Analysis of the Mechanical Behaviour for the External Fixation Device under the Impact of Torque

: In this research, an analysis of the mechanical behaviour for the Orthofix external fixation device under the impact of torque was performed. Research considers application of the Orthofix device on the tibia bone for the case of unstable fracture. 3D (Three Dimensional) model of the O rthofix device was created in the CATIA (Computer Aided Three-Dimensional Interactive Application) software, based on the real device construction. Structural analysis was used to monitor and analyse the stress magnitudes on the specific areas of the fixation device and fracture. With usage of the interfragmentary displacement data for the bone fragments, degrees of stiffness are introduced for the fracture and fixation device. Obtained results are used to specify the mechanical behaviour of the Orthofix fixation device.


INTRODUCTION
With ever increasing number of traffic accidents which involve motorcycle drivers, especially in recent years, external fixation devices are essential due to open fractures that may occure. External fixation device is a construction used for the purposes of the bone surgery and treatment of various types of trauma. These devices are used to fixate the bone fragments with application of pins, which are fastened into the bone fragments on the one side, while their other side is connected with the construction i.e. frame of the fixation device [1].
Design solutions for the fixation devices were developed along with the expansion of technology and medicine. For an example, simple design solutions accomplish fracture stability requirements, modular designs enables simple and fast utilization and circular devices with thin pins provide control of the small bone fragments. External fixation devices are often used with the adjustable couplings which enable dinamization in order of providing specific pressure on the bone segments [2].
Rapid evolution of computer sciences and software development has led to various softwares for 3D modeling and numerical analysis. In recent period, implementation of these softwares is inevitable for structural analysis of the fixation devices. With the 3D model and numerical analysis, a lot of data can be obtained, such as values of von Mises stress, displacement for the points of interest, as well as stress distributions and displacements of the fixation device itself [3][4][5][6][7][8][9].
The goal of this research is to examine the mechanical behaviour of the Orthofix external fixation system applied to the tibia bone under the impact of torque, for the case of unstable fracture.

DEVELOPMENT OF CAD MODEL
Orthofix fixation device represents one of the modern solutions developed for the needs of external fixation. Device is made of the austenite stainless steel (AISI 304 according to EN 10088 i.e. EN 58E) and anodized alloy of the aluminium (T6-7075 according to EN 573-3 i.e. AlZn5MgCu), coated with the layer of Polytetrafluoroethylene (PTFE). Fig. 1. shows the appearance of the Orthofix fixation device with distinguished aluminium and steel parts, in black and grey color, respectively.  Aluminium is a non-magnetic and corrosion resistant in various environments, and it is also less expensive when compared to other metals. Black aluminium color for the device components is acquired with the anodizing surface treatment. Austenite stainless steel is attributed with great resilliance to intercrystalline corrosion, while it has reduced yield strength, due to smaller proportion of carbon and a different structure. Mechanical properties of the Orthofix fixation device components are shown in Tab. 1 [10].
Development of the CAD model for the Orthofix device, based on properties of the physical model, is performed in the CATIA software. Device components are formed with the parametrization method, which enables connectivity between specific dimensions and reduces the time needed for corrections. Each component is created in the Part Design module, while complete fixation system is created by assembling these components in the Assembly Design module.
Apart from the Orthofix CAD model, tibia bone model is also created. Tibia is modeled as an ortotropic material with specifications according to Tab. 2 [11].

