
==== Front
BMC Musculoskelet Disord
BMC Musculoskelet Disord
BMC Musculoskeletal Disorders
1471-2474
BioMed Central London

7832
10.1186/s12891-024-07832-0
Research
Biomechanical study of spinal cord and nerve root in idiopathic scoliosis: based on finite element analysis
Ma Jibin 12
Wang Jian 1
Yang Yuming 1
Wu Jincheng 3
Liu Ziwen 1
Miao Jun mj6688@tju.edu.cn

4
Yan Xu pumc@sina.com

5
1 https://ror.org/02mh8wx89 grid.265021.2 0000 0000 9792 1228 Clinical School/Colledge of Orthopedics, Tianjin Medical University, No. 22 Qixiangtai Road, Heping District, Tianjin, China
2 Department of Orthopedics, The Second People’s Hospital of Changzhi, No. 83 Peace West Street, Luzhou District, Changzhi, Shanxi Province China
3 https://ror.org/004eeze55 grid.443397.e 0000 0004 0368 7493 Department of Orthopedics, Hainan Medical University Second Affiliated Hospital, No. 48 Baishuitang Road, Longhua District, Haikou, Hainan Province China
4 grid.33763.32 0000 0004 1761 2484 Department of Spine Surgery, Tianjin Hospital, Tianjin University, Jiefangnanlu 406, Hexi District, Tianjin, China
5 grid.33763.32 0000 0004 1761 2484 Department of Hand Surgery, Tianjin Hospital, Tianjin University, Jiefangnanlu 406, Hexi District, Tianjin, China
6 9 2024
6 9 2024
2024
25 71724 1 2024
29 8 2024
© The Author(s) 2024
2024
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Background

Current research lacks comprehensive investigation into the biomechanical changes in the spinal cord and nerve roots during scoliosis correction. This study employs finite element analysis to extensively explore these biomechanical variations across different Cobb angles, providing valuable insights for clinical treatment.

Methods

A personalized finite element model, incorporating vertebrae, ligaments, spinal cord, and nerve roots, was constructed using engineering software. Forces and displacements were applied to achieve Cobb angle improvements, designating T1/2-T4/5 as the upper segment, T5/6-T8/9 as the middle segment, and T9/10-L1/2 as the lower segment. Simulations under traction, pushing, and traction + torsion conditions were conducted, and biomechanical changes in each spinal cord segment and nerve roots were analyzed.

Results

Throughout the scoliosis correction process, the middle spinal cord segment consistently exhibited a risk of injury under various conditions and displacements. The lower spinal cord segment showed no significant injury changes under traction + torsion conditions. In the early correction phase, the upper spinal cord segment demonstrated a risk of injury under all conditions, and the lower spinal cord segment presented a risk of injury under pushing conditions. Traction conditions posed a risk of nerve injury on both sides in the middle and lower segments. Under pushing conditions, there was a risk of nerve injury on both sides in all segments. Traction + torsion conditions implicated a risk of injury to the right nerves in the upper segment, both sides in the middle segment, and the left side in the lower segment. In the later correction stage, there was a risk of injury to the upper spinal cord segment under traction + torsion conditions, the left nerves in the middle segment under traction conditions, and the right nerves in the upper segment under pushing conditions.

Conclusion

When the correction rate reaches 61–68%, particular attention should be given to the upper-mid spinal cord. Pushing conditions also warrant attention to the lower spinal cord and the nerve roots on both sides of the main thoracic curve. Traction conditions require attention to nerve roots bilaterally in the middle and lower segments, while traction combined with torsion conditions necessitate focus on the right-side nerve roots in the upper segment, both sides in the middle segment, and the left-side nerve roots in the lower segment.

Keywords

Adolescent idiopathic scoliosis
Biomechanics
Finite element analysis
Spinal cord
Nerve roots
Patient-specific model
Tianjin Key Medical Discipline(Specialty) Construction ProjectTJYXZDXK-026A TJYXZDXK-026A TJYXZDXK-026A TJYXZDXK-026A TJYXZDXK-026A TJYXZDXK-026A TJYXZDXK-026A Tianjin Municipal Health Bureau Science and Technology Fund2014KR15 2014KR15 2014KR15 2014KR15 2014KR15 2014KR15 2014KR15 issue-copyright-statement© BioMed Central Ltd., part of Springer Nature 2024
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pmcIntroduction

