Finite element study on effect of follower load on intersegmental rotation, facet joint force and nucleus pressure of the cervical spine

Background: The follower load is used to simulate the physiological compressive load of human spine. These compressive loads can maintain cervical spine’s mechanics stability and play a significant role in improving load-carrying capacity of the cervical spine. However, under different follower loads the biomechanical response of the cervical spine is unknown. So the aim of this study is to investigate the effect of follower load on biomechanics of the cervical spine. Results: In this study, a three-dimensional nonlinear finite element (FE) model of the cervical spine (C3-C7) was built and validated. Using this FE model of the cervical spine, we evaluated the effect of different follower loads on intersegmental rotation, facet joint force, and nucleus pressure in the cervical spine. The results indicated that with the follower load increased, the intersegmental rotation of the cervical spine in extension decreased, but the intersegmental rotation in other postures increased. The follower load increased the facet joint forces in all postures. In lateral bending (LB), the facet joint forces were only generated in the ipsilateral facet joints. In axial rotation (AR), there was a large asymmetry in the facet joint forces, and this asymmetry worsened with the follower load increased. The nucleus pressure of each segment nonlinearly increased with the follower load increased in all postures. Conclusion: An comprehensive analysis in intersegmental rotation, facet joint force and nucleus pressure under different follower loads can provide us a deeper understanding of the follower load in the human spine.

technical barriers and ethical conflicts in vivo experimental studies., later most researchers have chosen to investigate nucleus pressure by utilizing in vitro experiments methods. However, to date few researchers have used FE models to determine the changes of nucleus pressure of the cervical spine under different follower load [15]. It is worth noting that the FE models is easier to modify the material properties of cervical spine and is more suitable for performing parameter analysis.
Accordingly, the purpose of this study is to determine the effect of the follower load on biomechanics of cervical spine. To do so, a three-dimensional nonlinear FE model of the C3-C7 segment of cervical spine was developed and validated. Using this FE model of the cervical spine, we evaluated the effect of various follower loads (0 N, 50 N, 100 N, 150 N) on intersegmental rotation, facet joint force, and nucleus pressure in cervical spine.

Calibration and validation
The calibration processes are shown in Figs. 1 (a-c) and the validation results are shown in Figs. 2 (a-c), and Figs. 3 (a-d). The intersegmental rotation obtained by this finite element model were compared with the cadaver experiment data [40][41][42][43][44].

Facet joint force
In different postures, the predicted facet joint forces of different segments when under various follower loads are shown in Figs. 5 (a-c). In flexion, some facet joints had no facet joint forces, but the facet joint forces also increased with follower load increased. In extension, the facet joint forces of the C3-C4 segment were higher than other segments, while the load transmitted through the facet joint at the C4-C5 segment was the smallest. At the same time, the facet joint forces increased with an increase in the follower load. The facet joint forces on the left and right sides were not significantly different.
During LB, a facet joint force was generated only in the ipsilateral facet joint. For example, during right bending a facet joint force was generated only in the right side facet joint, and during left bending a facet joint force was generated only in the left side facet joint. As shown in Fig. 5 (b), the contact force of the facet joints on the left and right sides were not significantly different. And the facet joint forces increased with the follower load increased in LB. However, as shown in Figs. 5 (c), there was a large asymmetry in facet joint forces during AR. For example, during right axial rotation the facet joint forces on the left side were much larger than the facet joint forces on the right side. Similarly, during left axial rotation the facet joint forces on the right side were much larger than the facet joint force on the left side.
This asymmetry was even more obvious with higher follower loads. During AR, the facet joint force of the facet joints on both sides increased with an increase of the follower load. The nucleus pressure significantly increased as the follower load increased during LB and also during AR. And during LB or AR, the values of the nucleus pressure were not significantly different.

