Finite-Element Computer Modeling of Spatial Displacement of the Pterygoid Venous Plexus During Mandibular Movements

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript addresses an interesting and clinically relevant question: how the pterygoid venous plexus may shift during mandibular movements and whether this information could help improve the safety of mandibular anesthesia. The finite element approach is potentially useful, and the topic may be of interest to readers in dental anatomy, oral surgery, and dental anesthesia. However, the current version requires substantial revision before it can be considered for publication.

Major comments

1. Methodological detail is insufficient for reproducibility.
   The manuscript states that a 3D finite element model was built from CT data and BodyParts3D, and that simulations were performed for several jaw positions, but the actual FEM workflow is not described in enough detail. Important information is missing, including mesh characteristics, element types, boundary conditions, contact definitions, how muscle loads were implemented, and whether any sensitivity analysis was performed. Without these details, the study cannot be adequately evaluated or reproduced. The current Methods section remains too general.
2. The model is based on a very limited anatomical dataset and lacks validation.
   The study appears to rely on CT data from a single 48-year-old female subject, while muscles were partly modeled from an atlas. This should be stated more clearly as a major limitation. In addition, the manuscript does not provide direct validation of predicted venous plexus displacement against dynamic imaging or another reference standard. The authors later acknowledge the lack of direct validation, but this limitation should be more explicitly integrated into the interpretation of the findings.
3. The terminology is inconsistent and sometimes incorrect.
   The main structure is introduced as the pterygoid venous plexus (PVP), but elsewhere the manuscript uses other abbreviations and even anatomically incorrect terms such as “choroid plexus,” “CEP,” “PIC,” and “CVO.” This creates major confusion and should be corrected throughout the manuscript for consistency and anatomical accuracy.
4. The conclusions are somewhat overstated relative to the evidence provided.
   The authors conclude that maximum mouth opening is the safest position for injection. However, the model only shows predicted displacement of the venous plexus under simplified assumptions and does not directly measure puncture risk, clinical success, complication rate, or anesthetic spread. Therefore, the conclusion should be reframed more cautiously, for example as a hypothesis-generating biomechanical observation rather than a direct clinical recommendation.
5. Presentation of results needs improvement.
   The results are mostly descriptive. No uncertainty estimates, repeatability analysis, or sensitivity testing are presented. It would be helpful to provide a clearer explanation of the coordinate system, the clinical meaning of positive and negative directions, and why right and left movements behave differently. A schematic may help. In addition, the manuscript should better distinguish between absolute displacement magnitude and directional displacement components.
6. Table and figure presentation require careful revision.
   Table 2 contains obvious language/formatting problems, including mixed scripts and corrupted text. Several figure legends are minimal and the figures themselves do not yet communicate the results clearly enough for readers unfamiliar with FEM. The tables and figures should be professionally edited and standardized.

Author Response

Dear Reviewer!

Thank you for your careful review of our manuscript, your valuable comments, and the time you spent on it.

Comment 1
We have completely revised Section 2.4, "Finite Element Model." It now includes the following: element type and number (second-order, tetrahedrons; 487,000 elements, 712,000 nodes), mesh convergence analysis, boundary conditions (rigid fixation of the skull base, non-contact interaction in the TMJ), muscle load application method (distributed loads across attachment areas), and sensitivity analysis (changing the elastic modulus by ±20% resulted in a less than 12% change in the result). The methodology is now reproducible.

Comment 2
Thank you for this important comment. We explicitly stated in the Discussion that the model was based on data from only one subject, and that the muscles were taken from an atlas, not from the CT scan itself. We also explicitly acknowledged the lack of direct in vivo validation (dynamic MRI or cadaver measurements) and emphasized that the absolute displacement values ​​require confirmation in future studies. We have strengthened this section as recommended.

Comment 3
The authors express their gratitude for this comment, which helped us make the necessary corrections. We carefully reviewed the entire text and replaced all erroneous abbreviations ("choroid plexus," "CEP," "PIC," "CVO") with the correct "pterygoid venous plexus (PVP)." These errors have been corrected in the submitted version.

