The Effect of External Fixator Configurations on the Dynamic Compression Load: An Experimental and Numerical Study
Round 1
Reviewer 1 Report
The paper presents interesting approach to problem of fracture treatment, specifically compares different configurations of pins positions and resulting compression loads. Results obtained by authors can by considered an advance in current knowledge. The size of the submitted manuscript is quite long as it covers both experimental and numerical analysis of the topic.
Although the description of the load cell-based system that intends to simulate the bone callus is clear, it would be good if the authors considered including an enlarged view of this system somewhere within Fig. 2., or maybe introduce Fig. 2c.
Line 147: How was the time of 10 minutes for recovering of the samples determined? Why not 5 or 20? Explain.
Line 197: Value of COD (R2) given twice.
Line 90-91: “The average values obtained for each group were used to establish a qualitative comparison with the finite element results.” – this statement is very dangerous as it justifies completely skipping the effect of variation of experimental results. Author report testing each configuration five times. The only places in the manuscript where the SD of obtained results is mentioned are: raw results in Tab. 4 and error bars in Fig. 8-9. Within the paper body multiple statements can be found where authors compare the mean experimental result with each other or with result obtained using FEA (for example Discussion, starting from Line 392). It is always better each time to mention that the mean value is compared, as the obtained percentage ratio of such comparison is, due to SD, not precise but also subjected to the same variation of results. The mean value does not precisely represent results of series of test… For example calculated CL/TL for AB at 50mm /Tab.4/ is 15% (30.66N/200N) while 30.66N is only a mean value with SD of ±4.97 (COV=16.2%)…
See Fig. 5/7 – what does the each point on the line represent? Mean value of 5 test at that specific tensile/compression load? Or maybe the line represents a single test? But then the linear regression equation would represent only this single test within the configuration and not the combined results of all 5 tests within the configuration…
Please specify goodness of fit of the model in fig 5., for example R2 values, and refer to them in the text. Also in fig 12a.
Please examine and describe what would happen if the nonlinear curves (fig.5-6) were divided into two, separate, linear ones. Compare them (linear regression and R2) and compare the second part of the separated curve to wider axis distance configurations (fully linear ones 70/90mm).
Line 264-266. A non-linear function does not have a constant slope.
Line 400: Significantly? Was it tested statistically? α=0.05?
Fig. 12b – Why the clearly linear relation is missing the linear model?
It is quite unusual that the list of references contains not a single paper by authors of the reviewed paper, especially when authors widely publish papers discussing usage of FEA in biomechanics, etc. This creates the impression that the reviewed work is in no way related to the scope of scientific interests of the authors, while it of course is.
Language needs careful review. Minor English errors can still be found (WW2, higher instead of highest, etc.)
Author Response
Reviewer 1
The authors would like to thank the reviewers for reading the manuscript and for the comments and suggestions to improve the manuscript. Changes in the revised manuscript are highlighted with blue color.
the paper presents interesting approach to problem of fracture treatment, specifically compares different configurations of pins positions and resulting compression loads. Results obtained by authors can be considered an advance in current knowledge. The size of the submitted manuscript is quite long as it covers both experimental and numerical analysis of the topic.
Authors response: yes, we agree with this understanding.
Although the description of the load cell-based system that intends to simulate the bone callus is clear, it would be good if the authors considered including an enlarged view of this system somewhere within Fig. 2., or maybe introduce Fig. 2c.
Authors response: we agree and we added a new image on figure 2, which is identified as Fig. 2c.
Line 147: How was the time of 10 minutes for recovering of the samples determined? Why not 5 or 20? Explain.
Authors response: this time was selected randomly to assure creep-recovery, but because the compressive yield strength is about 107 MPa and the stresses were much lower than this value, it is expected that the material behaves linearly. Creep-recovery is the phenomenon observed in a body immediately after reduction of the fixed imposed creep load and in which deformation decreases exponentially over time. In order to clarify this idea, we changed the text as following:
“… the specimens were allowed to creep-recovery for 10 min.” (see Line 129)
Line 197: Value of COD (R2) given twice.
Authors response: we removed the value in parenthesis. (see line 176).
