Stochastic Strength Analyses of Screws for Femoral Neck Fractures

Round 1

Reviewer 1 Report

Authors present a Stochastic Strength Analyzes of Screws for Femoral Neck Fractures.

The role of the stochastic approach in orthopedic is a well establish approach thanks to its capability to cover a large range of configuration. This study is based on a simple Monte Carlo approach by using

 Anthill software.

Simplified screw model are presented

Several issues should be address before publication

Unfortunately the reader is not supported in the during the manuscript since this paper seems to be presented as a sort of appendix of previous paper of the same group (ref 1: Strength Analyses of Screws for Femoral Neck Fractures)

The continuing remanding to ref 1 do not simplify the reading mainly because no sufficient informations are provided in the introduction and MM.

These limitations are reflected in the Abstract. Authors say "

 As a continuation of the previous work, this article, therefore, aims to offer our own new numerical model of femoral screws together with their stochastic (probabilistic, statistical) assessment. "

The reviewer  suggest a reorganization of the manuscript to make self-sustainable the concept of this work. It is opinion of the review that this will increase the quality of the work. Reviewer suggest to reduce significantly the use of sentences in round brackets.

Figures should be improved. Fig 15 in particular. "Body liquids" what does it mean ?, please correct "tissues".

 

Author Response

The new version of the manuscript with highlighted changes was submitted.

Author Response File: Author Response.docx

Reviewer 2 Report

Thank you for givig me the opportunity to review this paper. Although the subject of the manuscript has a high relevance there is, from a clinical perspective, a lack of discussion how this apporach would improve current medical practice. The authors should explain more clearly what the medoical implication / improvement of current medical practice derived from your method would be. How to do expect to improve medical practice with your method?

The abstract should also present the authors findings as well as the main implications and conclusions.

Introduction

Give a brief description of your previous work as this will help the readers to understand your paper.

The term AO is not properly introduced and it is unclear to what medical perspectives refer to.

Methods

Page 5 - SBRA method has already been introduced (partly) in the previous sections, please be more concise by introducing it properly at one section of the manuscript.

 

 

 

Author Response

Dear reviewer, thank you for your work.

Clinical perspective, discussion about the approach were extended.

Introduction and abstract were corrected.

The term AO was properly introduced.

SBRA method introduction is more concise.

There was added more equation.

The English was checked again.

See the attached file with highlighted changes

Author Response File: Author Response.docx

Reviewer 3 Report

The authors present work concerning an approach to femoris neck (Colum) fractures with two types of screws:  full and cannulated. The work, based on a simplified 2D model, is interesting since it implies the use of current techniques.

There remains the idea of confusion in the writing of the work. Authors refer to previous papers of their authorship, as also future work to be done. This work is presented as step 2, requiring a careful reading of previous works, and implies the self-referencing of those works. This situation leads to an excess of referral to other works by the same authors, making the context and objectives less clear in the writing they present.

As an example: “This article is a direct continuation of our former work; see [1].”, or “Medical perspective and medical limitations are presented in [1].”, or “A comparison of the results acquired by the Finite Element Method and the method presented in this paper demonstrates the accuracy of our simple 2D model; see [1].”

Some ideas concerning the improvement of the paper:

In my opinion, the objectives of the work and its limitations can be improved and must be clearly stated, making it possible that, when reading the article, everyone understands what has been done and what is proposed. It should be clear that fractures at the level of the neck of the femur can be of various types. Only some of these can be treated using this type of screws, defined by the authors as minimally invasive treatment.

The basic considerations for the simplifications that are taken should be presented and discussed. The authors use a 2D model, with the limitations that are associated with it. In figure 14 an image is presented which has claimed to have been obtained with a finite element model in Ansys. However, they do not describe how this model was obtained, nor do they compare results with the 2D model. Why use 3 cannulated screws? Can the foundation be considered the same with the use of more than 1 screw?

It remains the idea that the discussion of the results could be presented in a more clear and sustained way. It is not clear the interest of figure 15 in the context of the work presented. This figure refers to ideas for future work.

Regarding the visual aspect of the work, the figures should be improved. They contain characters that are too disproportionate to the text and some of them are not well clear.

Author Response

Dear rewiewer, thank you for your work

There was added more text to explain the previous and future work.

 

The objectives of the work and its limitations and disscussion were improved and extended. Types of fractures and medical perspectives were extended.