Scoliosis is a three-dimensional deformity that initiates with transverse or horizontal decompensation and culminates in rotational decompensation, characterized by transverse rotation, coronal lateralization, and sagittal lordosis or extension [1]. Complications arising from spinal cord and nerve root injuries during the operation of adolescent idiopathic scoliosis (AIS) can result in severe consequences, ranging from mild sensory dysfunction to profound motor loss. Diab et al. [2] conducted a retrospective statistical analysis of 1301 consecutive surgical cases across multiple databases and identified three cases of spinal cord injury, resulting in a neurological complications incidence of 0.69%. Notably, one case of femoral nerve injury resolved within six months post-operation. In 2020, Kwan et al. [3] assessed the incidence and trends of surgeon-reported postoperative complications in AIS using the Scoliosis Research Society (SRS) morbidity and mortality database over a 13-year period, encompassing 84,320 patients. The overall complication rate was 1.5%, with new-onset neurological impairment being one of the most common complications (293 cases, 0.35%). Despite favorable outcomes for most AIS patients undergoing spinal surgery, it is not without medical or surgical complications. Buckland et al. [4] conducted a multicenter prospective study involving patients undergoing surgical treatment for AIS and identified neurological complications in 7 out of 2210 cases. While the incidence of acute and chronic spinal cord and nerve injury is low [5–8], the associated consequences are significant. Notably, nerve root injuries have been reported even under intraoperative neuroelectrophysiological monitoring [2, 9]. Therefore, surgical treatment for AIS carries a low but realistic incidence of spinal cord and neurological complications.

The models used in the biomechanical study of spinal scoliosis include various types such as animal models, physical experimental models, and cadaveric models. The scoliosis model in animals has not been observed in nature, making it challenging to select appropriate models. Although some researchers [10–12] have successfully established scoliosis models in animals, there are significant structural differences between reptiles and humans who walk upright, and animal models cannot fully replicate the actual conditions in humans. Physical experimental models have limited applicability due to the lack of changes in geometric and structural properties similar to biological tissues. Human cadaveric models theoretically provide results closer to actual human conditions. However, postmortem changes in the structure and properties of the spinal cord and nervous tissues introduce biomechanical discrepancies. Additionally, challenges such as difficulty in obtaining scoliosis cadaveric specimens and high experimental costs limit their widespread use.

Finite element studies on idiopathic scoliosis have been reported in etiological research, brace treatment, surgical simulation, and other areas [13]. However, There is a limited body of literature addressing the stress analysis of the spinal cord and nerves resulting from orthopedic procedures [14], with even fewer reports delving into stress changes specific to each spinal cord and nerve root segment.

We hypothesize that during the corrective process, significant stress changes may occur at the upper vertebra, lower vertebra, and apex vertebra in the spinal cord and nerve roots. Therefore, we focus on observing the stress variations in these segments. In this study, a comprehensive finite element model of the entire spine, including the spinal cord and nerve roots, was established for an AIS patient. Biomechanical analysis was conducted on the stress changes in the spinal cord and nerve roots under different Cobb angles. This approach aims to better estimate the potential risks to the spinal cord and nerve tissues, enhance our understanding of the stress variations in the spinal cord and nerve roots under different corrective actions, and provide improved guidance in clinical surgeries.

Methods

Individuation of finite element model.

A patient with AIS (male, 14 years old, height 165 cm, weight 50 kg) was selected, with the exclusion of other related diseases. Informed written consent was obtained from the patient for participation in this study, and all clinical investigations adhered to the principles outlined in the Declaration of Helsinki. The study received approval from the Tianjin hospital ethics committee. Figure 1 displays the anteroposterior and lateral views of the entire spine upon admission. Using a 64-slice helical computed tomography scanner (GE, Siemens Sensation16 Slice, Germany), T1-S vertebral bodies were scanned to obtain DICOM format tomographic image data with a slice thickness of 0.625 mm. The imaging data were imported into Mimics 20.0 software (Materialise, Belgium) to create a STL format three-dimensional surface model of the T1-S vertebrae. Subsequently, the data were imported into 3-Matic 12.0 software (Materialise Inc.) for wrapping and smoothing operations, removal of artifacts, and preliminary establishment of the structures of the nucleus pulposus and annulus fibrosus. The data were then exported to Geomagic Studio 12.0 software (Geomagic, Cary, NC, USA) for further smoothing and precise surface processing. Finally, the model was imported into Hypermesh 2017 (Altair Engineering, Troy, MI, USA) for mesh segmentation and ligament construction. Creo 2.0 software (PTC, USA) accurately constructed the size, location, and adjacent relationships of the T1-L1 nerve root at the exit of the intervertebral foramen based on cross-sectional and sagittal MRI images. After importing these images into Geomagic Studio 12.0 software for smoothing and surface treatment, they were transferred to Hypermesh 2017 software for mesh segmentation. Sagittal T2-weighted 3D fat-suppressed images were obtained from magnetic resonance imaging (Inginacx 1.5T, Philips), and the geometric scan data of T1-L1 spinal cord were acquired in DICOM format with a slice thickness of 1.0 mm. Geomagic Studio 12.0 software facilitated smoothing and surface processing, with subsequent importation into Hypermesh 2017 software for mesh segmentation. The spinal cord and nerve roots were spliced using Boolean operation in Hypermesh 2017 software. Finally, the above models were imported into Abaqus 2019 software (Simulia, Johnston, RI, USA) for model assembly, material property definition, and finite element analysis. Refer to Fig. 2 for the technical roadmap. The intervertebral disc comprises matrix and nucleus pulposus, with the nucleus pulposus accounting for 43% of the total intervertebral disc [15]. The elements representing vertebral bodies, intervertebral discs, spinal cord, and nerve roots are tetrahedral elements. The vertebral body, intervertebral disc, spinal cord, and nerve root were modeled as tetrahedra elements, while the ligament was simulated using a tension-only truss element [16]. The facet joint plane contact surface was defined as a face-to-face contact with a friction coefficient of 0.02. Material properties were defined based on previously reported literature [17–24] (see Table 1), and then mesh convergence testing was performed for the T1-S model in Hypermesh software.

