A Novel Optimized Finite Element Model of Lenke 1 Adolescent Idiopathic Scoliosis Based on Dynamic Flexibility in Vivo


 Bacground: It is of great significance to optimize the finite element model by spinal flexibility of adolescent idiopathic scoliosis (AIS) patients. The elastic modulus of the intervertebral disc is of critical importance in determining the overall flexibility of the spine. The aim of the present study was to optimize the finite element model of Lenke 1 AIS based on the dynamic flexibility in vivo by matching the optimal elastic modulus of the intervertebral disc.Methods: The Cobb angles under different longitudinal traction loads of one patient with Lenke 1 AIS were dynamically measured by using a spine morphometer with a posture sensor to plot the Cobb angle-longitudinal traction load characteristic curve. A 3D finite element model of the patient was established. The patient’s Cobb angle-longitudinal traction load characteristic curve was used as the dynamic flexibility in vivo to determine the optimal intervertebral disc elastic modulus of the model. Results: The dynamic flexibility curve in vivo of one Lenke 1 AIS patient was successfully obtained, and the patient’s optimal elastic modulus of the intervertebral disc for the finite element model was 5 MPa according to the dynamic flexibility curve in vivo.Conclusions: The use of dynamic flexibility in vivo to optimize the finite element model can provide a new perspective and approach for model optimization, which can reproduce the biomechanical characteristics in vivo of AIS patients.


Introduction
Adolescent idiopathic scoliosis ( AIS ) is the most common form of scoliosis with a prevalence of 0.47-5.2% and a female/male ratio that increases substantially with increasing age from 1.5:1 to 3:1 [1,2].
Changes in the physical appearance of AIS patients would affect their self-e cacy and con dence [3], and those with severe syndromes may also experience negative impact on their cardiopulmonary function and body balance, thus reducing the quality of their life. With the in-depth understanding of the pathophysiology and clinical treatment of AIS and the development of spinal orthopedic technology and internal xation equipment, there has been a consensus that brace treatment is suitable for mild and moderate AIS patients, and surgical treatment is suitable for patients with progressive or severe deformities [4][5][6]. Body mass index (BMI), scoliosis type, surgical strategy and other factors would affect the surgical outcome [7]. An ideal surgical strategy should include inherent characteristics(i.e. curve exibility), the complexity of speci c correction maneuvers, selection of fusion levels, instrumentation parameters, surgeon experience and correction objectives [8][9][10]. Biomechanical mechanisms may also have impact on the occurrence and progression of AIS. The biomechanical characteristics (especially spinal exibility) of each individual patient are an important premise for formulating an appropriate surgical strategy. The nite element model can simulate the spine anatomical structure and biomechanical characteristics of AIS patients in a reverse manner, and therefore has been widely used in the study of the etiology of scoliosis [11,12], brace development and treatment [13], biomechanical analysis for surgical strategy formulation and e cacy prediction [14]. The nite element model simpli cations and assumptions are the key to make the model suitable to a research. The authenticity of the model is the basis of the research application, and even a slight change in the model parameters would cause obvious deviation in the research results. In order to maximize the simulation of the biomechanical characteristics of the spine in vivo, it is essential to optimize the nite element model. At present, the nite element model is commonly optimized through the spinal exibility of AIS patients in a speci c state to present their inherent biomechanical characteristics [15][16][17][18]. We believe that the spinal exibility in a speci c state is a kind of static exibility and cannot fully re ect the overall exibility of the deformed spine, knowing that the dynamic exibility in vivo of AIS patients is a comprehensive re ection of the biomechanical characteristics of the spines. To the best of our knowledge, there is no research to optimize the model basing on the dynamic exibility in vivo so far. The aim of the present study is to use the dynamic exibility in vivo to optimize the Lenke 1 AIS nite element model.

Acquisition of dynamic exibility in vivo
We selected one Lenke 1 AIS patient(patient A) without tumors, infections, rheumatic immune diseases, cardiopuimonary dysfunction, old spinal injury and other diseases that cannot withstand the subsequent trial. Before the initiation of the trial, the patient and the families were fully informed and signed the medical ethics informed consent forms. This research project was approved by the ethics committee of Shanghai Changhai Hospital (Shanghai, China). The patient took a sitting position, with the upper body upright and the lumbosacral part xed. The traction occipital band was xed to the patient's mandible, and the vertical traction force was applied to the patient through the occipital band. The traction force gradually increased from 0N to 160N (about 30% of the patient's weight). The Cobb angles were measured every 20N with a posture sensor-based spine morphometer (Fig. 1). The scoliosis longitudinal traction device was used to control the traction force through a highly sensitive mechanical sensor ( Fig.   1).
The trial was conducted by two experienced orthopedic spine surgeons. The patient was measured three times by the two surgeons and the interclass correlation coe cient (ICC) for Cobb angles was 0.93(p < 0.05). The mean value of the Cobb angles was used as the nal result. The characteristic curve of Cobb angle-longitudinal traction load, also known as the dynamic exibility curve in vivo, was drawn according to the measurement result (Fig. 5).

