Manipulations of Oblique Pulling Affect Sacroiliac Joint Displacements and Ligament Strains: A Finite Element Analysis

Objective Clinical studies have found that manipulation of oblique pulling has a good clinical effect on sacroiliac joint pain. However, there is no uniform standard for manipulation of oblique pulling at present. The purpose of this study was to investigate the effects of four manipulations of oblique pulling on sacroiliac joint and surrounding ligaments. Methods A three-dimensional finite element model of the pelvis was established. Four manipulations of oblique pulling were simulated. The stresses and displacements of sacroiliac joint and the strains of surrounding ligaments were analyzed under four manipulations of oblique pulling. Results Manipulation of oblique pulling F2 and F3 caused the highest and lowest stress on the pelvis, at 85.0 and 52.6 MPa, respectively. Manipulation of oblique pulling F3 and F1 produced the highest and lowest stress on the left sacroiliac joint, at 6.6 and 5.6 MPa, respectively. The four manipulations of oblique pulling mainly produced anterior-posterior displacement. The maximum value was 1.21 mm, produced by manipulation of oblique pulling F2, while the minimal value was 0.96 mm, produced by manipulation of oblique pulling F3. The four manipulations of oblique pulling could all cause different degrees of ligament strain, and manipulation of oblique pulling F2 produced the greatest ligament strain. Conclusions The four manipulations of oblique pulling all produced small displacements of sacroiliac joint. However, they produced different degrees of ligament strain. Manipulation of oblique pulling F2 produced the largest displacement of sacroiliac joint and the greatest ligament strain, which could provide a certain reference for physiotherapists.


Introduction
Lower back pain usually caused by lumbar diseases, including myofasciitis, lumbar disc herniation, and lumbar spondylolisthesis, is a common clinical symptom [1][2][3]. In recent years, it has been found that the lesion of sacroiliac joint (SIJ) can also cause lower back pain, accounting for 14.5%∼22.5% [4]. Commonly, abnormal gait, heavy physical exertion, leg length discrepancy, and scoliosis may be factors related to SIJ pain without specifc causes. Te mechanism may include the following processes: pathogenic factors acting on the auricular surface of the sacrum and ilium may cause injury to the ligaments or muscles around the SIJ, which will result in slight movement of the SIJ, making the joints difcult to reset. Te mechanical environment of the joints may ultimately be imbalanced, and the soft tissues will be damaged. Tis condition is clinically referred to as SIJ subluxation [5].
Tere are many treatment methods for SIJ subluxation, mainly including the following: (1) take nonsteroidal antiinfammatory drugs (NSAID) and drugs for promoting blood circulation, so as to achieve the efects of antiinfammatory, and promote blood circulation and remove blood stasis [6,7]. (2) Inject glucocorticoids into the SIJ via a guide wire to produce a direct anti-infammatory efect [8][9][10]. (3) Pull the subluxated SIJ back to the normal position by manipulation to reduce nerve stimulation and relieve pain [11][12][13][14]. At present, the three methods have been applied in clinical treatment, and manipulation is the most widely used [15,16].
Manipulation relieves the low back pain by changing the mechanical environment of SIJ and surrounding tissue. Tis treatment method has little side efects, and can be easily accepted by patients. A large number of clinical studies have shown that manipulation of oblique pulling (MOP) has a good efect on SIJ subluxation [17][18][19]. Te detailed procedure are as follows: the patient is in the right decubitus position. Te right lower extremity is straight, and the left lower extremity is slightly bent. Te therapist stands at the patient's ventral side. Te therapist holds the patient in position with one hand on the back of the sacrum, the other hand on the anterior-superior spine, pushing the ilium towards the back. However, the position and direction of the manipulative force varies from therapists. Tere is no uniform standard for MOP at present. Does MOP with diferent force points and directions produce diferent efects on the SIJ and its surrounding ligaments? None of these issues has been studied. Terefore, this study intends to establish a three-dimensional fnite element model of the pelvis and explore the efects of MOP on the stress and displacement of SIJ and strain of the surrounding ligament by simulating four common MOPs.

