Finite element analysis of the stability of tibiofibular fractures treated with various combinations of external fixators

Abstract

Background

External fixators have been extensively applied in the treatment of open tibiofibular fractures and have yielded positive outcomes. The stability of an external fixator primarily hinges on its structure. Employing additional external fixation components can undoubtedly enhance stability. However, there is scant research on the topic of achieving superior stability with fewer external fixation components.

Methods

Utilizing 3D modeling software, constructed three different external fixation models in middle tibial fractures in Group A, constructed four external fixation models in proximal tibial fractures in Group B, and constructed four external fixation models in distal tibial fractures in Group C.Simulate the load under the assistance of a walker to stand up, obtain the displacement of fractures and the stress of the external fixator for each group. Analyze and compare the results of each model.

Results

In a mid-tibial fracture, the stability of the crossbar increases by 21% with each 2 cm closer to the tibia. Model B3 achieves superior stability with the use of more fixed clamps and connecting rods in the “H” shaped model. Although the triangular cross-bar structure used in Model B4 is less stable than that of Model B3, it has achieved 83.2% of the stability of Model B3, despite using fewer components. The stability of Model C4 has increased by 73.44% compared to Model C3.

Conclusions

The external fixator should be configured to keep the crossbar as close to the skin as possible. For proximal tibial fractures, to minimize the use of external fixation components, the triangular cross-bar structure of Model B4 can be employed. In the case of distal tibial fractures, while the triangular cross-bar structure of Model C4 offers good stability, the risk of displacement is greater. Therefore, it is advisable to use an H-shaped fixation method with additional external fixation components, such as those found in Model C3.

Introduction

For open tibial and fibula fractures, external fixators provide a conducive environment for wound healing and offer adequate mechanical stabilization for bone healing [1, 2]. Therefore, external fixation has become the preferred treatment for high-energy open tibiofibular fractures [3]. Currently, a variety of external fixators, differing in type and material, are employed clinically to treat open fractures of the tibia and fibula. Doctors have considered various configurations of external fixators, depending on the patient’s condition, fracture classification, surgical experience, and the availability of rods and schanz [4]. First, for fractures in the middle segment of the tibia, ordinary straight rods are initially used for external fixation, with two fixing screws placed at each end of the fracture [5]. Second, for fractures in the proximal or distal thirds of the tibia, where two screws cannot be optimally placed in both segments, to maintain the biomechanical stability of the reconstructed fracture structure, it is often necessary to use fixation pins distant from the fracture site. In such cases, an external fixation frame spanning the knee or ankle joint is frequently chosen. Installing a circular or semicircular external fixation frame can certainly enhance fracture stabilization [6,7,8]; however, for many primary hospitals, only hybrid external fixation frames are available, and circular models are lacking. Circular external fixation often significantly increases hospitalization costs. Utilizing multiple sets of nail-rod external fixation brackets certainly enhances fracture fixation, but it also significantly increases hospitalization costs. For complex proximal and distal tibial fractures, a multiplanar external fixation configuration, such as the cross and H-type nontransarticular models, may be a more advantageous choice for minimizing joint stiffness associated with transarticular fixation. In the treatment of open tibial fractures with external fixators, we frequently face the challenge of determining the optimal placement for stable fixation.

Finite element analysis (FEA) is a widely accepted computational method in orthopaedic research that converts three-dimensional models of bone implants under simulated physiological loads into finite elements to analyse and predict bone formation outcomes [9,10,11]. This study employed finite element analysis to compare the impact of fixation screws and connecting frame placements on the stability of mid-tibial fractures, as well as the influence of various external fixator modalities on fracture stability in either the proximal or distal third of the tibia. On the one hand, the mechanical performance parameters of the bracket are obtained through mechanical performance testing in experimental research, and its reliability and stability are evaluated. On the other hand, the finite element method is used to analyse the force‒deformation behaviour and the mechanical weakness of the external fixator, and then, optimization suggestions are proposed to provide certain data to support the development of industry standardization and the performance of the external fixator.

