Finite Element Analysis and in Vitro Biomechanical Experiment on the Effect of Unilateral Partial Facetectomy Performed by Percutaneous Endoscopy on the Stability of Lumbar Spine

Purpose: To investigate the lumbar biomechanical effects of unilateral partial facetectomy (UPF) of different facet joint (FJ) portions under percutaneous endoscopy. Methods: A 3D nite element (FE) model of the lumbar spine and 40 fresh calf spine models were used to simulate UPF under a physiological load performed through 3 commonly used needle insertion points (IPs) : (1) The apex of the superior FJ (as the rst IP), (2) The midpoint of the ventral side of the superior FJ (as the second IP), (3) The lowest point of the ventral side of the superior FJ (as the third IP). The range of motion (ROM) and the L4/5 intradiscal maximum pressure (IMP) were measured and analyzed under a physiological load in all models during exion, extension, left-right lateral exion, and left-right axial rotation. Results: When UPF was performed through the rst and the third IPs, the ROM of the lumbar spine and the L4/5 IMP in the FE model were signicantly increased compared with those in the intact FE model. When UPF was performed through the second IP, the ROM of the lumbar spine and the L4/5 IMP were not signicantly different compared with those in the intact FE model. When UPF was performed through the second IP, the ROM of the lumbar spine and the L4/5 IMP in the calf spine models were not statistically different from the intact calf spine model. Conclusion: UPF through the second IP resulted in a minimal impact on the biomechanics of the lumbar spine. Thus, it might be considered as the most appropriate IP for UPF. endoscopic lumbar surgery under local anesthesia: Discectomy, foraminoplasty, and ventral facetectomy.


Introduction
Lumbar instability often occurs after traditional open spinal surgery, leading to chronic pain in patients [1,2]. Thanks to the development of minimally invasive technology, percutaneous endoscopic transforaminal discectomy (PETD) is widely used in clinical practice due to its advantages, such as less damage and fast recovery [3,4]. However, PETD has its limitations. In order to effectively perform the endoscopic decompression and expand the working channel of the endoscope during the surgery, part of the bone structure of the superior facet joint (FJ) is often removed by facetectomy. Numerous studies showed that the integrity of the FJs is important to maintain the stability of the lumbar spine, since they are the main load-bearing structure of the spine [5][6][7][8]. The FJ can bear various forms of load such as compression, shear and axial rotation [9,10]. However, when the FJ cartilage is damaged, the concentration of in ammatory mediators in the joint cavity increases, stimulating the nerve ber endings in the FJ capsule, thus causing chronic pain in the FJs and accelerating their degeneration [11,12].
Clinical studies revealed that some patients show lumbar instability after PETD [13][14][15], demonstrating that different methods of facetectomy have different effects on the stability of the lumbar spine.
Biomechanical studies showed that the stability of the lumbar spine changes when more than 30% of the unilateral FJ is removed [16]. However, the method used for FJ resection in this study was not performed in the same way as it is performed in clinical practice, and the effect of resection of different FJ portions on lumbar spine stability has not been studied yet. Therefore, this study used 3D nite element (FE) models and calf spine models to simulate unilateral partial facetectomy (UPF) performed by PETD technology to explore the best approach to remove the FJ to achieve an adequate decompression without causing lumbar instability.
Material And Methods

