Biomechanical Evaluation of Cortical Bone and Traditional Trajectories for Lumbar Single Level Segment Fixation

Background: The aim of this study was to evaluate the biomechanical stability of a lumbar internal xation system with 3 different xation techniques by the establishment of a three-dimensional nite element (FE) model of lumbar single level xation. Methods: A three-dimensional osseoligamentous nonlinear FE model of osteoporosis lumbar 4-5 (male, aged 57 years, height 170 cm, weight 70 kg, bone mineral density T value -2.8SD) was built to detect the biomechanical stability of an internal xation system with the following 3 screw trajectories: traditional pedicle screw trajectory xation (TT), cortical bone trajectory (CBT) screw and hybrid pedicle screw xation (CBT + TT). The location and area of maximal equivalent stress and the angular displacement of this lumbar model with different screw trajectories were measured in anterior bending, posterior extension, lateral bending and during rotation. Results: The angular displacement of this lumbar model with the 3 different screw trajectories was similar, all of which could restrict the angular displacement of lumbar vertebrae. The maximal equivalent stress was located at the border of the CBT screw and rod, with the hybrid screw xation technique in axial rotation. Conclusion: The use of CBT and TT screws in lumbar internal xation had similar stability. The CBT screw could be an alternative solution to lumbar short-segmented xation, but temporary immobilization would be required to avoid the failure of CBT screw xation due to the increasing stress in position of extensive lateral bending and rotation.

stress was located at the border of the CBT screw and rod, with the hybrid screw xation technique in axial rotation.
Conclusion: The use of CBT and TT screws in lumbar internal xation had similar stability. The CBT screw could be an alternative solution to lumbar short-segmented xation, but temporary immobilization would be required to avoid the failure of CBT screw xation due to the increasing stress in position of extensive lateral bending and rotation. Background A pedicle screw xation system with excellent biomechanical stability is bene cial to the reconstruction of stability of spinal sequence and its fusion. It is the key to the curative effect of surgery for lumbar fusion [1,2]. However, cases of internal xation failure are not uncommon, due to loosening of the pedicle screw, screw exit or breakage and other complications. This failure occurs more commonly in elderly patients [3,4]. The current study suggests that elderly patients with osteoporosis or degenerative lumbar instability need more powerful internal xation and holding forces to maintain the stability of postoperative spinal stabilization [4].
In 2009, Santoni et al. [5] reported a new method -cortical bone trajectory (CBT). They tried to increase the screw in the nail holding force by changing the screw trajectory. Compared to the traditional trajectory (TT), axis of the pedicle was applied as a channel, so that the inclined screw could make better use of the pedicle cortical bone part, to ensure that the screw and cortical bone are embedded in each other. A subsequent biomechanical study con rmed its pullout strength was better than a TT screw [5].
At present, a CBT screw has been applied to lumbar internal xation systems by some surgeons, and they found that the fusion rate in patients with CBT screw internal xation was similar to those with traditional screws; The operative time and intraoperative blood loss were signi cantly reduced [6,7]. However, the CBT screw has not been widely applied in the clinic, which may be mainly attributed to the fewer biomechanical studies on CBT screw internal xation, with the clinical use of a CBT internal xation system still lacking a su cient theoretical basis.
The FE method is a standard engineering technique in general used in the design of airplanes, machines and bridges. In the analyze of bone joints such as spines, which have complicated shapes, load and boundary conditions, FE method can be a useful tool [8]. Using special software, it allows the modeling of complex structures by splitting the structure into numerous, simple FEs, each of which is easy to characterize and model mathematically. The lumbar FE model includes the vertebrae, intervertebral discs, endplates, posterior bony elements and all seven ligaments (the anterior and posterior longitudinal ligaments, ligamentum avum, facet capsules, and the intertransverse, interspinous and supraspinous ligaments) had been set up during last decades and facilitated the study of lumbar biomechanical characteristics [9][10][11][12].
Therefore, we conducted this study to investigate the biomechanical characteristics of TT and CBT screw internal xation by the establishment of a three-dimensional FE model of lumbar spine short segmental xation.

