1. Introduction
External fixation is one method of treatment for fractures, especially for patients who are at high risk for systematic complications [
1]. They are frequently applied for combat and disaster related casualties [
2,
3,
4], but also to manage bone defects [
5]. Since World War II, design and wearing comfort of the external fixators has been improved significantly. The main biomechanical principle of external fixation remains almost the same, i.e., providing sufficient stability at the fracture focus [
6], but nowadays it is well known that micromovements in bone callus are also important to the bone consolidation process [
7,
8,
9,
10]. Hence, the challenge for external fixation research on fracture healing is to improve the biomechanics of fracture fixation, and therefore, after good initial fixation stability, a fracture heals as fast as possible. In fact, fixator stability and stiffness are very important since they influence not only the amount of interframentary movement (IFM) and alignment at fracture focus, but also affect pin-screw loosening [
1,
11,
12].
Although there is a great variety of external fixator devices and fixator configurations, the Orthofix Limb Reconstruction System (LRS) was developed fkor the following three main indications: bone loss with shortening; bone loss without shortening; and deformity, with and without shortening, and extreme shortening. Previous studies have recommended its use in the treatment of bone defects since it offers several advantages over others [
5,
13,
14,
15], such as ease of application, versatility, stronger fixation, less fixator related complications, early weight bearing and primary bony union, patients satisfaction, etc. Nevertheless, there are also reports of higher complications and less patients’ satisfactions when it is used for femoral lengthening [
16,
17]. In fact, LRS is a telescopic device in which joints are locked in order to assure a rigid fixation or unlocked to allow load sharing, or even to carry out day-to-day lengthening or transport by the patient himself. Normally, under this condition, the external fixator is extremely loaded during the treatment and pin-tract infections, as well as pin angulation is the commonest complications.
To the best of our knowledge, data comparing the mechanical performance of this fixator at different configurations and, especially, with unlocked joint, is not available. Therefore, the aim of this work is to study the behavior of the LRS fixator and optimize the distance between the external fixator frame and the bone, as well as the number of pins used to connect the external fixator to the bone, in order to promote ideal external fixator stability and decrease healing time. A load cell-based system was developed to identify and quantify the load value that is transferred to the fracture focus, when the bone is being solicited under compression. Experimental and numerical analyses were completed and the results were compared. Good correlations between the values were obtained.
4. Discussion
The aim of our study was to investigate the viability of the Orthofix Limb Reconstruction System (LRS)
® in the dynamic compression mode. Although it is well accepted that the Orthofix ProCallus fixator was designed to incorporate controlled axial compression at the fracture site [
1,
25], the LRS external fixator it is also often used in the dynamic compression mode. Actually, the LRS fixator is especially indicated for bone correction through the techniques of bone transport, compression-distraction, partial acute shortening and transport, multifocal surgery, and bifocal lengthening [
5,
13,
15,
16]. However, for these clinical situations, patients are encouraged to perform partial weight-bearing exercises, such as walking with crutches, as early as the third or fourth day after the surgery [
5,
14] and, afterward, in the consolidation phase, to promote dynamic compression of the callus; releasing one of the clamps from the fixator rail, while the others remains locked, allows the LRS fixator compression mode. There are some published studies reporting comparisons of functional and clinical performance of the LRS system with other external fixators, such as Ilizarov and AO fixators [
5,
14,
15,
26]. The generality of these works concludes that the LRS fixator offers several advantages, such as ease of application, versatility, stronger fixation, less fixator related complications, early weight bearing, and early bony union. However, in their reports, researchers have not explicitly provided information of fixation strategies, such as the distance between the fixator body and the tibia axe or, even, the average value of bending span of Schanz screws, the number of pins in each bone segment, etc., thereby limiting the applicability of their results to the development of a strategy that optimizes the stress of pin-bone interfaces and the interfragmentary displacement. In fact, fracture healing by callus formation normally happens when the periosteal callus becomes stiffer, reducing interfragmentary movement while the loading amplitude is kept constant [
27]. Under external fixation, the amount of interfragmentary motion is dependent not only on the fixation system, but also on other equally important factors, such as the inherent stability of fracture, the accuracy of fracture reduction, the amount of physiologic loading, and the performance of pin-bone interfaces [
28]. Hence, the latest three factors were controlled in this study to investigate how the dynamic compression of the fracture site was influenced.