Comment 4
Thanks to your comment, we have significantly revised this issue and softened the wording in the abstract, discussion, and conclusions. It is now explicitly stated that the recommendation to use maximum mouth opening is a hypothesis based on biomechanical modeling and requires clinical validation. The phrases "hypothetically," "pending clinical validation," and "biomechanical rationale" have been added.

Note 5
The authors are grateful for this comment. A paragraph has now been added to Section 3, "Results," explaining that all values ​​were obtained on a single model without repeated measurements, but sensitivity analysis showed stability in the direction of displacement (<12% change in magnitude). The asymmetry in right/left displacements is explained in the Discussion section by different muscle load vectors while maintaining the geometric symmetry of the model.

Note 6
Thank you for your attention to our article. Table 2 has been completely reformatted: technical artifacts have been removed, headings have been standardized, and ± signs have been added for the direction of displacement. All figures (4–8) have had their captions clarified: an explanation of the color scale (blue = 0 mm, red = maximum) has been added, and it has been noted that the analysis was performed for the geometric center of the right vascular complex.

We hope that the revised version of the manuscript meets all requirements. Thank you for your constructive review, which has significantly improved our work.

Reviewer 2 Report

Comments and Suggestions for Authors

In this study, the authors constructed a three-dimensional finite element model based on the CT data of a single individual to simulate the spatial displacement of the pterygoid venous plexus under different vertical openings (15, 25, 35 mm) and horizontal lateral displacements (5 mm) of the mandible. The results showed that the displacement amplitude of the pterygoid venous plexus was positively correlated with the mandibular opening, with a total displacement of 1.24 mm (backward, inward, and downward) at the maximum opening (35 mm), while the displacement direction was asymmetric during lateral movement. This is a very interesting article. However, there're still the following issues which should be addressed. 

1. This study employed three-dimensional finite element method to simulate the displacement of the pterygoid venous plexus during mandibular movement. However, the model construction involved several key simplifying assumptions:
- All tissue structures (bones, muscles, ligaments, and blood vessels) were assumed to be uniform, elastic, and isotropic materials, while actual biological tissues have obvious anisotropic, nonlinear, and viscoelastic mechanical properties;
- The model was assumed to be geometrically symmetrical, ignoring the anatomical asymmetry that exists in the human body;
- The loading conditions only considered the "primary load", without specifying the exact values and directions of the muscle forces;
- Many parameters in the material property table were marked as "Not Specified", and no reliable literature sources were provided.
As a computer simulation method, the clinical reference value of three-dimensional finite element research is highly dependent on the physiological authenticity of the model. In the absence of animal experiments or clinical studies for verification, the above simplifying assumptions result in a significant gap between the computational results and the actual physiological conditions, making it difficult to directly apply the results to clinical decision-making. The authors did not perform any form of validation on the model (such as comparison with dynamic MRI, 4D Flow MRI, or cadaveric dissection data), raising doubts about the reliability of the results. 

2. The main conclusion of this study is that the displacement of the pterygoid venous plexus is the greatest (1.24 mm) at the maximum mandibular opening position (35 mm), thus suggesting that "the maximum opening position is the safest for injection." However, this conclusion has long been a common sense in clinical practice for anesthesia procedures. Clinicians usually choose the appropriate opening degree based on the specific conditions of the patient and the operational requirements when performing inferior alveolar nerve block anesthesia. The maximum opening position helps to avoid blood vessels and clearly expose the operational field of view, and this principle has been widely reflected in the teaching of anesthesia techniques and clinical practice. This study merely "confirms" this known common sense through numerical simulation and does not provide quantified guidance beyond clinical experience (such as the specific degree of risk reduction at different opening degrees, the impact of individual differences on safety, etc.), and its incremental clinical value is limited. 

3. The author did not systematically expound the specific guiding significance of the research results for clinical operations in the discussion, nor did they explain whether a displacement of 1.24 mm is sufficient to significantly reduce the risk of vascular injury in clinical practice (for example, by comparing it with the typical distance between the pterygoid venous plexus and the tip of the injection needle). The absence of such a discussion on clinical value further weakens the significance of this study. 

4. In Table 1, many material parameters are marked as "Not Specified", and no references for the material properties are provided. The reliability of the finite element analysis results highly depends on the accuracy and completeness of the input parameters. The absence of key parameters makes it difficult to reproduce and verify the analysis results. 

