Dynamic Parallel Traction's Impact on Femoral Neck Fracture Biomechanics: A 3D Finite Element Study

doi:10.21203/rs.3.rs-4851027/v1

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Dynamic Parallel Traction's Impact on Femoral Neck Fracture Biomechanics: A 3D Finite Element Study

https://doi.org/10.21203/rs.3.rs-4851027/v1

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Objective: This study aims to investigate the impact of dynamic parallel traction on the biomechanical characteristics of femoral neck fractures, with the goal of identifying a more effective traction method for the repair of such fractures.

Methods: We constructed a three-dimensional finite element model of the femoral neck based on CT images. Using linear regression analysis, we explored the optimal adjustment strategy for traction weight over time by analyzing the relationship between different traction weights and the maximum tolerable traction time. Additionally, we validated the stress characteristics under various traction angles and analyzed the interplay among traction weight, time, and angle.

Results: Among the relationships between traction weight, maximum tolerable traction time, and femoral neck stress values, the regression equation was F=175.9, R²=0.9513 (linear regression analysis), indicating that as traction time increased from 0s to 10s, the traction force decreased from 500N to 360N, while the stress value remained relatively stable. In terms of the relationship between traction angle and femoral neck stress values, the regression equation was F=123.2, R²=0.8864 (linear regression analysis), showing that the stress value rose from 5.592MPa under parallel traction to 18.944MPa at a 60-degree angle. When considering the combined effects of these factors on stress values, the regression equation was F=139.5, R²=0.9610 (linear regression analysis), demonstrating that dynamic parallel traction resulted in significantly lower stress values compared to other traction methods.

Conclusion: Dynamic parallel traction can effectively reduce the force experienced by patients, promoting healing and reducing complications. This finding holds significant implications for the development of related medical devices, offering valuable insights and benchmarks for future research and design.

Physical sciences/Engineering/Biomedical engineering

Health sciences/Medical research/Experimental models of disease

Dynamics

Parallel

Femoral Neck

Traction

In the contemporary landscape of medical and orthopedic treatment, the management of femoral neck fractures[1,2] remains a significant challenge, particularly concerning the efficacy of traction techniques and their influence on the biomechanical properties of the fracture site. Traction is employed to realign fractured ends through external forces, alleviate pain, prevent further damage, and facilitate fracture healing. However, conventional traction methods, due to potential malalignment of force vectors and fixed traction weights, may lead to suboptimal healing, delayed union, nonunion, and an increased risk of complications.

Addressing the issues of misaligned force vectors and static traction weights, this study introduces the concept of dynamic parallel traction, which is shown in Fig. 1. Dynamic parallel traction involves the dynamic adjustment of traction weight in relation to traction duration, coupled with automatic alignment adjustments to maintain a parallel traction state throughout the process. By constructing a three-dimensional finite element model of the femur, this study systematically evaluates the impact of varying traction angles, weights, and durations on stress distribution and its changes at the fracture site. Through meticulous biomechanical analysis, our aim is to substantiate whether the dynamic parallel traction technique can more effectively promote proper alignment of the fracture ends and enhance fracture healing.

Material Preparation and 3D Reconstruction: Our study commenced with the acquisition of high-precision CT images of the femur, serving as the foundational data for constructing subsequent three-dimensional finite element models. Employing MIMICS, a specialized medical image processing software, we meticulously extracted the geometric information of the femur from these images, culminating in a detailed 3D reconstruction.

Model Optimization: Post-reconstruction, models often exhibit imperfections such as sharp edges, overlapping surfaces, and voids. To rectify these issues, we utilized GEOMAGIC software to optimize the model, focusing on smoothing sharp edges, eliminating overlapping surfaces, and filling voids. This process ensured the geometric integrity of the model, closely mimicking the authentic femoral geometry and laying a robust foundation for subsequent finite element analysis.

Finite Element Analysis: Following optimization, the enhanced IGES file was imported into ANSYS for three-dimensional finite element analysis. Within the simulation, two distinct material properties were defined: cortical bone and trabecular bone. Cortical bone was assigned a Young's modulus of 17,000 MPa and a Poisson's ratio of 0.3; trabecular bone had a Young's modulus of 50 MPa and a Poisson's ratio of 0.4. For element selection, we consistently used Quadratic Tetrahedral elements, with an element size set at 5 mm.