Methods
The establishment of the FE model All study procedures and experiment protocols were performed in accordance to standard guidelines approved by the Ethics Committee of Experimental Research, Huashan Hoapital, Fudan University (Shanghai, China). An osteoporosis volunteer (male, 57 years old, height 170 cm, weight 70 kg, bone mineral density T value − 2.8SD) was used to create a three-dimensional osseoligamentous nonlinear FE model ( Fig. 1). No Congenital bone disease and lumbar disease were found in volunteer. The geometry of the bony structures was generated from computed tomography images (slice thickness 0.625 mm) of L4-L5 segments. After that, a 3D reconstruction of the model based on computed tomography images was performed using Mimics 10.0. Then we used Geomagic 12.0 software to translate the reconstruction to a Nurbs surface model according to its anatomical structure. At last, the FE model was conducted in Hypermesh 12.0 and the output imported into Abaqus 6.12 for nonlinear FE analysis. Written informed consent was obtained from this volunteer and ethical approval was given by the medical ethics committee of Fudan university.
The L4-L5 vertebra were simpli ed as isotropic and elastic materials and described by 2 parameters, namely the elastic modulus and Poisson's ratio. The material property was assigned in the FEA module of software Mimics 10.0 according to the grey value. The number of materials was set to 15. The Poisson ratio of the L4-L5 vertebra was 0.3. The relationship between density and grey value was determined using the following empirical equation: The relationship between density and Young's modulus was determined using the following empirical equation: The intervertebral disc consisted of nucleus pulposus, annulus brosus and cartilaginous endplates. The nucleus pulposus comprised 43% of the total disc volume and was positioned slightly posterior to the disc center [9]. The annulus consisted of annulus bers and annulus ground substance. The orientations of the annulus bers were ± 23° at the anterior side and increased to ± 58° at the posterior side. The ratio of ber volume to the volume of surrounding annulus ground substance was 5% at the inner layers and increased to 23% at the outer layers [10,13]. The annulus ground substance and nucleus were modeled with tetrahedral solid elements (C3D8), and the annulus bers were modeled with tension-only truss elements (T3D2). The surfaces of the facet joints were simulated using a cartilaginous layer (C3D6). The contact between the facet joints was simulated with surface-to-surface hexahedral solid elements without friction. All 7 ligaments (anterior and posterior longitudinal ligaments, inter-and supraspinous ligaments, facet capsular ligaments, ligamentum avum, and intertransverse ligaments) were modeled as tension-only truss elements with nonlinear elastic properties. The materials used in the model were assumed to be homogeneous and isotropic. The material properties of the various spinal components were derived from the literature as speci ed in Table 1 [11,12].

FE models of implants
The size of the TT pedicle screw was 45 mm × 6.5 mm. The size of the CBT pedicle screw was 35 mm × 5.5 mm. We placed TT screws into the vertebral body along an anatomical axis of the pedicle and parallel to the vertebral endplate. According to Matsukawa's research, the origin of CBT was situated at the lateral aspect of the pars interarticularis projecting in the 5 O'clock orientation in the left pedicle and the 7 O'clock orientation in the right pedicle. As a result,CBT screws were placed 10°laterally in the axial plane and 25°cranially in the sagittal plane [14].
Three types of xation technique using TT and CBT were studied: traditional trajectory pedicle screw xation (TT) (Fig. 2a), cortical bone trajectory for lumbar pedicle screw xation (CBT) (Fig. 2b), and hybrid pedicle screw xation (cortical bone trajectory screws in upper vertebrae and traditional trajectory screws in lower vertebrae) (Fig. 2c). The compressive constructs were modeled by Abaqus version 6.12. The FE L4-L5 model underwent bilateral facetectomy and partial laminectomy to replicate the improved transforaminal lumbar interbody fusion surgery when titanium alloy screws and connecting rods were used. The friction coe cient among the screws, connecting rods, and bone was set as in nite. A tie constraint at the interface of the pedicle screw and rod was used to simulate the rigid xation.