Development of the 3D FE Model
A healthy male volunteer (30 years old, height 175 cm, weight 70 kg) with no previous family history of lumbar disease was selected to participate to our experiment. After the exclusion of the presence of low back pain, lumbar deformity and other lumbar diseases in the volunteer, the informed consent form was signed, and a 3D computed tomography (CT) scan of the lumbar spine was performed (General Electric Company, Boston, Massachusetts, USA) to obtain the lumbar CT data. The high-resolution CT data were stored in DICOM (Digital Imaging and Communications in Medicine) format and imported into the Mimics 15.0 software (Materialise, Leuven, Belgium) to develop the L3-S1 3D geometric model. The model was imported into the 3-matic 7.0 software (Materialise), and its modeling tools were used to build a model of intervertebral discs and the upper and lower cartilage endplates. Then the mesh derivation function in Geomagic Studio 12.0 software (Geomagic, Raleigh, North Carolina, USA) was used to repair and encapsulate the model, which was built as a surface model and exported to Pro/Engineer 5.0 (Parametric Technology Corporation, Needham, Massachusetts, USA) in IGES (Initial Graphics Exchange Speci cation) format to generate a solid model of each segment. Then, the model was imported into Hypermesh 14.0 (Altair, Troy, Michigan, USA) to obtain a mesh model and to select the material, and the obtained model was uploaded in the ANSYS 13.0 software (ANSYS Company, Canonsburg, Pennsylvania, USA) to facilitate the FE analysis.
The FE model was constructed and consisted of the cortical and cancellous bone, posterior elements, nucleus, annulus ground substance, annulus ber, anterior longitudinal ligament, posterior longitudinal ligament, ligamentum avum, transverse ligament, capsular ligament, interspinous ligament, supraspinous ligament, and bone graft. The elastic modulus and Poisson ratio for each element were obtained from a previous report [17]. The material parameters that were most appropriate to de ne the behavior of the FE model of the nucleus pulposus were modi ed to simulate a moderate degeneration of the L4-L5 intervertebral disc [18], while the speci c values of the material properties used in the model are presented in Table 1. The FE model of the L3-S1 segment was nally developed. Figure 1 shows the anterior, left side, and posterior view of the FE model. The model was composed of a total of 536741 grids and 874956 nodes.

Calf Spine Specimen Preparation
Forty fresh calf lumbar spinal segments (L3-L6) were collected from 15-month-old calves with homogeneous weight and spinal condition. All calf spine specimens were acquired following the National Institutes of Health Guidelines for the Use of Laboratory Animals, and all procedures were approved by the Nanjing Medical University Committee on Animal Care. The structural integrity of all specimens were checked by X-ray, and specimens with fractures, tumors and severe osteoporosis were excluded. All specimens were wrapped in gauze soaked in saline, and sealed with a double-layer plastic bag, and stored at -20°C. The fresh specimens, once stored at -20°C, did not show any alteration in the structure of the bones and ligaments, and their biomechanical properties did not change [19]. Before the test, the specimens were defrosted in an environment at 4°C for 12 hours and the muscle and adipose tissue were removed. The integrity of the bony structure, lumbar intervertebral disc, FJ and ligament tissue should be maintained by paying attention during the handling of the specimen, which was then covered with gauze soaked in saline to keep it moist. Since the calf specimens possessed a long transverse process, all calf specimens were partially cut (retaining approximately 7 cm in length) in order to facilitate the experiment operation. The two ends of the L3 and L6 segments of the specimen were xed in a special test mold using Kirschner wires, embedded in self-curing denture powder (dental polymethyl methacrylate), and kept horizontal to facilitate the installing of the specimen on the loading device.

Insertion point (IP) Determination
According to the actual clinical surgery method, facetectomy was performed by removing the ventral side of the superior FJ up to the dorsal side. Thus, three commonly used clinical needle IPs were selected: (1) The apex of the superior FJ (as the rst IP), (2) The midpoint of the ventral side of the superior FJ (as the second IP), (3) The lowest point of the ventral side of the superior FJ (as the third IP). In this experiment, a trephine with a diameter of 7.5 mm commonly used in clinical surgery was used to simulate the UPF.  Figure 3 shows the FE models after UPF. Figure 4 shows the percutaneous lumbar facetectomy instrument (Spinendos, Germany) used in the experiment. First, the tip of the duckbill protective sleeve was pushed from the lateral posterior approach through the lower half of the left intervertebral foramen of the specimen to the level of the upper endplate of the L5. The oblique opening of the sleeve faced the back side of the lumbar spine and the sleeve pressed against the IP on the L5 superior FJ. The sleeve formed an angle of 20° with the coronal surface of the lumbar spine specimen and was parallel to the plane of the intervertebral disc. The intervertebral foramen was formed and enlarged by the matching trephine through the inner cavity of the protective sleeve. The inner diameter of the enlarged protective sleeve was 8.0 mm, and the outer diameter of the trephine was 7.5 mm. Forty fresh calf spine specimens were randomly divided into 4 groups with 10 specimens in each group. The control group was represented by the intact calf spine. The Group A was represented by the calf spine model in which UPF was performed through the rst IP. The Group B was represented by the calf spine model in which UPF was performed through the second IP. The Group C was represented by the calf spine model in which UPF was performed through the third IP. Figure 5 shows the calf spine models after UPF.

