Evaluation of the Structural Behaviour of a Unilateral External Fixator for Osteosynthesis

2.1. Unilateral External Fixator

A modular unilateral external fixator (Fixus 66, distributed by Unimedical Bio. Tech. Srl, Torino, Italy) was selected for this study. It is composed of a radiolucent carbon bar with an elliptical section (12.3 x 11.1 mm) and a length of 400 mm, four 4-hole aluminium clamps (two at each end of the fracture) for 3 to 6 mm diameter pins, two bar-clamp aluminium adapters that can slide on the bar up to the insertion height of the pins, where the adapter is locked. In this study, a total number of 6 pins were used per test, three for each end with the symmetrical arrangement, two on the right clamp and one on the left clamp. With the aim of testing the relation between fixator stability and pins diameter, self-tapping and self-drilling pins (150 mm long) with 3 mm and 4 mm diameter, respectively, were selected.

2.2. Samples Preparation

In order to neglect the high intrasubject variability linked to the use of cadaveric bones, the external fixator was implanted on 8 simulacra of tibia and 8 simulacra of femur produced by Sawbones (Sawbones, Pacific Research Laboratories, Inc., Vashon, WA). The tibia of 4th generation medium size version (model SKU:3401) was selected and for mimicking the femur diaphysis, a short hollow fiber reinforced epoxy cylinder with 30 mm of outer diameter and 4.3 mm of wall thickness (model SKU:3403-15) was selected. The 16 bone samples were divided into the subgroups according to (1) anatomic region (tibia or femur), (2) bone status (intact or fractured), and (3) pins diameter (3 mm or 4 mm), obtaining 8 subgroups, as summarized in Table 1.

Table 1.

Anatomic Region	Tibia		Femur
Pins Diameter Bone Status	3 mm	4 mm	3 mm	4 mm
Intact	1	1	1	1
Fractured	3	3	3	3

In the fractured samples, prior to implant, a diaphyseal transverse fracture was created using a surgical saw. The external fixation was thus performed on each sample, following the manufacturer's instructions.

2.3. Testing Set-up

To test the stability of the system in a load configuration that mimics the realistic stress as much as possible to which the bone-fixator construct is subjected in a hospital setting, a fixture for a uniaxial testing machine has been designed to replicate the lifting of the limb by gripping on the external fixator bar. This loading application is compatible both with the manoeuvring performed by the surgeon to check the post-implant stability and with the handling manoeuvring carried out by the medical staff during patient’s hospitalization. The designed testing setup is shown in Fig. (1A).

A lower fixture (Fig. 1A-(1)) able to fix the bone (Fig. 1A-(2)) to the base of the MTS Q-Test 10 Elite (MTS Systems Corporation, Eden Prairie, Minnesota, USA) (Fig. 1A-(3)) was therefore designed, while the upper fixture (Fig. 1A-(4)), equipped with two spherical joints, constrains the vertical movement of the fixator bar to the moving crosshead, adapting to the different positions of the fixator with respect to the bone and avoiding over-constraints. A 2.5 kN load cell (Fig. 1A-(5)) was interposed between the upper fixture and the moving crosshead. Each test was recorded with a full-frame digital camera (Canon EOS 5D Mark II) equipped with an autofocus lens for macro photography (Canon EF 100 mm f /2.8 Macro USM) and positioned on a tripod (Fig. 1A-(6)). Tests and videos were acquired simultaneously from two computers (Fig. 1A-(7) and (8)). Local movements around the fracture zone were measured through the optical tracking of four markers (M1, M2, M3, and M4, Fig. 1B and 1C).

2.4. Mechanical Tests

Two types of mechanical characterization have been designed for the evaluation of two important aspects of external fixation: (1) the static characterization, suitable for evaluating the stiffness of the bone-fixator construct with and without the fracture, and (2) the dynamic characterization, designed to evaluate the stability of the construct when repeatedly stressed. The testing of the external fixator implanted on non-fractured bones, albeit devoid of clinical motivation, is aimed at characterizing the stability of the external fixator in the absence of bone instabilities and producing reference values for comparisons. For this reason, only one test per combination of parameters was performed in the intact configuration.