Fig. 1 Biplane X-ray of the patient with Lenke1 AIS. (A) Frontal film; (B) Lateral film

Fig. 2 Technology roadmap

Table 1 Mechanical properties of FEM anatomical structures

Component	Young’s modulus (MPa)	Poisson ratio	Cross-sectional area (mm2)	
Vertebra	12,000	0.3		
Nucleus pulpous	1	0.49		
Ground substance	4.2	0.45		
Spinal cord	0.26	0.49		
Nerve root	1.19	0.44		
SSL	8		25	
ISL	6		30	
ALL	8		63.7	
PLL	2.5		20	
LF	5		40	
ITL	4.17		25	
CL	2.5		30	
SSL, supraspinal ligament; ISL, interspinous ligament; ALL, anterior longitudinal ligament; PLL, posterior longitudinal ligament; LF, ligamentum flavum; ITL, Intertransverse ligament; CL, capsular ligament

Given the focus of this experiment on stress changes in the spinal cord and nerve root at the intervertebral foramen outlet, the model was streamlined. The gray matter, white matter, dura mater, arachnoid membrane, pia mater, and dentate ligament were intentionally omitted. The cancellous bone was not modeled. The finite element model was created with shared nodes between the spinal cord and nerve roots, as well as shared nodes between vertebral bodies and intervertebral discs, and between the nucleus pulposus and annulus fibrosus. Contact relationships were established between the spinal cord and vertebral bodies/intervertebral discs, and also between vertebral bodies and nerve roots.

Verification of model

The biomechanical properties of the finite element method must align with the actual patient’s condition. Prior to conducting simulated biomechanical analysis, it is imperative to validate the established model. Given the absence of biomechanical experimental data encompassing the entire spine, spinal cord, and nerve roots for AIS, this study adopted the validation approach from previous investigations [25, 26]. The spine’s geometry was reconstructed in various motion states, and a comparison was made between X-ray films and finite element models (FEM).

Loading model

Traction conditions

The sacral bone was immobilized, restricting its rotation, restricting its movement in the X, Y, and Z directions. The spinal cord was secured at the upper edge of T1, limiting its movement in the X and Y directions, while permitting only axial movement along the Z-axis to simulate traction conditions.

Pushing conditions

Fixation of the sacrum restricts movements in the X, Y, and Z directions, as well as limits sacral rotation. The spinal cord was fixed at the upper edge of T1 to limit movement in the X and Y directions, allowing movement solely along the Z-axis. Uniform displacements of 20 mm, 40 mm, and 60 mm were applied to the T8 vertebral body, corresponding to the convex side of the upper vertebra. The force direction was oriented horizontally from the convex side to the concave side, simulating a dynamic condition.

Traction + torsion conditions

Apply a load to the T1 vertebra with displacements of 20 mm, 40 mm, and 60 mm along the Z-axis. Secure the spinal cord at the upper edge of T1, limiting its movement along the X and Y axes while allowing movement solely along the Z-axis. Securing the sacrum restricts its movements along the X, Y, and Z axes and confines sacral rotation. Configure the load to couple with the T8 vertebra and impart a 30° twist along the Z-axis to simulate the traction + torsion condition.

The loading diagram is illustrated in Fig. 3.