Discussion
A three-dimensional FE model of the cervical spine(C3-C7) was built and validated.
Using this three-dimensional FE model of the cervical spine, we evaluated the influence of the follower load on intersegmental rotation, facet joint force, and nucleus pressure in the cervical spine.
With an increase on follower load, the intersegmental rotation of all segments increased when in flexion, and the intersegmental rotation of all segments decreased when in extension. This result is similar to a previous study by Ng et al., who found similar increases in intersegmental rotation during cervical flexion when applying 100 N and 150 N compressive preloads at C5-C6 segment [3]. Kevin et al.
applied a 100 N follower load to cadaver specimens of the cervical spine using a robot tool and reported that the intersegmental rotation of C4-C5 segment and C5-C6 segment increased slightly in flexion, similar to the results in our study [13]., Barrey [48][49]. Therefore, the inclusion of LB and AR in our study make it difficult to directly compare the findings of the present study to previously published work.
In this study, the change characteristics of multi-segmental cervical facet joint forces when under physiological compressive load were studied, which. can be used as a supplement to the follower load research. After static analysis, different response values of the facet joint forces when under follower load were observed at different postures (Figs. 5 (a-c)). In flexion, the gap between the two articular cartilage will become larger, so most of the facet joints have no contact forces. An obvious increase in facet joint force due to a follower load while in an extension posture is observed in Fig. 5 [20], and the reported facet joint forces of the C67 segment from that study are similar to our results in extension and LB, but our reported joint forces are slightly greater during axial rotation. The reason for this difference may be partially due to some facet joint forces not being recognized as a result of the compressive load impact in the experimental study. In addition, Barrey et al. found that the facet joint force increased systematically when applying a compressive preload to cervical spine specimens [15]. Patwardhan et al. reported that the cervical spine's carrying capacity increased sharply under a follower compression load and the facet joint force also increased [1]. The above change trends of the facet joint forces are all in general agreement with the results of our study.
To our knowledge, only Hattori et al. has attempted to measure the nucleus pressure of the cervical spine using in vivo experiments method. They found that the nucleus pressure of a healthy intervertebral disc was more and more larger from the supine position to sitting position and the nucleus pressure in sitting position was approximately 1.5 times greater than in supine position. Therefore, the effect of increasing follower load can be considered to be similar to the effect of moving a person from supine to a sitting position.
Pospiech et al. explored the relationship between the muscle strength and pressure into disc and found that the muscle strength played a significant role in increasing nucleus pressure [50]. And the follower load is generated by the synergy of muscle tissue. That is to say, the application of a follower compressive load will cause nucleus pressure of the cervical spine increase and the above change trend is agreement with our result. At the same time, Pospiech et al. specifically investigated the nucleus pressure of C3-C4 and C5-C6 under muscle load, finding that their values showed an increase to 1.2 times and 2.7 times respectively. Our findings confirmed those of the previous literatures, with a significant increase in nucleus pressure at both the C3-C4 and C5-C6 intervertebral discs with application of the follower load. In addition, Kevin et al. tested twelve human cervical spine cadaver specimens using a robotic test device and found that the nucleus pressure of C4-C5 segment and C5-C6 increased by 4.6 times and 2.6 times respectively after applying a 100 N follower load [13]. These results are very similar to the results of our study. Barrey et al. evaluated the change trend of nucleus pressure in cervical spine under 50 N follower load and their findings also indicated that nucleus pressure increased with the application of a follower load [15]. Additionally, in our study the nucleus pressure varied nonlinearly as increasing follower load, which may be because nucleus pulposus and annulus ground were defined as incompressible hyper elastic materials. The material properties of the different cervical spine tissues (Tables 1) were taken from the literature [28, [34][35]. The facet cartilage and each part of the vertebra were defined as linear isotropic elastic material. The nucleus pulposus and annulus ground were simulated as incompressible hyper-elastic materials [35]. As specified by Shirazi-Adl et al. [36], the fibers were simulated as tension-only truss. The ligaments were simulated as connector elements with nonlinear properties and their nonlinear material properties were determined according to previous research [37].
The material properties and element types of each component of cervical spine model (C3-C7) are shown in Table 1. Loading and boundary conditions

Calibration and validation
The FE model was calibrated and validated before being used to calculate data. The calibration processes were implemented according to the method proposed by Nicole et al. [39]. The correction factors of the collagen fibers and ligaments were modified, and the intersegmental rotation of each segment under the action of moment load was calculated and compared with the experimental data from previous research to validate the finite element model [40][41][42][43][44]. The effect of the follower load on the nucleus pressure of the cervical spine in six directions.

Figure 7
A three-dimensional nonlinear FE model of the cervical spine (C3-C7).