The basic considerations for the simplifications a 2D model that are taken were presented and discussed. The finite Element application was explained. Elastic foundation, in connection to a number of screws, was explained.

It remains the idea that the discussion of the results could be presented in a more clear and sustained way. It is not clear the interest of figure 15 in the context of the work presented. This figure refers to ideas for future work.

Some Figures were improved. The English language was checked again.

See highlighted changes in the attachment file

Author Response File: Author Response.docx

Reviewer 4 Report

Dear Authors,
The article describes the studies aimed to investigate uncertainties in the modeling process, which are related for example to the natural variability of the mechanical properties of the bones, physiological loading, and the response of the model to these uncertainties. The applied research methodology made it possible to explore the research problem using a probabilistic approach, which is a good way to investigate individual dependence on data. Although the topic is interesting, I consider this work should be improved before publication for the following comments and suggestions: 
•    about bibliography I believe it is of absolute importance to cite the article "Biomechanical evaluation of human lumbar spine in spondylolisthesis”, Authors: Kamil Joszko, Marek Gzik, Wojciech Wolański, Bożena Gzik-Zroska, Edyta Kawlewska, Publicised in Journal of Applied Biomedicine, 2018, Volume 16, Issue 1, Pages 51 – 58. 
and “Biomechanical analysis of plate stabilization on cervical part of spine” Authors: Marta Kiel, Jan Marciniak, Janusz Szewczenko, Marcin Basiaga, Wojciech Wolański, Publicised in Archives of Materials Science and Engineering, 2009, Volume 38, Issue 1, Pages 41-47. 
Both articles present a deterministic numerical approach to biomechanics and I suggest discuss applications of stochastic mechanics, together with probabilistic reliability assessment in a similar investigation. Regarding these articles, what advantages will/would your proposed method carry out at practical applications in biomechanical engineering or in the field of traumatology and orthopaedics?
•    regarding the approach to this case, I believe that the calculation must be increased the changing range of stiffness k (the elastic foundation), which should demonstrate the influence of properties of healthy or osteoporotic bone on results. Authors use a constant coefficient k= 2.2222×10^7Pa, does it fit a healthy bone or a specific bone?
•    the results presented in this paper are applied to cancellous screws used in fractured bones. But model (also 3D FE model) and the boundary conditions don't present a fracture plane (type of fractures). I suggest explaining it. Additionally, Why did the authors divide the model into 3 sections: 15mm, 53mm, and 22mm (total length 90mm)? Does each section represent part of the screw or have other physical sense?
•    in my opinion too many figures are taken from the paper [1] (Frydrýšek, K.; Šír, M.; Pleva, L. Strength Analyses of Screws for Femoral Neck Fractures. J. Med. Biol. Eng. 38, 816–834 (2018). https://doi.org/10.1007/s40846-018-0378-x). Authors should the same iconographic information change or modify (or quote). 
I accept the article after minor revision (corrections) and I recommend it to publish in Applied Sciences Journal.

Author Response

Dear reviewer

Thank you for your work. We are sending our answers.

With regards Karel FRYDRÝŠEK

The article describes the studies aimed to investigate uncertainties in the modeling process, which are related for example to the natural variability of the mechanical properties of the bones, physiological loading, and the response of the model to these uncertainties. The applied research methodology made it possible to explore the research problem using a probabilistic approach, which is a good way to investigate individual dependence on data. Although the topic is interesting, I consider this work should be improved before publication for the following comments and suggestions:

•    about bibliography I believe it is of absolute importance to cite the article "Biomechanical evaluation of human lumbar spine in spondylolisthesis”, Authors: Kamil Joszko, Marek Gzik, Wojciech Wolański, Bożena Gzik-Zroska, Edyta Kawlewska, Publicised in Journal of Applied Biomedicine, 2018, Volume 16, Issue 1, Pages 51 – 58. 
  and “Biomechanical analysis of plate stabilization on cervical part of spine” Authors: Marta Kiel, Jan Marciniak, Janusz Szewczenko, Marcin Basiaga, Wojciech Wolański, Publicised in Archives of Materials Science and Engineering, 2009, Volume 38, Issue 1, Pages 41-47. 
  Both articles present a deterministic numerical approach to biomechanics and I suggest discuss applications of stochastic mechanics, together with probabilistic reliability assessment in a similar investigation. Regarding these articles, what advantages will/would your proposed method carry out at practical applications in biomechanical engineering or in the field of traumatology and orthopaedics?

