Adolescent idiopathic scoliosis (AIS) is the most commonly encountered pediatric musculoskeletal disease presenting a three-dimensional (3D) deformity of the spine. Standard measurement in scoliosis is the Cobb angle, which is the coronal plane angle measured between the vertebrae at the upper and lower bounds of the curve on a standing radiograph. Patients with severe (Cobb angle >40°–50°) or progressive curves may require surgery to correct the deformity.

An optimal surgical strategy is to provide maximal deformity correction while preserving spinal mobile segments to the best extent and obtaining a balanced posture. For instance, inadequate selection for instrumentation length may lead to a postoperative postural imbalance. In addition, although surgical technique as well as spinal instrumentation has been developed in which the 3D correction is achieved, there is still a possibility of implant-related complications such as pedicle screw loosening, screw or spinal rod breakage, and pedicle fracture. Load levels of the screws and rods are important concerns in surgical outcomes. Furthermore, although a rod shape considerably affects postoperative spinal alignment (Salmingo et al., 2014; Kokabu et al., 2016; Sudo et al., 2016; Le Navéaux, et al., 2017), the rod-bending maneuver relies excessively on surgeons’ experience. If the rod curvature does not match the patient’s deformity and does not allow for deformity correction, such situations will lead to an inadequate correction or implant-related complications due to the overstress on the implant and spine (Sudo et al., 2018). These issues require some innovative systems to assist surgery or predict the most probable outcome of surgery (Aubin et al., 2008; Sudo et al., 2021).

The typical thoracic AIS presents itself with thoracic hypokyphosis. Therefore, the surgical goal should be a correction of the thoracic kyphosis (TK) and achieves an anatomically correct thoracic curve. Post-surgery hypokyphosis can occur after using pedicle screw instrumentation. Several posterior surgical techniques have been developed to maintain and/or improve the TK (Clement et al., 2008; Sudo et al., 2014). However, next-generation surgical techniques are required in order to achieve true anatomical correction. In a healthy human population, the apex of the TK is typically located at T6–T8, when viewing standing sagittal films (Hasegawa et al., 2017). However, for some AIS, the postoperative apex of the TK is almost identical with the apex of the preoperative thoracic scoliosis (Sudo et al., 2018), which is not anatomically correct. This insufficient correction resulting in a postoperative non-anatomical TK is thought to be, because the spinal rods are being bent to match the curvature of scoliosis. From the standpoint of spatiotemporal deformity correction, we recently showed that anatomical four-dimensional (4D) spinal correction could be accomplished by curving the rod (Figure 1) (Sudo et al., 2018; Sudo et al., 2021). In the surgical procedure, two rods are bent in a nearly identical fashion to confirm spinal anatomical alignment without reference to the intraoperative alignment of the deformity (Sudo et al., 2018; Sudo et al., 2021). Consequently, pre-bent rod geometries were obtained from intraoperative tracings of the rod shapes, and optimized rod shapes were derived using iterative closest point method followed by hierarchical cluster analysis (Kokabu et al., 2018). Currently, 11 types of pre-bent cobalt-chrome (CoCr) alloy rods are available based on the deformity types and its lengths in Japan that can guide anatomical spinal correction regardless of the surgeons’ experience (Figure 1, Sudo et al., 2021).

In addition to providing the best spinal instrumentation configurations as pre-bent rods, prediction of surgical outcome along with its biomechanical impact can be obtained by simulation of the surgical procedures with computer modeling (Aubin et al., 2008). However, an objective model that can simulate the 3D outcome of the AIS surgery by considering the preoperative spinal alignment and the surgical intervention has not been completely elucidated (Pasha and Flynn, 2018). In addition, most planning tools in AIS surgery only simulate morphology-based changes of the spinal alignment, lacking the biomechanical analysis (Ferrero et al., 2008; Pasha and Flynn, 2018; Shao et al., 2018). A planning simulator based on spatiotemporal morphological postoperative 4D changes with a patient-specific finite element analysis (FEA) can allow surgeons to predict postoperative outcomes and effectively assist in performing AIS surgery (Galbusera et al., 2015; Wang et al., 2016; Le Navéaux et al., 2016; Cobetto et al., 2020; La Barbera et al., 2021; Galbusera et al., 2021).

The hypothesis of the present study was that our newly developed 4D planning simulation system incorporating pre-bent rods would significantly correlate with the actual postoperative spinal alignment after anatomical 4D spinal correction surgery. The current study aimed to compare simulated and actual deformity corrections in patients with AIS.

