Finite Element Analysis of Different Locking-Plate Fixation Methods for the Treatment of Ulna Head Fracture

Background: Ulnar head fractures are increasingly higher with the growing proportion of the elderly in the population. Failure to achieve stable anatomic reduction of ulna head fracture may lead to the DRUJ dysfunction and nonunion of distal radius. Due to the lack of the postoperative reporting outcomes and the biomechanical studies, it has not been well established about the optimal management of the comminuted distal ulna head fracture. This study aimed to explain the advantages and disadvantages of the ulnar-side locking plate xation, compared with the dorsal-side one, and its screws arrangement in the treatment of the ulnar head fracture by using nite element analysis. Methods: FE models of the ulnar head fracture and the models of ulnar-side locking plate and dorsal-side plate with two or three distal screws was constructed. In order to simulate forces acting on the ulnar and the osteosynthesis material during daily-life activity in subjects who underwent reconstructive surgery, we applied three loading conditions to each model, viz. axial compression 20N, 50N, and torsion moments 1Nm. Under these conditions, values of the von Mises Stress (VMS) distribution of the implant, peak VMS, and model displacement were investigated. Results: Both the stress values and model displacement of ulnar-side plate were lower than those of dorsal-side plate. When adding a screw in the middle hole of the ulnar head, the values of model displacement and the peak stress in xation system are lower, but it may evidently concentrate the stress on the middle screw. Conclusions: In conclusion, our study indicated that plating locking plate on ulnar side had lower stress distribution on the plate and better stability than on dorsal side in ulnar head fracture xation. Adding the additional screw on the ulnar head could reduce the displacement of the xation system and increase the stability of the xation system. This study requires clinical conrmation as to its practicality in the treatment of ulnar head fracture.

on the middle screw.
Conclusions: In conclusion, our study indicated that plating locking plate on ulnar side had lower stress distribution on the plate and better stability than on dorsal side in ulnar head fracture xation. Adding the additional screw on the ulnar head could reduce the displacement of the xation system and increase the stability of the xation system. This study requires clinical con rmation as to its practicality in the treatment of ulnar head fracture.

Background
Wrist joint is one of the main joints of a human body, which has high activity frequency. Previous studies suggested that the stability of the DRUJ(distal radius and ulna joint) greatly affected the function of wrist joint, not only for forearm rotation, but also for load and force transmission [1,2]. If it is not treated in time, the fracture of DRUJ often leads to the occurrence of post-traumatic chronic pain and limitation of wrist joint activity, which causes great inconvenience to the work and daily life of patients. Ulna head fracture may be seen in up to 6% of patients with unstable fractures of the distal radius [3], which is increasingly higher with the growing proportion of the elderly in the population [4]. During past years, researchers suspected that the fracture of ulna head may cause nonunion of distal radius [5], instability of DRUJ and the decreased forearm rotation [6]. Failure to achieve stable anatomic reduction of ulna head fracture may also lead to the loss of ulnar variance and the distal ulna nonunion, thus may cause DRUJ dysfunction, ulnar-sided wrist pain, and post-traumatic arthrosis [5,[7][8][9].
Due to the lack of the postoperative reporting outcomes and the biomechanical studies [10], it has not been well established about the optimal management of the comminuted distal ulna articular head fracture. Ring et al. [11] reported the Condylar Blade Plate Fixation could achieve healing with good alignment, satisfactory function, and an acceptable rate of secondary surgery. David et al. [12] showed us the bene t of the application of a locked plate including the locked or xed angle support, ability to insert variable lengths of locked pegs, and the low-pro le design. But Dorsal locking plate may bring about the soft tissue complication [13]. Recently, distal ulna hook plate has been introduced for the treatment of distal ulna fractures, yet the limitation of the vertical arrangement of distal screws may result in instability of the construct [14,15]. In the present study, we found that ulnar side micro locking plate could achieve good outcomes. However, the distal radius fracture combined with ulnar head fracture is not a common clinical case and the application of ulnar side locking plate has never been reported before. Since the number of cases is relatively small, it becomes indispensable to apply nite element analysis to evaluate the mechanical properties of implants.
Therefore, the purpose of this study is to explain the advantages and disadvantages of the ulnar-side locking plate xation, compared with the dorsal-side one, and its screws arrangement in the treatment of the ulnar head fracture by using nite element analysis.