Line 90-91: “The average values obtained for each group were used to establish a qualitative comparison with the finite element results.” – this statement is very dangerous as it justifies completely skipping the effect of variation of experimental results. Author report testing each configuration five times. The only places in the manuscript where the SD of obtained results is mentioned are: raw results in Tab. 4 and error bars in Fig. 8-9. Within the paper body multiple statements can be found where authors compare the mean experimental result with each other or with result obtained using FEA (for example Discussion, starting from Line 392). It is always better each time to mention that the mean value is compared, as the obtained percentage ratio of such comparison is, due to SD, not precise but also subjected to the same variation of results. The mean value does not precisely represent results of series of test… For example calculated CL/TL for AB at 50mm /Tab.4/ is 15% (30.66N/200N) while 30.66N is only a mean value with SD of ±4.97 (COV=16.2%)
Authors response: we agree with the reviewer, because in the text within the first paragraph of the results, section 3.1, it was not clear that the results of Fig. 5 and table 3 are only for one test of each situation, i.e. the values of table 3 are those of Fig.5 at specific loads. So, it seems that in this table we did not give the SD values, but in this case is not necessary, because the results are specific for one measurement only. In order to clarify this idea, it can now be read as:
“Figure 5 presents the results of measurements in the AC pins position and shows how the load in the callus varies with the applied load in one tensile/compressive test, for the callus stiffness of 220 N/mm, of each one of the several free pin spans.”
In fact, a very important thing to keep in mind, when learning how to design experiments and collect experimental data, is that our ability to observe the real world is not perfect. The observations we make are never exactly representative of the process that we think we are observing [1]. The error is a combined measure of the inherent variation in the phenomenon and the numerous factors that interfere with the measurement.
Peters, C.A. Statistics for Analysis of Experimental Data; Ramos, A.; Simões, J.A. Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. Med. Eng. Phys. 2006, 28, 916–924.Nevertheless, we removed that statement.
See Fig. 5/7 – what does each point on the line represent? Mean value of 5 test at that specific tensile/compression load? Or maybe the line represents a single test? But then the linear regression equation would represent only this single test within the configuration and not the combined results of all 5 tests within the configuration…
Authors response: Actually, I think that the answer to the previous question is also valid to answer this question. Each line represents a single test.
Please specify goodness of fit of the model in fig 5., for example R2 values, and refer to them in the text. Also in fig 12a.
Authors response: R2 of all regressions were added to both figures.
Please examine and describe what would happen if the nonlinear curves (fig.5-6) were divided into two, separate, linear ones. Compare them (linear regression and R2) and compare the second part of the separated curve to wider axis distance configurations (fully linear ones 70/90mm).
Authors response: Figure 5 and figure 6 were changed according reviewer suggestion. Moreover, in section 3.2, experimental results, the following text was added:
Line 206-210: “. In this figure, the numbers 50, 70 and 90 are used to identify the distance between the axis of nylon tubes and of the external fixator, there is also presented the trend line of each measurement: in Figure 5a) all the data is approximated by one regression line; Figure 5b) the AC50 data is approximated by two different regression lines.”
Line 216-221: “Some nonlinearity is observed in the CL/TL curve for the AC50 pins configuration and, because of this, the goodness-of-fit measure for this linear regression model is about 10% smaller than the R2 of the other two regression models of figure 5a). In figure 5b) it is possible to see that the use of two linear regression models for this distance between axes improves the R2 value of models' fit, but the second line shows a non-null intercept value. This observation at the origin may associated with the discontinuity of behavior produced by the locking effect of the free clamp,..”
Line 225-230: “. In this figure, the goodness-of-fit measures are always higher than 0.96, i.e. the R2 values are higher than 0.96. The slopes of the first lines of AB and AC linear regressions are similar, but the second lines of those linear regressions do not show so similar slopes. Moreover, the slop of the second line of the AC linear regression is more similar to that of the second line of the ABC linear regression, whereas the slope of the AB second linear regression is closer to the slope of the BC second linear regression.”
Line 264-266. A non-linear function does not have a constant slope.