5. This study did not conduct any form of validation on the accuracy of the finite element model. As a computational simulation method, the results of the finite element model must be compared with in vitro experiments, in vivo imaging data, or previously validated models to confirm its reliability. The results of finite element analysis without validation should be regarded as preliminary exploration rather than conclusions that can guide clinical practice. 

6. The discussion section is poorly structured and illogical. 
The current discussion section has the following issues:
- Loose structure: The content jumps between "ethical significance - clinical significance - methodological advantages - model validation - limitations", lacking a clear logical thread;
- Missing key content: It fails to systematically explain the guiding significance of the research results for clinical operations, and does not compare the displacement value (1.24 mm) with clinically relevant anatomical parameters (such as the distance between the injection needle tip and the blood vessel);
- Disconnected from the results: A large portion of the discussion merely restates the research results rather than delving into their mechanisms, significance, and limitations. 
It is suggested that the discussion section be reorganized into the following logically clear levels:
(1) Summary of main findings;
(2) Comparison with previous studies (anatomical, finite element studies, etc.);
(3) Analysis of clinical significance (quantitative guidance value);
(4) Methodological advantages and limitations;
(5) Future research directions. 

7. Missing references in the literature. 
- There is a lack of citation of systematic reviews on the application of the finite element method in oral and maxillofacial surgery.
- There is no reference to relevant studies on the anatomical variations of the pterygoid venous plexus, which is a key factor affecting the safety of anesthesia.
- Previous clinical studies on the impact of mandibular position on the safety of anesthesia have not been cited for comparative analysis. 

8.Is "ianb" in the keywords "jaw"? 

9. "Pterygoid venous plexus" is abbreviated as both "PVP" and "CEP". It is recommended to unify it as "PVP". 

10. In Table 2, there is a Russian phrase "Смещение 5 мм влево", which has not been uniformly translated into English. 

11. The resolution of Figure 1-8 is relatively low, and the axis labels and color scale legends in some of the graphs are hard to recognize. 

12. Some entries in the references lack the abbreviation of the journal name, and the format of volume, issue and page numbers is not uniform. 

Author Response

We sincerely thank you for your thorough and insightful review of our manuscript entitled "Finite Element Computer Modeling of Spatial Displacement of the Pterygoid Venous Plexus during Mandibular Movements" (ID: jpm-4192900). Your comments have significantly improved the quality and clarity of our work.

Reply to comment 1

Thank you for your comment. We agree that these are important limitations. In the revised manuscript, we have added a mesh convergence analysis (Section 2.4) to ensure numerical stability, as well as a sensitivity analysis (Section 2.4): changing the elastic modulus of soft tissue by ±20% changed the overall displacement by less than 12%, while the direction of displacement remained unchanged.
We have added a "Verification and Validation" subsection (Section 2.4), which explicitly states that direct in vivo validation was not performed and that our results should be considered hypothesis-generating.
We provide literature references for material properties (Koolstra & van Eijden, 2005; Darawsheh et al., 2023; Atif et al., 2024).

As per your comment, we clarified that muscle forces were derived from physiological cross-sections and EMG data from the literature, and were not arbitrarily selected.

In the Discussion section, we also explicitly acknowledge that "absolute displacement values ​​should be considered approximate and model-dependent." Direct clinical validation is not claimed.

Response to comment 2
We agree that the qualitative recommendation is not new. However, the quantitative aspect—the magnitude of displacement (1.24 mm) and its relationship to anatomical safety margins (25–60% of the needle-to-SVP distance)—has not previously been described.
We have revised the Discussion section to emphasize that the primary contribution lies in the biomechanical quantification of a known clinical observation, not the qualitative result itself. We also added a simplified geometric model estimating a 40–50% reduction in the cross-sectional area between the needle and vessel at maximum opening.

Response to Comment 3

Dear Reviewer, Thank you for this important point.
We have added a separate paragraph to the Discussion section (the third paragraph of Section 4) to precisely address this issue: we have included a literature source on anatomical studies (Khoury et al., 2011), which report that the distance from the needle tip to the PVS during a typical mandibular nerve block ranges from 2.0 to 4.5 mm. Thus, a displacement of 1.24 mm represents 25–60% of the available safety margin.
Using a simplified cylindrical model (PVS diameter ~3 mm), a perpendicular displacement of 1.24 mm reduces the needle-vessel overlap area by approximately 40–50%. This suggests that maximal mouth opening could potentially reduce the risk of intravascular injection by nearly half—a hypothesis that now requires clinical testing.
Here, we emphasize that this shift is clinically significant.