Establishment of the nite element model
Several simpli cations and assumptions were necessary for this ne element model. a. The mandible, cervical spine, ligamentum avum, supraspinous ligament, interspinous ligament, facet joint and muscles were not included in the model. b. The model did not discriminate the nucleus pulposus from the annulus brosus, made of ground substance and layers of bers. c. The intervertebral disc was assigned a value mainly based on the annulus brosus and modelled as isotroptic with the same mechanical properties. d.
The tractional load should counterbalance for the gravity loads and muscle forces, which are applied on the spine in vivo. However, it is di cult to determine the actual traction load in the nite element model test. The study neglected the gravity loads and muscle forces. Therefore, most of the other parameters cannot be validated and many results of the nite element analysis only indicate trends and do not necessarily represent the correct absolute values. Furthermore, patient A had surgical indications, a CT scan was needed to provide a reference for pedicle screw placement. CT DICOM format data of T1-L4 spinal segments of patient A were obtained, and the details are shown in Table 1. Referring to the material properties reported in the previous literature, the cortical bone, cancellous bone, intervertebral disc and anteroposterior longitudinal ligaments of the model were assigned an initial value [19][20][21][22]. The material properties for the model were extracted from the literature available (Table 2)   Optimization of the nite element model

Calculation of Cobb angle in the nite element model
Taking the coronal axis of the model as a horizontal straight line, two points of the superior endplate of the upper end vertebrae were selected and their coordinates were recorded as (X1, Z1), (X2, Z2), which were connected to obtain a straight line a, with the slope being k1; then the two nal points of the inferior endplate of the lower end vertebrae were selected and their coordinates were recorded as (X3, Z3), (X4, Z4), which were connected to get a straight line b, with the slope being k2. The angle between the two straight lines was the Cobb angle and calculated by using the following equation (Fig. 4): Optimization of the intervertebral disc elastic modulus of the model The intervertebral discs are of critical importance in determining spinal exibility [16]. This study mainly optimized the nite element model by matching the elastic modulus (E) of the intervertebral disc. The intervertebral disc was not divided into the nucleus pulposus and annulus brosus, but was assigned a value mainly based on the annulus brosus. By referring to the literature, E of the annulus brosus was 4.2 MPa [14,23]. Based on the results of the pre-experiment, the disc E of model A was set to 3MPa-7MPa in sequence to facilitate calculation. The traction loads were set to 0N, 20N, 40N, 60N, 80N, 100N, 120N,  140N and 160N, and then a dynamic exibility test was performed on model A. Using Matlab2017a, the characteristic curve of Cobb angle-longitudinal traction load, the t curves and equations of patient A and model A with different E were obtained. The goodness of t was expressed by the coe cient of determination(R²). The sum of squared differences (SSD) of Cobb angles under the same traction loads between patient A and model A with different E were also calculated. The minimum SSD value indicated that the two curves were closest, and the E of that curve was the optimal intervertebral disc E of model A.

Results
As shown in Fig. 5, the dynamic exibility curve in vivo of patient A was obtained successfully. The 3D nite element model A of patient A was established (Figs. 2 and 3), and the characteristics of patient A are shown in Table 1. Five dynamic exibility curves of model A with different disc elastic moduli and the dynamic exibility curve of patient A were obtained (Fig. 5, Table 3). The t curves (with all the R² greater than 0.9) and equations between Cobb angles and longitudinal traction loads of model A with different E and patient A were obtained (Fig. 6, Table 4). The SSD value of Cobb angles under the same traction loads between patient A and model A with disc E = 5MPa minimally demonstrated that 5MPa was the optimal disc elastic modulus of model A ( Table 4). The t curves between Cobb angles and longitudinal traction loads of patient A and model A with disc E = 5MPa were the closest (Fig. 6).

