Regional mechanical matching dictates vertebral rotation improvement in severe rigid idiopathic scoliosis with halo-pelvic traction: a finite element analysis

Abstract

Purpose

Halo-pelvic traction (HPT) safely improves spinal deformities by applying continuous, controlled axial traction between the skull and pelvis, creating favorable conditions for subsequent surgery. The regional mechanical relationship between spinal stress and improvement of vertebral axial rotation in severe rigid idiopathic scoliosis with HPT was clarified in this study.

Methods

A finite element (FE) model of C3–S1 spine was constructed to simulate three displacement conditions of HPT (5 cm, 10 cm, 15 cm). The regional mechanical relationship between spinal stress and the improvement of vertebral rotation was clarified.

Results

Vertebral body rotation improvement ratio, cortical/cancellous stress ratio, bilateral facet joint cartilage stress ratio were highly constant under traction displacement of 5 cm, 10 cm and 15 cm. The junctional area (T4–T5) achieves the most efficient vertebral body axial rotation improvement with moderate cortical/cancellous stress relief, high disc stress drive, and extreme asymmetry between left and right joints. The main thoracic curve apex T9 has a high cortical/cancellous ratio due to extremely low cancellous bone stress, a decrease in disc stress, and high bilateral facet joint stress, and a very low rotation improvement. Cortical overload was observed at T7 adjacent to the main thoracic curve, but there was still significant rotation improvement. Cortical/cancellous coordination was observed at upper thoracic curve apex T2, and axial rotation was significantly improved. Cortical/cancellous simultaneous unloading was observed at lumbar curve apex L2, and axial rotation was extremely low.

Conclusions

Vertebral body axial rotation improvement in severe rigid idiopathic scoliosis with HPT was dominated by regional mechanical matching.

Introduction

Severe rigid idiopathic scoliosis (Cobb angle > 90°) is one of the most challenging conditions in spinal surgery. This deformity is not only characterized by severe coronal imbalance, but also by significant vertebral rotation, sagittal alignment imbalance, and spinal stiffness. Direct posterior corrective surgery has a high risk of nerve damage, a high rate of internal fixation failure, and many postoperative complications [1, 2]. One-stage halo-pelvic traction (HPT) combined with second-stage posterior fusion has become the standard staging strategy for the treatment of this deformity. Through slow, continuous, controlled axial distraction, HPT can effectively release soft tissue, partially correct deformity, improve cardiopulmonary function, and reduce terminal surgical risk [3–5].

However, the potential for regional correction of HPT cannot be accurately predicted preoperatively. Previous study only focused on the overall Cobb angle change and failed to reveal region-specific mechanical response [6]. Finite element (FE) analysis further revealed that the application of corrective force not only changed Cobb angle, but also significantly affected the axial rotation of vertebral body, and the magnitude of corrective force was not simply linearly related to Cobb angle, emphasizing the complexity of rotational correction [7, 8]. Vertebral body rotation is a core component of spinal three-dimensional kinematics and biomechanics, especially in the assessment of scoliosis, degenerative diseases, and postoperative stability [9]. Finite element analysis is a powerful computational tool capable of simulating the stress, strain and range of motion of spinal structures under complex loads, providing a unique perspective for in-depth understanding of the mechanisms of vertebral body rotation and its clinical effects [10, 11].

In recent years, domestic and foreign scholars have applied finite element method to explore the biomechanical mechanism of scoliosis. Yahara et al. found by finite element analysis that the concave facet joint of idiopathic scoliosis withstands more than 91% of the load transmission, resulting in subchondral osteosclerosis and joint hyperplasia [12]. A recent study by Raftery et al. demonstrated that disc degeneration can lead to higher strains in the anterior region adjacent to cancellous bone, and the stress distribution is significantly shifted anteriorly [13].

The relationship between the vertebral cortical bone stress, cancellous bone stress, intervertebral disc stress, bilateral articular cartilage stress and the improvement of vertebral rotation angle is still unclear. Our team found a regular phenomenon in the early clinical observation: the vertebral rotation at the junction of the upper thoracic curve and the main thoracic curve improved most significantly during HPT, while the improvement at the apex of the main thoracic curve was extremely limited. However, the biomechanics mechanism behind it is still unclear. How does traction force redistribute in various regions of the spine? What is the spatial distribution law of stress in vertebral cortical bone and cancellous bone, intervertebral disc and bilateral facet joint cartilage?