Our personalized finite element spinal biomechanical model and its simulated response to surgical instrumentation allowed to evaluate the effect of the 4D anatomical correction technique on AIS deformity correction and on loads in the instrumentation. Not only geometric aspects of the deformity correction but also biomechanical results were simulated using existing pre- and postoperative information of 47 patients and 11 types of pre-bent rods. Despite the heterogeneity in the cohort of patients with various Lenke types, this study analyzed a cohort of patient-specific surgery models and found that our newly developed 4D planning simulation system incorporating pre-bent rods showed a significant correlation with the actual postoperative spinal alignment after anatomical 4D spinal correction surgery. The simulated measurements were all within 5° agreement with the clinical values, equivalent to the generally accepted clinical error of 5° (Majdouline et al., 2009).

The present study demonstrated the feasibility of our simulation system and the ability to simulate the surgical procedure using the pre-bent rods. The preoperative assumption for rod shape and length will help reduce operative time, thereby decreasing blood loss and risk of infection. However, in this model, the values of intervertebral stiffness matrix components were same through thoracic to lumbar spines and not personalized. We consider this as a main factor that may justify imperfect correlations of the slope and intercept. It may be important to consider the personal stiffness matrix for improving the capability of the model in predicting the perfect values. Other factors affecting the correlations could be that boundary conditions applied during simulation were not the same as during the actual surgery for each patient, and there was an issue that clinical measurements of the parameters of interest were not perfect. In addition, we cannot provide a quantitative justification regarding the prediction accuracy because no steps were used to ensure the credibility of our model in predicting the right values. Although computational models are increasingly used to support surgical planning, varying levels of model verification and validation limit the level of confidence in their predictive potential (Poncelas et al., 2021). Recently, Poncelas et al. performed a credibility assessment of their model to investigate proximal junctional failure in clinical cases with adult spine deformity using ASMEV&V40 standard (Poncelas et al., 2021). We should also assess the credibility of our model for AIS surgery using the recommended strategies in the future.

In the present study, the surgical simulations were conducted using the DICOM CT scans in a supine position and approximated with the surgical procedures performed on patients lying prone. In addition, the postoperative corrected angles were measured clinically using the DICOM CT data in a supine position. Consequently, supine CT scans were obtained after surgery, while the patient was still recovering; therefore, it was not yet load-bearing, and provided a better comparison between the clinical and simulated measurements (Little et al., 2013). The difference between the present simulation model and reality was small in the instrumented segments. Conversely, there is a possibility that the results for the uninstrumented regions are not accurate because the gravity and postural control were not simulated in the standing posture (Robitaille et al., 2009). Due to the aforementioned reasons, we performed comparisons using standing radiographs. Consequently, while there were significant differences in preoperative measurement values between standing radiographs and simulation model, there were no significant differences in postoperative measurement values between the standing radiographs and simulation model, indicating that the simulation model can predict postoperative spinal alignment in standing position including uninstrumented lumbar segments in the case with selective thoracic instrumentation for Lenke 1 A curves.

There have been computational studies that similarly predicted 3D correction and implant loads (Wang et al., 2016; Le Navéaux et al., 2016; La Barbera et al., 2021; Galbusera et al., 2021). These studies determined how several instrumentation parameters such as screw density and rod contouring angle affected correction and stress in the instrumentation. Because our previous studies have shown that multilevel facetectomy and screw density on the concave side significantly impact the amount of scoliosis correction and also TK restoration, especially in preoperative hypokyphotic (TK <15°) thoracic spine (Kokabu et al., 2016; Sudo et al., 2016), we currently attempt on inserting the screw as much as possible on the concave side. Also, rod curvatures were limited to up to 11 types. We have analyzed the correlation between preoperative rod angle and rod stress in the apex of the MT curve or TL/L curve. In addition, the correlation between postoperative TK in the simulation model and screw density on the concave side or preoperative rod angle in patients with hypothoracic (TK <15°) Lenke one curves was analyzed. The results showed that there were no significant correlations between the simulated correction and rod stress and instrumentation parameters (Supplementary figures S1, S2). Therefore, we could not confirm that clinical observation reported by Sudo et al. (2016) and Kokabu et al. (2016) was confirmed by the present biomechanical models. Because there was no range of numbers for the screw density and rod curvature, as well as sufficient quantity of sample numbers, there may be limitations in statistical analysis.