Discussion
Studies have shown that assessment of the spinal exibility of AIS patients is of great signi cance in determining fusion segments, selecting surgical approaches, and predicting postoperative orthopedic effects [24]. For AIS patients with relatively better exibility, orthopedic surgery can be completed by reducing the screw density or shortening the xed fusion segment. In comparison, patients with comparatively poorer exibility need to increase the screw density or extend the xed fusion segment to achieve the designated orthopedic purposes [24][25][26]. In addition, the role of spinal exibility assessment in conservative treatment is also important [27]. Scoliosis exibility evaluation is the overall deformability of the spine under active or passive external force, and it is a quanti cation of the degree of spinal stiffness. At present, the commonly used methods for clinical evaluation of scoliosis exibility include the supine bending method, fulcrum bending method, traction method, push prone method, and suspensiontraction method [28,29]. Berger et al. [30] used exibility index for systematic review of the predictive effect of the above ve methods on the surgical orthopedic outcome, and concluded that the supine bending method was the most commonly used method, and the fulcrum bending method was the most accurate method. However, both assessment methods are conducted in a static and speci c state [31], which hinders the overall assessment of spinal exibility. In addition, the stiffness degree of AIS patients is often different under the same traction loads, which emphasizes the necessity of overall assessment of the patients' exibility.
Although the nite element model has been widely used in the eld of spinal surgery, especially in the spinal biomechanical analysis of AIS patients [32,33], for the rst time it was used to simulate scoliosis correction surgery by comparing the effect of lateral and longitudinal forces on the correction of scoliosis [34]. Viviani et al. [35]  optimized the nite element model by using the fulcrum bending method, and after a detailed report of the speci c simulation process and the adjustment of the relevant soft tissue stiffness index, they believed that the stiffness of the intervertebral disc ber had a relatively strong impact on the exibility of the spine. In a subsequent study, the authors also found that spinal exibility in the fulcrum bending test was not governed by any single soft tissue structure acting in isolation. More detailed biomechanical characterisation of the fulcrum bending test is required to provide better data to determine the properties of patient-speci c soft tissues [41]. Kamal et al. [39] achieved optimization by adding muscle simulation to the nite element model. In addition, other scholars were also committed to improving the simulation accuracy of the model [42]. The individualized nite element model based on hexahedral meshing can simulate the structural characteristics of different scoliosis spines with more precision and make the stress distribution more uniform [43]. However, the construction of a high-precision individualized model requires manual matching with the details of scoliosis features, which can be extremely time-consuming. As a result, Hadagali et al. [17] proposed a block template method to construct a scoliosis thoracic spine model to improve the e ciency of modeling.
We believe that spinal exibility in AIS patients is an important manifestation of biomechanical characteristics, and optimization of the nite element model needs to consider spinal exibility. However, to the best of our knowledge, most models currently used to optimize the exibility statically and in a speci c state, and only the reduction degree in the range of exion, extension, lateral exion and rotation of the spine is consistent with AIS patients [18,44]. In this study, we utilized the dynamic exibility of AIS patients to optimize the nite element model. Although the dynamic exibility in vivo is only under a longitudinal traction load, it can still be viewed as an exploration of a novel method of model optimization.
The present study has some limitations. Firstly, only a one-case model was optimized, the type (Lenke 1) of scoliosis was simple, and the representativeness of the main curve Cobb angle was questionable. Secondly, the exibility of the spine in patients with scoliosis is affected by many factors, such as softtissue properties, but the model of the present study only optimized the elastic modulus of the intervertebral disc which was modelled as isotroptic with the same mechanical properties, while they may change depending on the spinal level. Meanwhile, the intervertebral disc was not distinguished between the nucleus pulposus and the annulus brosus. Instead, the annulus brosus was used as the main assignment subject. However, this does not affect the purpose that provide a new perspective and approach for model optimization of this study. Thirdly, the model was too simpli ed neglecting speci c anatomical structure (i.e. nucleous pulposus, facet joints) and simplifying the boundary conditions.
Although the purpose was to present a novel optimization method, more sophisticated model and realistic boundary conditions would undoubtedly increase the applicability. Finally, the dynamic exibility was only under longitudinal traction load and may not represent the overall exibility of one speci c patient. And also, it is not clear to which degree the disc properties are related to the traction forces. More comprehensive dynamic exibility evaluation methods would be worth studying in the future.

Conclusion
The use of dynamic exibility in vivo to optimize the nite element model can provide a new perspective and approach for model optimization in that it can reproduce the biomechanical characteristics in vivo of AIS patients.    Calculation method of Cobb angle in the nite element model. Two points of the superior endplate of the upper end vertebrae were selected and their coordinates were recorded as (X1, Z1), (X2, Z2), which were connected to obtain a straight line a, with the slope being k1; then the two nal points of the inferior endplate of the lower end vertebrae were selected and their coordinates were recorded as (X3, Z3), (X4, Z4), which were connected to get a straight line b, with the slope being k2. The angle between the two straight lines was the Cobb angle. Dynamic exibility curve of patient A and dynamic exibility curves of model A with different E(elasticity modulus).

Figure 6
Fit curves of dynamic exibility curve of patient A and dynamic exibility curves of Model A with different E(elasticity modulus).