The aim of this study is to construct an individualized finite element model of the whole spine with severe rigid idiopathic scoliosis (Cobb angle 165°of main thoracic curve), simulate three displacement conditions of cephalopelvic ring traction of 5 cm, 10 cm and 15 cm, systematically extract the improved angle of T1-L5 full-segment vertebral rotation, vertebral cortical bone stress, vertebral cancellous bone stress, intervertebral disc stress and bilateral facet joint cartilage stress, and reveal the spatial distribution and displacement evolution law of the above indexes.

Materials and methods

Establishment of the severe rigid idiopathic scoliosis FE model

The data were obtained from a 30-year-old adult with severe rigid idiopathic scoliosis (Cobb angle 165°). The computed tomography (CT) images of the whole lumbar spine were imported into Mimics 21.0 in Dicom format. After processing, a three-dimensional spinal model (C3–S1) was established. After smoothing and other processing, STL format was exported. In GeomagicStudio2014, reduce nails, remove surface features, fast-smooth and other operations, trace contours in precise surfaces, construct surface patches, construct grids, generate fitting surfaces, and then convert spine models to STP format, where cortical bone thickness is 1.5 mm. In SOLIDWORKS 2024, cone assembly is performed, and lumbar intervertebral discs, endplates, facet joints and other structures are created according to the surface contours of adjacent vertebral bodies, in which the nucleus pulposus accounts for about 50% of the disc volume. After the assembled assembly passes interference inspection, import the model into ANSYS, set material properties, boundary conditions, contact, analysis steps, load steps and other operations, add ligaments, and finally mesh, all structural meshes share nodes (Fig. 1).

Fig. 1.

Modeling process of severe rigid idiopathic scoliosis

Material properties and FE modeling

In this study, cortical bone, cancellous bone, facet cartilage and endplate are isotropic uniform linear elastic materials, while annulus fibrosus and nucleus pulposus are hyperelastic materials. Anterior longitudinal ligament, posterior longitudinal ligament, flaval ligament, intertransverse ligament, interspinous ligament and supraspinous ligament are all replaced by spring connection method. All ligaments in this study were modeled using tension-only spring elements. Material parameters of each tissue are taken from literature [14–18]. Specific material parameters and unit types were seen in Table 1.

Table 1.

Specific material parameters and unit types

Spinal tissue	Young’s modulus (MPa)	Poisson ratio	Stiffness (N/mm)
Facet joint articular cartilage	50	0.30
Endplate	25	0.25
Cortical bone	12,000	0.30
Cancellous bone	100	0.30
Annulus fibrosus	Hyperelastic material(Mooney-Rivlin) C1 = 0.56, C2 = 0.14
Disc nucleus	Hyperelastic material(Mooney-Rivlin) C1 = 0.12, C2 = 0.09
Flaval ligament			15.38
Anterior longitudinal ligament			8.74
Posterior longitudinal ligament			5.83
Intertransverse ligament			0.19
Interspinous ligament			10.85
Suspraspinous ligament			2.39

Mesh convergence tests were performed on a finite element model of the spine. Articular cartilage was meshed with a cell size of 0.5 mm, and the rest of the model was meshed with cell size of 1.5, 2, and 2.5 mm. The inferior surface of the sacrum was constrained in all directions and tested with a vertical downward force of 5N on the C3 surface. Maximum von Mises stresses in different tissues in the finite element model were calculated and compared. The mesh was considered convergent when the predicted results of the two mesh schemes compared differed by less than 5%.

Validation of the FE model

The constructed spinal finite element model was overlapped and compared with the original spine full-length X-ray and CT data of the patient before traction, and the similarity of the model was verified based on the coincidence degree of the two angles. Clinically, the patient increased about 17 cm after the final traction, so the model endowed with material attributes was compared with the simulated 17 cm traction condition X-ray of the patient after the final traction after mesh convergence analysis.

In order to ensure the validity of this finite element model, based on the established model, select part of vertebral body for verification. Select L1-L5 segment model, limit the lower surface of L5 to all degrees of freedom, apply a vertical downward force of 300N on the upper surface of L1 vertebral body, and apply a moment of 10N·m along the axial, sagittal and coronal planes to simulate the six movements of lumbar flexion, extension, left and right lateral flexion and left and right rotation [19, 20]. The mobility of L1 relative to L5 under different working conditions is calculated by ANSYS (Fig. 2), and the loading results are compared with the experimental results of literature research to verify the validity of the vertebral body model.

Fig. 2.