Experimental Design: We devised multiple experiments to evaluate the impact of three independent variables—traction duration, traction force[3,4], and traction angle[5]—on the stress characteristics and deformation of the femur. Our experimental plan was as follows:

Investigating Traction Force and Duration:

Established three traction force levels (360N, 400N, 500N) representing insufficient, adequate, and excessive traction forces, respectively.

Analyzed the variation in stress values across different traction forces and determined the maximum tolerable traction duration for each force level.

This exploration aimed to elucidate the relationship between traction force and duration, guiding the dynamic adjustment of traction force over time.

Utilized least squares linear regression analysis to validate the correlation between traction force, maximum tolerable duration, and stress values.

Traction Angle Variability:

Maintaining constant traction force and duration, we adjusted the traction angle in a two-dimensional space.

Examined the stress features and deformation across the femur under varying traction angles.

Employed least squares linear regression analysis to confirm the association between angle and stress values.

We also do theoretical analysis and derivation for offset in three-dimensional space, and the schematic diagram is shown in Fig. 2:

To begin with, let L1 represent the line of normal traction force, and L1′ denote the line of traction force after deviation. Next, select point P on L1′, and construct plane n parallel to L1 passing through P, along with plane m perpendicular to plane n. Then, project L1 onto plane m to obtain L2 within the same plane, where the angle between L2 and L1′ is denoted as θ. Following that, project L2 onto plane n to yield L3, and the angle between L3 and L2 is designated as ϕ. The angle between L1′ and L3 is noted as ψ. Our goal is to solve for angles θ and ϕ so that compensations can be made in the corresponding directions.

The detailed steps for solving these angles are as follows:

Choose point Q on L1, measure the distance between points P and Q, denoted as d′.

Measure the distance from point Q to plane n, designated as d, and the angle between d and d′ is recorded as α.

Determine the distance between the perpendicular from point P to L3 and point V, referred to as d′′.

Using the Law of Cosines, d2 + d′2 − d′′2 = 2dd′cos(α), calculate d′′.

Let W be the intersection point of L1′ ,L2, and L3. Calculate angle θ using the distances dwv (from W to V), dwp (from W to P), and d′′.

Applying the Law of Cosines again, dwv2 + dwp2 − d′′2 = 2dwvdwpcos(θ), find θ.

Utilizing the Triple Cosine Formula, determine the product of cos(θ) and cos(ϕ).

Measure the distance from point P to plane m. Since L2 is the projection of L1′ onto plane m, the foot of the perpendicular from L1′ to plane m will fall on L2, marked as X.

Measure dpx and dwx at points P and W, respectively.

In triangle pwx, applying the Law of Cosines, calculate β.

Finally, derive ϕ from the calculated values.

Compensate for the angles θ and ϕ to re-establish parallelism between the lines of traction force and fracture force.

Integrating the findings from the aforementioned two sets of experiments, we explored the interrelationship between traction weight, traction time, and traction angle. Our focus was on investigating the impact of dynamic adjustments in traction weight and time, along with the effect of maintaining parallel traction angles on stress characteristics. The results substantiated that dynamic parallel traction yields the most favorable outcomes. And Table 1 shows the attribute setting of 3D finite element analysis.

Table 1

Settings for Material Properties
Part	Young’s modulus(E)[MPa]	Poisson’s ratio(v)	Element type	Element Size
Cortical bone	17000	0.3	Quadractic tetrahedral	5mm
Cartilage	50	0.4	Quadractic tetrahedral	5mm

Impact of Dynamic Adjustments in Traction Time and Weight on Stress Characteristics of the Femur:

As the traction weight escalated from 360N and 400N to 500N, the stress values correspondingly rose from 5.592MPa and 6.213MPa to 7.767MPa. Under identical traction weight conditions, a notable increase in stress values across the femoral neck was observed as the traction duration extended. Specifically, at a traction weight of 360N, the stress value escalated from 5.592MPa to 18.944MPa; at 400N, the stress value climbed from 6.213MPa to 21.049MPa; and at 500N, the stress value surged from 7.767MPa to 26.311MPa. During the validation phase for dynamic adjustments of traction weight in relation to traction duration, a 500N traction weight was applied for 10 seconds, followed by a reduction to 400N at the 20-second mark, and a further adjustment to 360N when the traction time reached 30 seconds. The dynamic adjustment of traction weight, compared to a static weight, yielded notably reduced stress values across the femoral neck. Their relationship is shown in Fig. 3.