However, because both pre- and postoperative rod measurements were available in the current study, it was possible to utilize the initial rod shape and simulate its elastic deformation precisely. In this simulation model, the maximum power delivered to the rod was 1,000 N. We previously documented that the notch-free, pre-bent CoCr alloy rod (φ5.5 mm) showed an approximated linear loaddisplacement curve under 1000 N of load (Yamada et al., 2020). Due to these reasons, we opine that almost only elastic deformation occurred. However, elastoplastic phenomena involved in rod contouring may be considered in future studies to better elucidate whether both elastic and plastic deformation may be involved in vivo to explain any change in rod shape in vivo. Although it has been demonstrated that the amount of curvature incorporated into the rods before their insertion impacts TK restoration (Salmingo et al., 2014; Kokabu et al., 2016; Sudo et al., 2016; Le Navéaux, et al., 2017), there are a few studies that have estimated the loads in the rod during and after deformity collection (Galbusera et al., 2015). To our knowledge, this is the first study to show that the simulation model can predict the deformation of the implanted rod. The simulation model determined significant changes in the rod contours, especially on the concave side which has been clinically reported (Sudo et al., 2021). In addition, based on the changes in rod geometry and FEA, the highest stress was found at the apex of the rod curvature and the extremities of the instrumented levels, which is in agreement with previous results (Belmont et al., 2001; Aubin et al., 2008; Abe et al., 2015). Qualitative understanding of the stress in the rods is useful to estimate the risk of implant failure and loosening intraoperatively and/or postoperatively, which currently depends on the surgeon’s experience (Galbusera et al., 2015).

Further understanding of bonescrew forces in AIS instrumentation is essential as high-stresses at the bonescrew interface can cause screw loosening or breakage. Shear forces on the screws are more relevant to be reported rather than only pull-out values. In addition, because we did not observe intraoperative complications such as screw pull-out and bending, we could not analyze the predicted forces in cases with complications. However, in this study, the forces generated at the bonescrew interface (peak 497 N) were lower than the thoracic pedicle screws pull-out forces of approximately 800 N reported in experimental studies (Liljenqvist et al., 2001). The present study validated only the geometrical aspects, and more investigations are needed to validate the model in terms of forces at the bonescrew interfaces. However, the implants tested by Liljenquist et al. were monoaxial pedicle screws which were different from the screws in the current study (poly-axial screws). Bonescrew forces were higher for monoaxial screws than polyaxial screws, indicating that in patients with large and stiff spinal deformities or in patients with compromised bone quality, screws with more degrees of freedom would offer better perspective to reduce bonescrew connection failure (Wang et al., 2012). Although the thresholds may serve as a comparison in the present study, therefore, those simulated cases exceeding the threshold may not be considered necessarily unsafe, it is likely that the anatomical correction technique may be used safely.

Our study has some limitations. First, we applied boundary conditions only to the pelvis and did not include the cervical spine, ribs, and scapulae. Although this simplification of the real spine represents a condition wherein the vertebral levels are not entirely fixed, including the cervical vertebrae could demonstrate a more naturalistic behavior of the uninstrumented spinal segment (Majdouline et al., 2012). Second, we only simulated one diameter although the screw diameter is known to have the highest effect on the force to failure compared to screw length (Cho et al., 2010; Bianco et al., 2019). Since this was a first phase study to simulate the surgical procedure, the simulation was maintained as simple as possible. Additionally, model validation was purely based on the final rod geometry and the main spinal curves. However, to ensure that the simulation model can predict postoperative alignment, a more detailed validation on single vertebra position and rotation, together with individualized screw’s models and trajectories, would be needed. Third, this study did not analyze other forces and moments such as medio-lateral forces and screw bending moments. The other loading components may play a role in other clinically relevant failure modes and may be addressed in the future. Finally, in this surgical simulation, preoperative curve flexibility was not considered, and distractioncompression force was not applied on each screw head. Nonetheless, the simulation model can predict postoperative surgical alignments. However, we are currently improving the model to incorporate both preoperative curve flexibility based on bending radiographs and distractioncompression procedures, as well as actual screw length and diameter. There may be a limit to improve the comparison between model prediction and actual postoperative correction; however, the incorporation may further improve the estimation of rod stress and screw force because this information will contribute to set stiffness matrix components and connections between the geometries.

Our newly developed 4D planning simulation system incorporating pre-bent rods showed a significant correlation with the actual postoperative spinal alignment after anatomical 4D spinal correction surgery. The present study demonstrated the feasibility of our simulation system and the ability to simulate the surgical procedure using pre-bent rods. The FEA results in the simulation system measured for each individual patient would also provide a more realistic representation of the surgical procedures.