The experimental setup was developed using a simplified model of a human tibia, consisting of a nylon bar with 30 mm of diameter. The bone callus was included in the experimental setup by means of a load cell-based system, consisting of two carbon epoxy laminated composite plates with a final stiffness of 220 N/mm. The experimental results have shown that it was possible to quantify the load transferred to the fracture focus, during tests, and register the sensibility of the results to the distance between the external fixator and the bone.
The results of the symmetric configurations, shown in the
Table 4, indicate that increasing the distance between the bone and fixator body from 50 mm to 70 mm increases the percentage of the load passing through the callus by approximately 6% to 11%. This behaviour could be justified by the global stiffness variation of the external fixator. A smaller free pin span makes the whole structure stiffer than a larger one [
29,
30], and for any given regenerate stiffness of callus, a more flexible fixation tends to increase the ratio of the total load supported by the callus [
31,
32]. Nevertheless, the results of
Figure 5, and
Table 3 and
Table 4 show also that increasing the axial distance from 70 mm to 90 mm does not change load share ratios very much. Moreover, the values of the interfragmentary deformation presented in
Table 3 for the AC configuration agree with the previous conclusion. The interfragmentary strain is defined as the ratio of the relative displacement of fracture ends to the length of the initial gap. According to the interfragmentary strain hypothesis proposed by Perren [
33], if the local interfragmentary strain is smaller or equal to 2% it is possible to sustain the formation of compact bone, and therefore it seems that there is no significant difference in the callus strain level between both axial distances. Nevertheless, the distance between axes of 50 mm is more sensitive to changes of the intensity of loading than the other two distances. In fact, comparisons of interfragmentary deformation among different load intensities at this axial distance, show that if the initial load is increased four times the interfragmentary deformation increases 7.4 times, whereas for the distances of 70 to 90 mm relationships are only of 4.94 and 3.98, respectively. Moreover, the variation of the interfragmentary deformation among the three axial distances is more significant at the smallest loads than at the highest. For instance, for a load of 50 N the interfragmentary deformation for distances between axes of 70 mm and 90 mm is about 2.3 and 3.1 higher than that verified at the distance between axes of 50 mm, respectively. However, for a 200 N load the relationships are only 1.6 and 1.7 respectively. Therefore, these results show that there are at least two parameters that should be included on the external fixation comparisons purpose, the average bending span of Schanz screws and the weight of patient, i.e., the maximum load that is self-imposed. In fact, these two parameters should be accounted for, because the early weight bearing and bony union capabilities that are achieved with one external fixator are not only related to the geometric characteristics of the device (components of the fixator) or even with the psychological effect of those characteristics on patients, but also to their static or dynamic characteristics at several loads and fixator configurations (the number and spread of the pins along the bone segments, the distance between the main body of fixator and the bone) [
1,
25,
34,
35]. Nonetheless, the dynamic compression of the callus, which was induced by releasing one of the clamps from the fixator rail and the patient weight bearing, seems to be more sensitive to variations of the distance between axes of the fixator and the nylon bar than to the fixator configuration, see
Table 4.
