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

Manipulations of Oblique Pulling Affect Sacroiliac Joint Displacements and Ligament Strains: A... Hindawi Journal of Healthcare Engineering Volume 2023, Article ID 2840421, 10 pages https://doi.org/10.1155/2023/2840421 Research Article Manipulations of Oblique Pulling Affect Sacroiliac Joint Displacements and Ligament Strains: A Finite Element Analysis 1,2 2 2 3 2 Zhun Xu , Ziyu Feng, Zhaocong Zhang, Kunmu Zhang , and Yikai Li Department of Spine Surgery, Te First Afliated Hospital, Hengyang Medical School, University of South China, Hengyang 421000, Hunan Province, China School of Traditional Chinese Medicine, Southern Medical University, No. 1838, Guangzhou Avenue North, Baiyun District, Guangzhou 510515, Guangdong Province, China Te Second Afliated Hospital of Fujian University of Traditional Chinese Medicine, No. 282 Wusi Road, Gulou District, Fuzhou 350003, Fujian Province, China Correspondence should be addressed to Kunmu Zhang; 277873495@qq.com and Yikai Li; lyk_doc@163.com Received 6 October 2022; Revised 11 December 2022; Accepted 15 December 2022; Published 3 January 2023 Academic Editor: Elisabetta Zanetti Copyright © 2023 Zhun Xu et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Objective. Clinical studies have found that manipulation of oblique pulling has a good clinical efect on sacroiliac joint pain. However, there is no uniform standard for manipulation of oblique pulling at present. Te purpose of this study was to investigate the efects of four manipulations of oblique pulling on sacroiliac joint and surrounding ligaments. Methods. A three-dimensional fnite element model of the pelvis was established. Four manipulations of oblique pulling were simulated. Te 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. Te four manipulations of oblique pulling mainly produced anterior-posterior displacement. Te 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. Te four manipulations of oblique pulling could all cause diferent degrees of ligament strain, and manipulation of oblique pulling F2 produced the greatest ligament strain. Conclusions. Te four manipulations of oblique pulling all produced small displacements of sacroiliac joint. However, they produced diferent 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. which will result in slight movement of the SIJ, making the 1. Introduction joints difcult to reset. Te mechanical environment of the Lower back pain usually caused by lumbar diseases, in- joints may ultimately be imbalanced, and the soft tissues will cluding myofasciitis, lumbar disc herniation, and lumbar be damaged. Tis condition is clinically referred to as SIJ spondylolisthesis, is a common clinical symptom [1–3]. In subluxation [5]. recent years, it has been found that the lesion of sacroiliac Tere are many treatment methods for SIJ subluxation, joint (SIJ) can also cause lower back pain, accounting for mainly including the following: (1) take nonsteroidal anti- 14.5%∼22.5% [4]. Commonly, abnormal gait, heavy physical infammatory drugs (NSAID) and drugs for promoting exertion, leg length discrepancy, and scoliosis may be factors blood circulation, so as to achieve the efects of anti- related to SIJ pain without specifc causes. Te mechanism infammatory, and promote blood circulation and remove may include the following processes: pathogenic factors blood stasis [6, 7]. (2) Inject glucocorticoids into the SIJ via acting on the auricular surface of the sacrum and ilium may a guide wire to produce a direct anti-infammatory efect cause injury to the ligaments or muscles around the SIJ, [8–10]. (3) Pull the subluxated SIJ back to the normal 2 Journal of Healthcare Engineering Table 1: Material properties of the sacrum, ilium, pubic symphysis, position by manipulation to reduce nerve stimulation and and endplate. relieve pain [11–14]. At present, the three methods have been applied in clinical treatment, and manipulation is the Young’s modulus Poisson’s ratio most widely used [15, 16]. (MPa) Manipulation relieves the low back pain by changing the Cortical 12,000 0.3 Sacrum mechanical environment of SIJ and surrounding tissue. Tis Cancellous 100 0.2 treatment method has little side efects, and can be easily Cortical 12,000 0.3 Ilium accepted by patients. A large number of clinical studies have Cancellous 100 0.2 shown that manipulation of oblique pulling (MOP) has Pubic 5 0.45 a good efect on SIJ subluxation [17–19]. Te detailed symphysis procedure are as follows: the patient is in the right decubitus Articular 100 0.3 position. Te right lower extremity is straight, and the left cartilage lower extremity is slightly bent. Te therapist stands at the Endplate 1000 0.4 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 according to the literature [20]. In total, the pelvic model contained 458,867 elements and 201,982 nodes. Figure 1 towards the back. However, the position and direction of the shows the intact model with ligamentous attachments. 