Fig. 3 Loading diagram

Observation parameters

Changes in Cobb Angle were examined under each working condition. The average von Mises stress distribution across T1/2 to L1/2 segments of the spinal cord and the average von Mises stress distribution of the left and right nerve roots at the intervertebral foramen exit were recorded.

Statistical analysis

To validate the finite element model, GraphPad Prism 9.5.1 was utilized for a paired t-test comparing FEM and X-ray measurements, with α = 0.05. The upper segment was defined as T1/2-T4/5, the middle segment as T5/6-T8/9, and the lower segment as T9/10-L1/2. The mean von Mises stress for the spinal cord and nerve root in the upper, middle, and lower segments was assessed using the non-parametric Mann-Whitney U test (α = 0.05). A significance level of P < 0.05 was applied for statistical interpretation.

Results

Figure 4 illustrates the successful construction of a three-dimensional finite element model incorporating T1-S vertebrae, intervertebral discs, T1-L1 spinal cord, nerve roots, and seven spinal ligaments. This model comprises 1,212,995 elements and 254,301 nodes. Morphological validation of the model demonstrates a shape highly consistent with X-rays (see Figs. 5 and 6). The central position of the vertebrae, lateral convex angles in the sagittal and coronal planes, align well with the corresponding X-ray images of the patient. Finite element simulation results for the convexity reveal that the distance from the T1 center to the perpendicular line through the sacrum closely matches the measured data from left and right bending X-rays (see Fig. 7; Table 2).

Fig. 4 Finite element model of spine with spinal cord and nerve roots. (A) Anterior view; (B) Posterior view

Fig. 5 Morphological validation of the FEM morphological validation of the FEM

Fig. 6 Morphological validation of lateral bending of the model. (A) Right bending. (B) Left bending

Fig. 7 Comparison of the offset distance between the center of each vertebral body of the spine and the midline of the sacrum between the FEM and X-ray film. (A) Left bending; (B) Upright position; (C) Right bending

Table 2 The offset distance between the model and X-ray film (mm)

Spinal segment	Frontal	Left bending	Right bending	
X-ray	Model	X-ray	Model	X-ray	Model	
T1	-0.6	-0.8	-30.7	-29.6	25.3	23.5	
T2	-0.2	0	-27.8	-26.8	23.2	26.6	
T3	4.2	4.2	-24.6	-26.8	23	26.2	
T4	10.5	9.5	-19.4	-20.3	24.6	22.4	
T5	18.7	20.5	-14.1	-13.8	27.7	25.6	
T6	27.3	25.8	-8.7	-9.1	29.9	28.5	
T7	35.3	37.2	-3.4	-3.5	31.7	33.6	
T8	39.3	36.8	0.7	-0.7	31.4	32.8	
T9	39.7	40.5	3.7	2.8	30.4	27.9	
T10	34.6	35.5	3.9	2.8	26.9	29.8	
T11	26.2	27.2	2	4.2	21.4	21.5	
T12	17.1	18.1	-0.1	-0.5	14.9	12.3	
L1	6.7	6.9	-3.6	-3.2	8.5	7.9	
L2	-0.8	-0.8	-4.8	-5.1	3.2	3.3	
L3	-3.7	-3.2	-4.1	-3.8	-0.3	-0.1	
L4	-3.4	-3.2	-2.9	-2.4	-1.5	-1.2	
L5	-0.3	-1.1	-1.3	-1	-1.2	-1.6	
	t1 = 0.54	t2 = 0.37	t3 = 0.01	
	P = 0.599	P = 0.716	P = 0.990	

Model simulation results

The concave side of the main thoracic curve in AIS experiences compressive stress, while the convex side undergoes tensile stress. Across the three conditions, the Cobb Angle progressively decreases with increasing displacement at the action site (Table 3), leading to gradual improvement in the correction of the curve shape. The von Mises stress distribution for each segment of the spinal cord from T1/2 to L1/2, and the von Mises stress contours for the bilateral nerve roots at the intervertebral foramen exits, are illustrated in Figs. 8 and 9.