Methods

Establishment of three-dimensional models for tibiofibular fractures (middle, proximal 1/3, distal 1/3 tibial fractures)

This research was in accordance with Institutional Ethical approval of Ethicsommittee of Dongguan Eighth People’s Hospital (Approval number: LL20201225024).Select a healthy adult male with no orthopedic diseases of the lower limbs as the research subject.This participant gave his consent to participate in the study and obtained written informed consent. Experimental work was performed in accordance with the Helsinki Declaration. A thin-layer scan of the left lower leg was conducted with a 128-row helical CT at a layer thickness of 0.67 cm to acquire the scanning information of the tibia and fibula. Ethical approval to obtain the CT images of the health male was granted by the Eighth People’s Hospital of Dongguan City, China, during the collection process. The DICOM format data were collected and compiled on DVDs for storage. The CT data, which were saved in DICOM format, were imported into Mimics software (Materialise, Leuven, Belgium). Following image import, threshold establishment, editing, model segmentation, and data export, a preliminary 3D model was established, and the final 3D model data were exported in STL format. Subsequently, the data were imported into the reverse engineering software Geomagic Wrap 17.0 (Geomagic Company, USA) in STL format for processes such as smoothing, triangulation reduction, and scaling to create complete surface models of the tibia and fibula.

The 3D models of the tibia and fibula were imported into ANSYS Workbench 14.0 for surface fusion, Boolean operations, and other DM module (DesignModeler) activities. Bone blocks measuring 5 mm were extracted from the middle, proximal third, and distal third of the tibia and fibula to develop models of the tibiofibular fractures [12] (Group A: middle tibia and fibula fracture model; Group B: proximal one-third tibia and fibula fracture model; and Group C: distal one-third tibia and fibula fracture model).

Establishment of three-dimensional models with various components of hybrid external fixation brackets

Based on the anatomical parameters and self-measured dimensions of the external fixation brace products from the Stryker Company (Fig. 1), SolidWorks software was used to model the external fixation brace. The external fixation brace was simplified, and modelling was completed using functions such as sketching, extrusion, chamfering, and assembly. SolidWorks can also interface with ANSYS Workbench software for bidirectional data exchange.

The modelling process included the following steps: (1) Dimensional Measurement: Carefully measure the length, width, height, outer diameter, inner diameter, hole diameter, and span of each component. (2) Component Modelling: Begin sketching based on the measurements of each component, and complete the modelling using functions such as extrusion, rotation, chamfering, drilling, and offsetting. This results in three-dimensional model files for five components (a. rod clamp block, b. rod clamp block, c. 8 mm long carbon fibre connecting rod, d. 8 mm short carbon fibre connecting rod, and e. 5 mm fixation schanz), which are saved separately (Fig. 1).Combine the fixed clamp for manual measurement to simplify the external fixator, model the external fixator through SolidWorks software, and obtain the model of the external fixator.Due to the characteristic of different fiber orientations in each layer of carbon fiber materials, our research difficulty has been significantly increased. We simplified the carbon fiber material into a linear, isotropic, and homogeneous material model. To reduce the impact of model variations, bones and schanz are also simplified into linear, isotropic, and homogeneous materials. (3) Model Assembly: Access the software’s assembly module to add components individually. Apply fixed constraints to each component, add assembly constraints, and so on.

Fig. 1

Physical photos of external fixators

Establishment of the finite elements for each model

Import the previously existing three sets of three-dimensional models into Solidworks software. Then, assemble the components of the external fixator with the three sets of tibia and fibula fracture models. The assembly mode of the external fixator is carried out according to the following groups, and finally, save these data as IGES files (Fig. 2).

Model A1: Four Kirschner wires are positioned at the three-point bisectors of the upper and lower segments of the mid-shaft tibial fracture, all perpendicular to the tibial axis and traversing through two cortical layers. The crossbar is connected to the Kirschner wires via a rod clamp and is positioned parallel to the axis, 10 cm away.

Model A2: Based on Model A1, the crossbar is moved laterally by 2 cm, so it is now 12 cm parallel to the central axis.

Model A3: Based on Model A1, the crossbar is moved laterally by 4 cm, so it is now 14 cm parallel to the central axis.