In the analysis conducted via the method of least squares[6], variance analysis revealed that the sum of squares due to regression (SS) was 734.6, with degrees of freedom (DF) equal to 2, resulting in a mean square (MS) of 367.3. The F-statistic was determined to be 175.9, accompanied by a P-value less than 0.0001, strongly suggesting the statistical significance of the model. The parameter estimation outcomes indicated an intercept (β0) of -43.57, a traction force coefficient (β1) of 0.07233, and a maximum tolerable traction time coefficient (β2) of 2.718. All parameters featured P-values below 0.05, underscoring their highly significant impact on the model. The coefficient of determination (R2) stood at 0.9513, signifying the model's ability to account for 95.13% of the variability in the dependent variable, thereby confirming a well-fitted model. Furthermore, multicollinearity diagnostics confirmed VIF values of 1.158 for both traction force and maximum tolerable traction time, substantially below the threshold of 10, ruling out any presence of multicollinearity within the model. Consequently, the analysis unequivocally substantiated a significant positive correlation between traction force, ultimate traction time, and stress values.

Impact of Parallel Traction Angle on Stress Characteristics of the Femur:

The investigation into the effect of varying traction angles on the stress characteristics of the femur revealed a progressive increase in stress values as the angle deviated from parallel alignment. At a traction angle of 0°, corresponding to perfect parallelism, the stress value recorded at the femoral neck was 5.592MPa. As the angle increased to 10°, the stress value escalated to 5.721MPa. Further increments in angle to 20°, 30°, 40°, 50°, and finally 60°, resulted in stress values of 8.090MPa, 10.941MPa, 13.870MPa, 16.667MPa, and a peak value of 18.944MPa, respectively. And the results of three dimensional analysis are shown in Fig. 4.

In the analysis conducted via the least squares method, variance analysis disclosed a sum of squares due to regression (SS) of 669.0, with a degree of freedom (DF) of 1, yielding a mean square (MS) of 669.0. The computed F-statistic was 123.2, paired with a P-value less than 0.0001, strongly suggesting the statistical significance of the model. Parameter estimation outcomes indicated an intercept (β0) of 4.838 and an angle coefficient (β1) of 0.2822. All parameters featured P-values below 0.05, underscoring their highly significant impact on the model. The coefficient of determination (R2) stood at 0.8664, signifying the model’s capacity to explain 86.64% of the variability in the dependent variable, thereby affirming a well-fitted model. Multicollinearity diagnostics confirmed a Variance Inflation Factor (VIF) of 1.000 for the angle, excluding any presence of multicollinearity within the model. These findings unambiguously substantiated a significant positive correlation between the angle of traction and stress values. The results map is displayed in Fig. 5. And in Table 2, we show the results of stress value of different situations including dynamic parallel traction.

Table 2

Relationship Between Traction Weight, Traction Time, Traction Angle, and Stress Value
Traction Weight(N)	Ultimate Traction Time(s)	Traction Angle(°)	Stress Value(MPa)
360	7.78	parallel	5.592
		10	5.721
		20	8.090
		30	10.941
		40	13.870
		50	16.667
		60	18.944
400	6.67	parallel	6.213
		10	6.356
		20	8.989
		30	12.157
		40	15.411
		50	18.519
		60	21.049
500	5.56	parallel	7.767
		10	7.945
		20	11.236
		30	15.196
		40	19.263
		50	23.149
		60	26.311

In this study, we explored the impact of traction time and weight on stress characteristics of the femur, further validating the efficacy[7,8] of dynamic parallel traction. Our experimental outcomes highlighted that increases in traction time and weight led to substantial escalations in stress values across the femoral neck. Specifically, under traction weights of 360N, 400N, and 500N, stress values surged from 5.592MPa to 26.311MPa, indicating that augmented traction weight significantly amplifies stress endured by the femoral neck. Moreover, elongated traction duration also prompted a pronounced rise in stress values. Under consistent traction weight, as traction time expanded from 10 to 30 seconds, stress values witnessed a notable ascent. This phenomenon might stem from the femoral neck’s gradual acclimatization to applied traction forces, culminating in progressively mounting stress values.

Additionally, dynamic adjustments in traction weight markedly alleviated stress values across the femoral neck. Amidst the escalation of traction time from 10 to 30 seconds, modulating traction weight from 500N down to 360N substantially diminished stress values on the femoral neck. This underscores that dynamic alterations in traction weight can effectively mitigate stress borne by the femoral neck, thus curtailing the risk of femoral neck injury.