Authors response: we agree with the reviewer. So, we changed this statement, it can now be read as:
Line 236-237: “Some of the CL/TL ratios presented in table 4 are quite similar to the slope of equations that are depicted in figure 5. “
Line 400: Significantly? Was it tested statistically? α=0.05?
Authors response: we did not perform statistical analysis. The statement is not correct, se it can now read as:
Line 338-339: “… does not change load share ratios very much.”
Fig. 12b – Why the clearly linear relation is missing the linear model?
Authors response: we don’t understand the reviewer question. The finite element model is not linear, because we have contact conditions and frictional contact. Figure 12b) shows the slip distance on the two configurations and it is clear that the 90 mm distance shows higher slip distance than the distance of 70 mm.
It is quite unusual that the list of references contains not a single paper by authors of the reviewed paper, especially when authors widely publish papers discussing usage of FEA in biomechanics, etc. This creates the impression that the reviewed work is in no way related to the scope of scientific interests of the authors, while it of course is.
Authors response: actually, we detected some reference errors that were created during the insertion of text in the Journal template. Hence, references [21 and 22] are related with authors biomechanic research works.
Language needs careful review. Minor English errors can still be found (WW2, higher instead of highest, etc.)
Authors response: authors perform a careful English revision. The modifications are highlighted with blue color.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The aim of the present article is to evaluate the behaviour of the Orthofix Limb Reconstruction System in the dynamic compression mode. The topic of the manuscript is very interesting and gives a significant contribution in the field of biomechanics. In addition, the manuscript is well written and well organized. Carefully analyzing the paper, I have found only minor issues. As such, in my opinion once the issues reported in the specific comments are properly treated, the paper should be published in Applied Sciences.
Specific comments:
Section “Finite element modelling”:
Page 7 line 179: I did not find the reference 43 in the References section. Please carefully check.
Page 7 line 179: The choice of the average element length of the mesh is related to a convergence analysis? If so, could you provide some details about the convergence analysis?
Page 7 line 179: Could the authors declare the number of degrees of freedom of the FE model?
Page 7 line 179: Could the authors specify and comment the algorithm used to generate the mesh?
Moreover, could the authors discuss the choice of hexahedral elements instead of tetrahedral elements?
Section “Experimental results”:
Figure 5: Could the authors use a greater font size for the x and y axes? Use please a gretaer font size also for the equations inside the plot.
Figure 6: Could the authors use a greater font size for the x and y axes?
Section “Comparison of FEM and experimental results”:
Figure 7: Could the authors use a greater font size for the x and y axes?
Page 12 line 284: Put figure with f in capital letter
Page 12 line 288: Put figure with f in capital letter
Figures 8 and 9: Could the authors use a greater font size for the x and y axes?
Page 13 line 300: Put figure with f in capital letter
Page 14 line 317: Put figure with f in capital letter
Figures 10-11: The color bars are not clear. I think they are too small. Moreover, the font size is too small. Please make some changes.
Section “Discussion”:
Figure 12: Could the authors use a greater font size for the x and y axes?
Page 22 line 551: I suggest to add as a limitation the use of bar instead of the realistic geometry of the tibia.
I suggest to discuss the possibility to apply this study to a realistic bone such as a cadaver bone. Do you think that using a realistic shape could change the results?if so, to what extent?
In the context of biomechanics many computed tomography (CT)-based FE modelling strategies have been developed to study the risk of fracture of bone and to evaluate the performance of prosthetic devices (put some recent references, you can see some recommended references below). Do you think that it could be possible develop a subject-specific image-based FE modelling strategy for this kind of study as a future work? Moreover, do you think that in addition to consider the realistic shape of the bone the hetoregeneity of material properties that is possible to obtain from diagnostic images could impact the resuls? If so, to what extent? To contextualize, I suggest to put some references such as:
- Katz Y. et al, Clinical Biomechanics, 2019, 58 pp 74-89
- Falcinelli C. et al, Journal of Mechanical Behavior of Biomedical Materials 2019, 93 pp 9-22
- Haider IT. et al, Journal of Biomechanical Engineering 2020, 142(2): 021010
Comments for author File: 
Comments.pdf
Author Response
Reviewer 2:
The authors would like to thank the reviewers for reading the manuscript and for the comments and suggestions to improve the manuscript. Changes in the revised manuscript are highlighted with blue color.