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 2.2. Simulation of MOPs. Te simulation of MOP was as on the SIJ and its surrounding ligaments? None of these follows: the magnitudes of the forces were determined by issues has been studied. Terefore, this study intends to determining the manipulative power of fve therapists using establish a three-dimensional fnite element model of the a biomechanical testing machine. Te average manipulative pelvis and explore the efects of MOP on the stress and force was 600 N [22]. Terefore, a large part of the sacrum displacement of SIJ and strain of the surrounding ligament and the right iliac crest were fxed. Ten, a push force of by simulating four common MOPs. 600 N along the ventral-dorsal direction was applied to the left anterior-superior spine or anterior-inferior iliac spine. 2. Materials and Methods Tere were four MOPs. MOP-F1: the force was applied at the left anterior-inferior iliac spine in a direction of 30 2.1. Model Construction. A 3D fnite element model of the from the sagittal plane which roughly paralleled to the SIJ pelvis was established. Tree-dimensional models of the surface. MOP-F2: the force was applied at the left anterior- sacrum and ilia were reconstructed from the computed inferior iliac spine, parallel to the sagittal plane. MOP-F3: the tomography (CT) images of a healthy male volunteer force was applied at the left anterior-superior iliac spine in (34 years old, 170 cm in height, and 65 kg in weight) using a direction of 30 from the SIJ surface. MOP-F4: the force Mimics 20.0 (Materialise Company, Leuven, Belgium), and was applied at the left anterior-superior iliac spine, parallel the cortical and cancellous regions of the bones were to the sagittal plane. Te detailed loading and boundary distinguished. Axial slices 0.5 mm thick spanning the entire conditions, as well as the x-, y-, and z-axes, are described in pelvis were selected for model construction. All surface Figure 2. Te compressive stresses and displacements of SIJ models were meshed using Geomagic 2013 (Raindrop and the strains of ligaments for four MOPs were then in- Company, Marble Hill, USA). Te SIJ was composed of vestigated using Abaqus 2018 (Dassault Systemes S. A cartilage and the endplate of the sacrum and the ilia, with Company, Massachusetts, USA). their surrounding ligaments. Te cartilage was recon- structed with a uniform thickness. Te regions of the ar- ticular surfaces were based on CT images, and the 2.3.MeshConvergenceStudy. In order to evaluate the degree thicknesses of the cartilage were acquired from the liter- of accuracy of the pelvic model, the mesh convergence study ature [20]. Te sacral and iliac cartilages had thicknesses of was carried out. Four mesh models were established 2 mm and 1 mm, respectively. Te bone endplate thick- according to diferent mesh fneness. Te number of ele- nesses of the sacral and iliac parts of the cartilage were ments and nodes in each model are shown in Table 2. assumed to be 0.23 mm and 0.36 mm, respectively. Te gap Following boundary conditions and material properties, between the two cartilages was set at 0.3 mm [20]. Te loads, and constraints were described in detail in the material properties chosen from previous studies [20, 21] abovementioned sections. MOP-F1, F2, F3, and F4 were are summarized in Table 1. applied to these meshes. Finally, the maximum stresses and Te anterior sacroiliac ligament (ASL), short posterior displacements of the four models on the left SIJ surface of the sacroiliac ligament (SPSL), long posterior sacroiliac ligament sacrum under four MOPs were analyzed. (LPSL), sacrospinous ligament (SS), interosseous sacroiliac ligament (ISL), and sacrotuberous ligament (ST) complexes were