Model Construction.
A 3D fnite element model of the pelvis was established. Tree-dimensional models of the sacrum and ilia were reconstructed from the computed tomography (CT) images of a healthy male volunteer (34 years old, 170 cm in height, and 65 kg in weight) using Mimics 20.0 (Materialise Company, Leuven, Belgium), and the cortical and cancellous regions of the bones were distinguished. Axial slices 0.5 mm thick spanning the entire pelvis were selected for model construction. All surface models were meshed using Geomagic 2013 (Raindrop Company, Marble Hill, USA). Te SIJ was composed of cartilage and the endplate of the sacrum and the ilia, with their surrounding ligaments. Te cartilage was reconstructed with a uniform thickness. Te regions of the articular surfaces were based on CT images, and the thicknesses of the cartilage were acquired from the literature [20]. Te sacral and iliac cartilages had thicknesses of 2 mm and 1 mm, respectively. Te bone endplate thicknesses of the sacral and iliac parts of the cartilage were assumed to be 0.23 mm and 0.36 mm, respectively. Te gap between the two cartilages was set at 0.3 mm [20]. Te material properties chosen from previous studies [20,21] are summarized in Table 1.
Te anterior sacroiliac ligament (ASL), short posterior sacroiliac ligament (SPSL), long posterior sacroiliac ligament (LPSL), sacrospinous ligament (SS), interosseous sacroiliac ligament (ISL), and sacrotuberous ligament (ST) complexes were modelled as 3D tension-only truss elements. Te material properties of each ligament were obtained from the literature [21]. Te attachment regions were chosen according to the literature [20]. In total, the pelvic model contained 458,867 elements and 201,982 nodes. Figure 1 shows the intact model with ligamentous attachments.

Simulation of MOPs.
Te simulation of MOP was as follows: the magnitudes of the forces were determined by determining the manipulative power of fve therapists using a biomechanical testing machine. Te average manipulative force was 600 N [22]. Terefore, a large part of the sacrum and the right iliac crest were fxed. Ten, a push force of 600 N along the ventral-dorsal direction was applied to the left anterior-superior spine or anterior-inferior iliac spine.
Tere were four MOPs. MOP-F1: the force was applied at the left anterior-inferior iliac spine in a direction of 30°f rom the sagittal plane which roughly paralleled to the SIJ surface. MOP-F2: the force was applied at the left anteriorinferior iliac spine, parallel to the sagittal plane. MOP-F3: the force was applied at the left anterior-superior iliac spine in a direction of 30°from the SIJ surface. MOP-F4: the force was applied at the left anterior-superior iliac spine, parallel to the sagittal plane. Te detailed loading and boundary conditions, as well as the x-, y-, and z-axes, are described in Figure 2. Te compressive stresses and displacements of SIJ and the strains of ligaments for four MOPs were then investigated using Abaqus 2018 (Dassault Systèmes S. A Company, Massachusetts, USA).

Mesh Convergence Study.
In order to evaluate the degree of accuracy of the pelvic model, the mesh convergence study was carried out. Four mesh models were established according to diferent mesh fneness. Te number of elements and nodes in each model are shown in Table 2. Following boundary conditions and material properties, loads, and constraints were described in detail in the abovementioned sections. MOP-F1, F2, F3, and F4 were applied to these meshes. Finally, the maximum stresses and displacements of the four models on the left SIJ surface of the sacrum under four MOPs were analyzed.

