Comminuted fractures associated with soft tissue injury and high contamination should be fixed immediately to minimize post-traumatic complications (18). In these cases, external fixators are used as temporary or definitive treatment (19, 20). The goal of this numerical study was to assess the biomechanical and mechano-biological distinction between the bi-cortical and mono-cortical groups of varying pin configurations to treat diaphyseal tibial fractures using unilateral-uniplanar external fixators.
This study shows that the BiC fixations are conducive to higher axial stiffnesses compared with the MoC designs (Fig. 1). It stands to reason the pins in BiC fixation are anchored at two cortices, and bone fragments are displaced less than the MoC group under the applied load. The finding for the relation between the anchored length of the pin and the construct stiffness is consistent with the current literature. Varady et al. (8) performed a clinical test on the porcine tibia fixed by an external fixator and came to the same conclusion. Ochman et al. (21) used locking and non-locking plates to treat metacarpal fractures in domestic pigs and showed that the axial stiffness provided by mono-cortical screws is lower than bi-cortical types. As well, the results observed by Bonner et al. (22) in treating the distal tibial extra-articular fracture were similar to those found here. Of note, the axial stiffness obtained for the MoC system was slightly smaller than the BiC, but both are in the same range (Fig. 1). This result correlates well with that seen in the in-vitro experiment by Mladenovic et al. (4), who found that external fixators mounted by uni-cortical and Schanz pins almost exhibit the same stability in the latero-lateral direction. Even though adding pins makes the construct stiffer, more than four pins did not substantially ameliorate the stiffness. Even though there is always a tendency to employ more pins to create a more stable construct, it should be kept in mind that increasing the number of pins elevates the risk of infection around the pin insertion area (8).
Figure 2 indicates that the mean Young's modulus of the tissue obtained throughout the callus increases by adding pins and enhancing the stiffness of the construct. This effect is rooted in the coherence between the construct stiffness and the pathway of bone healing applied by the mechano-regulation theory of this study (23). Meanwhile, since the difference between the axial stiffness of MoC and BiC groups emerged as negligible (Fig. 1), it was also expected that there would be a slight difference between the mean of Young's modulus within their differentiated tissues. The most noticeable difference was found between the fixators with 2 and 4 pins, which can be explained by the axial stiffness reported for these two models (see Fig. 1).
Fibrous tissue produced at the fracture gap in all models indicated that granulation tissue elements experienced high magnitudes of mechanical stimuli at the initial stage of healing (Fig. 3). This result agrees with the findings of other studies, which showed that mechanical stimulus is higher at the central callus, and fibrocartilage tissue is expected to emerge (23–25). In addition, Fig. 3 shows that for a similar number of pins, the distribution of Young's modulus throughout the callus tissue is accordant in both MoC and BiC cases, given the identical mechanical stiffness provided by both fixation systems.
Although the entire configuration is under an axial vertical load, stiffness mismatch between implant and bone induced bending moment in the fracture zone, while a neutral axis is located outside the bone, closer to a component with higher stiffness, i.e., external fixator. Because of this factor, far cortex callus elements at the far distance from the neutral axis are bent more and tended to be displaced higher than near cortex elements close to the neutral axis (Fig. 4). Based on the mechano-regulation algorithm of bone healing employed in this study, the difference in axial displacements leads to regions with higher and lower Young's modulus at near and far cortices, respectively (Fig. 3). The findings from this study correspond to those of Bottlang et al. (26), who conducted a histological evaluation of fracture healing with various locking plate constructs in a sheep tibia. They found that minimal gap motion at the near cortex suppresses fibro-cartilage callus formation.
According to a comparative evaluation of uniformity in different pin configurations illustrated in Table 1, at least four pins are required to achieve a uniform differentiation and even distribution of tissue phenotypes across the callus. Besides, it can be observed that changing the MoC to BiC fixation did not substantially improve the uniformity.
The present computational research incorporated some assumptions and limitations that should be kept in mind when interpreting the results. The models did not realize the threads of pins but instead assumed smooth surfaces tied to the bone tissue at pin-bone interfaces. Considering the fair corroboration that the FE model showed with the in-vitro experiment, this simplifying assumption was inappreciable. Therefore, it cannot be regarded as a significant source of error in this mechano-biological study. However, determining the local effects of pin threads on the stress distribution across the bone cortices awaits further studies. In addition, this study did not investigate pin loosening, one of the challenging problems that depend on the quality of pin-bone interaction. It is worth mentioning that the FE bone model was generated based on the CT images of a healthy adult tibia, which did not suffer from osteoporosis and bone disorders, thus exhibited a dense cortical thickness. Conversely, in patients with skeletal disorders, the risk of cortical bone thinning is escalated (27). Therefore, comparing the BiC and MoC fixations in the occurrence of pin loosening needs a deep consideration of the bone quality. Another parameter that can influence the analyses of this study was the simple transverse fracture geometry with perfectly flat surfaces and a gap size of 3 mm. A broader study that considers the fracture severity and complexity, e.g., oblique, butterfly, and comminuted fractures with irregular shapes and larger gap sizes, could increase the robustness of the FE models and the accuracy of the predicted healing. Moreover, simulations were just limited to the immediate phase of healing, in which the granulation tissue only presents at the fracture gap. Referring to the numerical study by Nourisa and Rouhi (28), we concluded that this limitation does not invalidate the overall reliability of the current results. They showed that the predicted tissue phenotype in the early bone healing stage correlates with the ultimate healing outcome. Nevertheless, it seems that extending the investigations to the entire healing process that could imply periosteal callus formation may likely yield a more rigorous comparison between BiC and MoC fixations.