The FE method has been proven to be useful for postoperative modeling of different orthopedic applications and has been used to evaluate different fixation methods for PAO [20, 27, 28]. Despite TPO being a mainstay of advanced surgical treatment of multiple conditions, FE analysis has, to our knowledge, not previously been applied to evaluate the stability of different implant constructs.
In this study, we present a FE analysis of how screw placements affect the stability of a standardized TPO. Model E, with the most entry points available, clearly had the best results from a stability point of view. Model C, with a distally placed screw, also showed high stability, but placing a screw from the acetabular fragment has drawbacks. Firstly, extraction of a screw (or pin) from this entry point can be challenging, secondly the antero-lateral corner superior to the acetabulum is small and can potentially break, and thirdly implants in this location may also interfere with hip abduction. In the other models with all screws placed from the superior fragment (A, B and D), the option to place the screws from more entry points (D) outperformed the models with less entry points available (A and B).
Adamczyk et al. used an in vitro model to compare the stability of bioabsorbable (PLLAFootnote 5) and metal screws after a TPO  in weight-bearing conditions. No significant difference was found at physiological loads, when comparing the two materials in both the standing and spica cast positions. This was likely, according to the authors, due to the inherent stability of the remaining intact pelvic ring, as compression of the osteotomy will cause bony contact that carry the load regardless of implant material. This result is in line with our findings for Z+ loading, where implant position had a limited effect on stability when compressing the osteotomy. Hence, it can be suspected that the osteotomy and graft position are more important than the strictly mechanical properties of the implant when studying a weight-bearing scenario. For loading directions where the implants are mainly subjected to bending forces, e.g., in the X- and Y-directions, the resulting stability will be a trade-off between strong material properties and optimal placement. Bioabsorbable screws enable a superior implant placement which should be considered along with other benefits, like not needing extraction and less risk of implant migration, when making a judgment for the best procedure. Our present findings show, in line with two basic orthopedic principles, that implants should be spread out in all dimensions over the osteotomy and that implant placements more perpendicular to an osteotomy improve stability. Both principles are easier to adhere to when more entry points are available. Bioabsorbable screws are not as strong as an equivalent metal screw, but the benefit of more placement options may, to a certain degree, compensate this limitation. A TPO can, however, also be performed on adults, and in these cases, extraction of metal screws may not be necessary and the benefit and indication of bioabsorbable implants thus decrease.
In the present study, we have not used physiological loads but rather focused on a generic prescribed displacement of 1 mm or 1 degree in a given direction. The displacements for different fixation methods are in the same order of magnitude as found by Yassir et al.  (< 2 mm displacement and < 3 deg rotation), supporting the load used in the present study.
A load analysis based on everyday motions or standing loads might have modified the results , but this was out of the scope of the study. Since the TPO is normally followed either by a hip spica, an orthosis or non-weight-bearing in a wheelchair, physiological loads in a standing position are of less relevance until bony healing has occurred (6–8 weeks postoperatively). The present study, therefore, focused on these, crucial, first weeks postoperatively rather than stability during a later stage.
A validation of the FE model by comparing the model predictions to a physical test was not feasible in the current study, since no physical experiment measuring stiffness in all DOFs exists in the literature. The only relevant study with a similar test setup, performed on cadaver specimens, is Yassir et al.  enabling a plausibility check of the model predictions in vertical loading (Z+ in the current study). In the study by Yassir et al., the authors report a 0.7 mm deformation for a screw configuration similar to present Model C, and a 1.2 mm deformation for a screw configuration similar to present Model A/B with vertical loading (Z+ in the current study), for an external load of 450 N (equivalent to 225 N per hip joint). The Z + stiffness in the current study ranged from 626 to 748 N/mm (see Additional file 1: Appendix) for Models A-C, corresponding to a 0.30–0.36 mm deformation. This is slightly smaller to the deformations measured by Yasser et al., but it should be pointed out that the FE model used in this study represents a “perfect” osteotomy, with all bony parts perfectly cut and aligned. This is not the case in reality, where any imperfections will result in larger deformation. In addition, Yasser et al. point out the risk of “increased osteotomy fragment motion secondary to screw loosening in the later trials,” regarding the repeated testing. In the light of this, the model predictions seem to be plausible, at least for vertical loading in the Z + direction.