Verification of lumbar spine model mobility during forward flexion (a) extension (b) concave lateral bending (c) convex laateral bending (d) left ratation (e) and right rotation (f)

Loading and boundary conditions of the FE model

The finite element model of spine established in this study adopts two kinds of contact relations: one is binding, that is, there is no relative sliding displacement between the two parts of binding under force, and binding constraints are defined between the vertebral body segmentation part and the intervertebral disc; the other is frictional contact, and relative displacement can occur between the two sides. Due to the existence of synovial fluid, the friction coefficient between the facet joint surfaces of upper and lower vertebral bodies is determined to be 0.01 [19, 21]. Three severe scoliosis models with different traction displacement conditions were set up in this paper. The working displacement applied to the upper surface of C3 was 50 mm, 100 mm and 150 mm respectively to simulate the traction process of the cephalopelvic ring of the patient. The boundary conditions of all models were to restrict all degrees of freedom of the lower surface of the sacrum, and the displacement along the positive Z axis was applied to the upper surface of C3 (Fig. 3).

Fig. 3.

Stress nephogram of spine under three displacement conditions of 5 cm (a),10 cm (b) and 15 cm (c)

Biomechanical analysis using the established model

Von Mises stress is an equivalent stress used to assess whether ductile materials yield, a scalar value that converts complex multiaxial stress states into uniaxial tensile stress. Therefore, von Mises stress was used as the main evaluation standard to observe the stress changes of T1–L5 vertebral cortical bone, T1–L5 vertebral cancellous bone, T1/2–L5/S1 intervertebral disc and bilateral facet joint cartilage under different working conditions, and to analyze the stress and change trend of vertebral cortical bone, vertebral cancellous bone, intervertebral disc and bilateral facet joint cartilage. The stability of the ratio was assessed using the coefficient of variation (CV). A fixed global coordinate system is established in ANSYS software, which does not change with the deformation of the model. The directions of coordinate axes are defined as follows: Z axis points to the cephalad side, Y axis points to the front of the spine, and X axis points to the right side of the patient. The axial rotation of the vertebral body is defined as the rotation angle around the Y axis. Measure the change value of the axial rotation angle of 17 vertebral bodies in T1-L5 under three working conditions relative to the state before traction (Fig. 4). Negative values indicate de-rotation, and for ease of presentation, this study is presented as absolute values.

Fig. 4.

Improvement of vertebral body axial rotation of main thoracic curve apical region and junction region at 15 cm displacement

Results

Mesh convergence effectiveness analysis

Scheme 1 has 2,278,045 cells and 3,607,682 nodes, Scheme 2 has 1,120,772 cells and 1,872,348 nodes, Scheme 3 has 706,045 cells and 1,228,031 nodes. The table shows the percentage difference of vonMises stress between scheme 1 and scheme 2 and scheme 3 respectively. The difference of vonMises stress between scheme 1 and scheme 2 is less than 5%. Therefore, scheme 2 is considered as mesh convergence. Considering the complexity of calculation in this study, the second mesh generation scheme can not only ensure the reliability of simulation results, but also reduce calculation time and improve efficiency (Table 2).

Table 2.

Comparison of three mesh division schemes

Meshing scheme	Scheme 1	Scheme 2	Scheme 3
Size(mm)	1.5	2	2.5
Cell count	2,278,045	1,120,772	706,045
Number of nodes	3,607,682	1,872,348	1,228,031
Maximum stress of cortical bone(MPa)	13.9850	14.2200	14.105
Change rate relative to scheme 1 ( %)	–	1.68	0.86
Maximum stress in cancellous bone(MPa)	7.0553	7.3320	6.5010
Change rate relative to scheme 1 ( %)	–	3.92	7.86
Maximum stress in endplates(MPa)	3.7936	3.8378	3.8059
Change rate relative to scheme 1 ( %)	–	1.17	0.32
Maximum stress in disc nucleus(MPa)	0.1472	0.1410	0.1485
Change rate relative to scheme 1 ( %)	–	4.40	0.88
Maximum stress in facet joint articular cartilage(MPa)	8.3550	8.6048	8.7047
Change rate relative to scheme 1 ( %)	–	2.99	4.19
Maximum stress in annulus fibrosus(MPa)	1.9019	1.9180	1.9696
Change rate relative to scheme 1 ( %)	–	0.85	3.56
Time(min)	43	26	21

Model validation

The finite element model of severe scoliosis was compared with the X-ray and CT data images of the whole spine before traction (Cobb angle error < 1°), and the finite element model under the working condition displacement of 17 cm was compared with the X-ray of the whole spine after final traction (Cobb angle correction error < 1%). It can be seen that both of them have good consistency (Fig. 5).

Fig. 5.