Loading and boundary conditions
The L5 vertebra in the load simulation was restrained, while the superior surface of L4 was given a 500 N compressive preload to mimic upper body weight. The nodes on the upper surface of the L4 vertebra were used as a reference node for load application. The exion/extension, lateral bending, and axial rotation were simulated by a bending moment generated through a 15 Nm force applied to the superior surface of the L4 vertebra. Data analyses were performed by Abaqus 6.12.

Observed indicators
The location and area of maximal equivalent stress and the angular displacement of this lumbar model with different screw trajectories were measured in anterior bending, posterior extension, right lateral bending and right rotation.

Results
The validation of FE model In order to ensure the accuracy of the intact L4-L5 FE model, we compared the results with previous studies [11,15,16]. The entire moment-rotation curve on the conditions of exion, extension, lateral bending and axial rotation demonstrated the nonlinear behavior of our FE model. Furthermore, the axial displacement curve of the vertebral body under different distribution pressure was compared with the previous FE studies in literature [17][18][19].

Angular displacement of FE models and stress of implants
The angles of the normal lumbar model in anterior bending, posterior extension, lateral bending and rotation were 1.17°, 1.17°, 1.15°and 1.24°, respectively. The axial displacement of lumbar 4-5 FE model was 0.29 mm, 0.54 mm, 0.78 mm, and 1.03 mm under a pressure of 500 N, 1,000 N, 1,500 N and 2,000N, which was in accordance with previous studies [20,21]. Figure 3 shows the normal lumbar model and its angular displacement with the 3 types of xation technique in anterior bending, posterior extension, right lateral bending and rotation. The angular displacement in the CBT lumbar model was slightly higher than those in the other 2 models; however, the 3 types of xation technique could restrict obviously the angular displacement of lumbar vertebrae when compared with the angular displacement of normal lumbar spine.
The maximal equivalent stress with the 3 types of xation technique was located at the border of the screw and rod, but the individual location had some slight change for these techniques (Fig. 4). The maximal equivalent stresses in anterior bending with TT, CBT and hybrid xation techniques were located at the border of lower vertebral screw and rod, which were 176 Mpa, 207.6 Mpa and 152.2 Mpa, respectively. Similarly, the maximal equivalent stresses in the posterior extension with TT, CBT and the hybrid xation technique were also located at the border of the lower vertebral screw and rod, which were 151.3 Mpa, 217.4 Mpa and 232.2 Mpa, respectively. In the condition of right bending, the lower vertebral screw at the left side was bearing a higher load for the TT and CBT screws xation (220 Mpa, 288 MPa). The maximal equivalent stress with the hybrid xation technique was located at the CBT screw in the left upper vertebra (380.7 MPa). In the condition of axial rotation to the right, the stress concentration with the TT screw was located at the border of the upper vertebral screw and rod, with 320.1 MPa of maximum equivalent stress. For CBT screw internal xation, the maximum equivalent stress was located at the border of the lower vertebral screw and rod (778.9 MPa). For hybrid screw internal xation, the maximum equivalent stress was located at the border of CBT screw and nail rod (812 Mpa) (Fig. 5).