DEVELOPMENT OF FEM MODEL
Development of the FEM (Finite Element Method) model is performed in the CATIA software. One of the greatest advantages of the mentioned software is reflected in associativity, compared with other analysis softwares. This means that any change of CAD model parameters will be automatically updated in the FEM model.
FEM model development starts with discretization and selection of the finite element type. Discretization must be performed with the elements which are sufficiently small, so that usable results may be obtained. Also, the size of finite elements must be in accordance with computer performance capability [12,13]. Components of the Orthofix fixation device are modeled with the linear and parabolic tetrahedron finite elements. Linear tetrahedrons are used for couplings, spherical joints and fasteners, while parabolic tetrahedrons are used for truss, tibia, and half-pins.
Once discretization is complete, connection properties for the Orthofix device are defined. Interaction between halfpins and bone models is established via fastened connection property (Fig. 2a). Fastened connection is a feature defined over the boundaries of the selected parts, where these parts are than handeled as one body. Second type of connection used to establish Orthofix system is contact connection property (Fig. 2b). With this connection property, penetration of bodies is restricted i.e. bodies can still move but only up to point where they reach strictly defined clearence.
Once virtual parts are applied, it is necessary to define torque. When analysing the basic strains, torque is the case where any cross-section of a rod is influenced with the external forces. This effect is reduced to a moment Mt, corresponding to a vector parallel to the longitudinal axis of the rod. This moment is called torque moment [14].
whereas: θ -torque angle, p -translational displacement of the considered point, l -distance between axis of the segments and considered point (Fig. 5).
Without any doubt, the stiffness of the fixation device construction is important, but it does not provide direct insight about the fracture movement. More precise information may be obtained by investigating real relative movements of the bone ends under simulated load conditions.
Fracture stiffness is defined as ratio of the applied load and resultant relative displacement for the considered pair of points, as shown with Eq. (5) [16]:    Fig. 7.

RESULTS
Values of the displacements for the maximum torque moment of 15 Nm, are presented in Tab.3.
For the maximum torque, greatest displacement of the fracture area amounts 4.84 mm and it is located at the top of the bone model i.e. brim of the upper segment. Greatest displacement for the fixation construction is located at the top and at the end of the half-pins, and it amounts 4.84 mm.
Stress values are variable and dependant of the construction shape. Most critical and most loaded zones of the construction are half-pins and contact areas between halfpins and couplings (Fig. 8).  These critical zones are used to collect data about intensity and direction of principal stresses (Fig. 9). Result of the 2 observed zones (MM1 & MM2) are shown in Tab. 4.

CONCLUSION
Mechanical behaviour of the external fixation device have an enormous impact on the fracture treatment, by influencing the biomechanical fracture environment. The main task of the external fixation device is to stabilise the fracture during the treatement. In order of accomplishing this task without any mistakes and defects, it is necessary to adjust the size, shape and the relative position for each of the fixation device component. This adjustements need to correspont to the clinical needs i.e. information about the constructive parameters and loads are mandatory for the construction process.
In this research, an analysis of the mechanical behaviour for the Orthofix fixation device under the impact of torque was performed. With usage of the CATIA software, 3D model of the fixation device was formed. This model is fundamental for further FEM analysis, used for observing mechanical behaviour of the fixation device, which involve fracture movements, construction behavior under load and stiffness definition.
Structural analysis showed that maximum displacement of the fracture is located at the top of the tibia bone model with value of 4.84 mm, while maximum fixation construction displacement also amounts 4.84 mm, and it is located at the top and at the bottom of the half-pins. Displacements for the distal bone segment have small values, due to clamp restrain.
Using the displacement values for the fracture zone, obtained with analysis, fracture stiffness which amounts 3.875 Nm/mm is defined. Similarly, using the values of the angular rotation of the bone model, construction stiffness which amounts 180.72 Nm/rad is defined. Both of the defined stiffnesses satisfy the permitted limits for these types of constructions.
Values and directions of the principal stresses were observed for the 2 critical zones under the impact of maximum torque load. These zones are half-pins and area of the connection of the half-pins and couplings. Greatest stress is located on the critical zone 1 (MM1) and amounts 274.79 MPa, which satisfies the permitted stress value for the halfpin material.
By analysing the intensities and directions of the principal stresses it is noticeable that the truss is conducted to the effects of the uneven stresses of tension and pressure in two perpendicular directions, due to length of threaded connection and the bone asymmetry.
Based on the presented results and their analysis, it can be concluded that Orthofix device shows good mechanical behaviour under the impact of torque. These behaviour can be further improved by using new materials for fixation device components or with redesign process of the device.