modelled as 3D tension-only truss elements. Te 2.4. Model Validation. Two studies were performed to material properties of each ligament were obtained from the validate this model. For the pelvic model, the distribution of literature [21]. Te attachment regions were chosen the main strain of the pelvis was compared with that Journal of Healthcare Engineering 3 SPSL ASL LPSL SS ST (a) (b) Figure 1: Ventral (a) and dorsal (b) views of the fnite element model. Ligaments are represented in color lines, with red arrows identifying each ligament complex (note the interosseous sacroiliac ligament is not visible in anterior-posterior views). ASL indicates anterior sacroiliac ligament; LPSL, long posterior sacroiliac ligament; SPSL, short posterior sacroiliac ligament; SS, sacrospinous ligament; ST, sacrotuberous ligament. L L L L F3 F1 F4 F2 PA PA PA PA (a) (b) (c) (d) RLRLRL RL F3 F1 F4 F2 (e) (f ) (g) (h) Figure 2: Loading and boundary conditions for four manipulations of oblique pulling. Te yellow triangles represent the fxed sites of the pelvic model. Te superior view (a, b, c, and d) and frontal view (e, f, g, and h) of the pelvis are shown, (a) and (e) manipulation of oblique pulling-F1; (b) and (f ) manipulation of oblique pulling-F2; (c) and (g) manipulation of oblique pulling-F3; (d) and (h) manipulation of oblique pulling-F4. reported in the study of Zhang et al. [23]. In our model, the and superior S2 vertebral endplates were calculated. In this distribution of the main strain of the pelvis was analyzed model, the displacements were investigated under the same loading. 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 3. Results studies [20, 25]. When the bilateral ilia were fxed, fve translational forces (anterior, posterior, superior, inferior, 3.1. Mesh Convergence Study. Te maximum stress and and mediolateral) of 294 N and three moments (fexion, maximum displacement on the left SIJ surface of the sacrum extension, and axial rotation) of 42 Nm were applied to the were analyzed for each of the meshes, under MOP-F1, F2, centre of the sacrum, respectively. Te displacements of F3, and F4, which are shown in Figure 3. Te diferences in a node lying in the midsagittal plane between the inferior S1 maximum stress and maximum displacement between mesh 4 Journal of Healthcare Engineering Table 2: Element and node numbers for four diferent mesh resolutions. Element number Node number Mesh 1 142,007 58,480 Mesh 2 243,492 101,724 Mesh 3 458,867 201,982 Mesh 4 1,051,834 481,435 0.12 0.09 0.06 0.03 2 0.00 0 500000 1000000 1500000 0 500000 1000000 1500000 Number of Mesh Elements Number of Mesh Elements MOP-F1 MOP-F3 MOP-F1 MOP-F3 MOP-F2 MOP-F4 MOP-F2 MOP-F4 (a) (b) Figure 3: (a) Maximum stresses on the left SIJ surface of the sacrum for diferent number of mesh elements, under MOP-F1, F2, F3, and F4. (b) Maximum displacements on the left SIJ surface of the sacrum for diferent number of mesh elements, under MOP-F1, F2, F3, and F4. 3 and mesh 4 under four MOPs were less than 5%, which was pubis, while the stress of the dorsal pelvis was mainly con- considered as reasonably close ranges. According to these centrated on the left iliac crest and the greater sciatic notch. results, mesh 3 with 458,867 elements was selected for Te maximum stress value was 52.6 MPa. Under MOP-F4, further study. the area of stress concentration was roughly the same as that under MOP-F3. Te maximum stress value was 80.0 MPa. Te distributions of stresses on the SIJ surface of the 3.2. Model Validation. Te stresses were located mainly in sacrum are shown in Figure 6. Under four MOPs, the the upper and posterior areas of the acetabulum and extended principal stresses were concentrated on the anterior and to the iliac crest, the incisura ischiadica major, and the rear inferior part of the left SIJ. Higher stress was observed on the acetabulum. Te area of stress concentration and maximum left SIJ for the four MOPs. Among them, MOP-F3 produced value of stress were consistent with those reported in a pre- the highest stress on the left SIJ, at 6.6 MPa, while MOP-F1 vious study [23]. Under eight loading conditions, the dis- produced the lowest stress on the left SIJ, at 5.6 MPa. placements 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. 