2.5. Data Elaboration

Force-displacement plots were produced from static results, resulting in the setting of the zero displacements when a 5 N force was recorded. Obtained trends were revealed to be bilinear in each test. For this reason, a unique stiffness parameter (i.e., the slope of the whole experimental curve) was not computable. Therefore, two different stiffness indexes were assessed, describing the sample behaviour at the beginning and at the end of the load application. In detail, the initial stiffness K_i was computed as the linear regression of the curve in the 5 – 30 N load range, whereas the final stiffness K_f was computed as the linear regression of the curve in the 250 – 350 N load range.

The videos acquired during static tests were imported in the GOM Software 2019 (GOM GmbH, Braunschweig, Germany) to track the displacement of the markers. Two lines were created between markers M1 and M2 and markers M3 and M4, respectively (Fig. 2) and, as a stability indicator, the angle α formed between the two lines was measured along with the test, with respect to the initial reference angle measured at time t = 0.

Dynamic results were post processed through a force normalization with respect to the first force peak of each test. This was considered indispensable since the maximum force values, although calibrated by static tests to be equal to 350 N, turned out to be variable according to the test rate. From the so obtained force-displacement hysteresis loops, areas were computed and compared, being indicative of the energy involved. Energy trends with respect to the cycle number (from 1 to 10) were then fitted with a two-parameter power function in the form y = b x^m, aiming to assess the rates of decay m.

3.1. Static Characterization

Fig. (3) shows force-displacement trends for the 16 performed tests. The bilinear behaviour is clearly visible in almost every curve, with particular preponderance in the more rigid configurations. Moreover, sudden failures are visible in the configurations with fractured segments and thinner pins, represented by solid red lines. These are due to the failures in correspondence with the pin threads, which generate an instantaneous relative sliding between the pin and the bone.

Focusing on the computed stiffnesses K_i and K_f (Table 2), the initial stiffness was revealed to be systematically higher than the final stiffness, up to 4-fold higher in the intact configurations and up to 3-fold higher in the fractured ones. The only exception is the configurations with tibia and 3 mm diameter pins, which are globally less stiffer and are characterized by a less pronounced bilinearity. By comparing the two anatomic regions, the fixator behaves stiffer when mounted on the femur, regardless of the pins used, while stiffnesses comparable to the femur ones are reached by the tibia when 4 mm diameter pins are used.

The optical analysis allowed the evaluation of the bone segment's stability by maintaining alignment of the segments during load application. Figs. (4 and 5) show that the angle increased for each fractured configuration (intact configurations would generate a null angle increase, therefore, it was not monitored).

Steep angle increases are visible in three 3 mm diameter pin tests, which are the ones characterized by failures in pin holds. On the contrary, 4 mm diameter pins allowed the maintenance of the segment misalignment to be always below 1.7°.

Fig. (6) summarizes the total angle variation experienced by the two anatomic regions, confirming the higher stabilizing effect of the 4 mm diameter monocortical pins.

3.2. Dynamic Characterization

Fig. (7) shows the normalized energy loss trend at three different test rates for a representative sample. The curves revealed to be always almost identical, albeit translated vertically, therefore, the variation in the rate of application of the load led to very similar results in the power fitting procedure. Hence rates of decay m were reported only for the 1 mm/min test rate.

Table 3 lists the rates of decay computed for the 16 tested samples, and no macroscopic differences result from the comparison between both anatomic regions and pin diameters. Indeed, the rate of decay m settles around -2 for each test. Therefore, no substantial differences between configurations arise when the fixator is repeatedly stressed.

From a visual inspection, no further pin-bone damage was noted after the dynamic characterization. The failures indeed occurred exclusively during static stresses, and the application of the dynamic load did not lead to further damage to the samples.