Validation of FE model of severe rigid idiopathic scoliosis before and after HPT. a–b The FE model of severe scoliosis was compared with the X-ray and CT data images of the whole spine before traction. c the FE model under the working condition displacement of 17 cm was compared with the X-ray of the whole spine after final traction. FE, finite element; CT, computed tomography

The lumbar spine model was extracted separately to verify the range of motion of L1-L5 vertebrae. The simulation results were compared with the experimental results of previous study [19]. Under different working conditions, the lumbar range of motion (ROM) of the model in flexion, extension, rotation and lateral bending is consistent with the experimental result(Fig. 6).

Fig. 6.

Comparison of lumbar ROM between this model and previous lumbar spine models. ROM, range of motion

Stress distribution in cortical and cancellous bone of vertebral body

Figures 7 and 8 showed that the stress distribution of vertebral cortical bone was stable and bimodal under three kinds of traction displacement. T2 of the upper thoracic curve apex was 3.38 MPa at 15 cm, T3 reached 4.19 MPa, forming the first peak. T4 stress decreased significantly from the junction region, only 2.51 MPa at 15 cm, which was significantly lower than that of adjacent segments. Main thoracic curve region stress from T5 gradually increased until T7 in the vicinity of the main thoracic curve reached the peak value of the whole spine, then decreased. T9 of the main thoracic apex was 3.71 MPa, and the stress in the lumbar region decreased sharply. L2 of the lumbar apex was only 0.93 MPa at 15 cm, which was lower than 1.3 MPa in all lines. With the increase of traction displacement, the cortical bone stress increased nonlinearly. The stress increased most rapidly at T4 and T5, with the ratio of 15 cm/5 cm reaching 2.95 and 3.06 respectively.

Fig. 7.

Stress nephogram of T1-L5 vertebral body under three displacement conditions of 5 cm,10 cm and 15 cm

Fig. 8.

Stress changes of cortical bone a and cancellous bone b of T1-L5 vertebral body under three displacement conditions of 5 cm, 10 cm and 15 cm

The stress distribution in cancellous bone was different from that in cortical bone. The stress distribution in cancellous bone was unimodal. The stress in upper thoracic curve was the highest, T2 was 1.59 MPa at 15 cm, which was the peak value of the whole spine. The stress in junction area T4 was 1.33 MPa, which was still at a high level. After entering the main thoracic curve area from T5, the stress in cancellous bone decreased sharply, T5 was only 0.86 MPa. T6–T11 maintained 0.33–0.49 MPa, and T9 was 0.49 MPa. The stress in T12–L5 was low continuously, L2 was 0.49 MPa, and the stress in other segments was 0.27–0.45 MPa. With the increase of traction displacement, the stress in cancellous bone also increased nonlinearly, and the stress in T4 and T5 increased most rapidly in junction region (15 cm/5 cm ratio was 2.96 and 3.07 respectively).

Cortical/cancellous stress ratio was highly stable at three displacements: T2 ratio was 2.13, 2.13 and 2.13 respectively (CV 0.1%), T4 was 1.89, 1.89, 1.89 respectively (CV 0.1%), T5 was 3.86, 3.88 and 3.85 respectively (CV 0.4%), T7 was 11.32, 11.40, 11.39 respectively (CV 0.4%), T9 was 7.59, 7.58, 7.57 respectively (CV 0.1%), and L2 was 1.90, 1.88, 1.90 respectively (CV 0.6%).

Intervertebral disc stress

Figures 9 and 10 showed that The disc stress distribution along the spine showed two peaks. The disc stress at T3/4 was the highest at the upper thoracic curve, reaching 1.20 MPa at 15 cm. The disc stress of T4/5 was 1.54 MPa, and that of T5/6 was 1.65 MPa. The disc stress at T6/7 adjacent to the main thoracic curve reached the peak value of the whole spine (1.70 MPa), T7/8 disc stress was 1.43 MPa, T8/9 disc stress decreased significantly to 1.20 MPa, T9/10 disc stress decreased rapidly. Lumbar curve disc stress was lower than 0.25 MPa, showing a resting state. With the increase of traction displacement, the intervertebral disc stress increased nonlinearly.

Fig. 9.

Stress nephogram of T1/2-L5/S1 intervertebral disc under three displacement conditions of 5 cm,10 cm and 15 cm

Fig. 10.

Stress changes of T1/2-L5/S1 intervertebral disc under three displacement conditions of 5 cm, 10 cm and 15 cm

Articular cartilage stress in facet joints

Figures 11 and 12 showed that the stress distribution of articular cartilage of left facet joint was bimodal, the main peak was located at T9/10 (20.94 MPa at 15 cm) in the top of main thoracic curve, the second peak was located at T3/4 (14.55 MPa) in the upper thoracic curve, and the stress decreased significantly (8.48 MPa) at T4/5 in the junction region.

