The most stable pinning configurations in transverse supracondylar humerus fracture fixation in children: A novel three-dimensional finite element analysis of a pediatric bone model

Background : This study aimed at finding out the effect of exit height of pins, pin trajectory and pin number on the stability of crossed and lateral pinning configurations used in the fixation of extension-type supracondylar humerus fracture (SHF) in children, through finite element analysis of a novel pediatric humerus bone model. Method : Distal humerus model consisting of the ossific nucleus of the capitellum (ONC) and distal cartilage of a 6-year-old boy was developed computationally. Various crossed and lateral pinning fixation models with either two or three pins were simulated on an extension-type, transverse SHF and tested in six loading directions. Results : Two-crossed pins and 2-lateral pins were respectively more stable in rotation and compression loadings, while 3-crossed pins were the most stable in all loading directions. The crossed pins exiting at the upper border of the distal metaphyseal-diaphyseal junction (MDJ) had the best stiffness among the 2-crossed pins, while the lateral pins with a mid-ONC distal pin provided the best stiffness among the 2-lateral pins. A third pin however, going through the olecranon fossa led to improved stability of the 2-lateral pins in flexion, extension, internal and external rotations. Conclusion : In the fixation of extension-type, transverse supracondylar humerus fractures, 2-crossed pins are only superior to 2-divergent lateral pins in rotational loadings. Two-crossed pins exiting at the upper border of the MDJ provides the best stability, whereas 2-lateral pins with a distal pin going through the middle third of the ONC provides the best stability against compression forces for these fractures. Three-crossed pins however offer the best stability against both compression and rotation forces.This study offers important clues in the preoperative evaluation and management of extension-type supracondylar fractures in children.

of the MDJ provides the best stability, whereas 2-lateral pins with a distal pin going through the middle third of the ONC provides the best stability against compression forces for these fractures. Three-crossed pins however offer the best stability against both compression and rotation forces.This study offers important clues in the preoperative evaluation and management of extension-type supracondylar fractures in children.

Background
3 Supracondylar humerus fracture (SHF) is a commonly encountered pediatric trauma. It accounts for about 60% of all elbow fractures in children [1]. Closed reduction and percutaneous pinning is commonly used as the mainstream treatment for displaced SHFs.
However, loss of reduction with the technique is a major concern to pediatric orthopedic surgeons. Causes of loss of reduction with pinning techniques have been attributed to pinning configuration, pin size, pin number and pin spread [2][3][4][5][6][7].
Crossed pins and divergent lateral pins are said to have comparable stiffness in numerous clinical and biomechanical studies [8,9]. Many authors have however advocated for the lateral-only pins due to the risk of ulnar nerve injury with medially placed pins [10,11].
However, the use of crossed pins may be inevitable in some cases, such as in medially oblique fractures, high fractures or fractures with medial comminution, which may have a higher incidence of loss of reduction in clinical practice [5]. Crossed pins are also preferred by many surgeons because of its torsional stability, an important factor considered in the prevention of cubital varus [12].
Acceptable but controversial results have been shown with multiple biomechanical studies comparing crossed and divergent lateral pins [3,9,[13][14][15][16]. However, most of those studies were heterogeneous in fixation details. Influencing factors such as the positions where the pins entered and exited the bone were not studied in detail. This might be one of the reasons for the different results from those studies. By using a novel pediatric bone model, our study aimed at finding out the effect of these detailed features of crossed and lateral pinning through finite element analysis.

Methods
Computational modelling of the pediatric distal humerus A normal computed tomography (CT) data of the right elbow of a 6-year-old male child 4 who was evaluated for occult elbow fracture, was downloaded from our hospital's picture archiving and communications systems software (PACS) in Digital Imaging and Communications in Medicine (DICOM) format after approval from our institution's Medical Ethics Committee. The data was then imported into Simpleware's image processing software (Synopsis Inc., California, USA) for data processing. This CT data was selected because no pathology was found on the elbow and also due to its clearness of the elbow

Pinning Fixation And Finite Element Models Generation
The finished surface model was imported into SolidWorks 2016 edition (Dassaut Systemes-Simula, France) to generate a solid model of the distal humerus. A typical, transverse supracondylar humerus fracture, with a 20 degrees sagittal obliquity, was created at the level of the olecranon fossa, to mimic the most common fracture pattern [17]. Various crossed and lateral pinning configurations were then simulated using 1.6 mm diameter cylinders as Kirschner-wires, generating a total of eleven models (Fig. 2, Fig. 3). The entry points of the lower pin in the 2-lateral pinning configurations, were altered with respect to the ONC in the sagittal plane, to generate a total of 3 configurations (Fig. 3, Fig. 4). A third pin was added laterally or medially to the stiffest 2-lateral pinning configuration (2LCap) after testing the lateral pins, to give the 3-pinning configurations 3LLC, 3LOF and 3CP (Fig. 2). The fixated models were imported into HyperMesh14 (Altair Engineering, Michigan, USA) for pre-processing and meshing. Material properties for the finite element analysis were assigned according to Table 1[18, 19].