3.4. Displacement of SIJ. In MOP-F1, the displacements of the left SIJ were 1.088, 0.305, and 0.033 mm in the anterior- posterior (AP), superior-inferior (SI) and medial-lateral 3.3. Stress of the Pelvis and SIJ. Te stress distributions of the (MI) direction, respectively. In MOP-F2, the displace- pelvis under four MOPs are shown in Figure 5. Under MOP- ments were 1.211, 0.186, and 0.064 mm in the AP, SI, and MI F1, the stress of the ventral pelvis was mainly concentrated on direction, respectively. In MOP-F3, the displacements were the left SIJ, extended to the arcuate line, the right SIJ, the right 0.962, 0.048, and 0.117 mm in the AP, SI, and MI direction, anterior-inferior iliac spine, the upper part of the right ac- respectively. In MOP-F4, the displacements were 1.105, etabulum, and the outer upper edge of the right pubis. While 0.064, and 0.094 mm in the AP, SI, and MI direction, re- the stress of the dorsal pelvis was mainly concentrated around spectively. Te four MOPs mainly produced anterior- the left posterior inferior iliac spine and the greater ischial posterior displacement. Te displacement of the left SIJ notch. Te maximum stress value was 76.9 MPa. Under under four MOPs are shown in Figure 7. MOP-F2, the area of stress concentration was roughly the same as that under MOP-F1, but the maximum stress value was higher, at 85.0 MPa. Under MOP-F3, the stress of the 3.5. Strain of Ligaments. Te strains of six ligaments under four MOPs are shown in Figure 8. For most of the ligaments, ventral pelvis was mainly concentrated on the left iliac crest, the left SIJ, the arcuate line, and the superior ramus of the the strain of the left ligament was greater than that of the Max stress (MPa) Max Displacement (mm) Journal of Healthcare Engineering 5 Superior Inferior Anterior Posterior Mediolateral Flexion Extension Axial rotation (mm) (mm) (mm) (mm) (mm) (degree) (degree) (degree) Present model (computational) Eichenseer et al. (computational) Miller et al. (experimental) Kim et al. (computational) Figure 4: Comparison of sacral displacements under eight loadings comparable to those in previous experimental and computational studies. right ligament under four MOPs. In MOP-F1, the left SS, greater stress on the right hemi-pelvis. Terefore, MOP-F2 ASL, and ISL had a higher strain value, which were 3.71, 1.41, and F4 produced greater stress on the left and right pelvis and 1.36%, respectively. In MOP-F2, the left SS, ST, and ASL than MOP-F1 and F3. had a higher strain value, which were 4.29, 1.51, and 1.28%, 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 respectively. In MOP-F3, the left SS, ASL, and ST had a higher strain value, which were 3.05, 1.61, and 1.09%, interosseous ligaments [30], so the motion of SIJ is mainly undertaken by the lower 1/3 part of SIJ. Te stresses on SIJ respectively. In MOP-F4, the left SS, SPSL, and ASL had a higher strain value, which were 2.85, 1.90, and 1.04%, surfaces of the sacra produced by four MOPs mainly dis- respectively. tributed 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 4. Discussion observed on the left SIJ surfaces under four MOPs. Com- SIJ subluxation is a common clinical disease [26, 27]. Te pared with MOP-F2, MOP-F1 produced a smaller maximum main cause of the disease is the minor displacement of SIJ or stress on the left SIJ surface, which was connected to the the injury of surrounding ligaments. According to many direction of MOP-F1 parallel to the SIJ surface. Compared with MOP-F4, MOP-F3 produced a greater maximum stress clinical reports [17, 28, 29], MOP could achieve good results in the treatment of SIJ subluxation. However, MOP has had on the left SIJ surface. Tis phenomenon suggested that the SIJ surface was compressed and the motion forms of SIJ no uniform standard for force point and direction. In this study, we established a three-dimensional fnite element included translation and rotation. model of the pelvis to explore the efects of MOP with Te displacement of the left SIJ was greater than that of diferent force points and directions on SIJ. the right side under four MOPs. Te displacement of the MOP-F1 and F2 were applied at the anterior-inferior left SIJ was 0.96∼1.21 mm in AP direction, 0.03∼0.12 mm in iliac spine, while MOP-F3 and F4 were applied at the MI direction, and 0.05∼0.31 mm in SI direction. Te values anterior-superior iliac spine. Te force direction of F1 and were all within 3 mm, which was consistent with previous F3 were roughly