The aim of the present article is to evaluate the behaviour of the Orthofix Limb Reconstruction System in the dynamic compression mode. The topic of the manuscript is very interesting and gives a significant contribution in the field of biomechanics. In addition, the manuscript is well written and well organized. Carefully analyzing the paper, I have found only minor issues. As such, in my opinion once the issues reported in the specific comments are properly treated, the paper should be published in Applied Sciences.
Authors response: yes, we agree with this understanding.
Specific comments:
Section “Finite element modelling”:
Page 7 line 179: I did not find the reference 43 in the References section. Please carefully check.
Authors response: thanks, we detected some reference errors that were created during the insertion of text in the Journal template. We gave our best to check the references and we think that now are all there.
Page 7 line 179: The choice of the average element length of the mesh is related to a convergence analysis? If so, could you provide some details about the convergence analysis?
Authors response: yes, it is. In order to clarify this idea, authors added the following text and reference:
“The accuracy of this numerical model was verified previously by a mesh convergence study and by a comparison with the numerical solution obtained with 10-noded tetrahedral finite elements [23].”
Ramos, A.; Simões, J.A. Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. Med. Eng. Phys. 2006, 28, 916–924.
Page 7 line 179: Could the authors declare the number of degrees of freedom of the FE model?
Authors response: yes, authors added the following text:
Line 165-166: “… nodes (degrees of freedom 263,651x3=790,953) and …”
Page 7 line 179: Could the authors specify and comment the algorithm used to generate the mesh?
Authors response: yes, mesh was created using the rule-based (mapped) meshing algorithm with a preferred hexahedral (brick) cell shapes, which is available in ADINA software. Therefore, we added the following text:
Line 165-167: “… The complete finite element mesh was built with 263,651 nodes (degrees of freedom 263,651x3=790,953) and 267,780 elements, using the rule-based (mapped) meshing algorithm with a preferred hexahedral (brick) cell shapes, which is available in ADINA software, and simulations were also obtained using the ADINA standard solver.”
Moreover, could the authors discuss the choice of hexahedral elements instead of tetrahedral elements?
Authors response: Actually, in the reference of Ramos and Simões the readers can check some particularities of both geometries and the number of nodes per element too. Nevertheless, it is well known that 4-node tetrahedral elements and 8-node hexahedral elements are too stiff in bending solicitations. Nevertheless, if the incompatible modes are added as additional degrees of freedom in the 8-node hexahedral elements, the solution behaves gets more flexible, like a shell structure.
Section “Experimental results”:
Figure 5: Could the authors use a greater font size for the x and y axes? Use please a gretaer font size also for the equations inside the plot.
Authors response: The font size was changed from 12 to 14, nevertheless, because we have also diminished the size of the image, it could seem smaller.
Figure 6: Could the authors use a greater font size for the x and y axes?
Authors response: The font size was changed from 12 to 14, nevertheless, because we have also diminished the size of the image, it could seem smaller.
Section “Comparison of FEM and experimental results”:
Figure 7: Could the authors use a greater font size for the x and y axes?
Authors response: The font size was changed from 12 to 14, nevertheless, because we have also diminished the size of the image, it could seem smaller.
Page 12 line 284: Put figure with f in capital letter.
Authors response: Thanks, we changed to Figure 7 (pag. 9, line-252).
Page 12 line 288: Put figure with f in capital letter.
Authors response: Thanks, we changed to Figure 8 (pag. 9, line-255).
Figures 8 and 9: Could the authors use a greater font size for the x and y axes?
Authors response: The font size was changed from 12 to 14.
Page 13 line 300: Put figure with f in capital letter
Authors response: Thanks, we changed to Figure 9. (pag. 10, line 262)
Page 14 line 317: Put figure with f in capital letter.
Authors response: Thanks, we changed to Figure 10. (pag. 10, line 270
Figures 10-11: The color bars are not clear. I think they are too small. Moreover, the font size is too small. Please make some changes.