Model B1: The first Kirschner wire is positioned at the midpoint of the upper segment of the tibial fracture. The second wire is positioned at a distance from the fracture site in the upper segment, equal to the distance from the first wire to the fracture line. The third wire is positioned at the same distance from the fracture line as the second wire, and the crossbar is positioned parallel to the central axis, 10 cm away.

Model B2: Building on Model B1, an additional crossbar is added 14 cm parallel to the central axis, connected by a rod clamp.

Model B3: Building on Model B1, three Sterling schanz and a crossbar fixation system are added to the front of the tibia, with a short connecting rod between the two crossbars connected by a b. rod clamp block, forming an “H”-shaped multiplanar configuration.

Model B4: Building on Model B1, a triangular crossbar structure is formed by adding a transverse bar connecting the third transverse bar of Model B1 to the proximal front of the tibia.

Model C1: The third Kirschner wire is positioned at the midpoint of the lower segment of the tibia following a fracture. The second Kirschner wire is positioned at a distance from the upper segment of the tibia to the fracture site, equivalent to the distance from the third Kirschner wire to the fracture line. The first Kirschner wire is positioned at the same distance from the second wire. The crossbar is positioned 10 cm parallel to the central axis.

Model C2: Building on Model C1, an additional crossbar is added 14 cm parallel to the central axis.

Model C3: Building on Model C1, three Sterling schanz and a crossbar fixation system are added to the front of the tibia, with a short connecting rod between the two crossbars connected by a b. rod clamp block, forming an “H”-shaped multiplanar configuration.

Model C4: Building on Model C1, a triangular crossbar structure is formed by adding a single Kirschner wire in front of the distal tibia and.

connecting it to the first Kirschner wire crossbar in Model C1.

Table 1 Material properties used in finite element models

Fig. 2

Schematic diagram of three different external fixation models for tibiofibular fractures

FEA data calculation for each model

All models were imported into Abaqus CAE 2022 (Dassault Systemes Simulia, Providence, RI, USA) for analysis. The material properties of those used in each model, including the elastic modulus, Poisson’s ratio, density, etc., were also uploaded [13, 14]. Select appropriate material properties to describe the behavior of bone and external fixation materials. The three materials used in the study can be found in Table 1. The mesh generation tool in Abaqus was used to create a finite element mesh, dividing it into discrete finite elements. Choose an appropriate mesh density to balance computational accuracy and computational time.The finite element mesh size is 2 mm. The mesh element types for both bone and external fixator are C3D10(A 10-node quadratic tetrahedron).For critical areas such as fracture zones and the junctions of fixation devices, the mesh has been refined to enhance the accuracy of the analysis. After meshing, a mesh quality check was performed on the model to ensure there were no distorted or overlapping elements, thus guaranteeing the accuracy of subsequent analyses. In order to balance computational accuracy and time, we can refine the mesh in critical areas, while in regions far from critical areas and where stresses are relatively smooth, we can use coarser meshes to reduce the computational load and improve efficiency. Furthermore, by employing C3D10 quadratic tetrahedral elements, we can further enhance accuracy even with coarser meshes. On this basis, the mesh type and density selected in this paper are combined with the evaluation of mesh density based on computer hardware resources (CPU/GPU performance, memory, etc.), ensuring that the computation is feasible and efficient.

Boundary conditions and model validation

In the finite element software Abaqus, binding constraints are set to simulate the contact states between the “bone-schanz”, “rod-clamp block”, and “schanz-clamp block”. The distal end of the tibia is fixed completely, a reference point is established above the tibial condylar eminence, and the reference point is coupled with the upper articular surface (Fig. 3). Axial loads of 50 N/62.5 N/75 N/82.5 N/100 N are applied on the tibial condylar plane. A static analysis is selected with an initial step size of 0.1 set by the solver [15, 16]. After configuration, the simulation can be executed. A plethora of resulting data, including stress, strain, and displacement, are generated. The results are exported to an OBD file for further analysis.

The results are visualized and analysed using Abaqus visualization tools or other post-processing tools. The results are compared with known biomechanical principles to validate the model’s accuracy.