Fig. 11.

Stress nephogram of articular cartilage of left a and right b facet joints under three displacement conditions of 5 cm,10 cm and 15 cm

Fig. 12.

Stress changes of T1/2-L5/S1 articular cartilage of left a and right b facet joints under three displacement conditions of 5 cm, 10 cm and 15 cm

The main stress peaks of articular cartilage of right facet joint were located at T7/8 and T8/9 (21.93 MPa and 21.92 MPa at 15 cm) adjacent to the main thoracic curve, and the secondary stress peaks were located at T4/5 (19.98 MPa) and T10/11 (18.70 MPa) transitional zone.

The ratio of left to right stress (L/R) was highly stable at 5 cm, 10 cm and 15 cm. T4/5 ratio was 0.46, 0.47 and 0.42 respectively. T8/9 ratio of the main thoracic apex was 0.80, 0.78 and 0.77 respectively (CV 1.9%). T9/10 ratio of the main thoracic apex was 1.28, 1.33, 1.38 respectively (CV 3.8%). T4/5 ratio showed extreme asymmetry (left unloading, right loading), T8/9 and T9/10 ratio showed bilateral high pressure.

Axial rotation angle of vertebral body

Figures 13 and 14 indicated that vertebral rotation improvement showed a unimodal distribution, with the peak located at T5 (27.5° at 15 cm), T2 improved 21.3° at 15 cm displacement, T4 improved 24.5°, T7 improved 20.2°, T9 decreased sharply to 6.0°, L2 improved 5.5°, T10 was the lowest point of total spinal rotation improvement (0.44°).

Fig. 13.

Stress nephogram of T1-L5 vertebral rotation under three displacement conditions of 5 cm,10 cm and 15 cm

Fig. 14.

Vertebral axial rotation changes of T1-L5 under three displacement conditions of 5 cm, 10 cm and 15 cm

The improvement ratio of critical area was highly constant at 5 cm, 10 cm and 15 cm, T2/T5 ratio was 0.72, 0.73 and 0.77 respectively. T4/T5 ratio was 0.88, 0.90 and 0.89 respectively. T7/T5 ratio was 0.71, 0.71 and 0.73 respectively (CV 1.6%), T9/T5 ratio was 0.20, 0.20, 0.22 respectively (CV 5.6%), L2/T5 ratio was 0.19, 0.19, 0.20 respectively (CV 3.0%).

Relationship between axial rotation angle and spinal stress change

Figure 15 showed that the vertebral rotation in the junctional region (T4–T5) was improved by 24.5–27.5° under 15 cm traction displacement, which was the highest in the whole spine (2.51–3.31 MPa). Facet joints showed extreme asymmetry, forming “left sliding, right fulcrum” guiding mechanism.

Fig. 15.

Relationship between vertebral axial rotation angle and spinal stress change under three displacement conditions of 5 cm (a) 10 cm (b) and 15 cm (c)

At 15 cm traction displacement, the rotation of the apical region of the main thoracic curve (T9) improved only 6.0°. The cortical stress in this region was moderate (3.71 MPa), the cancellous bone was disabled (0.49 MPa), the cortical/cancellous ratio was as high as 7.57, the disc stress in T8/9 was 1.20 MPa. Bilateral facet joint locking: 21.92 MPa on the right side of T8/9, 20.94 MPa on the left side of T9/10 (L/R≈0.8–1.4). The rotation of T7 was improved by 20.2°, it was still at a high level. Cortical bone stress peaked at 5.58 MPa, cancellous bone was seriously unloaded at 0.49 MPa, and cortical/cancellous ratio was as high as 11.39, indicating critical overload of structure. The peak stress of T6/7 disc was 1.70 MPa. The right facet joint was locked at 21.93 MPa, and the left facet joint was compressed at 16.22 MPa (L/R = 0.74). The rotation of that upper thoracic curve apex (T2) was improve by 21. 3° under the traction displacement of 15 cm, the stress of cortical bone was 3. 38 MPa, and the stress of cancellous bone was the highest in the whole spine. L2 rotation improved only 5.5° under 15 cm traction displacement, cortical bone 0.93 MPa, cancellous bone 0.49 MPa, cortical/cancellous ratio 1.90, intervertebral disc rest (0.20 MPa), left facet joint 0.88 MPa, right facet joint 5.09 MPa (L/R = 0.16), showing passive compensation mode.