Model Validation.
Two studies were performed to validate this model. For the pelvic model, the distribution of the main strain of the pelvis was compared with that reported in the study of Zhang et al. [23]. In our model, the distribution of the main strain of the pelvis was analyzed under the single-legged stance. For the sacrum model, the relationship between displacement and load was compared with that indicated in cadaveric [24] and computational studies [20,25]. When the bilateral ilia were fxed, fve translational forces (anterior, posterior, superior, inferior, and mediolateral) of 294 N and three moments (fexion, extension, and axial rotation) of 42 Nm were applied to the centre of the sacrum, respectively. Te displacements of a node lying in the midsagittal plane between the inferior S1 and superior S2 vertebral endplates were calculated. In this model, the displacements were investigated under the same loading.    3 and mesh 4 under four MOPs were less than 5%, which was considered as reasonably close ranges. According to these results, mesh 3 with 458,867 elements was selected for further study.

Model Validation.
Te stresses were located mainly in the upper and posterior areas of the acetabulum and extended to the iliac crest, the incisura ischiadica major, and the rear acetabulum. Te area of stress concentration and maximum value of stress were consistent with those reported in a previous study [23]. Under eight loading conditions, the displacements agreed not only with those in an experimental study but also with those in some computational studies [20,24,25], and these results are shown in Figure 4.

