics for each of the three reference studies. This addition clarifies how these parameters influence torque generation, Brownian versus Néel relaxation, mechanical force transmission, and overall magneto-mechanical efficiency. We now explicitly describe the quasi-spherical superparamagnetic dextran-coated magnetite nanoparticles used by Jordan et al., the larger spherical single-domain Fe/MgO core–shell particles investigated by Chalkidou et al., and the multidomain, anisotropic clustered magnetite structures employed by Spyridopoulou et al. These distinctions, together with their corresponding surface coatings, colloidal stability, and intracellular behavior, are now discussed in detail to contextualize the theoretical force predictions of our study.
(See revised draft, lines 191-205, 211-219, 228-235.)
R1: These details could be added to the Materials and Methods section (around line 190) and summarised in Table 2 for clarity.
Author response:
We thank the reviewer for this valuable suggestion. In response, Table 2 has been expanded to include two additional columns reporting (i) the nanoparticle size and morphology and (ii) the experimentally observed biological outcome in each of the three case studies. These additions clarify the influence of particle geometry, magnetic regime, and surface chemistry on torque generation and MM efficacy. Furthermore, short descriptions were added in the text to summarize the experimental protocols and to indicate whether MM exposure resulted in cell destruction, hyperthermia-driven effects, or negligible mechanical action. These revisions provide a more complete and accessible contextualization of the theoretical force estimations presented.
(Updated Table 2, line 321.)
R1: MM applications have shown convincing results in vitro. Given the authors’ expertise in MM approaches, it would be very valuable if they could discuss potential pathways for developing this technique toward preclinical studies. Even a brief forward-looking perspective would significantly strengthen the impact of the manuscript.
Author response:
We thank the reviewer for this insightful suggestion. In accordance with the recommendation, we have expanded the Discussion section to include a forward-looking perspective outlining the key steps required for the transition of magneto-mechanical (MM) actuation from in vitro studies toward preclinical evaluation. This new paragraph discusses the influence of tissue-level mechanical constraints, heterogeneous nanoparticle uptake, and viscosity on MM force generation, and highlights the need for physics-based predictive models that incorporate these biological variables. Additionally, we now describe the requirements for developing magnetic field applicators capable of producing spatially localized field gradients at tissue-relevant depths, as well as the potential integration of targeted or stimuli-responsive MNP formulations for selective in vivo actuation. We believe that these additions provide a clearer roadmap for future preclinical development and significantly enhance the translational context of the manuscript.
(See revised Discussion, lines 428-483.)
R1: In summary, this is a well-written and relevant manuscript. I recommend its publication following the minor revisions suggested above.
Author response: We want to thank again the reviewer for his constructive input.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis study has developed a customized magnetic field device for cancer therapy applications based on the magnetomechanical effect, which possesses clear biomedical orientation value. However, there are critical information gaps and insufficient quantification in the systematic evaluation of the magnetic field device, which may affect the reproducibility of the study conclusions and the accuracy of translation to biological experiments. In light of the core objectives of the study, supplementary review comments are provided from the following three aspects for the authors to improve the work:
- The manuscript only mentions that the device can generate three magnetic field configurations (static, rotating, and alternating), and the existing simulations only focus on the "single configuration that produces the highest mechanical force" (main text). It fails to conduct systematic simulation and numerical presentation of the core magnetic field parameters for the three configurations—there is neither intuitive characterization of the spatial distribution of magnetic field lines nor key quantitative indicators such as magnetic field intensity (maximum, average), root mean square (RMS) amplitude, and frequency response. This makes it impossible to establish a quantitative correlation in biological experiments based on clear magnetic field parameters. It is recommended to supplement magnetic field simulation data according to the type of magnetic field and provide specific parameters including the spatial distribution of magnetic field lines, magnetic field intensity (maximum, average), RMS amplitude, and frequency.
- The manuscript only refers to "cell culture petri dish" and "hypothetical petri dish position" (e.g., z=0 plane), but does not provide specific dimensional parameters of the petri dish (e.g., diameter, height, base thickness), nor does it evaluate the uniformity of magnetic field distribution across the entire petri dish surface. It is recommended to specify the size of the cell culture petri dish and the uniformity of the magnetic field on its surface, and supplement the parameters of the experimental carrier and the evaluation of spatial uniformity.