The predicted cell load values correlated well with the experimental results, especially for the axial distance of 70 mm, see
Table 4 and
Table 5 and
Figure 8. The highest errors of the load share ratio are for the ABC and ABCAC configurations, where the numerical results give values that are 14.5% and 16.7% smaller, respectively. Nevertheless, for the 90 mm axial distance, the numerical load share ratios are on average 17.4% higher than those obtained experimentally and the highest error of 20.2% was obtained for the AB configuration. Although the numerical results of the load share ratio for the 90 mm axial distance were higher than those of the 70 mm axial distance, the interfragmentary deformations increase only 0.5% on average, see
Table 5. The difference between the behaviour of numerical and experimental results for the 90 mm axial distance is also visible in
Figure 7, showing that the numerical model shows higher flexibility than the experimental model. This behaviour is justified by the difference of clearances between the numerical and experimental models, which influences the locking stiffness of the external fixator. In fact, from the comparison of experimental and numerical locking stiffness values for the 70 mm axial distances, as shown in
Figure 9, shows that the fixator configuration has a significant effect on its experimental values. Actually, the values change from 12.92 N/mm to 22.63 N/mm, when the pin configuration changes from BC to AB, respectively. Higher values of the locking stiffness are associated with less load passing to the callus bone, due to the higher blocking effect of the free clamp, which is affected by the clearances between the free clamp and the rail body of the external fixator. Nevertheless, the y-displacement (compression displacement) of the free nylon bar depends also on the equivalent stiffness of the Schanz screws that are connected to it, hence, the cell load values are dependent on this parameter too. Combining these insights with the knowledge that the ABC pin alignment is the assemblage that is more rigid and, simultaneously, has the highest variation of the numerical and experimental locking stiffness values, it seems feasible to use this fixator configuration to make comparisons of the differences between experimental and numerical behaviour at both axial distances. For the 70 mm distance between axes, the predicted callus force was about 14.5% smaller than that measured, whereas, for the 90 mm distance between axes, it was 11.3% higher, but the numerical models of both experimental tests were created with the same number of degrees of freedom (three times the number of nodes). Hence the numerical flexibility was always the same, except the part which is inherent to the span length of the pins, and the main difference concerns the real and geometrical values of clearance between the fixator body and the clamps of the fixator.
Numerical clearance has a direct relation with the contact forces developed at contact areas and, because the numerical models have included frictional contact in the free clamp, these dry contact forces were modelled according to Coulomb’s law. In this friction law, the relative tangential velocity has an important role in detecting sliding and sticking between contact surfaces. In static or quasi-static analyses the slip velocities are calculated using the nodal incremental displacements divided by the time step [
24], and therefore the time step increment has some effect on the final solution. In this study, the time step was always the same for all fixator configurations, but the automatic time stepping (ATS) method controls the time step size in order to obtain a converged solution. If there was no convergence with the specified time step, the program automatically subdivides the time step until it reaches convergence. Nevertheless, no significant time step differences were detected among the several fixator configurations.
Figure 12a shows the average values of slip velocities of the two surfaces of the free clamp that contact with the two exterior surfaces of fixator rail in the ABC configuration and the distance between axes of 70 mm and 90 mm.
The initial slip velocity predicted for the 70 mm axial distance is about 0.7 μm/s higher than that predicted for the 90 mm axial distance and, after an initial increase, it remains almost constant, but with trends to decrease, as shown by the negative slope of trendline that is depicted in the graphic. Although the trendline of the predicted slip velocity for the 90 mm axial distance shows an inverse relationship, i.e., the slope is positive, therefore, the main factor behind these differences can only be justified by the variation of span length between both fixator configurations, since the clearance is constant between numerical models. Nonetheless, from this behaviour is not possible to make a straightforward conclusion about what is the effect of fixator clearance on the force passing to the callus. Perhaps increasing the geometrical clearance between the free clamp and the fixator rail can change the slope signal of trendline of the predicted slip velocity for the 70 mm ABC fixator configuration, achieving, in this way, higher slip distance and higher callus force, as in the case of
Figure 12b. Thus, improving the concordance between numerical and experimental results. But, if the increase of the same geometrical clearance would have a similar effect on the results of the 90 mm ABC fixator configuration, the force passing to the callus could get higher and, in this case, the agreement between numerical and experimental results would be lower. From this critical analysis, it is possible to confirm that fixator axial distances change the free clamp movement within the fixator rail and it is feasible that clearance could also have influence on this movement.
In addition, the contact pressure distributions predicted on the cell load, as shown in
Figure 11, confirms that loads passing to the callus depend not only on the number of pins placed on the bone segment, but also from the distance between the artificial callus and first pin. In fact, it was possible to verify that decreasing this distance, i.e., changing from BC to AB pin configuration, reduces the contact pressure, but also diminishes the in-plane rotation of pins, i.e., smaller rotational misalignment, leading to a smaller misalignment of the axes of nylon bars. Moreover, the von Mises stresses presented in
Table 6 show that the ABC pin configuration achieves a more homogeneous distribution of stress, which is an important factor to avoid pin site infection [
36].