parallel to the SIJ surface, and the force research results [31, 32]. Under four MOPs, the displace- direction of F2 and F4 were parallel to the sagittal plane of ment in the AP direction was the largest in the three di- rections, which might be related to the fact that MOP could the pelvis. Anatomically, the anterior-inferior iliac spine is located inside and below the anterior-superior iliac spine, turn the pelvis outward. In the AP direction, MOP-F2 and F4 produced the largest displacement of the left SIJ. Te closer to the SIJ surface. Terefore, under the same direction of manipulation, MOP-F1 and F2 could produce greater directions of forces applied by MOP-F2 and F4 were maximum stress on the left hemi-pelvis than MOP-F3 and parallel to the sagittal plane, which was more likely to cause F4. In addition, since the anterior-superior iliac spine was SIJ movement in the AP direction than the directions of the closer to the iliac crest region, MOP-F3 and F4 also caused force parallel to the SIJ surface. In the MI direction, greater stress on the left iliac crest region than MOP-F1 and MOP-F3 and F4 produced the largest displacements. Te F2. From the perspective of the mechanical mechanism, the force points of the two manipulations were at the anterior- direction of manipulation parallel to the sagittal plane is superior iliac spine, which were far from the SIJ surface. more likely to produce greater stress on the left hemi-pelvis Tus, the force arm was longer, which was easier to produce displacement in the MI direction. Te sacrum is broad at than that parallel to the SIJ surface. Furthermore, the torque on the right hemi-pelvis was also greater, which could lead to the top and narrow at the bottom. It is wedge-shaped and Displacement (mm or degree) 6 Journal of Healthcare Engineering S, Mises SNEG, (fraction = -1.0) ( : 75%) +7.687e+01 +7.046e+01 +6.406e+01 +5.765e+01 +5.125e+01 +4.484e+01 +3.843e+01 +3.203e+01 +2.562e+01 +1.922e+01 +1.281e+01 +6.406e+00 +0.000e+00 MOP-F1 S, Mises SNEG, (fraction = -1.0) ( : 75%) +8.504e+01 +7.795e+01 +7.087e+01 +6.378e+01 +5.669e+01 +4.961e+01 +4.252e+01 +3.543e+01 +2.835e+01 +2.126e+01 +1.417e+01 +7.087e+00 +0.000e+00 MOP-F2 S, Mises SNEG, (fraction = -1.0) ( : 75%) +5.261e+01 +4.823e+01 +4.384e+01 +3.946e+01 +3.507e+01 +3.069e+01 +2.631e+01 +2.192e+01 +1.754e+01 +1.315e+01 +8.768e+00 +4.384e+00 +0.000e+00 MOP-F3 S, Mises SNEG, (fraction = -1.0) ( : 75%) +8.010e+01 +7.342e+01 +6.675e+01 +6.007e+01 +5.340e+01 +4.672e+01 +4.005e+01 +3.337e+01 +2.670e+01 +2.002e+01 +1.335e+01 +6.675e+00 +0.000e+00 MOP-F4 General view Local view Local view General view Ventral Dorsal Figure 5: Distribution of compressive stresses on the cortical bone of the pelvis under MOP-F1, F2, F3, and F4. Te images of the local view are enlarged images in the red box of the general view. Journal of Healthcare Engineering 7 S, Mises S, Mises SNEG, (fraction = -1.0) SNEG, (fraction = -1.0) ( : 75%) ( : 75%) +5.602e+00 +6.550e+00 +4.500e+00 +5.000e+00 +4.125e+00 +4.583e+00 +3.750e+00 +4.167e+00 +3.375e+00 +3.750e+00 +3.000e+00 +3.333e+00 +2.625e+00 +2.917e+00 +2.250e+00 +2.500e+00 +1.875e+00 +2.083e+00 +1.500e+00 +1.667e+00 +1.125e+00 +1.250e+00 +7.500e-01 +8.333e-01 +3.750e-01 +4.167e-01 +0.000e+00 +0.000e+00 Right Lef Right Lef MOP-F1 MOP-F3 S, Mises S, Mises SNEG, (fraction = -1.0) SNEG, (fraction = -1.0) ( : 75%) ( : 75%) +5.862e+00 +5.960e+00 +4.500e+00 +4.500e+00 +4.125e+00 +4.125e+00 +3.750e+00 +3.750e+00 +3.375e+00 +3.375e+00 +3.000e+00 +3.000e+00 +2.625e+00 +2.625e+00 +2.250e+00 +2.250e+00 +1.875e+00 +1.875e+00 +1.500e+00 +1.500e+00 +1.125e+00 +1.125e+00 +7.500e-01 +7.500e-01 +3.750e-01 +3.750e-01 +0.000e+00 +0.000e+00 Right Lef Right Lef MOP-F2 MOP-F4 Figure 6: Distribution of compressive stresses on the SIJ surface of the sacrum under MOP-F1, F2, F3, and F4. 1.5 1.0 0.5 0.0 MOP-F1 MOP-F2 MOP-F3 MOP-F4 MOP-F1 MOP-F3 MOP-F2 MOP-F4 AP SI Figure 8: Ligament strains under MOP-F1, F2, F3, and F4. L: left; MI R: right; ASL: anterior sacroiliac ligament; ISL: interosseous sa- Figure 7: Te displacements of the left SIJ under MOP-F1, F2, F3, croiliac ligament; SS: sacrospinous ligament; ST: sacrotuberous and F4. AP: anterior-posterior direction; SI: superior-inferior di- ligament; LPSL: long posterior sacroiliac ligament; SPSL: short rection; MI: medial-lateral direction. posterior sacroiliac ligament. Displacement (mm) Strain (%) ASL (L) ASL(R) ISL (L) ISL (R) SS (L) SS (R) ST (L) ST (R) LPSL (L) LPSL (R) SPSL (L) SPSL (R) 8 Journal of Healthcare Engineering lies between the iliac bones on both sides forming SIJ [33]. 