Table 3 The value of Cobb angle under different working conditions

Loading condition	Displacement(mm)	Cobb angle (°)	Correction rate(%)*	
Traction Condition	20	53.4	37	
40	32.4	62	
60	7.2	91	
Pushing Condition	20	47.9	43	
40	27.1	68	
	60	12.1	86	
Traction + Torsion Condition	20	47.7	44	
40	32.8	61	
60	8	91	
Footnote: Correction rate = (Pre-correction Cobb angle - Post-correction Cobb angle) / Pre-correction Cobb angle × 100%

Fig. 8 Stress nephogram of the spinal cord and nerve roots under traction and pushing conditions

Fig. 9 Stress nephogram of the spinal cord and nerve roots under traction + torsion conditions

Comparative analysis of spinal cord stress

At a significance level of α = 0.05, the impact on the middle spinal cord is consistently significant under various conditions and displacement changes. However, under pushing conditions, a significant impact on the lower spinal cord is observed when displacement ranges from 20 mm to 40 mm. For the upper and middle spinal cord segments, the influence on the spinal cord is consistently significant only under the traction + torsion condition when the displacement ranges from 20 mm to 60 mm. In the case of the other two conditions, the impact on the spinal cord is significant only at lower displacement levels. Column analyses of the average von Mises stress in the upper, middle, and lower spinal cord segments under the three conditions are presented in Fig. 10A.B.C, and the corresponding statistical summaries are provided in Table 4.

Fig. 10 Column analysis charts of the spinal cord and nerve roots under three conditions. (A) Stress of the spinal cord in traction condition. (B) Stress of the spinal cord in pushing condition. (C) Stress of the spinal cord in traction + torsion condition. (D) Stress of bilateral nerve roots in traction condition. (E) Stress of bilateral nerve roots in pushing condition. (F) Stress of bilateral nerve roots in traction + torsion condition. * represents P < 0.05

Table 4 Compares spinal cord Von Mises stress at varied displacements under three conditions

Working condition	Segment	P-value
displacement
(20 mm vs. 40 mm)	P-value
displacement
(40 mm vs. 60 mm)	
Traction Condition	T1/2-T4/5	0.029*	0.057	
T5/6-T8/9	0.029*	0.029*	
T9/10-L1/2	0.056	0.222	
Pushing Condition	T1/2-T4/5	0.029*	0.057	
T5/6-T8/9	0.029*	0.029*	
T9/10-L1/2	0.016*	0.100	
Traction + Torsion Condition	T1/2-T4/5	0.029*	0.029*	
T5/6-T8/9	0.029*	0.029*	
T9/10-L1/2	0.151	0.310	
* Indicates a significant difference, α = 0.05

Figure 11 A.D.G respectively show the average von Mises stress distribution of the spinal cord in the T1/2-L1/2 segments under different displacements during traction, pushing, and traction + torsion conditions. It can be observed from the figures that with a decrease in Cobb angle, the maximum average von Mises stress in the spinal cord appears in the T7/8 and T8/9 segments.

Fig. 11 Line chart of the average von Mises stress of the spinal cord and nerve roots under three conditions. (A) The average von Mises stress in each spinal cord segment under the traction condition. (B) The average von Mises stress in each segment of the left nerve root under the traction condition. (C) The average von Mises stress in each segment of the right nerve root under the traction condition. (D) The average von Mises stress in each spinal cord segment under the pushing condition. (E) The average von Mises stress in each segment of the left nerve root under the pushing condition. (F) The average von Mises stress in each segment of the right nerve root under the pushing condition. (G) The average von Mises stress in each spinal cord segment under the traction + torsion condition. (H) The average von Mises stress in each segment of the left nerve root under the traction + torsion condition. (I) The average von Mises stress in each segment of the right nerve root under the traction + torsion condition

Comparative analysis of nerve root stress

At a significance level of α = 0.05, the results indicate that during the corrective process with a displacement ranging from 20 mm to 40 mm, the impact of pushing on the nerves on both sides shows significant differences across the three segmented regions. Traction, on the other hand, does not exhibit significant differences for the upper nerves on both sides but shows significant differences for the middle and lower nerves on both sides. Under the traction + torsion condition, there are no significant differences observed in the left upper and right lower nerves, while significant differences are present in the nerves of other segments. With increasing displacement, the effects of different conditions on nerves on both sides seem nonsignificant, except for the significantly different impact of the left nerves in the middle segment under traction and the right upper nerves under pushing.

Column analyses of the average von Mises stress on the left and right nerves in the upper, middle, and lower segments under the three conditions are depicted in Fig. 10D.E.F, and detailed statistical summaries are provided in Table 5.