Even though there are differences between the numerical and experimental models, namely concerning the clearance and the continuity of connections between the free clamp and Schanz screws, and of all components connected to the locked clamp, it is worth noting that both models confirm that the fixator configuration has a significant effect on the percentage of load passing to the callus. Moreover, disagreements between recent studies on whether mechanical stimulation is required during consolidation and remodelling healing stages [
37,
38] could also be related to differences between the external fixator configurations in the several studies. In fact, Claes et al. [
37] performed an elastic dynamization by decreasing the stiffness of the fixation and assuming that, within the dynamization weeks, the load bearing on the operated leg does not changed considerably. In this case, the load passing to the callus was higher, and thereby increased the interfragmentary movement. On the contrary, in the work of Tufekci et al. [
38] the dual unilateral fixation was maintained in all healing weeks and the dynamization was performed in the mobile fragment by a DC motor. The first main difference between these two studies is associated with the rate of change of movement in the fracture. In the first study this decrease was self-regulated by the fixation, weight bearing, and callus stiffness, while in the second study the load transmission across the bridged fracture was very limited and dynamization was controlled locally in the mobile fragment. This localized dynamization has a different impact in the remodelling process. Actually, the success of bone remodelling depends on adequate blood supply and on the gradual increase of mechanical stability [
39,
40], the localized modification of one condition has different effects than a global modification of both conditions. Moreover, in the physiological-like group [
38], the active fixator applied 1 mm axial compressive IFMs, commencing on the fifth post-operative day, and, after three weeks, the movements were decreased in 0.25 mm increments until week six, when the applied movements were stopped [
38]. This decrease of IFM does not seems related to the physiological loading on bone healing phases. If we accept that during the fracture healing process patients tend to increase weight bearing on the affected leg and that the bone callus tends to get stiffer, then it is expected that IFM should not decrease so fast [
35].
In fact, one of the limitations of this work is related to the difference in IFM between the cell load and that of bone fragments, i.e., the bone callus. The IFM of bone callus is not limited to the axial displacement, there are three other movements which include: transverse, angular, and axial rotation (torsional shear) [
18]. In addition, the natural weight-bearing loads include bending and shear (transverse and torsional). Actually, the natural loading is very complex and difficult to simulate. Moreover, it would require considerable resources to validate an experimental and/or numerical model that were able to predict important parameters. Nevertheless, because the generality of studies concerning the fracture healing process has been focus on the compression load [
28,
35,
38,
41,
42] and the main goal of this work was to investigate the viability of the LRS fixator in the dynamic compression mode on different configurations, we were interested in relative rather than absolute results. Another limitation of this work is associated with the use of a nylon bar instead of a realistic geometry of the tibia. Nowadays, there is a great number of published works wherein realistic CAD geometries of femur and tibia have been generated using the computed tomography (CT) imaging technique [
43,
44,
45,
46]. Despite the excellent quality of these results, they are subject-specific finite element studies and, because strain variability for cadaveric specimens is larger than 100% [
47], their use in test specimens concerning the external fixator configurations would require a sample of several hundred specimens. Moreover, as in any other FE model, reliable subject-specific numerical models need to ensure that modeling assumptions reflect the in vivo environment. Hence, considering the low availability of donors and the large variability of human anthropometry and material properties, it seems that synthetic bones could be an attractive alternative to this study [
22]. Nevertheless, it would be interesting to develop subject-specific image-based FE models for all healing phases and try to establish a relationship between the experimental and numerical displacements of the free clamp, in order to obtain comparative results that could contribute to the evaluation of the consolidation phase and help decide when the clamp can be unlocked. Yet, these results should not be used in a quantitative way, but to compare the patient outcome between two different moments of consolidation phase. In addition, this procedure can be used on other patients and avoid exposure to additional X-ray radiation for consolidation level information.
The findings of this work cannot be applied blindly to address issues concerning the external fixation of fractured tibia, for instance the sensitivity values of load share ratios to the distance between the external fixator body and the bone. In fact, this ratio is affected not only by the distance between mentioned axes but also by the nylon stiffness, and therefore different stiffness values in real bones are expected. Nevertheless, the trends identified in this work could remain valid on real bones.