What causes different coronal curve patterns in idiopathic scoliosis?

Background Adolescent idiopathic scoliosis (AIS) is a three-dimensional deformity of the spinal column in otherwise healthy adolescents. The underlying mechanisms associated with the spinal deformity development have been explored which delineated the role of the sagittal curvature of the spine. The patterns of the spinal deformity vary between the AIS patients as shown in several classification systems. It remains to further investigate how variations in sagittal profiles result in different coronal plane deformities in AIS and how these deformation patterns are intrinsically different. Methods A total of 71 Lenke 1 and 52 Lenke 5 AIS patients were included retrospectively. The 3D models of the spine were generated from biplanar radiographs to calculate the clinical spinal parameters, vertebral axial rotations, and the 3D centerline of the spinal curvature. A classification based on the centerlines’ axial plane projection was developed. The 3D curvature of the centerline was calculated at each point. A 2D elastic rod finite element model (FEM) of the sagittal spinal curvature for each axial subtype was developed to calculate the 3D deformity of the spine under gravity and axial torsion. Differences in the axial clusters’ clinical parameters, curvature of the spine, and the deformation patterns of the FEM were compared. The characteristics of the sagittal curvature of these axial clusters were determined. Results Lenke1 was divided into two axial groups (I and II) whereas the Lenke 5 cohort all had the same axial projection pattern (loop shape). T5-T12 kyphosis was significantly different between Lenke1-Group I and the other two groups, p=0.04. The vertebral rotation in both Lenke1-Group I and Lenke 5 had only one maximum value and the FEM deformed in a loop shaped whereas Lenke1-group II showed two maximum values for vertebral rotation and the FEM of the centerline deformed in a lemniscate shape. The ratio of the spinal arc lengths above and below the sagittal inflection points for Lenke1-Groups I and II and Lenke 5 were 0.52, 1.16, and 3.24, respectively. Conclusion Variations in the axial plane projection of the curve were observed within Lenke types. Lenke 1- Group I and Lenke 5 showed similar 3D curve characteristics suggesting one 3D curve whereas Lenke1-Group II, with two 3D curves, behaved differently. The length of the spinal arcs above and below the sagittal inflection point related to the patterns of axial deformity.


Introduction
Classification systems of adolescent idiopathic scoliosis (AIS) play an important role in clinical management of the disease [1,2]. The current widely-used classification system of AIS, Lenke classification, primarily is based on the curve appearance in the frontal plane, with a minor role for the sagittal plane [2]. 3D curve subtypes have been identified within the Lenke subtypes [3,4]. However, it has not been determined whether the 3D characteristics of the curves follow the current clinical classification of the AIS.
Lenke determined 6 subtypes of AIS with complementary modifiers to provide guidelines for surgical treatment [2]. This system classifies the AIS patients, based on the number of structural curves in the frontal plane to one curve scoliotic types (Lenke1 and Lenke5), twocurve scoliotic types (Lenke 2, 3, and 6), and a three-curve scoliosis (Lenke 4). Threedimensional classification of the curves resulted in more than 6 curve patterns in AIS, sub classifying the patients within the Lenke types [3][4][5]. But it was not determined how different aspects of the 3D curves vary within and between the Lenke types. More importantly, it was not determined whether the mechanism of the scoliotic curve development can be explained using the similarity or differences between the 3D curve types. A better description of the fundamental 3D characteristics of the scoliotic curves can have an important role in understanding the pathogenesis of the curve development and subsequent clinical management of the disease [6,7].
As shown previously, the axial projection of the curve carries important information for surgical and non-surgical management of the right thoracic AIS [6,[8][9][10]. It was also shown that the sagittal profile strongly relate to the patterns of axial deformation using mechanics of deformation in an elastic rod [3,11,12]. Here, it is studied if the axial projection of the curve varies within the Lenke types and whether that variation relates to the sagittal curvature of the spines within these subtypes. As the prevalence of Lenke 1 (thoracic curve) (51%) and Lenke 5 (thoracolumbar/lumbar curve) (12%) is among the highest in AIS patients [13], it was aimed to determine the differences in the 3D curve characteristics of the Lenke 1 and Lenke 5 curves based on an axial classification of the curves. The hypothesis was that variation in the axial plane projections of the curves exists independent of the frontal curve classification but related to the sagittal profile of the spine. The differences between the 3D characteristics of the axial subtypes were used to discuss the mechanics of the various frontal curve pattern developments in these AIS subtypes.