Discussion
At present, most tests have been performed through cadaver simulation of pedicle screws in screw detection, and the results have shown that the CBT screw has good biomechanical properties, but the results of the same index are not entirely consistent. For example, in the cadaver experiments of Santoni et al. [5] and Matsukawa et al. [14], the CBT screw had a stronger anti-pullout force and torque. But in the study of Baluch et al. [22], the anti-pullout strength of the two kinds of screws was not obviously different. In the experiment of Perez-Orribo et al. [23], CBT screw and TT screw lumbar specimens had the similar performances in the aspect of anti-axial pullout. The differences are closely related to the objects of the researches. Although lumbar specimens can accurately re ect the biomechanical and morphological characteristics of lumbar vertebrae, during CBT screw placement, it cannot ensure the consistency and accuracy of the angle of pedicle screws. The deviation of position and the standard requirements of nail will lead to biased results. But in the case of screw misplacement, specimens cannot be replaced, so the repeatability of experiments is poor. Unlike cadaver studies, three-dimensional FE software with good repeatability and accuracy can completely copy each structure and simulate the lumbar biomechanical characteristics, and at the same time can choose the screw entry point and screw direction in accordance with appropriate standards [24].
The main purpose of lumbar internal xation is to restrict segmental motion, thus providing a good environment for fusion. Oshino [25] found that intervertebral stability after CBT xation was similar to that of TT xation by using a sheep cadaveric spine model. Through this experimental research, we found that the angular displacement of this lumbar model with the 3 different xation techniques was a little different in anterior bending, posterior extension, lateral bending and rotation, but all could restrict the angular displacement of lumbar vertebrae signi cantly when compared with normal lumbar vertebrae, thereby indicating that the 3 types of internal xation techniques could provide a relative stable fusion environment.
The maximum equivalent stress could estimate the risk of internal xation fracture [4]. The results of the present studies suggested that the equivalent stress with a CBT screw was obviously larger than that with a TT screw, which could result from: 1) the length of the CBT screw in the vertebral body being shorter; the CBT screw being shorter and only xed at the lumbar posterior column, which could cause screw stress concentration when lumbar stress was transmitted to the screw, and this was different from the TT screw [14]; 2) The direction of the CBT screw did not match with the normal direction of lumbar activities. In axial rotation, the implanting angle of the contralateral CBT screw was in the opposite direction of lumbar spine motion, leading to increased stress at the border of the screw and rod. Therefore, the authors thought that temporary postoperative immobilization would be required to avoid CBT screw loosening or fracture due to increased stress.
Regarding the lumbar internal xation method, surgeons should consider both the biomechanical characteristics of the internal xation system and the intraoperative speci c conditions. The entry point of the CBT screw was closer to the center line than that of the TT screw, thus less vertebral muscles detachment before screw implantation would be needed for a CBT screw, reducing the operative time and intraoperative bleeding. This would be bene cial when the operative eld is hard to expose due to obesity and patients with poor surgery tolerance [6,7]. With the advent of the CBT screw, some scholars used a combination of CBT and TT screws; the distance between the upper and lower vertebral screw nail was then shortened, which could shorten the incision in single segmental lumbar internal xation surgery to 5 cm, thus further decreasing intraoperative blood loss [26]. Therefore, a CBT screw would be of certain advantages in the clinical application compared with a TT screw.
Our research has its limitations. In the clinic, screw tap importing and screw selection bias before nailing can affect screw stability. In this paper, in terms of FE analysis, Because of the direct screw placement in the preset position and the lack of clinical prenail operation, therefore, it is impossible to simulate errors caused by the preset. Although the study of the single segment lumbar spine proved the biomechanical of CBT screw in internal xation of vertebral body. But there is still a need for long term follow-up, in order to understand the advantages and disadvantages of a CBT screw system in lumbar fusion xation.

Conclusion
In this study, we establish 3 different FE models of single level lumbar xation. According to our study, the use of CBT and TT screws in lumbar internal xation could provide similar stability for single level lumbar xation. The CBT screw could be an alternative solution to lumbar short-segmented xation, but temporary immobilization would be required to avoid failure of CBT screw xation due to the increasing stress in position of extensive lateral bending and rotation.
Abbreviations FE: nite element; CBT: cortical bone trajectory; TT: trajectory xation Declarations Ethics approval and consent to participate All study procedures and experiment protocols were performed in accordance to standard guidelines approved by the Ethics Committee of Experimental Research, Huashan Hoapital, Fudan University (Shanghai, China).

Consent for publication
Signed informed consent was obtained from volunteer.

Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests
The authors indicated no potential con icts of interest.