Discussion

In this study, a FE model of severe rigid idiopathic scoliosis (Cobb angle 165°) was successfully constructed. The model data covered 17 vertebral bodies (T1-L5), 17 intervertebral discs (T1/2–L5/S1), and 17 pairs of articular cartilage (T1/2–L5/S1). It is one of the most complete FE models reported so far. In previous studies, simplified modeling was often used, which could not reflect the mechanical effects of the whole spine. In the aspect of material attribute assignment, this study abandoned the traditional linear elasticity and systematically adopted Mooney-Rivlin hyperelastic constitutive model of intervertebral disc based on literature experimental data for the first time in the study of HPT, which lays a foundation for revealing the regional stress distribution law [17, 18]. Linear materials were frequently used in early spine FE studies due to their simple modeling and low computational cost. However, with the deepening of research, the limitations of linear materials in simulating the nonlinear large deformation behavior of the intervertebral disc are gradually recognized. The mechanical behavior of the intervertebral disc itself is highly nonlinear, and it would be more consistent with the real situation to use hyperelastic materials to characterize it [14–18]. Previous FE analysis showed that the stress of pelvic nail and halo nail increases with the traction distance at different traction displacement (50–150 mm). Even if the traction distance reaches 150 mm, the stress of pelvic nail and halo nail, the strain of nail channel and the reaction force of supporting rod do not reach the critical threshold [22]. However, there is no research on the distribution and variation of spinal stress during HPT. This study can provide important clinical reference value.

This study adopts geometric morphology verification and biomechanical response verification, which reaches the advanced level of similar international research and provides a solid guarantee for the reliability of subsequent conclusions. The study systematically revealed for the first time the regional mechanical matching law between cortical bone stress, cancellous bone stress, intervertebral disc stress, articular cartilage stress of left and right articular processes and improvement of vertebral body rotation under HPT. The cortical/cancellous stress ratio of vertebral body and articular cartilage stress ratio of left and right facet joint have definite clinical value. Finite element analysis can accurately calculate the stresses and displacements of spinal structures under complex loads, providing unprecedented possibilities for understanding the mechanisms of vertebral body rotation and its clinical effects [23–25].

Vertebral body rotation is a core component of three-dimensional kinematics and biomechanics of the spine, especially in the assessment of scoliosis and postoperative stability [9]. This study found that T5 vertebral body rotation in the junctional region improved by 27.5° at 15 cm displacement, while T9 of the main thoracic curve was only 6.0°, and the T9/T5 ratio was 0.20, 0.20, and 0.22 at 5, 10, and 15 cm, respectively (CV 5.6%). This finding provides a new perspective for understanding the nature of traction biomechanics.

Overgrowth of the anterior column may trigger flexion instability of the spine, and stress-related bone resorption may exacerbate the progression of the deformity, providing a biomechanical hypothesis for the etiology of idiopathic scoliosis [26]. Cortical bone is the main load-bearing structure, while cancellous bone plays more role in filling, dispersing stress and buffering [27]. Cortical/cancellous stress ratio reflects the load distribution pattern of vertebral body composite structure. The study found that a T5 ratio of 3.85 was benign unloading, corresponding to 27.5° of high vertebral rotation improvement; a T9 ratio of 7.57 was structural disability, corresponding to 6.0°of rotation collapse; and a T7 ratio of 11.39 was critical overload, corresponding to 20.2° of improvement but high risk warning.

Clinical studies have shown that HPT can lead to a significant decrease in bone mineral density (BMD) of the patient’s vertebral body, which may increase the risk of fixation failure in subsequent surgery; the length of traction is positively correlated with BMD loss, and the longer the traction is stretched, the more severe the “stress shielding” on the vertebral bone may be, resulting in greater BMD reduction [28, 29]. Studies have demonstrated that the correlation between mechanical strength of functional units and cortical bone strength is significantly higher than that with cancellous bone strength, and that total bone density predicts vertebral body strength more accurately than cortical or cancellous density alone [30]. This indicates that the cortical/cancellous stress ratio of vertebral body, as an integrated index, can reflect the structural integrity of vertebral body more comprehensively. When osteoporosis occurs, the load distribution is fundamentally reversed. When vertebral cancellous bone is lost, the load borne by cancellous bone drops sharply, while the load sharing of cortical shell increases significantly [31]. In this study, T7 cortical/cancellous ratio was as high as 11.39 and T9 was 7.57, which was direct evidence of load transfer to cortical bone after cancellous bone failure. The abnormal increase of this ratio suggested that cancellous bone in this region had undergone severe dysfunctional atrophy. Patients with very severe scoliosis may be at risk for regional osteoporosis in the apical region and adjacent regions, and BMD should be assessed before surgery. Extreme caution should be taken when placing screws in areas with cortical/cancellous ratio > 7.0 (T9) during surgery, and bone cement reinforced screws should be considered; satellite rod technique should be adopted in areas with cortical/cancellous ratio > 10.0 (e.g. T7) to avoid screw loosening caused by isolated bearing of cortical bone. Meanwhile, anti-osteoporosis treatment should be strengthened after surgery to prevent long-term fracture risk.