Establishment of the nite element models
A 45-year-old healthy female volunteer was recruited without the history of wrist and systemic diseases. A Canon Aquilion ONE ViSION Edition CT scanner was used to perform a high-resolution CT scan of her right forearm. The scanning layer thickness was 0.5 mm. The CT scan was stored as a DICOM format le into the Mimics 19.0. The reconstruction slice thickness was 0.5 mm. The 3D model of the right forearm was obtained based on the gray value of the tissue and segmentation of the region, and was exported as an igs le, then incorporated into Geomagic 12 for smoothing, meshing and tting surface processing ( Fig. 1).
Then the model was incorporated into the Creo Parametric 2.0. In this study, we used OsteoMED 2.0 HPS Y-plate system. Thus the cannulated screws with a diameter of 2.0 mm and Y-steel plate were fabricated using Creo Parametric 2.0. A model of ulnar head was established and stabilized with ulnar side plate and the dorsal side plate respectively according to the practical surgical method with no interfragmentary gap (Fig. 2). The implant material was modeled as Titanium Alloy Ti6Al4V with material constants: Elastic Modulus E [GPa] 110; Poisson's ratio µ 0.33.
Subsequently, the models were incorporated into ANSYS Workbench 15.0 for meshing and cut the fracture line of ulna head fracture described by Paksima [10]. When there are more than two geometric models, the relative relationship between the models should be set according to the actual situation, so we set the contact setting to binding relation in this report. (Fig. 3) The bone was de ned with linear elastic material properties using Young's modulus of 17 GPa for cortical bone and 1.5 GPa for cancellous bone. Poisson's ratio for both cortical and cancellous bones was 0.3 [16]. The elastic modulus and Poisson's ratio of various structural materials were shown in Table 1. The three-dimensional model of cortical bone and cancellous bone was developed by Boolean operation, and the proximal femoral bone model was built re-assembly. In vivo loading conditions in the human DRUJ have not been completely discovered. Bernal et al. [17] found that the mean grip force was 18.6N while performing a daily-life activity by measuring different subjects through wearable capacitive pressure sensors in the ngers. Putnam et al. [18] reported that each 10 N of grip force would transmit 26 N of force through the distal ulna metaphysis in the wrist neutral position. If the wrist was no longer in extension and ulnar deviation owing to the variation of hand position during power grip, the amount of force through the distal ulna metaphysis would reduce. In order to simulate forces acting on the ulnar and the osteosynthesis material during daily-life activity in subjects who underwent reconstructive surgery, we applied three loading conditions to each model, viz. axial compression 20N (Fig. 4A), 50N (Fig. 4B), and torsion moments 1 N m (Fig. 4C) [19].

Evaluation Criteria Of The System
First, the maximum displacement of the fracture end of the model was measured. Second, four models' von Mises Stress (VMS) distribution and peak VMS of both the xation plates and the internal xation system were observed [20]. These parameters were used to capture the mechanical factors involved in the xation stability and fracture healing [21].

Von Mises Stress (VMS) Distribution
The VMS patterns of the three loading settings in four xation systems were shown in Fig. 5. The stress values of ulnar-side plate were lower than those of dorsal-side plate. Obvious concentration of stress on 4 models in 3 loading settings was found near the fracture line. The VMS patterns of three loading settings in four implant plates were shown in Fig. 6 and the maximum Von Mises peak stresses on xation plate were recorded in Table 1. Thus, the maximum Von Mises peak stresses of ulnar-side xation plate was lower, which indicated the ulnar-side xation plate could smoothly transfer the load to the proximal cortical bone. The peak stress in xation system under torsion moments could be reduced by adding a screw in the middle hole of the ulnar head. Although it was decreased only in ulna side plate xation under axial compression, it may evidently concentrate the stress on the middle screw.

Fracture Displacement Changes
The model displacement patterns of three loading settings in four xation systems were shown in Fig. 7. The values of model displacement in ulna-side xation group were lower than those in the dorsal-side xation group. When adding a screw in the middle hole of the ulnar head, the displacement in xation system could be reduced. The maximum displacement of the 4 models was shown in Table 2.