Although it is unusual for reviewers to ask for a specific citations, we decided to cite only one you proposed, i.e. Joszko, K.; Gzik, M.; Wolański, W.; Gzik-Zroska, B.; Kawlewska, E., Biomechanical evaluation of human lumbar spine in spondylolisthesis. J. Appl Biomed 2018, 16 (1), 51-8, https://doi.org/10.1016/j.jab.2017.10.004. However, there are big differences between our work and citations you proposed. Your proposed citations are focused on spine and deterministic approach and on FEM. Those citations are solving only a few simulations (configurations) and our work is solving 5x10⁶ random Monte Carlo simulations (configurations). Otherwise, in our article, there is enough citation of FEM solutions too.

Advantages of our approach:

1. Simple, fast and easy way with similar results to FEM (we are solving set of 12 equations, i.e. there is a sparse matrix ).
2. Solved and evaluated 5x10⁶ random Monte Carlo simulations (configurations) in collum femoris. This is a good connection with the reality, because each operation of corpus humanum is different.
3. As is known, there no exist absolutely safe medical techniques or mechanical structures. Some treatments of fractures could be ended even by death. Hence, according to the chosen variabilities and many solutions, we calculated the biomechanical probability of possible failure. This is not possible to do it via the deterministic approach, because the deterministic approach is not based on the theories of statistics and probability. This information is usually interesting for producers, medics, insurance companies etc.
4. Other advantages are mentioned in our article too.

•    regarding the approach to this case, I believe that the calculation must be increased the changing range of stiffness k (the elastic foundation), which should demonstrate the influence of properties of healthy or osteoporotic bone on results. Authors use a constant coefficient k= 2.2222×10^7Pa, does it fit a healthy bone or a specific bone?

As is mentioned in our article, in the field of collum femoris fractures, this method cannot be applied for osteoporotic bone. This is a small “mini invasive” implant intended for young people with a good bone quality and healthy bones. For osteoporotic bone must be applied bigger and massive implants based on nails, plates and their combinations or ever full or partial alloplasty of hip joint. For more information see our reference [1].

Value of k = 2.2222×10⁷ Pa, fits well for a typical bone of a good quality of young people but with collum femoris fracture. However, in the future, we would like to recalculate our results together with a small variability o k. But, this is a little more complicated. Actually, k is parameter of a mechanical interaction between the screw and collum femoris. This parameter is mainly influenced by dimension and material of a screw, by type of fracture, by quality of screw inserting into bone and by material of a bone. Variability of dimensions of screws can be neglected (those variabilities are very small). Variabilities of a material properties of a screw were applied. Parameter k fits well for fracture but its variability was neglected. Variabilities of quality of a screw inserting are generally influenced by the application of a variable angle . Material properties of a bone are partly neglected via constant k. However, this is a new and original probabilistic approach applied firstly in the branch of collum femoris fractures. We did not find any different probabilistic solutions in the literature.

•    the results presented in this paper are applied to cancellous screws used in fractured bones. But model (also 3D FE model) and the boundary conditions don't present a fracture plane (type of fractures). I suggest explaining it. Additionally, Why did the authors divide the model into 3 sections: 15mm, 53mm, and 22mm (total length 90mm)? Does each section represent part of the screw or have other physical sense?

Our model is based on a simplified model of boundary conditions with a fracture. In our approach, there is only 12 boundary conditions and 3 differential equations. Because, the screw is a “short beam on elastic foundation”, the “switch off” or “switch on” or situation between these limits can be controlled via value k. This approach is easy but with a small error and the results are in accordance with FEM solutions and with our other probabilistic and deterministic solutions of fractures or other deterministic and probabilistic solutions of beams on elastic foundation. However, there is a way to applied boundary condition in a place of the fracture (it will leads to the solution of 4 differential equations with 16 boundary conditions) but this will bring small changes of the results.

The dimensions 15, 53, 22 and 90 mm are connected with real screw (Medin company) and for a typical loadings and screw position.

•    in my opinion too many figures are taken from the paper [1] (Frydrýšek, K.; Šír, M.; Pleva, L. Strength Analyses of Screws for Femoral Neck Fractures. J. Med. Biol. Eng. 38, 816–834 (2018). https://doi.org/10.1007/s40846-018-0378-x). Authors should the same iconographic information change or modify (or quote).

All figures from our references are al least modified or changed. There is not a problem with copyright.