Finite element analysis studies have revealed that asymmetric distribution of facet joint stress in degenerative scoliosis is an important mechanism for the development of the deformity. When the scoliosis angle is small, the convex facet joint bears more stress, while when the Cobb angle is large, the concave facet joint bears more stress [32]. The concave facet joints of idiopathic scoliosis are subjected to more load transmission, resulting in subchondral osteosclerosis and facet hyperplasia [12]. Thoracic scoliosis with low bone mass produces asymmetrical and higher stress concentrations on the concave side, especially in cortical bone, facet joint, and endplate [33]. This is consistent with the phenomenon that the stress of T9 bilateral facet joint cartilage is more than 16 MPa, and the peak stress of T7 cortical bone is 5.58 MPa. The stress ratio (L/R) of bilateral facet joints is the core index to distinguish joint motion mode. The results showed that T4/5 ratio 0.42 (8.48 MPa unloading on the left and 19.98 MPa fulcrum locking on the right) was the basis of “directional locking”, and T8/9 ratio 0.77 (16.83 MPa on the left and 21.92 MPa on the right) and T9/10 ratio 1.38 (20.94 MPa on the left and 15.19 MPa on the right) were “destructive locking”, with bilateral facet joints locked and vertebral body rotation severely restricted. The L/R ratio of facet cartilage was highly stable (CV < 6%) under three displacements, which proved that the joint motion pattern remained constant during the whole traction. This study distinguished for the first time two essentially different facet joint states: “guided locking” and “destructive locking”. The former is the mechanical basis for efficient de-rotation of vertebral bodies (T4/5), while the latter is the structural cause of rotation collapse (T8/9, T9/10). In clinical practice, if preoperative CT shows clear left joint space and narrow right joint space with osteophyte formation in the junction area (T4/5), the junction area has high traction potential; if preoperative CT shows bilateral joint space disappearance or bony fusion in the apical vertebral area T8/9, the apical vertebral area has low traction potential.

The stress distribution in the disc of scoliosis is asymmetrical and concentrated locally, mainly on the concave side of scoliosis, which is not only on the vertebral body but also on the disc, especially under rotational loads, the disc bears more stress than other types of loads [19]. The stress drop in the T8/9 disc in this study is a degenerative manifestation of long-term abnormal loading, resulting in the loss of the ability to actively drive rotation.

The core theoretical contribution of this study is to propose and demonstrate the “5 cm prototype law” of HPT: the regional mechanical framework has been completely established at 5 cm traction displacement, the absolute level and relative ratio of rotation improvement in each region remain highly stable throughout the traction, and subsequent traction only amplifies the prototype non-linearly, without changing the essential mechanical role of any region. Specifically, it is manifested as: Vertebral body rotation improvement ratio T4/T5 0.88–0.90 (CV 1.1%); T7/T5 ratio 0.71–0.73 (CV 1.6%); T9/T5 ratio 0.20–0.22 (CV 5.6%); T2/T5 ratio 0.72–0.77 (CV 3.6%); L2/T5 ratio 0.19–0.20 (CV 3.0%). At 5 cm traction displacement, the initial stress state of facet joint and initial tension distribution of intervertebral disc has been completely established, and the subsequent traction mainly causes quantitative change (stress amplitude increases, improvement amplitude enlarges) rather than qualitative change. The clinical significance of transformation is significant: if the T5 vertebral body rotation in the junction area is improved by more than 10° during 5 cm traction, it indicates that the full cycle curative effect is satisfactory; if the T9 vertebral body rotation is improved by less than 2.5°, the rotation correction in this area is ineffective; if the nerve monitoring abnormality occurs in the T7 adjacent to the main thoracic curve, combined with the critical overload state of its cortical/cancellous ratio > 10.0, the traction should be terminated immediately. This finding provides a basis for individualized traction planning.