Fig. 3

Finite element model showing boundary conditions and load direction

Results

Group A model results

In the middle tibial fracture scenario, the distribution of bone and stent deformation is illustrated in Fig. 4. Under axial loading forces of 50 N, 62.5 N, and 75 N, Model A1 demonstrated the smallest maximum displacement, followed by Model A2, with Model A3 exhibiting the largest displacement. However, under axial loads of 87.5 N and 100 N, Model A3 experienced compression and contact at both ends of the fibular fracture, reaching the maximum displacement value, leading to the conclusion that external fixation had failed. It can be inferred that Model A1 was the most stable and Model A3 was the least stable. The model suggests that the closer the crossbar of the external fixation bracket is to the longitudinal axis of the tibia, the stronger the external fixation bracket is. Within the tolerable pressure range, the stability increased by 21% for every 2 cm closer to the tibia.

Group B model results

In the proximal tibial fracture scenario, the displacement curves for the Group B models are depicted in Fig. 5. Under an axial load incrementally increasing from 50 N to 100 N, Group B1 exhibited the greatest maximum displacement, while Group B3 exhibited the least. The displacement in Group B4 ranked second, with B4 experiencing the least displacement at 50 N. Under a 100 N load, Model B1 experienced compression and contact at both ends of the fibular fracture, leading to external fixation failure, highlighting B1’s heightened instability.

During assisted walking, external fixation braces are typically applied with 10% of the patient’s body weight (75 N) to the axial direction of the proximal tibia [17, 18]. To replicate this assisted standing phase, a study was conducted with an axial load of 75 N. As shown in Fig. 6, Model B2 demonstrated a 28.8% increase in stability compared to Model B1, Model B3 exhibited a 67.8% increase, and Model B4 achieved a 59.4% increase in stability. The stability of Model B4 reached 83.2% of that of Model B3.

Figure 7 indicates that the maximum stress on the external fixation braces of all Group B models occurred on the first Kirschner wire, with Model B2 experiencing the highest Kirschner wire stress (average of 735.56 MPa). The maximum Kirschner wire stress in Model B3 was 346.57 MPa, and in Model B4, it was 331.65 MPa, with Model B4’s stress being lower than that of Model B3. The maximum stress at the schanz–bone interface occurred at the first pinhole. The pinhole stresses in both Model B3 and Model B4 were comparable and lower than that in Model B1.

Group C model results

In the distal tibial fracture scenario, the displacement of the C group models are illustrated in Fig. 8. Under an axial load incrementally increasing from 50 N to 100 N, Group B1 exhibited the greatest maximum displacement, while Group C3 exhibited the least, with Group C4 having the second-highest displacement. Under a 100 N load, Models C1 and C2 experienced compression and contact at both ends of the fibular fracture, leading to external fixation failure, indicating that both C1 and C2 were less stable than C3 and C4.

Similarly, a 75 N axial load was applied to simulate a patient standing with the aid of a walker. As shown in Fig. 9, Model C2 demonstrated a 17.35% increase in stability compared to Model C1, Model C3 a 66.63% increase, and Model C4 a 48.93% increase. The stability of Model C4 reached 73.44% of that of Model C3.

According to Fig. 10, the maximum stress on the external fixation bracket for all C group models occurred on the last Kirschner wire. The maximum stress on the Kirschner wire was comparable between Model C1 (736.87 MPa) and Model C2 (718.24 MPa), while Model C4 (359.59 MPa) exhibited the least stress, followed by Model C3 (466.61 MPa). The maximum stress at the schanz-bone interface occurred at the last pinhole, with similar maximum stresses at the pinholes in Models C4 (13.5 MPa) and C3 (28.48 MPa), both of which were lower than those in Model C1.

Fig. 4

(a) A group of different axial load of bone and stent deformation distribution cloud map. (b) Line chart of maximum deformation of bone and bracket in Group A under different axial loads

Fig. 5

Line chart of maximum deformation of bone and external fixators in Group B under different axial load

Fig. 6

(a) The displacement nephogram of bone and external fixator under 75 N axial load in Group B. (b) Bar chart of relative stability comparison under 75 N axial load in Group B

Fig. 7

(a) The stress nephogram of external fixator under 75 N axial load in Group B. (b) The stress nephogram of the pinhole under 75 N axial load in Group B

Fig. 8

Line chart of maximum deformation of bone and external fixators in Group C under different axial load