Furthermore, our results unveiled that enhancements in traction angle precipitated significant surges in stress values across the femoral neck. Upon increasing the traction angle from 0° to 60°, stress values escalated from 5.592MPa to 18.944MPa. This suggests that an elevated traction angle triggers a pronounced augmentation in stress endured by the femoral neck. This could potentially be attributed to the incremental shift of the traction force application point towards the distal end of the femoral neck, precipitating a gradual rise in stress values.

Via linear regression analysis[9,10] utilizing the least squares method, we discerned a significant positive correlation between traction force, ultimate traction time, traction angle, and stress values. The statistical significance of the model underscores the substantial influence of these factors on stress values across the femoral neck. Moreover, the model’s goodness-of-fit indicates that these variables can elucidate a considerable portion of the variability in the dependent variable, attesting to the model’s commendable predictive capabilities.

Synthesizing our experimental findings, we can deduce that augmentations in traction time and weight engender significant elevations in stress values across the femoral neck, whereas dynamic adjustments in traction weight can efficaciously diminish stress values. Additionally, enhancements in traction angle also precipitate substantial escalations in stress values across the femoral neck. These insights offer valuable guidance for femoral neck traction, facilitating the optimization of traction methodologies and mitigating the hazard of femoral neck injury.

In practical applications, healthcare providers can tailor traction time and weight according to individual patient specifics to achieve optimal traction outcomes. Simultaneously, the selection of traction angle should be predicated on patient-specific considerations to circumvent injuries stemming from excessive traction. Dynamic parallel traction, as an efficacious approach to femoral neck traction, merits further dissemination in clinical practice.

Nonetheless, our study harbors certain limitations. Firstly, the modest sample size might inadequately represent the broader population. Future studies could benefit from larger sample sizes to enhance reliability and generalizability. Secondly, our investigation solely scrutinized the influence of traction time and weight on femoral stress characteristics, neglecting other plausible factors such as individual variability and traction velocity. Subsequent research endeavors could delve deeper into the impacts of these additional factors on femoral stress characteristics, fostering a more holistic understanding of the mechanisms underlying femoral neck traction.

In summary, our experimental outcomes offer valuable guidance for femoral neck traction, elucidating the influence of traction time and weight on femoral stress characteristics, and corroborating the effectiveness[11] of dynamic parallel traction. These revelations hold pivotal clinical implications for refining femoral neck traction methodologies and curtailing the peril of femoral neck injury. Future research could further explore other potential factors, advancing the efficacy and safety of femoral neck traction methodologies.

In a pioneering study employing a three-dimensional finite element model[12] specific to the femoral neck, we comprehensively assessed the impact of diverse traction weights, durations, and angles on the critical stress characteristics intrinsic to this anatomical region. Our findings underscore the potential of dynamic parallel traction, a sophisticated technique that adeptly adjusts in tandem with alterations in traction time and weight, thereby maintaining a therapeutically optimal stress environment. Leveraging an innovative method for compensating angular deviations within a three-dimensional framework ensures the preservation of parallel traction, a crucial factor in achieving favorable outcomes.

Notably, this advanced traction methodology significantly diminishes stress exerted on the femoral neck, thereby catalyzing the healing process and mitigating potential complications. Moreover, our research offers invaluable guidance for the engineering and design of next-generation medical devices, tailored to harness the benefits of dynamic parallel traction. Given its demonstrated efficacy and safety profile, dynamic parallel traction emerges as a clinically advantageous approach, poised to revolutionize the treatment paradigm for femoral neck fractures, offering patients a more effective and secure pathway to recovery.

Author Contribution

Jiarui Li and Xiaolin Wu contributes equally to this research, and Dongming Xing is the corresponding author. Other persons contributes according to their sequence of the authors.

Acknowledgement

This research is supported by Qingdao Cancer Institute.

Data Availability

The datasets used or analysed during the current study available from the corresponding author on reasonable request.

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No competing interests reported.

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You are reading this latest preprint version

Dynamic Parallel Traction's Impact on Femoral Neck Fracture Biomechanics: A 3D Finite Element Study

Status:

Version 1

Abstract

Figures

Introduction

Materials and Methods

Investigating Traction Force and Duration:

Traction Angle Variability:

The detailed steps for solving these angles are as follows:

Results

Impact of Dynamic Adjustments in Traction Time and Weight on Stress Characteristics of the Femur:

Impact of Parallel Traction Angle on Stress Characteristics of the Femur:

Discussion

Conclusion

Declarations

Author Contribution

Acknowledgement

Data Availability

References

Additional Declarations

Status:

Version 1