Table 5 Nerve root Von Mises stress compared at various displacements under three conditions

Working Condition	Segment	P-value
displacement
(20 mm vs. 40 mm)	P-value
displacement
(40 mm vs. 60 mm)	
Left	Right	Left	Right	
Traction Condition	T1/2-T4/5	0.057	0.114	0.343	0.114	
T5/6-T8/9	0.029*	0.029*	0.029*	0.114	
T9/10-L1/2	0.008*	0.016*	0.222	0.841	
Pushing Condition	T1/2-T4/5	0.018*	0.015*	0.114	0.029*	
T5/6-T8/9	0.012*	0.019*	0.114	0.343	
T9/10-L1/2	0.007*	0.028*	0.421	0.095	
Traction + Torsion Condition	T1/2-T4/5	0.057	0.029*	0.486	0.343	
T5/6-T8/9	0.029*	0.029*	0.886	0.686	
T9/10-L1/2	0.008*	0.151	0.690	0.421	
* Indicates a significant difference, α = 0.05

Figure 11B.C.E.F.H.I respectively illustrate the changes in average von Mises stress of nerve roots on both sides of the thoracic curvature in the T1/2-L1/2 segments under traction, pushing, and traction + torsion conditions as displacement ranges from 20 mm to 60 mm. The figures depict that the maximum average von Mises stress of the thoracic concave-side nerve roots is observed in the T2/3, T3/4, and L1/2 segments, while for the thoracic convex-side nerve roots, it occurs in the T5/6, T6/7, and T9/10 segments. At a displacement of 40 mm, under traction conditions, the average von Mises stress of the left-side nerve roots in the T8/9 segment (0.0111 MPa) is lower than that of the right-side nerve roots (0.0118 MPa). Under pushing conditions, the average von Mises stress of the left-side nerve roots in the T8/9 segment (0.0246 MPa) is also lower than that of the right-side nerve roots (0.0420 MPa). Similarly, under traction + torsion conditions, the average von Mises stress of the left-side nerve roots in the T8/9 segment (0.0281 MPa) is lower than that of the right-side nerve roots (0.0209 MPa).

Discussion

This study constructed a three-dimensional deformity model of AIS and simulated three surgical methods during corrective surgery for AIS. The study primarily focused on observing the average von Mises stress changes in the spinal cord and bilateral nerve roots under different surgical methods. It is important to note that the stress values in the spinal cord and nerve roots may not directly represent the actual stresses experienced. Rather, we computed the stress trends in different segments of the spinal cord and nerve roots under various surgical methods. This information plays a crucial role in clinical guidance, although it does not provide direct measures of real stress in the spinal cord and nerve roots.

Biomechanical characteristics of the spinal cord

The biomechanical characteristics of the spinal cord encompass mechanical properties, morphological features, and biomechanical behaviors. Henao et al. [14] constructed a finite element model based on transverse sections of a cadaveric spinal cord, incorporating gray and white matter, soft and hard meninges, dentate ligaments, nerve ganglia, and nerve roots. In contrast, our study only constructed a finite element model based on the patient’s own CT and MRI geometry, without further detailing gray matter, white matter, or hard meninges. This decision stems from two main reasons: (1) Significant biomechanical differences exist between gray and white matter. Vallotton et al. [27] quantified and analyzed indicators of gray and white matter in 24 patients with mild to moderate degenerative cervical spine disease and 24 healthy subjects. Their findings revealed substantial atrophy and microstructural changes in cervical cord white and gray matter, while lumbar cord only exhibited white matter atrophy and microstructural changes. Thus, it is inferred that white matter is sensitive to pathological changes. Additionally, lumbar cord white matter atrophy was associated with lower limb sensory impairments. (2) Animal studies have shown variations in the longitudinal and transverse elastic moduli of the dura mater across different segments in adult sheep, with cervical segments having lower elastic moduli than lumbar segments [28]. Limited literature addresses the biomechanical properties of the arachnoid mater, although its inclusion can enhance the predictive accuracy of spinal finite element models [29]. Dentate ligaments offer stability to the spinal cord in both static and dynamic conditions, exerting direct mechanical stress on the spinal cord. Polak et al. [30] conducted uniaxial tensile experiments on 98 dentate ligaments from seven fresh porcine spinal cords, revealing segment-specific stress values, with a noticeable decrease in tensile force closer to the caudal end of the dentate ligament. In fresh human cadaver specimens, there is no literature documenting the biomechanical behavior of the dura mater, arachnoid membrane, pia mater, and dentate ligament. It is also possible that these spinal structures exhibit different biomechanical characteristics across different segments in humans. This underscores the significant challenges in comprehensively and accurately constructing a finite element model of the spinal cord. Therefore, this study simplified the spinal cord model due to the substantial difficulty involved in achieving a comprehensive and accurate representation.