Methods
Subjects: A total of 71 Lenke1 and 52 Lenke 5 AIS were selected retrospectively and consecutively. All patients had biplanar standing radiographs and bending films to verify the Lenke types. Male and female patients between 12-17 years old were included. Patients with previous spinal surgery, spondylolisthesis, congenital spinal abnormalities, and neuromuscular conditions were excluded.
Image processing: 3D reconstructions of the spinal radiographs were created in SterEOS 2D/3D (EOS imaging, Paris, France). The 3D reconstruction algorithm allows identifying several anatomical landmarks on the coronal and lateral radiographs to create the 3D morphology of the vertebral bodies based on a statistical model [14]. The 3D models then were used to extract the vertebral centroids and create the 3D centerline of the spine by connecting the 17 vertebrae centroids of the thoracic and lumbar spine [15]. This centerline was isotropically normalized in a way that all the spines have the same heights while modifying the antero-posterior and lateral coordinates by the same factor. The reliability of this method in evaluating the 3D spinal curves was shown previously [3,15].
Axial classification of the curves The 3D centerlines of the Lenke 1 and Lenke 5 patients were clustered based on the variations in the axial projections of the curves. The number of clusters was determined based on the silhouette values [16]. The silhouette value determines the maximum number of the groups with significantly different curve patterns [16]. K-means clustering then was performed to divide the cohort into the number of clusters determined by the silhouette value.
Spinal and pelvic parameters: The spinal and pelvic parameters (Thoracic and lumbar Cobb angles, T5-T12 Kyphosis, L1/S1 lordosis, pelvic incidence, sacral slope, and vertebral axial rotation) were calculated using the 3D models of the spine in each cluster. Vertebral rotation was determined by the angle between the axial projection of the vector connecting the posterior and anterior landmarks on the vertebral endplate and the true horizontal axis (Y-axis) connecting the femoral head centers [17]. The reliability of identifying these landmarks were determined previously [15].
Geometrical parameter: Using the spinal centerlines, the curvature of the 3D centerline at each vertebral level was calculated. The curvature of the centerline at each point can be considered as the inverse of the radius of a circle that best fits the curvature at that point and mathematically calculates as how rapidly the tangent to the curve changes direction between two consecutive points ( Figure 1).

Biomechanical parameters:
The sagittal curvature of the spine, without considering the frontal deformity, was used to develop a 2D reduced order finite element model (FEM) of the spine [12]. The S shaped (sagittal profile) 2D model of a homogeneous, isotropic, slender elastic rod (Young modulus=1000Pa and Poisson ratio=0.3) with a circular cross section, was loaded by vertical loading (gravity) at each vertebral level and a torsional moment representing the trunk mass asymmetry as shown in [18]. This model previously generated the 3D deformation patterns of the scoliotic spine [12]. The reduced-order FEM was created for all the axial clusters to calculate the 3D deformation patterns.
Finally, the sagittal curvature of the spine in each axial subtypes were characterized by the length of the positive and negative arcs and the position of the inflection point ( Figure 1).
The inflection point was determined at the center of the section without any curvature in the sagittal plane ( Figure 1).

Statistical analysis
The clinical, geometrical, and biomechanical parameters were compared between the clusters in Lenke 1 and Lenke 5 cohorts using an analysis of variance followed by a post hoc test (ANOVA and Turkey's test for normally distributed data and Kruskal-Wallis and Dunn's test when normality was rejected).  Figure S1). Although both anterior-posterior and lateral deviations of the axial projections were different between the two most distinguished clusters in Lenke 5 patients, the patterns of the axial deformity did not differ between the two clusters (supplementary materials, Figure S1). Table 1 summarizes the spinal and pelvic measurements in the two clusters of Lenke1 and in Lenke 5. Thoracic Cobb angles were statistically different between the Lenke 1 (Groups I and II) and Lenke 5 cohorts, p=0.032 and p=0.037, respectively. T5-T12 kyphosis was statistically different between Lenke 1-Group I and Lenke 5,p=0.041. Figure 3 shows the axial rotation of the vertebral bodies in the three clusters. Similar patterns were observed for Lenke 1-Group I and Lenke 5 patients with one peak (maximal) for vertebral rotation whereas the vertebral rotation plot for Lenke 1-Group II showed two peaks related to the axial rotation of the apical vertebrae in the thoracic and lumbar curves (Figure 3). This suggests Lenke 1-Group I and Lenke 5 are the true "single curves" whereas Lenke1-Group II has two 3D curves, without the lumbar being structural yet.

Spinal and pelvic parameters:
Geometrical parameters: Figure 4 shows the curvature vector, representing its magnitude, of the three curves at each vertebral level along the spine in three views ( Figure 4A Biomechanical parameters: Figure 5 shows the deformation patterns of the 2D finite element models, of the S shaped sagittal geometry as shown in figure 2A. The deformation patterns of the Lenke 1-Group I and Lenke 5 were looped shaped whereas the Lenke 1-Group II showed a lemniscate axial projection, as also was seen in the clinical data (Figure2 B).