FE model
After importing the intact model and the 3 UPF models into Ansys 13.0, the human physiologic parameters, boundary conditions, and applied loads were set to each model. All nodes at the bottom of the S1 segment of each model were set as fully constrained and then, a load of 400 N was applied to the upper end of the L3 vertebral body, which is equivalent to the force of the upper human body. A torque load of 10.0 Nm was set in various directions of the coordinate system (X, Y, Z) to simulate different movements [20]. The range of motion (ROM) and the L4/5 intradiscal maximum pressure (IMP) during exion, extension, left-right lateral bending, and left-right axial rotation were recorded and compared with the ones in the intact model.

Calf Spine Model
The calf spine specimens were thawed at room temperature for approximately 8 hours before the experiment, and the temperature of the specimens was kept cold before the test by surrounding the specimens with ice cubes to reduce tissue degeneration. A scalpel was used to perform a horizontal incision of 1 cm parallel to the endplate of the vertebral body in the center of the L4/5 intervertebral disc, the needle to test the pressure (approximately 1 mm in diameter) was inserted parallel to the endplate of the vertebral body into the posterior edge of the intervertebral disc, and the Gaeltec pressure sensor (Gaeltec Devices, UK) was connected to measure the IMP. Before the test, the calf spine specimens were xed on the Intron E10000 tension and torsion biaxial universal material biomechanical testing machine (INSTRON Corporation, USA) using a special xture for testing calf spine mechanics. An electronic digital level for spine biomechanical test installed above the special xture was present to measure lumbar spine ROM (Fig. 6). According to the standards of the calf spine specimen test proposed by Wilke et al. [21], the torque was set to 10 N·m and the constant axial pressure was set to 400 N. The specimens were loaded and unloaded twice to remove their viscoelasticity before measuring the ROM of the calf spine exion, extension, lateral bending, axial rotation and the L4/5 IMP, in order to ensure the accuracy of the data, and the results were recorded on the third round of measurements, so that relatively stable kinematic test data could be obtained. The specimens were continuously sprayed with saline during the entire test to keep them moist and minimize tissue degeneration.

Statistical Analysis
Statistical analysis was performed using SPSS (version 22.0; SPSS, USA). The independent-sample t-test was used to compare the difference between the intact and facetectomy group, the mean value and standard deviation (SD) were calculated and the measured data were expressed as "x ± s". All reported p values were two-tailed, and p values less than 0.05 were considered statistically signi cant. Then, the ROM of each segment in L3-S1 was measured. Our test data were compared with the data obtained by 3D FE models from a previous research study to evaluate the validity of the model [22]. Our results showed that the L3-S1 lumbar model in the normal physiologic state established in this simulation possessed an appropriate ROM under various conditions of motion, indicating that the model was appropriate (Figure 7).

L4/5 IMP
The cloud map of the stress distribution of the L4/5 intervertebral disc was generated using the Ansys 13.0 software. The L4/5 IMP increased the least in M2 and increased the most in M3 compared with its value in M0. The L4/5 IMP in M1 signi cantly increased in exion (45.2%) and extension (52.5%) compared with its value in M0. The L4/5 IMP in the exion, extension, left-right lateral exion, and leftright axial rotation was slightly increased in M2 compared with its value in M0, which was 9.4%, 10.5%, 6.6%, 7.3%, 9.3%, and 9.8% respectively. The L4/5 IMP in the exion, extension, and left-right axial rotation signi cantly increased in M3 compared with its value in M0, which was 55.5%, 68.2%, 56.9%, and 54.5%, respectively (P<0.05). The detailed data are listed in Figure 8.