Biomechanical impact of three surgical methods on the spinal cord

This study found that under all three conditions, the highest stresses occurred near the apex vertebrae. However, Henao et al. [14] employed a hybrid computational modeling approach to simulate three correction techniques. Their findings revealed that under traction conditions, the maximum stress on the spinal cord occurred in the thoracolumbar region, while the spinal cord stress values were minimized in the segmental torsion condition. This discrepancy could be attributed to the fact that, in both traction and pushing conditions, as well as traction + torsion conditions, the spinal cord is farthest from the midline. With the correction of deformities, the stress on the spinal cord contacting the vertebrae may decrease from the top vertebral region towards the distal end. Additionally, the disparity in results between the two studies may stem from differences in modeling approaches.

Table 4 presents the statistical results for the upper, middle, and lower spinal cord under three different conditions and varying displacements. The table indicates that the average von Mises stress in the middle spinal cord exhibits statistical differences under all three conditions and at three different displacements. Combining this information with Fig. 11A.D.G, it can be inferred that the risk of injury to the middle spinal cord appears to be the highest. Under pushing conditions, as the Cobb angle decreases from 47.9° to 27.1°, there is a significant difference in the lower spinal cord, suggesting a risk of injury in this segment. For the middle-upper spinal cord, when displacement varies from 20 mm to 60 mm, only the traction + torsion condition shows a consistently significant impact on the spinal cord. This implies a sustained risk of injury to the middle-upper spinal cord throughout the correction process. When displacement ranges from 40 mm to 60 mm, the upper spinal cord shows no significant difference between traction and pushing conditions, suggesting that spinal cord damage may have occurred in the displacement range of 20 mm to 40 mm. In contrast, the lower spinal cord under traction + torsion conditions remains consistent throughout the displacement range from 20 mm to 60 mm, indicating no significant change in injury risk.

Therefore, throughout the scoliosis correction process, there is a consistent risk of injury to the middle spinal cord segment under various conditions and displacements. In the early stages of correction, the upper spinal cord segment is at risk of injury under all three conditions. Additionally, the lower spinal cord segment faces a risk of injury under pushing conditions. In the later stages of correction, there is a risk of injury to the upper spinal cord segment under traction + torsion conditions. Interestingly, the lower spinal cord segment under traction + torsion conditions shows no significant change in injury risk from the early to later stages of correction.

Biomechanical impact of three surgical methods on nerve roots

To reveal the stress variations of the main thoracic curve nerve roots during the corrective process. As shown in Fig. 11B, E, and H, under three conditions with displacement ranging from 20 mm to 60 mm in the T1/2-L1/2 segments, the maximum average von Mises stress of the thoracic left-side nerve roots appears in the upper end vertebra and lower end vertebral regions, while for the thoracic right-side nerve roots, it occurs near the apex vertebra. This may be attributed to the fact that during the correction of spinal scoliosis, the left-side nerve roots experience the greatest stress in the intervertebral foramina of the upper end vertebra and lower end vertebral regions, while the right-side nerve roots experience the greatest stress in the intervertebral foramina near the apex vertebra. Furthermore, at a displacement of 40 mm, the average von Mises stress of the left-side nerve roots in the apex vertebra region is less than that of the right-side nerve roots under three conditions. Kim et al. [18] used finite element analysis to study the biomechanical changes of nerve roots in degenerative lumbar scoliosis and found that when there is no rotational displacement, the stress on the concave-side nerve roots is greater than that on the convex-side nerve roots, whereas with rotational displacement, the stress on the convex-side nerve roots is greater than that on the concave-side nerve roots. We hypothesize that rotational correction may cause the observed stress changes in the apex vertebra region during the corrective process in our study.

Table 5 presents the statistical outcomes for the nerve roots on both sides in the upper, middle, and lower segments under three conditions with varying displacements. The table reveals that during the displacement range of 20 mm to 40 mm, the impact of the pushing condition on the nerve roots exhibits significant differences in all three segments. This suggests a notable risk of injury to both sides of the nerve roots in the upper, middle, and lower segments under pushing conditions. This phenomenon may be attributed to the force applied on the convex side of the apex vertebra. As the apex vertebra moves from the convex side towards the midline, the convex side experiences compression while the concave side undergoes separation. Consequently, both sides of the nerve roots come into contact with the pedicle at the intervertebral foramen. Under the traction condition, significant differences in the nerve roots on both sides are observed in the middle and lower segments, indicating a risk of injury in these segments under this condition. In the traction + torsion condition, significant differences are noted in the upper right, both sides of the middle, and the lower left segments, suggesting a risk of injury in these regions. With increasing displacement, apart from the significant differences observed in the traction condition for the left nerve root in the middle segment and in the pushing condition for the right nerve root in the upper segment, the stress changes in the nerve roots of different segments under other conditions are not significant. This implies potential damage to the nerve roots in these segments under corresponding conditions, such as the right nerve root in the middle segment and both sides of the lower segment under traction conditions, the left nerve root in the upper segment and both sides of the middle and lower segments under pushing conditions, and the right nerve root in the upper segment, both sides of the middle segment, and the left nerve root in the lower segment under traction + torsion conditions.