The vertebral body at junction (T4–T5) achieved 24.5° and 27.5° ultimate rotation improvement due to moderate cortical/cancellous stress unloading, high disc stress driving and extreme asymmetry of left and right facet joints. Cortical overload (cortical/cancellous ratio 11.39) was observed at T7 adjacent to the main thoracic curve, but 20.2° improvement was maintained. The angle of T4–T5 and T7 should be paid attention to during the second stage operation. The nerve monitoring should be strengthened during the operation. The cortical/cancellous ratio of T9 of the main thoracic curve was 7.57, the intervertebral disc stress decreased, and the cartilage stress of bilateral facet joints was > 16 MPa, only 6.0° improvement was obtained. Low stress in cancellous bone can cause osteoporosis, so attention should be paid to the stability of screw placement during surgery. Traction has very limited effect on the rotation correction of T9 region of apical vertebra. The rotation correction of vertebral body mainly depends on intraoperative osteotomy operation. If screws are placed in apical vertebra region, bone cement can be considered to strengthen screws to avoid screw loosening. Cortical/cancellous load bearing pattern was found in T2 of upper thoracic curve apex (ratio 2.13), the screws could be placed according to conventional strategy, but not the key point of correction. Lumbar apex L2 showed passive compensation mode, traction contribution was weak, rotation correction mainly depended on intraoperative direct de-rotation operation and intervertebral release.

The occurrence of spinal cord injury during scoliosis correction is closely related to many factors. Preoperative spinal cord abnormalities and greater kyphosis angle are important risk factors for postoperative neurological complications, other risk factors include three-column osteotomy, revision surgery, thoracic osteotomy, etc. [34]. The pathophysiology of distraction spinal cord injury is multifactorial and involves a complex interaction of mechanical compression, vascular disturbances, and iatrogenic injury [35–38]. At the apex of the deformity, the spinal cord is pulled across the posterior edge of the vertebral body, resulting in dual damage of local mechanical compression and ischemia [39]. Spinal cord injury risk should be one of the core concerns in HPT biomechanical research. In the future, based on the FE model established in this study, it is feasible to further introduce spinal cord and nerve root components [22, 40]. Using FE analysis to explore changes in spinal cord stress during HPT has important clinical translation value.

FE analysis results show that there are significant differences in improvement of vertebral body axial rotation in different regions. This finding has direct clinical guiding significance for the second-stage posterior internal fixation surgery. The vertebral body rotation has been partially corrected after HPT. If the screw placement is still planned according to the original CT data before HPT, it may cause the screw to penetrate the medial wall of the vertebral pedicle and enter the spinal canal, or penetrate the lateral wall and damage the segmental vessels. The CT scan data at the end of traction should be used for three-dimensional reconstruction to re-plan the screw diameter, length and ideal screw insertion angle of each screwed vertebral body. Therefore, future research can also explore the impact of second-stage surgical screw trajectory planning after HPT on screw accuracy, neurological safety, and orthopedic effect.

There are some limitations in this study. Hyperelastic parameters are derived from experimental data of healthy tissues, and severe scoliosis patients have different degrees of disc degeneration and joint hyperplasia. The scoliosis model is static analysis, and the real traction is a slow process for months. Introducing viscoelastic constitutive model is the key to upgrade. This study is based on a typical patient with severe scoliosis, but different deformity patterns may present differential regional mechanical patterns and multi-case modeling is necessary. The model used in this study is Lenke type 4, which is not representative of all types of scoliosis. In the future, finite element analysis models of other types of idiopathic scoliosis in adults can be established to explore the mechanics of vertebral body derotation of different types of scoliosis during HPT. Model predictions need to be correlated with preoperative imaging and post-traction rotation improvement measurements from a large clinical cohort to achieve true clinical translation.

Conclusion

This model systematically reveals for the first time the regional mechanical matching law between cortical bone stress, cancellous bone stress, intervertebral disc stress, articular cartilage stress of bilateral facet joints and improvement of vertebral axial rotation in severe rigid idiopathic scoliosis with HPT, which provides a new perspective for understanding the essence of traction biomechanics. The “5 cm prototype law” in severe rigid idiopathic scoliosis of Lenke type 4 moves the decision node of traction therapy forward to the early stage of treatment, which provides a basis for the formulation of individualized traction plan. The characteristics of regional mechanical changes provide objective mechanical basis for screw placement strategy and intraoperative risk warning in secondary posterior surgery.

Author contributions

All authors contributed to the manuscript. Study conception and design: JW, LZ, YH; acquisition and analysis of data: JW, HY, JH, YZ, YZ, YW; methodology: YH, LZ; writing—original draft: JW, HY; writing—review and editing: JW, HY. All authors have read and agreed to the published version of the manuscript.

Funding

No funding.

Data availability

The dataset generated and analyzed during the current study is available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The study was conducted in accordance with the Declaration of Helsinki, and was approved by Ethics Committee of Beijing Chaoyang Hospital Affiliated to Capital Medical University (2024-ke-641). Written informed consent was obtained from participant.

Consent for publication

The authors affirm that all participants provided informed consent for publication.

Competing interests

The authors declare no competing interests.