ROM
The ROM of the L3-S1 FE model was calculated by Ansys 13.0 software. The ROM increased the least in M2 and increased the most in M3 compared with its value in the M0. The ROM in M1 regarding the left axial rotation increased by 35.5% compared with its value in M0. The ROM in the exion, extension, leftright lateral exion, and left-right axial rotation was slightly increased in the M2 compared with its value in M0, which was 4.6%, 9.4%, 5.3%, 4.8%, 8.5%, and 9.2% respectively, The ROM of the lumbar spine in the right lateral exion and left-right axial rotation was signi cantly increased in the M3 compared with its value in M0, which was 37.1%, 43.7%, and 40.4%, respectively (P<0.05). The detailed data are listed in Figure 9.

L4/5 IMP
The data of the pressure sensor in the L4/5 intervertebral disc of the calf spine specimen were recorded and analyzed. The L4/5 IMP signi cantly increased under extension in the group A compared with the control group (P<0.05). The L4/5 IMP slightly increased in the group B compared with its value in the control group during extension and left-right axial rotation, but the difference was not statistically signi cant. The difference in exion and left-right lateral exion was also not statistically signi cant compared with the control group. The L4/5 IMP signi cantly increased in the group C under extension and left-right axial rotation compared with its value in the control group (P<0.05). The detailed data are listed in Table 2.

ROM
The ROM of the calf spine specimens was obtained by recording the electronic digital level on the upper end of the specimen xture (Table 3). No signi cant difference in ROM was found under the six motions of exion and extension, left-right lateral exion and left-right axial rotation in group A and group B compared with the control group. However, the ROM was signi cantly increased under left-right axial rotation in the group C compared with its value in the control group (P < 0.05).