I accept the article after minor revision (corrections) and I recommend it to publish in Applied Sciences Journal.

Round 2

Reviewer 1 Report

FRYDRÝŠEK and co-authors addressed some aspects of the comments, but some issues remain

The stare of the art could be improved see e.g. Li et al. Journal of Orthopaedic Surgery and Research (2018) 13:272, more recently Xia, Y., Zhang, W., Zhang, Z. et al. Treatment of femoral neck fractures: sliding hip screw or cannulated screws? A meta-analysis. J Orthop Surg Res 16, 54 (2021). https://doi.org/10.1186/s13018-020-02189-1

Authors simplified screw as cylinder, what is the role of the thread? The 2d schematization is very strong.

Moreover, what is the variability of the cancellous bone material properties? does it affect the screw fixation?

The review does not understand some figures:

Figure 14 is the same reported in Journal of Medical and Biological Engineering https://doi.org/10.1007/s40846-018-0378-x

What is the difference between Figure 13 and Fig. 17 reported in Journal of Medical and Biological Engineering https://doi.org/10.1007/s40846-018-0378-x

what is the added value of figure 15?

In fig What is the meaning of \MPa\? Are they "\" round brackets?

Please correct it also in List of Symbols

Author Response

Dear reviewer

Thank you for your work. We are sending our answers.

With regards Karel FRYDRÝŠEK

 

The state of the art could be improved see e.g. Li et al. Journal of Orthopaedic Surgery and Research (2018) 13:272, more recently Xia, Y., Zhang, W., Zhang, Z. et al. Treatment of femoral neck fractures: sliding hip screw or cannulated screws? A meta-analysis. J Orthop Surg Res 16, 54 (2021). https://doi.org/10.1186/s13018-020-02189-1

We added mentioned references and other references to improve the state of the arts. However, Finite Element Method and other deterministic method are not based on the theory of probability and are not in the focus of our article. We calculated and evaluated 5x10⁶ random Monte Carlo simulations (configurations) and to perform it via Finite Element Method is very very complicated.

Authors simplified screw as cylinder, what is the role of the thread? The 2d schematization is very strong.

We are working with the beams. Therefore, this is possible to do it. If the screw is in a bone properly installed (i.e. surrounded by the bone, embedded in the bone), the influence of a thread (i.e. notch is decreased). There is a big difference between loading of surrounded and unsurrounded screw and our beam is a surrounded screw.

Moreover, what is the variability of the cancellous bone material properties? does it affect the screw fixation?

In this first original and new probabilistic approach, the Elastic foundation stiffness, i.e. femoral bone stiffness k, of the bone is constant and chosen as a value for typical bone of young people. This is because this way of treatment is not recommended for osteoporotic bone.

1. However, the quality of cancellous bone properties and the quality of screw bone contact, is partly included in coefficient n; which is between 2 and 3. An extreme is when n=2, i.e. the quality of bone-screw osteosynthesis in performed only by two of three inserted screws. We added some information about it in our text.
2. As noted in this article, this method of osteosynthesis is applied for young people and not for older people. The quality of bone of young people is better (i.e., there is smaller variability of bone material properties).
3. In the future, we would like to apply the variability of cancellous bone too via parameter k, but this relates to a new and more complicated calculation. According to our previous research, the variability of k as a kind of stiffness has average influence.

In this article as a new approach, there is only 6 basic and the most important probabilistic inputs connected with screw positions, loading and material properties of screws.

The review does not understand some figures:

Figure 14 is the same reported in Journal of Medical and Biological Engineering https://doi.org/10.1007/s40846-018-0378-x

Figure 14 was changed into a similar one.

What is the difference between Figure 13 and Fig. 17 reported in Journal of Medical and Biological Engineering https://doi.org/10.1007/s40846-018-0378-x

Figure 13 and Fig. 17 gives the same information but are different. Figure 13 has some added information. However, these Figures are based on SW Anthill output and modified. There is not a conflict with copyright.

What is the added value of figure 15?

It is an information about a biological staining of screw and plate by human tissues and liquids. We added more information in this picture. The goal is to make a small information about our general investigation of screws (global context).

In fig What is the meaning of \MPa\? Are they "\" round brackets? Please correct it also in List of Symbols

Brackets / / are used for an introduction of a physical unit. According to the basic reference [1], the physical units are noted by the same way. For example, megapascal is noted as a physical unit /MPa/ or in connection with a certain value as 1 MPa. However, in some places and figures we corrected it but not in the text. However, this way of writing is probably in concordance with publisher or publisher can correct it or ask for it.