Fig. 9

(a) The displacement nephogram of bone and external fixator under 75 N axial load in Group C. (b) Bar chart of relative stability comparison under 75 N axial load in Group C

Fig. 10

(a) The stress nephogram of external fixator under 75 N axial load in Group C. (b) The stress nephogram of the pinhole under 75 N axial load in Group C

Discussion

External fixators are a common treatment option for several clinical orthopaedic cases, including open fractures and dislocated injuries, which are typically encountered in high-energy trauma scenarios. The application of external fixators has demonstrated positive outcomes, facilitating soft tissue healing, allowing for the ability to perform additional surgeries, and offering improved and more comfortable wound dressing and care. All these benefits have been corroborated by previous clinical studies.

In this research, finite element models were utilized to analyse fractures in the middle, distal, and proximal segments of the tibia and fibula. For fractures in the middle segment, a classic model featuring two fixed crossbars on each side was examined to determine the relationship between the height of the crossbar and stability. Within the tolerable pressure range, the stability increased by 21% for every 2 cm of the crossbar positioned closer to the tibia. This suggests that the crossbar should be positioned as close to the tibia as possible within the constraints of the skin and external fixation device space, enhancing the stability of the external fixation frame.

In the proximal tibiofibular fracture models, the scarcity of bone at the proximal end often precludes the installation of two pins aligned vertically, thus impeding the classic external fixation approach of two pins on each side of the fracture. Consequently, we developed three alternative models that incorporate a single pin aligned vertically at the proximal end of the fracture. The stability of Model B2 was only improved by 28.8% by simply adding a crossbar without adding additional fixed schanz. Model B3 achieved superior stability with the use of more fixed clamps and connecting rods in the “H”-shaped model. Although the triangular crossbar structure used in Model B4 was less stable than that used in Model B3, it achieved 83.2% of the stability of Model B3 despite using fewer components. Additionally, Model B4 exhibited the least external fixation stress, reducing the risk of loosening and fracture of the external fixator. Furthermore, we observed that the maximum stress at the schanz-bone interface of these fractures occurred at the first pinhole. The higher stress at the schanz-bone interface increases the likelihood of loosening between the fixation pin and the bone, leading to potential fixation failure. This finding aligns with prior clinical findings [14, 19]. The results indicated that Models B3 and B4 exhibited comparable maximum stresses at the schanz-bone interface. Therefore, we recommend Model B4’s fixation method for the external fixation treatment of proximal tibiofibular fractures, as it employs fewer external fixation components while achieving robust stability, with optimal external fixation stress and maximum stress performance at the schanz-bone interface.

In the distal tibiofibular fracture models, typically, only one fixation pin can be installed on a vertical line at the distal end of the fracture. We also designed Model C3 with an “H” shape utilizing more external fixation components and Model C4 with a triangular crossbar structure requiring fewer components. Comparing the displacement data between the Group B and Group C models, it was found that the stability of distal tibiofibular fractures was more challenging to maintain, as these fractures to displace more easily and extensively under the same external fixation. The addition of crossbars improved the stability by only 17.35%, with the maximum stress reaching 718.24 MPa. Consequently, Model C2 was less suitable for surgical applications. Model C4 offered a 73.44% increase in stability compared to that of Model C3. This suggests that while the triangular crossbar external fixation method offers some stability, the maximum displacement of the fracture still reached 16.74 mm. Therefore, the authors recommend employing more external fixation components during surgery for distal tibiofibular fractures to further enhance the stability of these particularly unstable fractures. Similarly, the highest stress at the schanz-bone interface of these fractures was consistently observed in the final pinhole. The greater the stress at the schanz-bone interface is, the greater the stress in the final fixation pin, increasing the likelihood of loosening and failure of the fixation pin, wound exudation, and subsequent infection.