5. Conclusions Tis special structure makes the SIJ move up easily, but In this study, a three-dimensional fnite element model of move down difcultly. Te anterior-inferior iliac spine is the pelvis was established, and four manipulations with located inside and below the anterior-superior iliac spine. diferent force points and diferent directions were studied. Tus, MOP-F1 and F2 applied at the anterior-inferior iliac Te results showed that MOP-F3 and F4 caused greater spine could produce a larger upward displacement in the SI stresses on the SIJ surface. Te four MOPs all produced small direction. displacements of the SIJ and diferent degrees of ligament Ligaments play an important role in maintaining pelvis strain. Among them, MOP-F2 and F4 could produce greater stability. Abdelfattah and Moed [34] found that the pubic displacements of SIJ and ligament strains. MOP-F1 and F2 symphysis and the anterior sacroiliac ligament played a key applied on the anterior-inferior iliac spine mainly produced part in maintaining pelvis stability when the pelvis sufered the displacement in AP and SI directions, while F3 and F4 “book-turning” violence. Sichting et al. [35] considered that applied on the anterior-superior iliac spine mainly produced the ligaments around SIJ not only played a role in main- the displacement in AP and MI directions. taining mechanical stability of SIJ, but also acted as a neuromuscular feedback mechanism. Eichenseer et al. [25] through a fnite element model, demonstrated that Data Availability with the decrease of ligament stifness, the stress and Te data used to support the fndings of this study are movement of SIJ would increase. Bohme et al. [36] found available from the corresponding authors upon request. that the anterior sacroiliac ligament and the sacrotuberous ligament bore the largest load in the case of anterior and Conflicts of Interest posterior compression fractures of the pelvis, accounting for 80% and 17% of the total load, respectively. Te sac- Te authors declare that they have no conficts of interest. rospinous ligament played an important role in main- taining vertical stability of the pelvis. Our results indicated Acknowledgments that the strains of the sacrospinous ligament, the anterior sacroiliac ligament, and the interosseous ligament were Tis work is supported by the Natural Science Foundation of larger than the other three ligaments in most cases under Hunan Province (grant no. 2022JJ40403), the National four MOPs. Among them, the strain of sacrospinous lig- Natural Science Foundation of China (grant no. 81904316), ament caused by MOP-F2 was the largest, at 4.29%. Under and the Key Laboratory Project of Orthopaedic Plant Re- MOP-F2, the displacement of SIJ was the largest, which led search and Development of Hengyang City (grant no. to the largest ligament strain. Te anterior sacroiliac lig- 2018KJ115). Te authors would like to thank all their col- ament is a broad and thin ligament located in the front of leagues for their support on this project. Te authors really SIJ. Te main displacement under four MOPs was in the AP appreciate the Research Square for presentation of the direction, so the anterior sacroiliac ligament would pro- preprinted version of the manuscript [37]. duce a greater strain. In this study, there were four types of MOP. MOP-F2 References and F4 produced the larger displacement in the AP di- rection, at 1.21 and 1.11 mm, respectively. It showed that the [1] B. Minghelli, “Musculoskeletal spine pain in adolescents: epidemiology of non-specifc neckand low back pain and risk manipulation parallel to the sagittal plane could cause factors,” Journal of Orthopaedic Science, vol. 25, no. 5, a larger displacement. In addition, MOP-F2 and F4 also pp. 776–780, 2020. caused greater ligament strains. It could be seen that [2] A. Shmagel, R. Foley, and H. 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Zhang et al., “Manipulations of oblique pulling afect sacroiliac joint displacements and ligament strains: a fnite element analysis,” 2022. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Healthcare Engineering Hindawi Publishing Corporation