In the present model, the influence of muscle forces and soft tissues was also discarded. Muscles and soft tissues can provide stability to the pelvis, while on the other hand, muscle forces can cause greater loading . Due to the partial immobilization of the patient following a triple pelvic osteotomy, the variation in loading from muscles forces is considered to be of less importance.
All displacements are not of equal clinical relevance, and a distracting force on the osteotomy is, for example, irrelevant. In clinical practice, it is widely known that the movements normally are associated with instability and a collapse of an osteotomy is firstly a “closing” of the osteotomy (mostly Z+ movement in our model) and/or a postero-medial dislocation of the distal fragment (X− in our model). A rotation around the X-axis affects the ante/retroversion of the acetabulum with both being undesirable but an increased retroversion even less so. A displacement in both X− and Y− negates the correction achieved and means that the distal fragment may lose the hinge of cortical bone in the infero-medial corner of the osteotomy.
Due to the complexity of the three-dimensional shape of the pelvis, the theoretically possible entry points and subsequent angles and lengths of an implant are innumerable and the modeling had to be restricted to study only a few clinically feasible solutions. Our study does not present reference values but intend to serve as a guide for surgical planning of TPO by outlining factors affecting stability and support. Moreover, our study was performed with a singular type of implant, corresponding to a 4.5-mm resorbable 85L/15G PLGA screw. Compared to commonly used 2-mm-steel K-wires, the 4.5-mm bioabsorbable screw has 60% less bending stiffness. Thus, for loading directions where the implants are mainly subjected to bending forces, e.g., in the X- and Y-directions, the joint overall flexibility should be comparable. For loading directions where the implants are mainly subjected to axial loads, (Z-), a 2-mm K-wire is almost 10 times stiffer than a 4.5-mm bioabsorbable screw, but this is of less clinical relevance. Also, lacking threads, the K-wire cannot fully utilize its axial stiffness, so the pull-out strength of a 4.5-mm bioabsorbable screw remains superior. Depending on the specific type of implant, the absolute magnitude of the results will vary to some extent, but the relative stability/flexibility between different implant configurations is expected to be consistent.
Although the study demonstrated the comparison of different fixation systems, the modeling had its limitations. Similar to other established finite element models of the pelvis , the implant screws were simplified as homogeneous with isotropic materials. Furthermore, a constant cortical thickness and homogeneous and isotropic material properties were assigned to the pelvis bone. This is a simplification compared to some other models in the literature that include a non-homogeneous distribution of trabecular bone properties [28, 32, 33]. However, since the aim of this study was to compare the biomechanical performance of different implant configurations in identical conditions, and not to study the stress–strain state of the bone or the contact stress of the osteotomy, this simplification was justified. This is further motivated by analyzing differences of relative flexibility, as a small error in structural stiffness would be treated equally for all configurations by the normalization of the results.
Using a similar motivation, we have not performed any mesh converges study. Since flexibility (or stiffness) relates to the displacement while stress/strain relates to the derivative of the displacement, structural flexibility will converge much faster than stress/strain. Therefore, mesh convergence studies are of greater importance for stress or strain analyses. A relevant example is presented in the ABAQUS (2016) user guideline, where even a very coarse mesh consisting of just 14 elements gives a stiffness prediction within 3% of the accurate result, while the stress at the critical area is not converged even using the finest mesh consisting of 1800 elements.
Moreover, the individual shape of the pelvis may vary greatly, affected by sex, age, and as shaped by the underlying condition necessitating surgery. The shape of the pelvis should not, however, greatly affect the relative stability between the screw configurations. Nevertheless, additional studies are warranted to evaluate the applicability of our findings in clinical practice. While virtual models cannot completely replace experimental testing, they provide a valuable tool that is rapidly evolving.