Notably, previous studies have demonstrated that in external fixators, particularly at the schanz-bone interface, the stress ranges from 300 MPa to 800 MPa [20,21,22], varying with the model. One of the factors contributing to this high stress is the unstable fixation of the external fixator. The configuration of the external fixators, including the fixation frame installation, fixation angle, number of schanz, position of the schanz frame, and frame material, plays a crucial role in the stress distribution between each schanz frame and the bone. Incorrect choices can lead to high stress, potentially resulting in complications such as implant failure and stress shielding effects. Consistent with prior research, this study revealed that under all three loading scenarios, the maximum stress in the external fixator occurred at the schanz-bone interface. The displacement of the external fixation frame exhibited a similar trend, with the most unstable structures experiencing the greatest displacement. Several factors can contribute to high displacement, including the angle of the connecting clip, incorrect pin placement, the size of the fixing pin, and the fastening of the connecting clip, all of which can alter the direction of the external fixation frame’s load. Ideally, the schanz should be inserted perpendicularly into the bone, and the fixation frame should be aligned in a straight plane parallel to the bone or other planes. However, in practice, surgeons encounter challenges in achieving perfect perpendicularity between the schanz and the bone. This can compromise the stability of the external fixator and lead to significant displacement. From another perspective, incorrect pin placement can increase the risk of complications from schanz infection and loosening, affecting approximately half (50%) of patients [23, 24]. Technically speaking, repeated high levels of displacement may lead to the formation of voids at the schanz-bone interface, potentially resulting in schanz loosening.

Currently, numerous studies exist on the external fixation of tibial fractures; however, most of these studies have focused on clinical efficacy and biomechanical experiments. Finite element analysis is less commonly utilized, yet its repeatability and adaptability of variables enrich and diversify the research.

A minority of researchers have also studied the stability of external fixation braces for tibial fractures; however, their investigations primarily concerned the stability of proprietary new external fixation braces. A portion of peer studies have investigated the placement of single-layer cortical bone and two-layer external fixator Schanz pins [12]. A portion of peers discussed the stability of the same external fixation device under normal conditions and in patients with osteoarthritis and osteoporosis [14]. Research on diverse combinations of external fixation components is relatively scarce. A study on three different combinations of external fixation treatment for distal tibial fractures has provided me with many insights, and this study has conclusions similar to our research on the triangular crossbar external fixation structure.This study not only addresses distal tibial fractures but also examines three different types of fractures and investigates a more extensive array of external fixation models [25].

This study considered several limitations while simulating the finite element models of the external fixation frames. First, the models in this study accounted for only transverse fractures, omitting oblique, spiral, and comminuted fractures. Future research should test various fracture configurations, including those with bone loss and spiral and comminuted fractures, to better understand their effectiveness. Second, this study relied on CT images of healthy subjects with transverse fractures created using Mimics software, which may influence the predictive accuracy. Nonetheless, this approach is considered acceptable and is widely used by other researchers. For future studies, the use of CT data from actual patients for finite element analysis is recommended [25, 26].

In this study, we primarily simulated patients standing with the assistance of a walker, although we also analysed the main axial loads. However, in actual scenarios, patients face a variety of forces in different directions when standing, walking, or turning. This represents another limitation of the current research, given the limited computational resources and the time-consuming nature of simulating complex conditions. Therefore, additional research is necessary to simulate these scenarios, offering fresh insights into the biomechanical properties of patients treated with external fixators.

Finally, in this study, cortical and cancellous bones were categorized as linear, isotropic, or homogeneous. However, bones exhibit uneven properties in reality [27]. To minimize time consumption in finite element analysis and given the limitations of current computer resources for simulating nonuniform models, isotropic and uniform properties were employed. Additionally, numerous scholars have utilized similar approaches in simulating bones and implants, achieving acceptable outcomes [21].

Conclusions

The findings suggest that Models B4 and C4 exhibited superior schanz-bone interface stress compared to the other models. Moreover, they required minimal external fixation components and achieved a stability range of 73.44 − 83.2%, potentially serving as a viable alternative for treating distal and proximal tibial fractures. In light of the results from Model A, the crossbar should be positioned as proximal as possible to the skin. For proximal tibial fractures, to minimize the use of external fixation components, the triangular crossbar structure of Model B4 can be employed. In the case of distal tibial fractures, while the triangular crossbar structure of Model C4 offers good stability, the risk of displacement is greater. Therefore, it is advisable to use an H-shaped fixation method with additional external fixation components, such as those found in Model C3.