Discussion
SIJ subluxation is a common clinical disease [26,27]. Te main cause of the disease is the minor displacement of SIJ or the injury of surrounding ligaments. According to many clinical reports [17,28,29], MOP could achieve good results in the treatment of SIJ subluxation. However, MOP has had no uniform standard for force point and direction. In this study, we established a three-dimensional fnite element model of the pelvis to explore the efects of MOP with diferent force points and directions on SIJ. MOP-F1 and F2 were applied at the anterior-inferior iliac spine, while MOP-F3 and F4 were applied at the anterior-superior iliac spine. Te force direction of F1 and F3 were roughly parallel to the SIJ surface, and the force direction of F2 and F4 were parallel to the sagittal plane of the pelvis. Anatomically, the anterior-inferior iliac spine is located inside and below the anterior-superior iliac spine, closer to the SIJ surface. Terefore, under the same direction of manipulation, MOP-F1 and F2 could produce greater maximum stress on the left hemi-pelvis than MOP-F3 and F4. In addition, since the anterior-superior iliac spine was closer to the iliac crest region, MOP-F3 and F4 also caused greater stress on the left iliac crest region than MOP-F1 and F2. From the perspective of the mechanical mechanism, the direction of manipulation parallel to the sagittal plane is more likely to produce greater stress on the left hemi-pelvis than that parallel to the SIJ surface. Furthermore, the torque on the right hemi-pelvis was also greater, which could lead to greater stress on the right hemi-pelvis. Terefore, MOP-F2 and F4 produced greater stress on the left and right pelvis than MOP-F1 and F3.
Te lower 1/3 part of SIJ is the synovial joint, and the posterior and upper 1/3 part of SIJ is connected by the interosseous ligaments [30], so the motion of SIJ is mainly undertaken by the lower 1/3 part of SIJ. Te stresses on SIJ surfaces of the sacra produced by four MOPs mainly distributed in the front and lower part of SIJ surfaces, which was related to the anatomical structure of SIJ. Due to the force point located on the left pelvis, the greater stresses were observed on the left SIJ surfaces under four MOPs. Compared with MOP-F2, MOP-F1 produced a smaller maximum stress on the left SIJ surface, which was connected to the direction of MOP-F1 parallel to the SIJ surface. Compared with MOP-F4, MOP-F3 produced a greater maximum stress on the left SIJ surface. Tis phenomenon suggested that the SIJ surface was compressed and the motion forms of SIJ included translation and rotation.
Te displacement of the left SIJ was greater than that of the right side under four MOPs. Te displacement of the left SIJ was 0.96∼1.21 mm in AP direction, 0.03∼0.12 mm in MI direction, and 0.05∼0.31 mm in SI direction. Te values were all within 3 mm, which was consistent with previous research results [31,32]. Under four MOPs, the displacement in the AP direction was the largest in the three directions, which might be related to the fact that MOP could turn the pelvis outward. In the AP direction, MOP-F2 and F4 produced the largest displacement of the left SIJ. Te directions of forces applied by MOP-F2 and F4 were parallel to the sagittal plane, which was more likely to cause SIJ movement in the AP direction than the directions of the force parallel to the SIJ surface. In the MI direction, MOP-F3 and F4 produced the largest displacements. Te force points of the two manipulations were at the anteriorsuperior iliac spine, which were far from the SIJ surface. Tus, the force arm was longer, which was easier to produce displacement in the MI direction. Te sacrum is broad at the top and narrow at the bottom. It is wedge-shaped and     lies between the iliac bones on both sides forming SIJ [33]. Tis special structure makes the SIJ move up easily, but move down difcultly. Te anterior-inferior iliac spine is located inside and below the anterior-superior iliac spine. Tus, MOP-F1 and F2 applied at the anterior-inferior iliac spine could produce a larger upward displacement in the SI direction.
Ligaments play an important role in maintaining pelvis stability. Abdelfattah and Moed [34] found that the pubic symphysis and the anterior sacroiliac ligament played a key part in maintaining pelvis stability when the pelvis sufered "book-turning" violence. Sichting et al. [35] considered that the ligaments around SIJ not only played a role in maintaining mechanical stability of SIJ, but also acted as a neuromuscular feedback mechanism. Eichenseer et al. [25] through a fnite element model, demonstrated that with the decrease of ligament stifness, the stress and movement of SIJ would increase. Bohme et al. [36] found that the anterior sacroiliac ligament and the sacrotuberous ligament bore the largest load in the case of anterior and posterior compression fractures of the pelvis, accounting for 80% and 17% of the total load, respectively. Te sacrospinous ligament played an important role in maintaining vertical stability of the pelvis. Our results indicated that the strains of the sacrospinous ligament, the anterior sacroiliac ligament, and the interosseous ligament were larger than the other three ligaments in most cases under four MOPs. Among them, the strain of sacrospinous ligament caused by MOP-F2 was the largest, at 4.29%. Under MOP-F2, the displacement of SIJ was the largest, which led to the largest ligament strain. Te anterior sacroiliac ligament is a broad and thin ligament located in the front of SIJ. Te main displacement under four MOPs was in the AP direction, so the anterior sacroiliac ligament would produce a greater strain.
In this study, there were four types of MOP. MOP-F2 and F4 produced the larger displacement in the AP direction, at 1.21 and 1.11 mm, respectively. It showed that the manipulation parallel to the sagittal plane could cause a larger displacement. In addition, MOP-F2 and F4 also caused greater ligament strains. It could be seen that MOP-F2 and F4 are more efective manipulations to cause the displacement of SIJ and the strain of the surrounding ligaments.
Tere are some limitations in this study. First, the fnite element model was established based on a single individual, while there are individual diferences on age and gender for SIJ. Second, the ligaments in this model were built with linear materials, which had certain infuence on refecting the strain of ligaments. Tird, this pelvic model only contained bones and ligaments. Soft tissues such as muscles and the skin were not considered. Fourth, manipulations were analyzed based on a normal SIJ in this model, but manipulations were applied to the subluxated SIJ clinically, so the results could not fully refect the biomechanical characteristics of manipulations. Perhaps the diseased SIJ was less stable and easier to reduce under manipulation. Te establishment of the fnite element model of SIJ subluxation will beneft the further study of the disease.

Conclusions
In this study, a three-dimensional fnite element model of the pelvis was established, and four manipulations with diferent force points and diferent directions were studied. Te results showed that MOP-F3 and F4 caused greater stresses on the SIJ surface. Te four MOPs all produced small displacements of the SIJ and diferent degrees of ligament strain. Among them, MOP-F2 and F4 could produce greater displacements of SIJ and ligament strains. MOP-F1 and F2 applied on the anterior-inferior iliac spine mainly produced the displacement in AP and SI directions, while F3 and F4 applied on the anterior-superior iliac spine mainly produced the displacement in AP and MI directions.

Data Availability
Te data used to support the fndings of this study are available from the corresponding authors upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.