Authors response: The size of pictures was adjusted.
Section “Discussion”:
Figure 12: Could the authors use a greater font size for the x and y axes?
Authors response: The font size was changed from 12 to 14.
Page 22 line 551: I suggest to add as a limitation the use of bar instead of the realistic geometry of the tibia.
Authors response: the reviewer suggestion is included in the line 470-471.
I suggest to discuss the possibility to apply this study to a realistic bone such as a cadaver bone. Do you think that using a realistic shape could change the results? if so, to what extent?
In the context of biomechanics many computed tomography (CT)-based FE modelling strategies have been developed to study the risk of fracture of bone and to evaluate the performance of prosthetic devices (put some recent references, you can see some recommended references below). Do you think that it could be possible develop a subject-specific image-based FE modelling strategy for this kind of study as a future work?
Moreover, do you think that in addition to consider the realistic shape of the bone the heterogeneity of material properties that is possible to obtain from diagnostic images could impact the results? If so, to what extent? To contextualize, I suggest to put some references such as:
- Katz Y. et al, Clinical Biomechanics, 2019, 58 pp 74-89
- Falcinelli C. et al, Journal of Mechanical Behavior of Biomedical Materials 2019, 93 pp 9-22
- Haider IT. et al, Journal of Biomechanical Engineering 2020, 142(2): 021010
Authors response: In order to address all reviewer issues, the following text was added:
Line 470-492: “… Another limitation of this work is associated with the use of a nylon bar instead of a realistic geometry of the tibia. Nowadays, there is a great number of published works wherein realistic CAD geometries of femur and tibia were generated using the computed tomography (CT) imaging technique [43–46]. Despite the excellent quality of these results, they are subject-specific finite element studies and, because strain variability for cadaveric specimens can be larger than 100% [47], their use in tests specimens concerning the external fixator configurations would require a sample of several hundred specimens. Moreover, as in any other FE model, reliable subject-specific numerical models need to ensure that modelling assumptions reflect the in vivo environment. Hence, considering the low availability of donors, the large variability of human anthropometry and material properties, it seems that synthetic bones might be an attractive alternative to this study [22]. Nevertheless, it would be interesting to develop subject-specific image-based FE models for the all healing phase and to try to establish a relation between the experimental and numerical displacements of the free-clamp, in order to create comparative results than can contribute to the evaluation of the consolidation phase and help to decide when the clamp can be unlocked. Yet, these results should not be used in a quantitative way, but to compare the patient outcome between two different moments of consolidation phase. In addition, this procedure can be used on other patients and avoid exposure to additional X-ray radiation for consolidation level information.
The findings of this work cannot be applied blindly to address issues concerning the external fixation of fractured tibia, for instance the sensitivity values of load share ratios to the distance between the external fixator body and the bone. in fact, this ratio is affected not only by the distance between mentioned axes but also by the nylon stiffness and, therefore, are expected different stiffness values in real bones. Nevertheless, the trends identified in this work may remain valid on real bones.”
Katz, Y.; Lubovsky, O.; Yosibash, Z. Patient-specific finite element analysis of femurs with cemented hip implants. Clin. Biomech. 2018, 58, 74–89. Haider, I.T.; Goldak, J.; Frei, H. Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model. Med. Eng. Phys. 2018, 55, 1–8. Falcinelli, C.; Di Martino, A.; Gizzi, A.; Vairo, G.; Denaro, V. Mechanical behavior of metastatic femurs through patient-specific computational models accounting for bone-metastasis interaction. J. Mech. Behav. Biomed. Mater. 2019, 93, 9–22. Haider, I.T.; Baggaley, M.; Brent Edwards, W. Subject-Specific Finite Element Models of the Tibia With Realistic Boundary Conditions Predict Bending Deformations Consistent With In Vivo Measurement. J. Biomech. Eng. 2020, 142. Cristofolini, L.; Viceconti, M.; Cappello, A.; Toni, A. Mechanical validation of whole bone composite femur models. J. Biomech. 1996, 29, 525–535.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Thank you for submitting the revised version of the paper.