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

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Hindawi Publishing Corporation
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2040-2295
eISSN
2040-2309
DOI
10.1155/2023/2840421
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Abstract

Hindawi Journal of Healthcare Engineering Volume 2023, Article ID 2840421, 10 pages https://doi.org/10.1155/2023/2840421 Research Article Manipulations of Oblique Pulling Affect Sacroiliac Joint Displacements and Ligament Strains: A Finite Element Analysis 1,2 2 2 3 2 Zhun Xu , Ziyu Feng, Zhaocong Zhang, Kunmu Zhang , and Yikai Li Department of Spine Surgery, Te First Afliated Hospital, Hengyang Medical School, University of South China, Hengyang 421000, Hunan Province, China School of Traditional Chinese Medicine, Southern Medical University, No. 1838, Guangzhou Avenue North, Baiyun District, Guangzhou 510515, Guangdong Province, China Te Second Afliated Hospital of Fujian University of Traditional Chinese Medicine, No. 282 Wusi Road, Gulou District, Fuzhou 350003, Fujian Province, China Correspondence should be addressed to Kunmu Zhang; 277873495@qq.com and Yikai Li; lyk_doc@163.com Received 6 October 2022; Revised 11 December 2022; Accepted 15 December 2022; Published 3 January 2023 Academic Editor: Elisabetta Zanetti Copyright © 2023 Zhun Xu et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Objective. Clinical studies have found that manipulation of oblique pulling has a good clinical efect on sacroiliac joint pain. However, there is no uniform standard for manipulation of oblique pulling at present. Te purpose of this study was to investigate the efects of four manipulations of oblique pulling on sacroiliac joint and surrounding ligaments. Methods. A three-dimensional fnite element model of the pelvis was established. Four manipulations of oblique pulling were simulated. Te 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. Te four manipulations of oblique pulling mainly produced anterior-posterior displacement. Te 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. Te four manipulations of oblique pulling could all cause diferent degrees of ligament strain, and manipulation of oblique pulling F2 produced the greatest ligament strain. Conclusions. Te four manipulations of oblique pulling all produced small displacements of sacroiliac joint. However, they produced diferent 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. which will result in slight movement of the SIJ, making the 1. Introduction joints difcult to reset. Te mechanical environment of the Lower back pain usually caused by lumbar diseases, in- joints may ultimately be imbalanced, and the soft tissues will cluding myofasciitis, lumbar disc herniation, and lumbar be damaged. Tis condition is clinically referred to as SIJ spondylolisthesis, is a common clinical symptom [1–3]. In subluxation [5]. recent years, it has been found that the lesion of sacroiliac Tere are many treatment methods for SIJ subluxation, joint (SIJ) can also cause lower back pain, accounting for mainly including the following: (1) take nonsteroidal anti- 14.5%∼22.5% [4]. Commonly, abnormal gait, heavy physical infammatory drugs (NSAID) and drugs for promoting exertion, leg length discrepancy, and scoliosis may be factors blood circulation, so as to achieve the efects of anti- related to SIJ pain without specifc causes. Te mechanism infammatory, and promote blood circulation and remove may include the following processes: pathogenic factors blood stasis [6, 7]. (2) Inject glucocorticoids into the SIJ via acting on the auricular surface of the sacrum and ilium may a guide wire to produce a direct anti-infammatory efect cause injury to the ligaments or muscles around the SIJ, [8–10]. (3) Pull the subluxated SIJ back to the normal 2 Journal of Healthcare Engineering Table 1: Material properties of the sacrum, ilium, pubic symphysis, position by manipulation to reduce nerve stimulation and and endplate. relieve pain [11–14]. At present, the three methods have been applied in clinical treatment, and manipulation is the Young’s modulus Poisson’s ratio most widely used [15, 16]. (MPa) Manipulation relieves the low back pain by changing the Cortical 12,000 0.3 Sacrum mechanical environment of SIJ and surrounding tissue. Tis Cancellous 100 0.2 treatment method has little side