Discussion
This study aimed to show how the intrinsic characteristics of the 3D scoliotic curves vary within and between the two most prevalent AIS curve types i.e., Lenke1 and Lenke 5. Our results determined that a subgroup of Lenke 1 (Group I) and Lenke 5 patients present with similar shape of axial projection (loop shape) showing one true 3D curve whereas the Lenke 1-Group II showed two 3D curves and a lemniscate axial projection ( Figure 6). Comparing the sagittal curvature of these subtypes revealed that the length of the positive and negative curvatures of the sagittal profile was significantly different in Lenke1-Group I and Lenke 5 whereas the lengths of these two arcs were more similar, compared to the other two groups, in Lenke1-Group II ( Figure   6). This result showed the link between the axial projection, sagittal profile, and the coronal deformity of the spine in scoliotic subtypes.
It was previously showed that two axial subgroups exist in right thoracic AIS: loops shaped and lemniscate shaped [3,19]. The sagittal curvature of the spine relates to the pattern of the 3D deformity development, particularly the aforementioned axial subgroups of right thoracic AIS [19]. When the spine was considered as a curved elastic rod, it was shown quantitatively that the distribution of the moments along the spine are altered by the initial geometry of the sagittal spinal curvature which in turn results in different 3D deformation patterns among scoliotic patients [11,19]. Considering the sagittal profiles in the subgroups of Lenke1 (Figure 6 ), it is expected that the two sagittal subtypes deform differently. The sagittal profile of the spine is  Figure 6). As the moments that rotate the spine off the sagittal plane are a function of the sagittal curvature, particularly the angle between the tangent to the spine and horizontal line [11], it is expected that the maximum off-plane deformation occurs at different locations of the spine in these subtypes ( Figure 7A). The area above the lower apex in the sagittal plane in Lenke 5 and the area below the upper apex in Lenke 1-Group I are subject to maximum moment due to the inclination of the curves in those regions. These moments that bend the curve off the sagittal plane are responsible for frontal deformity in the thoracolumbar/ lumbar section in Lenke 5 and in the mid thoracic section in Lenke 1-Group 1 (figure 7B). As a result, the deformed spines, in both Lenke1-Group I and Lenke 5 when projected on to the axial plane form a loop shape, i.e., only one 3D curve. In Lenke 1-Group II the sections with minimal tangent angle (maximum moment) fall between the two apices of the sagittal curve resulting in deformation of the kyphotic curve above the inflection point and deformation of the lordotic curve below the inflections point, creating two 3D curves in this subtypes. These two curves when projected on the axial plane form a lemniscate shape (Figure 7). This explains why the axial plane curve characteristics are similar in Lenke1-Group I and Lenke 5 but differ from Lenke1-Group II.
The mechanics of elastic rods were used to explain scoliotic curve development in AIS from a mechanical standpoint [11,12]. It was shown that higher rod inclination results in an increased moment on the rod [11]. This theory is similar in concept to the posterior shear theory that believes an increased posterior shear in posteriorly inclined vertebrae results in rotational instability of the spine [20]. However, different from the shear theory, that was based on the preexisting rotation of the vertebral bodies [21,22], the rod theory showed that physiological loading of the spine can result in rotation of the kyphotic and lordotic sections of a 2D S shaped curve while exposing the most inclined vertebrae (posteriorly or anteriorly) to higher 3D deformations (Figure 7). The rod theory also differs from the shear theory, as in the latter the shear force is responsible for creating a moment that rotates the vertebrae whereas the rod theory  Figure 6A and Figure 7). It is expected that excessive forward tilt of the vertebrae above and below the cranial and caudal apices also result in the curve deflection, given that the moment is large enough to exhaust the bending modulus of the spine. If the two apices of the sagittal curve are close to each other, the anteriorly inclined vertebrae above or below the cranial and caudal curves can also rotate and create a third 3D curve as seen in Lenke 4 or compensatory curve in other curve types. Finally, while studies have alluded to the genetic factors affecting the morphology of the hip and knee and the pathway of developmental musculoskeletal diseases [24,25], the role of genetics in variation is sagittal alignment of the spine remains to be further explored.
The clinical classification of the spine should aim to guide the surgical decision-making.
In the context of selective fusion of the spine in AIS, considering the described 3D characteristics of the curve in this study can guide the fusion level selection. A short fusion that does not include the entire 3D curve in subjects with a loop shaped axial projection (Lenke 1-Group I and Lenke 5) can lead to postural compensation and need for revision surgery [26]. In Lenke 1-Group II with two 3D curves, and the secondary curve not being structural yet, it is expected that fusion of the main thoracic curve, as an adequate kyphosis is being imparted, can change the force distribution along the spine and de-twist the secondary curvature (lumbar) spontaneously. Finally, it is expected that the Lumbar modifier As and hypokyphosis Lenek1s are mostly in Lenke1-Group I and lumbar modifier Cs and normal/hyperkyphosis in Lenke1-Group II [3], however considering the true number of the 3D curves can eliminate the error associated with the classification of the borderline cases and improve the surgical planning.