Response to Comment 4
We appreciate the comment and have added a footnote to Table 1 clarifying that parameters such as Rm (ultimate tensile strength) are not required for linear elastic finite element analysis and do not affect the displacement results – they are included for completeness only.
Furthermore, we have added literature references for all non-empty mechanical properties (ρ, ν, E) directly below the table: [12, 13, 15] for bones, muscles, ligaments, nerves, TMJ, and arteries.

Response to Comment 5
Dear Reviewer, The authors appreciate your attention to this data presentation issue.
Section 2.4 (Validation and Validation) clearly states: "Direct quantitative validation using dynamic imaging (e.g., cine MRI or 4D flow MRI) or cadaveric measurements was not performed." In the Discussion section, we add: "Absolute bias values ​​should be considered model-dependent and require confirmation using independent methods."
We never claim clinical evidence—our conclusion is that the model provides biomechanical justification for clinical recommendations, not a substitute for clinical trials.

Response to Comment 6
Based on your comments, we have completely revised the Discussion section in accordance with your clear recommendation:
a) Summary of Key Findings (First Paragraph)
b) Comparison with Previous Studies (Second Paragraph)
c) Clinical Relevance (Third and Fifth Paragraphs – 1.24 mm Quantitative Analysis, Relationship with Aspiration Velocity, and the Gow-Gates Method)
d) Methodological Limitations (Seventh Paragraph – Single Subject, Isotropic Assumptions, Lack of Direct Validation)
d) Future Research Directions (Eighth Paragraph – Personalized Models, Cine MRI, Clinical Trials)
We believe the discussion is now logically structured and avoids simple repetition of results.

Response to Comment 7
Thank you for your feedback. We have added the following references to the revised manuscript:
a) Systematic Reviews/FEM Methods: Atif et al., 2024 [12]; Darawsheh et al., 2023 [13]
b) Anatomical variations and distances in the pterygomandibular space: Khoury et al., 2010 [25]; Khoury et al., 2011 [26]
c) Clinical studies of aspiration rates and comparisons of techniques: Ravi Kiran et al., 2018 [27]; Prabhu Nakkeeran et al., 2019 [28]

They now confirm our clinical interpretation and contextualize our findings within the existing literature.

Response to comment 8
Thank you for your careful and meticulous reading of the manuscript.

We checked the keywords. The abbreviation "IANB" is not used; the full phrase "mandibular nerve block" is present. The word "jaw" has been added as a keyword to improve the search.

Reply to Comment 9
We thank you for this emphasis, and we have corrected it throughout the manuscript. The abbreviation "CEP" (Russian) has been completely removed. Only PVP is used consistently.

Reply to Comment 10
We apologize for this oversight. The Russian phrase has been replaced with the English equivalent "Left shift by 5 mm" in Table 2.

Reply to Comment 11
Please review the updated figures in the revised version of the manuscript.

Reply to Comment 12
Thank you for your comment and guidance, dear reviewer. We have carefully reformatted the entire reference list in accordance with the journal's guidelines. All journal titles are now presented uniformly (using standard abbreviations where applicable), and the order of volume, issue, and page numbers has been adjusted across all entries.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for your thorough and constructive revision. The manuscript has improved substantially compared with the previous version. In particular, the finite element methodology is now described in much greater detail, including mesh type and size, convergence testing, boundary conditions, muscle load implementation, and sensitivity analysis, which significantly improves reproducibility. The terminology has also been corrected and standardized, and the presentation of Table 2 and the figure legends is clearer than before.

The discussion of limitations has also been strengthened appropriately. The authors now acknowledge that the model is based on a single subject, that muscles were atlas-based rather than individually segmented, and that no direct in vivo validation was performed. This is an important improvement and makes the interpretation more balanced.

Reviewer 2 Report

Comments and Suggestions for Authors

The revised version is much better. Most of the issues have been addressed. I have no further comments.