Discussion
Many studies reported that the deterioration of the biomechanical function is the most crucial reason for postoperative complications such as lumbar instability [23][24][25][26], which in turn causes chronic low back pain in the patients [27][28][29]. At present, lumbar instability is diagnosed by the relative displacement or angle of the vertebral body in the exion and extension positions. Hasegawa K. et.al also believe that the increase in the FJ space is the strongest predictor of lumbar instability [30]. Therefore, the integrity and health of the FJs are essential in the stability of the lumbar spine. FE analysis is considered as an important method in biomechanics research, since it effectively replaces the human body research and provides bio-realistic results in terms of trend analyses. According to different studies, the properties of materials can be changed by FE analysis, which can also generate and manipulate geometric shapes as needed [31][32][33]. The best choice for testing the biomechanics of lumbar spine is the use of specimens from a fresh human cadaver. However, it is di cult to obtain a su cient number of cadavers of the same age and gender. Therefore, animal specimens are the best choice for biomechanical experiments rather than specimens from human cadavers, and they can be obtained from several animals including dogs, pigs, calves, and sheep. Among them, calf vertebral bodies are similar in size to the human ones and have a wide variety of sources. Therefore, the experiments in this work were performed using 40 calf spine specimens to perform UPF.
During the PETD surgery, an insertion operation is performed under local anesthesia in the posterior aspect of the vertebral body to allow the direct entry into the spinal canal to perform the discectomy. The surgery is performed far from the outlet and dorsal root ganglia, avoiding as much as possible the muscles and ligaments adjacent to the vertebral body, but a partial destruction of the FJ is inevitable. Some biomechanical studies showed that the destruction of FJs increases the risk of spinal instability and spinal degeneration [34][35][36]. However, recent advances in FE research on facetectomy have been made. In 2014, Erbulut [37] performed an FE analysis and found that the FE model of the lumbar spine is severely affected in extension and axial rotation after the complete removal of one FJ side. Thus, lumbar fusion or pedicle screw xation is required after the removal of the bilateral FJs of the lumbar spine. However, in 2017, Zeng et al. [7] simulated the resection of the 50% of one FJ side on a lumbar FE model and they realized that the intradiscal pressure and intervertebral ROM were not signi cantly different from their value in the intact model. Thus, these patients do not need lumbar fusion or lumbar xation. On the other hand, in 2019, Li et al. [38] simulated the graded resection of the lumbar FJs through FE analysis and discovered that the removal of the 50% of the unilateral lumbar FJ increased the risk of biomechanical degeneration of the lumbar spine and the occurrence of failed back surgery syndrome. In 2020, S. Ahuja et al. [16] performed an FE analysis and discovered that the lumbar spine ROM, the pressure in the FJs and the pressure in the intervertebral disc signi cantly increase when more than 30% of an unilateral facet joint is removed. The conclusions of the above studies on the biomechanics of facetectomy are different, because none of these studies established a uni ed standard in the resection of the lumbar FJs. The experiments performed in previous works were mostly resection of the superior FJ from the dorsal side to the ventral side, which is not in agreement with what is performed in clinical practice, and the cutting method was a longitudinal cut of arti cial division [16,[37][38][39][40][41]. Indeed, a trephine is used in clinical practice to perform a cut from the ventral side of the superior FJ to the dorsal side, and from the head to the tail end [42][43][44]. The resected superior FJ is left with an arc-shaped gap. Therefore, the previous studies are not applicable in clinical surgery, thus having less signi cance.
The three IPs selected in our experiments were needle IPs currently used in clinical surgery, with the rst IP (the apex of the superior FJ) as the most commonly used IP. The percutaneous endoscopic discectomy was invented in 1993 by the German spine surgeon Hoogland Thomas [45] who chose the apex of the superior FJ as the needle IP [46,47]. Therefore, this IP was selected also in this work as one of the IPs to perform the experiments. In our experiment, the height of the L5 superior FJ of the lumbar FE model was 13.4 mm, the average height of the L5 superior FJ of the calf spine models was greater than 13 mm, and the radius of the trephine was 3.75 mm, thus, the height of the superior FJ was su cient to divide the three IPs, all placed at the edge of the superior FJ. Facetectomy performed through the ventral edge of the superior FJ can maximize the expansion of the intervertebral foramen. In addition, the test data on these three IPs could be compared with each other to evaluate the impact of facetectomy of the different FJ portions on the biomechanics of the lumbar spine.
The bilateral FJs and the intervertebral disc form a spine unit that shares the pressure of the trunk on the vertebral body [48][49][50]. Since the top of the superior FJ is triangular, a stress concentration may easily occur at the tip of the superior FJ under physiological conditions, meaning that the stress sustained in this point is relatively large. The facetectomy performed through the rst IP resulted in a destruction of the integrity of the superior FJ, leading to stress redistribution, and the larger stress sustained by the apex of the superior FJ was distributed to the adjacent intervertebral disc and the contralateral FJ. The FE analysis revealed that the ROM of the lumbar spine in M1 was increased by 35.5% compared with its value in M0 in the left axial rotation, and the L4/5 IMP during exion and extension was increased by 45 This work has a limitation. No specimens from cadavers were used to perform the in vitro biomechanical studies due to the reasons explained above in articles already published, thus, calf spine specimens were preferred since calf vertebral bodies are similar in size to the human ones, and because calf spine specimens represent the best replacement for cadaver spine specimens to perform biomechanical research. However, in the present experiments the FJs of the calf spine specimens possessed thicker joint capsules and greater bone density, which increased the di culty in the removal of the excess muscle and soft tissues from the specimens. The outer diameter of the trephine used in the experiment was 7.5 mm, therefore, the biomechanical effect of other size trephine or tools used for facetectomy on the lumbar spine needs further study and additional clinical research.

Conclusions
In conclusion, although the rst IP is the most commonly used IP in the PTED surgery, our results showed that it was not the most appropriate IP in the analysis of FE biomechanics and in vitro biomechanical experiment. UPF performed through the midpoint of the ventral side of the superior FJ resulted in a minimal impact on the biomechanics of the lumbar spine, suggesting that it might be the most appropriate IP for UPF. Our conclusion allows the re nement of the current guidelines in performing percutaneous endoscopy, providing a theoretical basis for clinicians in the choice of the most appropriate IP to perform UPF.