Discussion
The static stability of the DRUJ is achieved by the bony congruity between the sigmoid notch of the radius and the ulnar head and by the ligaments which hold the joint together [22]. Part of the ligaments constitute the main stabilizer of DRUJ, which run from the fovea of the ulnar head to the dorsal and palmar edges of the sigmoid notch on the distal radius. [23][24][25]. The distal interosseous membrane (DIOM) of the forearm acts as a secondary soft tissue stabilizer of DRUJ. DIOM originates from the distal ulna 54 mm (on average) proximal to the ulnar head and runs distally to insert on the dorsal inferior rim of the sigmoid notch of the radius, which is at the terminal of the central band of the interosseous membrane [26][27][28]. Therefore, when the ulnar head breaks, the ligament will lose its stable attachment point, resulting in the instability of DRUJ. Distal ulnar metaphyseal fracture can be deemed as a fracture ranging from the ulnar neck to within 5 cm of the distal dome of the ulnar head and the high incidence of it is related to osteoporosis [29]. Since 2000, with the development of internal xation technology and increasing aging population, people's requirements for the recovery of wrist joint function are gradually improved. More and more surgeons choose open reduction and internal xation to treat unstable distal ulnar fractures [30,31]. Palmer and Werner [32] showed up to 42% of force passing through the ulna, in which axial force passing down the ulnar head fracture end was closer to 20% [32]. The above studies indicated that the loss of the ulna head would disrupt the biomechanics and load-bearing capacity of the DRUJ. Therefore, the demand for internal xation treatment become higher owing to the biomechanical characteristics of ulna head fracture.
However, the number of reported cases and literatures is rather sparse, which is mostly limited by the low incidence, merely 5-6%, of distal radius fractures accompanied by a distal ulnar metaphyseal fracture. [3].
At present, it remains plenty of controversies around the treatment of distal ulnar head fracture. It is challenging to perform an internal xation of distal ulnar metaphyseal fractures because the distal fracture fragment is small, comminuted, osteoporotic, covered with articular surface over a 270° arc and surgical exposure of the distal ulna for hardware placement raises the possibility to damage the dorsal sensory branch of the ulnar nerve [33]. The most widely used xation methods are dorsal micro-locking plate and anatomical hook plate, but it remains unclear about their merits and drawbacks and mechanical properties. Although the hook plate conforms to the ulnar anatomical structure of the distal ulna, there are few screw holes in the head which are arranged vertically, and the screw placement is limited during operation. On the other hand, the locking plate has more screw holes and the characteristics of pre bending. Considering that the horizontal arrangement of screws has higher anti rotation ability, we propose a method of placing the micro-locking plate on the ulnar side. Nevertheless, limited by the number of clinical cases, retrospective study is di cult to carry out. Therefore, a new way of analysis is urgently demanded.
Nowadays, thanks to the latest development of nite element model generation, such as improved quality of CT imaging, segmentation algorithm and computing rate, the accuracy of nite element modeling has been greatly elevated [34]. With the maturity of technology, 3D nite element analysis (FEA) can simulate the biomechanical analysis of complex orthopedic diseases and get rid of the limitation of the lack of cases. In this study, we chose to use FEA to gure out whether placing the ulnar side locking plate had better biomechanical properties than the current choice of the dorsal side locking plate. We hope the mechanical results of this study provide experimental guidance to its application in clinical surgeries.
As shown in Table 2, the ulnar-side locking plate models provided more stable xation than the dorsalside models and the stability increased with the augment of head screws. Figures 5 and 6 illustrated that the stress of the four xation systems was concentrated at the fracture line. Both the stress concentration zone and the maximum displacement were decreased in ulnar-side locking plate xation. As shown in Table 1, under torsion moments, the peak VMS of the ulnar-side xation models are lower than the dorsalside one, and it reduced as adding the additional ulnar head screw, which evidently indicated the antitorsion function of the horizontally arranged ulnar head screw. Under the axial loading, the peak VMS increased on the dorsal-side xation models and concentrated at the middle additional screw, while it decreased on the ulnar-side xation models. The results mentioned above indicated that ulnar-side locking plate xation provided better stability, resulting in the lower stress distribution on the plate and greater security of the xation system. Ulnar-side plate xation could generate a rigid, stable mechanism and provide a strong resistance ability to counter compression and torsion effect. Adding the additional screw enabled the xation models to generate a better stability, but concentrated the stress on the middle screw, which will guide the design of subsequent plate improvement. This study is the rst FEA comparing the mechanical e ciency of dorsal-locking plate and ulnar-side locking plate in the xation of ulnar head fracture. However, with the limitation of no experimental validation was conducted and no soft tissue structure was built in the models, the application of these xation plates still requires more research.
This nite element simulation may facilitate the further mechanical research and give guidance to the treatment of the ulnar head fracture clinically.

Conclusions
In conclusion, our study indicated that plating locking plate on ulnar side had lower stress distribution on the plate and better stability than on dorsal side in ulnar head fracture xation. Adding the additional screw on the ulnar head could reduce the displacement of the xation system and increase the stability of the xation system. This study requires clinical con rmation as to its practicality in the treatment of ulnar head fracture. Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.  Stablishing the internal xation models of ulnar head fracture and importing the models into Abaqus software for meshing.