During the correction process of spinal deformity, stress changes occur as a result of displacement through the intervertebral foramen leading to contact with the nerve roots. In the early stages of correction, there is a risk of injury to the nerve roots on both sides in the middle and lower segments under traction conditions. Additionally, there is a risk of injury to the nerve roots on both sides in the upper, middle, and lower segments under pushing conditions. Specifically, there is a risk of injury to the upper right, both sides in the middle, and the lower left nerve roots under traction + torsion conditions. In the later stages of correction, there is a risk of injury to the left nerve root in the middle segment under traction conditions and a risk of injury to the right nerve root in the upper segment under pushing conditions.

In summary, a thorough understanding of the timing of spinal cord and bilateral nerve root injuries in various segments under different conditions can assist clinical practitioners in optimizing surgical strategies, enhancing surgical success rates, and reducing potential risks of complications.

The primary limitations of this study are as follows: (1) Simplification of spinal cord modeling: The modeling of the spinal cord was simplified, and the precise anatomical construction of nerve roots within the vertebral canal was not accurately represented. The elastic moduli of various model components were set based on reported experimental data, mostly derived from cadaveric sources, which could be influenced by tissue degradation. Future research should involve further studies on fresh specimens to obtain more accurate data on the viscoelastic properties of the spinal cord. (2) Modeling assumptions impacting mechanical response: In this study, these modeling assumptions affected the mechanical response of the spinal cord and nerve root models to imposed kinematic conditions. The mechanical properties of spinal cord finite element components were calibrated for quasi-static simulation analysis. While simulation results suggest the effectiveness of this method for comparative analysis of surgical maneuvers, it remains uncertain whether the detected issues truly represent real complications. Therefore, to gain further insights into the impact of personalized biomechanical properties on finite element stress evaluation of the spinal cord and nerve roots, we will enhance preoperative planning in the future. This will involve providing personalized preoperative correction plans for patients with complex spinal deformities to ensure safety in individual surgical procedures. Additionally, preoperative biomechanical simulations combined with intraoperative neurophysiological monitoring techniques will be employed to cross-validate each other, collect data, and establish a large sample database. This effort aims to further develop a safe correction system for the spinal cord and nerves.

Conclusions

In conclusion, our investigation on AIS involved the implementation of three surgical methods to induce biomechanical changes in the spinal cord and nerve roots. Through finite element analysis and statistical evaluation, valuable insights have been contributed for clinical guidance. The successful reconstruction of personalized finite element models accurately replicated spinal components, demonstrating morphological consistency with radiographic images. Simulation results indicated a gradual reduction in Cobb angles under various loading conditions, signifying an improvement in the correction of spinal deformities. Distinct spinal correction maneuvers, such as traction, pushing, and their combination with traction and torsion, exhibited variations across different spinal segments and loading conditions. The average Von Mises stress in the spinal cord consistently manifested significance in the midsection, while the stress distribution in nerve roots varied based on the corrective techniques applied and the specific spinal segments involved. These findings contribute to a better comprehension of the biomechanics implicated in AIS correction, forming a foundational basis for optimizing treatment strategies. The subsequent phase necessitates exploration through clinical validation to further solidify our research. In summary, our study delivers valuable biomechanical insights that can enhance the efficacy and safety of spinal scoliosis correction procedures in clinical practice.

Author contributions

JM conceived the original ideas of this manuscript. JBM, JW, YMY wrote the manuscript. JBM, JW, JCW performed the experiments. ZWL and JW were responsible for image production. JM and XY revised the manuscript. All authors read and approved the final manuscript.

Funding

Supported by Tianjin Key Medical Discipline(Specialty) Construction Project(TJYXZDXK-026 A).

Supported by Tianjin Municipal Health Bureau Science and Technology Fund (2014KR15).

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study was approved by the Ethics Committee of Tianjin Hospital. Informed consent to participate was obtained from the parent of the participant.

Consent for publication

Written consent for publication was obtained from the parent because the patient was a minor or incapacitated, and therefore unable to provide consent directly. We confirm that the parent gave written informed consent for the publication of their personal or clinical details, along with any identifying images, in this study.

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Jibin Ma, Jian Wang and Yuming Yang contributed equally to this work and should be considered co-first authors.
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