Reviewer 3 Report

The authors made some improvements in the writing and description of the work presented. Although the description is improved, some aspects could have been improved as well. For example, some of the figures are exactly the same as those in previous works by the authors (see figs 3, 4, and Ref [1]).

Concerning the developed work, I believe that “NEW multidisciplinary approach to biomechanics” is not an adequate indication. In fact, literature shows a lot of works using a multidisciplinary approach in biomechanics. And the authors present a simplified 2D model.

There is still the idea of the work presented as a step of teamwork. There is no problem with this, but it implies the self-referencing of those works, with a lot of self-citations. Perhaps in some of the citations that are based only on the authors' own descriptions, citations from other authors can be added.

The list of Symbols must be revised. Ex: m Patient mass (not weight). I also suggest using […] in the list of Symbols. See also paragraph before expression (4.4).

I still believe that the figures can be improved to a better visual aspect of the work. Ex: The dimension of the text in the figures can be adjusted to match the dimension of the redaction.

In fact, figures still contain characters that are too disproportionate to the text and some of them are not well clear.

There is still a question concerning figure 14. The image presented is claimed to have been obtained with a finite element model in Ansys. However, they do not describe how this model was obtained. What type of stress is there? Von Mises stress?  So, must be indicated. The comparation is important in the context of the results obtained with the 2D model and can be more detailed.

Concerning the redaction of “other opportunities for future work”, Fig. 15 and paragraph before figure 15.  It seems to me that this part has no interest in the context of the work presented, being disconnected. Not my opinion, this part should not be part of the writing of the work.

Author Response

Dear reviewer

Thank you for your work. We are sending our answers.
With regards Karel FRYDRÝŠEK

The authors made some improvements in the writing and description of the work presented. Although the description is improved, some aspects could have been improved as well. For example, some of the figures are exactly the same as those in previous works by the authors (see figs 3, 4, and Ref [1]).

We made more changes in the Fig. 3 and 4. However, we believe that there is not copyright conflict.

Concerning the developed work, I believe that “NEW multidisciplinary approach to biomechanics” is not an adequate indication. In fact, literature shows a lot of works using a multidisciplinary approach in biomechanics. And the authors present a simplified 2D model.

We deleted the word “new”. However, the most and original new thing is the application od probabilistic (stochastic) approach in this branch of science connected with evaluation of 5x10⁶ random Monte Carlo simulations (solutions of possible configurations).

There is still the idea of the work presented as a step of teamwork. There is no problem with this, but it implies the self-referencing of those works, with a lot of self-citations. Perhaps in some of the citations that are based only on the authors' own descriptions, citations from other authors can be added.

We added more citations from other authors.

The list of Symbols must be revised. Ex: m Patient mass (not weight). I also suggest using […] in the list of Symbols. See also paragraph before expression (4.4).

Brackets / / are used for an introduction of a physical unit. According to the basic reference [1], the physical units are noted by the same way. For example, megapascal is noted as a physical unit /MPa/ or in connection with a certain value as 1 MPa. However, in some places and figures we corrected it but not in the text. However, this way writing is in concordance with publisher or publisher can correct it during the final revision before a print.

We changed word “weight” into “mass”.

I still believe that the figures can be improved to a better visual aspect of the work. Ex: The dimension of the text in the figures can be adjusted to match the dimension of the redaction.

We checked, modified and improved the quality of some images.

In fact, figures still contain characters that are too disproportionate to the text and some of them are not well clear.

We checked, modified and improved the quality of some images. However, the publisher can change or ask us for a specific changes of pictures too.

There is still a question concerning figure 14. The image presented is claimed to have been obtained with a finite element model in Ansys. However, they do not describe how this model was obtained. What type of stress is there? Von Mises stress?  So, must be indicated. The comparation is important in the context of the results obtained with the 2D model and can be more detailed.

We corrected Fig. 14 and add there some desired information.

Concerning the redaction of “other opportunities for future work”, Fig. 15 and paragraph before figure 15.  It seems to me that this part has no interest in the context of the work presented, being disconnected. Not my opinion, this part should not be part of the writing of the work.

This figure, together with the paragraph, inform about our large focus on screws applied in traumatology, orthopaedics and surgery (i.e. global context of our research). We thing, it is an important information for Discussion.