Finite Element Calculation And Determination Of Stiffness
The finished meshed models were imported into Abaqus 6.14 (Dassaut Systemes-Simula, France). Near the position of the established geometric center, a node was selected as a reference point at the loading surface. A coupling constraint was then set between the loading surface and the reference point. The proximal end of the humerus was completely restrained and a concentrated force of 30N was applied to the reference point along the X, -X axes and Y, -Y axes to simulate flexion, extension, valgus and varus loadings. A torsional moment of 1.5 N m was also applied along the Z and -Z axes to simulate internal and external rotations. The maximum displacement of the distal fragments relative to the proximal fragments were recorded and the corresponding stiffnesses were computed.

Stress Analysis On Pins
In order to determine the technique that generated the most stress on pins, we recorded and analyzed the stress distribution regions and levels on pins, and also determined the highest stress levels on individual pins in each technique, in order to determine the pin that contributed more to the stability of techniques.

Results
We compared the stiffness of crossed pins at different exit points. The CP4 crossed pinning configuration, in which the pins exited at the upper border of the metaphysealdiaphyseal junction (MDJ), had the best stiffness in all directions. A further increase or decrease in exit height did not result in any further increase in stiffness (Fig. 5a). Among the 2-divergent lateral pinning configurations, stiffness was better when the distal pin entered through the ONC. The 2LCap configuration which had its distal pin going through the middle third of the ONC, had the best stiffness (Fig. 5). Overall, 2LCap had the best stiffness in compression tests, while CP4 had the best stiffness in rotational tests when all 6 the two pins configurations were compared (Fig. 5b).
When an additional pin was used with the 2LCap configuration, its overall stiffness significantly improved in all directions. The 3-crossed pinning configuration 3CP, had the best overall stiffness among the 3-pinning configurations. Stiffness more than tripled in both coronal and rotational loadings and doubled in sagittal loadings (Fig. 5b). The 3lateral configuration 3LLC, which had its third pin lying within the lateral column was only stiffer than 3LOF in sagittal loadings while the 3-lateral configuration 3LOF which had its third, middle pin going through the olecranon fossa was stiffer in coronal and rotational loadings.
When the 3-pins configurations were compared with the best 2-pins configurations, 3CP was still the stiffest in all directions, followed by the 3-lateral pins configurations in compression tests and CP4 in rotational tests. Stress analysis showed the highest stress levels generated during rotational tests to be located on the medial pins which means that, medial pins play a crucial role in maintaining torsional stability of crossed pins. In the divergent lateral pinning configurations, the distal (capitellar) lateral pins experienced the highest stress levels individually, also demonstrating their contributing role in the stability of lateral pins.