- The calculation of mechanical forces in the manuscript is limited to literature-reported data, and the correlation between mechanical forces and magnetic nanoparticle (MNP) uptake amount has not been verified through in-house experiments. On this basis, it is advisable to conduct a small-sample preliminary experiment to demonstrate the effectiveness of the magnetic field device.
The above comments focus on improving the quantitative evaluation of the magnetic field device. These data will help support basic biological experiments and provide a reliable methodological reference for product translation and subsequent magnetomechanical therapy.
Author Response
Reviewer 2
Comment 1: The manuscript only mentions that the device can generate three magnetic field configurations (static, rotating, and alternating), and the existing simulations only focus on the "single configuration that produces the highest mechanical force" (main text). It fails to conduct systematic simulation and numerical presentation of the core magnetic field parameters for the three configurations—there is neither intuitive characterization of the spatial distribution of magnetic field lines nor key quantitative indicators such as magnetic field intensity (maximum, average), root mean square (RMS) amplitude, and frequency response. This makes it impossible to establish a quantitative correlation in biological experiments based on clear magnetic field parameters. It is recommended to supplement magnetic field simulation data according to the type of magnetic field and provide specific parameters including the spatial distribution of magnetic field lines, magnetic field intensity (maximum, average), RMS amplitude, and frequency.
Response 1: We thank the reviewer for his insightfull comment. We have added Tables 3 and 4 (lines 382 and 392, lines 350-399) in the revised manuscript where we include all the parameters asked by the reviewer.
Comment 2: The manuscript only refers to "cell culture petri dish" and "hypothetical petri dish position" (e.g., z=0 plane), but does not provide specific dimensional parameters of the petri dish (e.g., diameter, height, base thickness), nor does it evaluate the uniformity of magnetic field distribution across the entire petri dish surface. It is recommended to specify the size of the cell culture petri dish and the uniformity of the magnetic field on its surface, and supplement the parameters of the experimental carrier and the evaluation of spatial uniformity.
Response 2: We thank the reviewer for this important comment. The cell culture petri dish used in both the numerical simulations and the experimental design has a diameter of 3.5 cm, and this information has now been explicitly added to the revised manuscript. We would like to clarify that the magnetic field over the petri dish surface is intentionally non-uniform, as the presence of spatial gradients is a necessary physical condition for the generation of magneto-mechanical forces on magnetic nanoparticles. A perfectly uniform magnetic field would only induce torque and would not give rise to translational forces. Therefore, the device is deliberately designed to produce controlled magnetic field gradients across the culture area. In the revised version, we now explicitly report the dish dimensions (line 252) and provide a quantitative evaluation of the magnetic field spatial gradients within the petri dish volume, allowing direct assessment of field non-uniformity and force-generating capability. We have added a relative discussion in the revised manuscript (lines 263-270). A respective paragraph has been aslo added at the conclusion session (lines 500-507).
Comment 3: The calculation of mechanical forces in the manuscript is limited to literature-reported data, and the correlation between mechanical forces and magnetic nanoparticle (MNP) uptake amount has not been verified through in-house experiments. On this basis, it is advisable to conduct a small-sample preliminary experiment to demonstrate the effectiveness of the magnetic field device.
Response 3: We thank the reviewer for this valuable comment. We would like to clarify that the present study is primarily a physics- and engineering-oriented proof-of-principle investigation, focusing on the precise characterization, numerical modeling, and validation of the magnetic field configurations and the resulting magneto-mechanical forces generated by the device. Our laboratory specializes in the design, calibration, and quantitative validation of electromagnetic field systems, rather than in biological experimentation. The cellular uptake values employed in this work were intentionally drawn from well-established in vitro studies reported in the literature, which were conducted by specialized molecular biology groups and provide experimentally validated benchmarks for superparamagnetic, single-domain, and multidomain nanoparticle systems. Moreover, biological validation of magneto-mechanical stimulation using this device has already been reported in previous collaborative studies with molecular biology departments, demonstrating its applicability in real cellular environments. The primary goal of the present manuscript is therefore to establish a quantitative physical framework that links magnetic field parameters, spatial gradients, and intracellular nanoparticle loading to the resulting mechanical forces acting on single cells. This framework is essential as a predictive tool for guiding future biological studies under well-controlled and reproducible magnetic field conditions. Additional dedicated in vitro experiments aimed at systematically correlating magneto-mechanical forces with cellular responses are currently part of our planned future work.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsAccept！
