## 2 Materials and Methods
### Experimental Model  
The purpose of this part of the study was to experimentally investigate the TSF setup used in the clinical investigation in order to correlate the clinical observations regarding callus formation presented in the previous section with the mechanical response of the TSF device. In the experimental investigation, axial compressive loading was considered the predominant loading mode during weight-bearing. For this purpose, an experimental model was set up, consisting of a TSF fixator with identical configuration to the clinical setup.  
The typical TSF configuration as applied in the clinical treatment of HTO (Section 2.1) is shown in Figure 2. The TSF configuration consists of an upper (open) and lower ring with internal diameters of 180 mm and 155 mm, respectively. The TSF rings are connected to each other with six triangulating struts. Universal joints are used at the ring-strut connection points in order to allow for the rotational movement of the struts.  
To simulate the upper and lower bone structure, two 30 mm diameter polyethylene bars were used, with lengths of 130 mm (upper part) and 139 mm (lower part). The upper bar was fixed on the open ring with two half-pins of 6 mm diameter and a pre-tensioned Kirschner wire of 1.8 mm diameter. The pre-tension applied on the wire during setup was 1000 N using the standard wire tensioner, included in the TSF instrumentation, and was confirmed by using an axial extensometer on the wire during pre-tensioning. As far as the element configuration is concerned with regard to the actual clinical case, clamping of the half-pins on the upper ring was such that the angle between them was 67\({}^{\circ}\) with respect to the center of the ring. The Kirschner wire had an internal angle of 45\({}^{\circ}\) and 112\({}^{\circ}\) with the first and second half-pin, respectively. The lower ring was fixed on the polyethylene bar using three half-pins of 5 mm diameter placed at an internal angle of 25-40\({}^{\circ}\). The Kirschner wire was attached to the upper ring with screws, while the half-pins were attached to the rings with special rancho cube connectors, as shown in Figure 2.  
Figure 2: Experimental setup of TSF fixator corresponding to the clinical case examined.  
Fixation of the half-pins with the polyethylene bars was made using internal screwing. The axes of the upper and lower polyethylene bars were aligned at the center of each ring, and were perpendicular to the plane of the rings in the direction of uniaxial loading. During compressive displacement, simple support conditions in the upper bar were implemented to allow free rotation of the bar by using a metallic cylindrical element for surface contact (Figure 2). During gripping, the axis of the cylindrical element was aligned to the loading axis by default. Next, alignment of the cylindrical element axis with the axis of the upper bar was achieved by ensuring firstly the surface flatness of the polyethylene bar and then by using a measuring caliper for adjusting the position of the surface at the contact location.  
The lower bar axis was aligned by default to the loading axis of the machine by including on the one edge of the bar a manufacturing detail in order to allow gripping of the bar directly on the machine wedges. Prior to the application of axial displacement resulting in compressive loading of the fixator frame, the space between bars was set at 35 mm.  
The TSF fixator was placed on an MTS 810 universal testing machine, and a constant displacement rate of 5 mm/min was applied for uniaxial compression. During testing, the total displacement of the end supports as well as the magnitude of the applied compressive force were measured.