Discussion
Biomechanical studies via computational finite element simulation can provide deeper insight into the stability and functionality of bone constructs, and therefore can be used to make comparisons among various fixation techniques that are difficult to be accomplished through other methods [20]. This study is the first to establish a pediatric bone model for three-dimensional finite element analysis through a novel combination of commonly available commercial software. In this model, we compared the stiffness of prevalent Kirschner wire configurations and the variations in fixation patterns of supracondylar 7 fracture of the humerus. We observed that 2-crossed pins are not stiffer than 2-divergent lateral pins in some circumstances, as it used to be believed by many surgeons. A third pin going through the olecranon fossa, inserted through the ossific nucleus of the capitellum substantially enhanced the stiffness of 2-divergent lateral pins configuration.
Previous finite element analytic studies on pediatric fractures exclusively utilized synthetic bone models [14]. The dramatic difference in the anatomy of the distal humerus between adults and children would inevitably lead to divergence from clinical reality. In It is mostly believed that, the more proximal pins exit, the more stable the fixation would be. In our crossed pinning configurations however, the best stiffness was achieved when both pins exited around the upper border of the metaphyseal-diaphyseal junction (MDJ).
This superiority was most obvious in the anti-rotation ability. It had been reported that proper pin spread at the fracture site could influence the stability of pins [5]. We observed from our study that, by exiting around the upper border of the MDJ in typical SHFs, the ideal pin spread could be achieved and therefore optimum stability may be obtained.
Although the higher the crossed pins exited the more pin spread achieved along the 8 fracture line, stiffness however reduced as they exited higher. This was probably because the center of rotation was brought closer to the crossing point as the pins exited higher, thereby making them less stable. Pins that crossed within the MDJ region would have their centre of rotation brought closer to the fracture line, also making them less stable. Similar observation was made with crossed pins in a previous biomechanical study conducted with composite bones using varying fracture heights of metaphyseal-diaphyseal fracture of the humerus[21].
The entry point and pin pathway had a major influence on the total stiffness of lateral pins. One pin entering through the ONC greatly enhances the stiffness of divergent lateral pins in all aspects. When entering from the ONC, there is more pin-cortical bone contact area, rendering pins more stability. This finding was consistent with that of Gottschalk et al, [3]. The distal lower pins of the two lateral-entry configurations (2LP, 2LD) in our model, with only a small or no ONC contact area, may have to penetrate and re-enter the bone through their course along the olecranon fossa giving them a shorter bone tunnel length and therefore less stability. Our study was however not the first to emphasize on the effect of lateral pin pathways. Using synthetic bone model, one study compared the influence of the distal lateral pin when the position of the other, proximal lateral pin was fixed. They came to the conclusion that, a lateral pin placed parallel to the metaphyseal flare of the lateral humeral cortex, in combination with a second diverging pin crossing the fracture site at the medial edge of the coronoid fossa, provides the optimum fixation [22]. It was however not clear whether the second pin was a capitellar entry one.
Adding a third pin to 2-divergent lateral pins in any configuration significantly enhances stiffness of lateral pins in all directions. From our study, we observed that a third, middle pin travelling all the way within the bony cavity of the lateral column increases stability of lateral pins in the sagittal plane, while that going through the olecranon fossa increases 9 stability in the coronal and rotational planes. We believe the increased stability demonstrated is due to the more reinforcement along the fracture line by the additional pin, longer bone tunnel length and more pin-cortical bone contact regions. The best stiffness was however generated by the 3-crossed pin configuration (3CP, 2-divergent lateral and 1-medial pins), which had a mid-ONC distal lateral pin. Stiffness values were far more than any other 3-pins configuration in all loading directions. Our finding differed from that of Feng C et al., who stated that an additional pin did not bring about increased stiffness in their model [6]. This difference may be partly due to the difference in testing models, fracture patterns and entry and exit points.
Despite the novelty of this model, our study had some limitations. First, the model was based on the computed tomography images of a 6-year-old boy, which may not represent the diverse pediatric population. However, since the majority of SHFs occur around this age, it was therefore used for our model. Secondly, we only looked at the most commonly encountered typical, transverse fracture pattern [17], which may not represent all clinical circumstances of pediatric supracondylar humeral fractures. Models of different age, gender and fracture pattern must be developed and tested, as well as clinical observations should be carried out to further verify the findings in this study.

Conclusion
This study demonstrated the influence of entry point, exit point, pin number and pathway on the stiffness of Kirschner wire fixation in pediatric transverse supracondylar humerus fractures. It offers important clues in the preoperative evaluation and management of these fractures. Compared to 2-crossed pins, 2-lateral pins with a mid-capitellar distal pin in maximum divergence would provide better stability against translational forces for satisfactorily reduced transverse fractures. Three-divergent lateral pins are however more stable than 2-divergent lateral pins and would be recommended in cases of unstable reduction. Despite the risk of ulnar nerve injury, crossed pins still provide the best stability against rotational forces with pins exiting at the upper border of the MDJ providing the best stability. For optimum stability against both translational and rotational forces, two-divergent lateral pins (with a mid-capitellar distal pin) and one medial pin is recommended for transverse supracondylar humerus fractures. If there is however any concern for ulnar nerve injury with medial pins, 3-divergent lateral pins with at least one mid-capitellar distal pin can offer comparable stability as crossed pins and should be used

Consent for publication
Not applicable.

Availability of data and materials
The datasets used or analysed during the current study are available from the corresponding author on reasonable request.

Funding
There was no funding for this work.     Stiffness values for pining configurations a. Two-pin configurations. CP4 and 2LCap were respectively stiffest among the crossed pins and lateral pins. In compression tests, 2LCap was stiffer than all crossed pins while CP4 was stiffer than all lateral pins in rotation tests. b. Three-pin configurations compared with the best 2-pin configurations. 3CP was the stiffest in all directions, followed by 3LOF in flexion and extension, 3LLC in valgus and varus and CP4 in internal and external rotations