Finite element analysis (FEA) is a sophisticated simulation method, and also an effective tool for elucidating biomechanics in the spine. In the biomechanical evaluations based on FEA, it is important to establish a model that can accurately reproduce the mechanical property of each part. Establishing such a model requires accurate data on anatomic structures and material properties [13
]. However, since ligaments show complicated material properties and large deformation, it is difficult to establish an accurate model of ligaments in FEA. Many researchers used two-dimensional tension-only truss or cable elements to describe the function of ligaments [11
]. In the present study, the surrounding ligaments were modeled with three-dimensional solid elements. The material properties of ligaments were simulated by hyper-elastic Ogden-3 formulation based on the experimental data. The validated results indicated that the model established in this study could effectively reproduce the mechanical behaviors of L1-S1 lumbar segment. In addition, another advantage of the model established in this study was that it could directly obtain the stresses and strains of the ligaments. The results may be useful to predict the chronic degeneration and disease of ligaments.
The intensive discussions among the three surgical scenarios were shown below.
Stresses of M8 PSF
The largest maximum stress on the M8 PSF was found in the PAIB model, with the PCP model following and the PCT model being the least in each loading condition. The increase in the stresses on the M8 PSF may induce the increase in the risk of the breakage of PSF. The maximum stress on the M8 PSF was significant larger in lateral bending and extension than in flexion and torsion. Therefore, clinically the patients were recommended to avoid excessive lateral bending and extension movements in the process of treatment and recuperation.
Stresses of cages
As the Ti material was stiffer than the PEEK material, both the maximum stress and the average stresses on the cages of PCT model were larger than those on the PCP model, which indicated that the Ti material cages in the PCT models suffered more stresses concentration than the PEEK cages. The greater stresses on cages may increase the risk of fine motion and mote on cages. The fine motion and mote of cages would cause inflammation of the fused segment and have adverse effect on the fusion process. So the PCT model was obviously inferior to the PCP model in this respect.
Stresses and strains on ligaments
Compared with the intact model, the stresses on ligaments of the three surgical models increased significantly and the maximum increase of the stresses located at the segments that proximally adjacent to fusion segment (See Table ). The greater stresses on ligaments were found in the PAIB model than the other two models. The maximum stress on PAIB model was about 8 times that of the PCT model and 5 times that of the PCP model, at the most.
The PAIB model also produced larger strains on the majority of ligaments. The ligaments were pre-stressed due to the increase of strains on ligaments, which reduced the ability of ligaments to resist stretching. The ligaments would be injured or fragmented more easily, when there is external load applied on the spine. The increase of stresses and strains on the ligaments also changed the normal physiological and mechanical environments of ligaments. These changes were likely relevant to the invocation of early pain and prone to cause chronic soft tissue injury and degeneration. In this respect, the PCP and PCT models were better than PAIB model. To our knowledge, there were few reports describing the stresses on ligaments in the PLIF procedure.
Stresses of the adjacent intervertebral discs
Both the postoperative following-up and biomechanical studies showed that the PLIF accelerated degeneration of adjacent segment and segmental instability [11
]. The FE results showed that great changes were found in the stresses on the discs proximally adjacent to the fusion segment. These great changes in discs could be used to interpret the clinical findings of early degeneration of adjacent disc [12
]. The increase of the maximum Von Mises stresses on adjacent discs during torsion was probably due to the following reasons: the M8 PSF restrained more ROM than other loading conditions. Thus, the ROM of the adjacent segment increased a lot. And the Von Mises stresses on adjacent discs also increased. The decreases of the stresses on the discs in the PAIB model were smaller than the other two surgical models, especially at fusion adjacent segments under extension, flexion and torsion. This result showed that the surgical method using AIB could decrease the risk of degeneration of fusion adjacent discs.
Maximum stress on the endplate of surgical segment
Of all the structures, the most significant changes in the maximum stress occurred on the L4 inferior endplate and L5 superior endplate. There were two main reasons that caused the tremendous increase in the stress on the endplates. Firstly, although the jagged edges of the cages avoided the relevant moments between endplates and cages, this design resulted in stress concentration. Secondly, the materials of PEEK and Ti were much stiffer than the bone grafts. So the phenomenon of stress shielding on cages was serious. The majority of the load was transferred onto the cages instead of the bone grafts. So the PLIF with cages caused tremendous increase in the stress on the endplates. Excessive stresses on the endplate may cause osteolysis of the endplate and subsidence of the fused segment. Compared with the surgical model using cages, the surgical model using AIB could reduce the stresses concentration on the endplates obviously, thus protect the endplate of the surgical segment.
From the results of stresses on the adjacent discs and the endplates, it was shown that the PAIB model was better than the other two models. Therefore, this surgical method was recommended for the elderly patients who had already suffered from the ASD and osteoporosis. This was because that the two major risks faced in the PLIF procedure were the further degenerative diseases of surgery adjacent segments and the subsidence or damage of endplate, which would eventually result in the failure of fusion surgery. Compared to the two models using cages, the PAIB model could effectively abate such phenomenon.
Average stresses on bone grafts
The ultimate purpose of the PLIF was to complete bone graft fusion, restoring the height of intervertebral space and finally achieving long-term stability of the lumbar spine. Therefore, the fusion rate of the bone grafts was the key point of the surgery, and it was also the issue that our study focused on. According to Wolff’s Law, bone can change its structure according to its mechanical environment. So the stresses on grafts may be used to predict the long-term fusion rate [20
]. As our FE results (see Table ) shown, the PCP and PAIB models got similar average stresses on bone grafts, and were both larger than the PCT model. This was mainly due to the low stiffness of AIB and PEEK material, which reduced the stresses shielding on bone grafts. Therefore, the average stresses on the bone grafts of the PCP and PAIB models were significantly larger than those on the PCT model. The contour plots of Von Mises stresses on the bone grafts were shown in Figure . It can be seen that the stresses of the PCT model mainly concentrated on the inferior or superior surface of the grafts, whereas not so much stresses traversed the central part of the grafts (see Figures
ab and c). On the other hand, the stresses distribution of the grafts in the PCP and PAIB models was more extensive (see Figures
d to g), which may better facilitate the fusion from grafts to endplate, and improve the efficiency of bone graft fusion.
Figure 5 Contour plots of Von Mises stresses on bone grafts for each surgical model in torsion. (a) the graft-1 in the PCT model, (b) the graft-2 in the PCT model, (c) the graft-3 in the PCT model, (d) the graft-1 in the PCP model, (e) the graft-2 in the PCP model, (more ...)
To conclude, the comparative results showed that the greatest stresses on cages and endplates were found in the PCT model, but the stresses on the bone grafts were found lowest in this model, so it may be inferior to the other two surgical models. The PCP model and PAIB model showed a similar considerable stresses on the bone grafts. However, the PCP model showed a decrease in the percentage change of ligaments and less stresses on PLIF. The PAIB model showed a decrease in the percentage change of adjacent discs and lower stresses on endplates.
There are certain limitations in this FE study. Firstly, The ANN was modeled with an isotropic hyper-elastic material model without the fiber-reinforced structure. Secondly, the facet joints and capsular ligaments were simplified to 30 spring elements. Under the actual condition, the structures are more complex. Thirdly, muscle contractions were not simulated in the current study. The muscle contractions may bring complicated external forces that have significant influences on the biomechanical perspective [9
]. The above factors will be considered in our further study. Although there were certain simplifications in our FE model, the FE model was well validated by the previous in vitro
study. Therefore, the model established in this study is reasonable and can be used as an efficient tool to evaluate the effects of three surgical scenarios on the lumbar spine.