efects, and can be easily Cortical 12,000 0.3 Ilium accepted by patients. A large number of clinical studies have Cancellous 100 0.2 shown that manipulation of oblique pulling (MOP) has Pubic 5 0.45 a good efect on SIJ subluxation [17–19]. Te detailed symphysis procedure are as follows: the patient is in the right decubitus Articular 100 0.3 position. Te right lower extremity is straight, and the left cartilage lower extremity is slightly bent. Te therapist stands at the Endplate 1000 0.4 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 according to the literature [20]. In total, the pelvic model contained 458,867 elements and 201,982 nodes. Figure 1 towards the back. However, the position and direction of the shows the intact model with ligamentous attachments. 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 2.2. Simulation of MOPs. Te simulation of MOP was as on the SIJ and its surrounding ligaments? None of these follows: the magnitudes of the forces were determined by issues has been studied. Terefore, this study intends to determining the manipulative power of fve therapists using establish a three-dimensional fnite element model of the a biomechanical testing machine. Te average manipulative pelvis and explore the efects of MOP on the stress and force was 600 N [22]. Terefore, a large part of the sacrum displacement of SIJ and strain of the surrounding ligament and the right iliac crest were fxed. Ten, a push force of by simulating four common MOPs. 600 N along the ventral-dorsal direction was applied to the left anterior-superior spine or anterior-inferior iliac spine. 2. Materials and Methods Tere were four MOPs. MOP-F1: the force was applied at the left anterior-inferior iliac spine in a direction of 30 2.1. Model Construction. A 3D fnite element model of the from the sagittal plane which roughly paralleled to the SIJ pelvis was established. Tree-dimensional models of the surface. MOP-F2: the force was applied at the left anterior- sacrum and ilia were reconstructed from the computed inferior iliac spine, parallel to the sagittal plane. MOP-F3: the tomography (CT) images of a healthy male volunteer force was applied at the left anterior-superior iliac spine in (34 years old, 170 cm in height, and 65 kg in weight) using a direction of 30 from the SIJ surface. MOP-F4: the force Mimics 20.0 (Materialise Company, Leuven, Belgium), and was applied at the left anterior-superior iliac spine, parallel the cortical and cancellous regions of the bones were to the sagittal plane. Te detailed loading and boundary distinguished. Axial slices 0.5 mm thick spanning the entire conditions, as well as the x-, y-, and z-axes, are described in pelvis were selected for model construction. All surface Figure 2. Te compressive stresses and displacements of SIJ models were meshed using Geomagic 2013 (Raindrop and the strains of ligaments for four MOPs were then in- Company, Marble Hill, USA). Te SIJ was composed of vestigated using Abaqus 2018 (Dassault Systemes S. A cartilage and the endplate of the sacrum and the ilia, with Company, Massachusetts, USA). their surrounding ligaments. Te cartilage was recon- structed with a uniform thickness. Te regions of the ar- ticular surfaces were based on CT images, and the 2.3.MeshConvergenceStudy. In order to evaluate the degree thicknesses of the cartilage were acquired from the liter- of accuracy of the pelvic model, the mesh convergence study ature [20]. Te sacral and iliac cartilages had thicknesses of was carried out. Four mesh models were established 2 mm and 1 mm, respectively. Te bone endplate thick- according to diferent mesh fneness. Te number of ele- nesses of the sacral and iliac parts of the cartilage were ments and nodes in each model are shown in Table 2. assumed to be 0.23 mm and 0.36 mm, respectively. Te gap Following boundary conditions and material properties, between the two cartilages was set at 0.3 mm [20]. Te loads, and constraints were described in detail in the material properties chosen from previous studies [20, 21] abovementioned sections. MOP-F1, F2, F3, and F4 were are summarized in Table 1. applied to these meshes. Finally, the maximum stresses and Te anterior sacroiliac ligament (ASL), short posterior displacements of the four models on the left SIJ surface of the sacroiliac ligament (SPSL), long posterior sacroiliac ligament sacrum under four MOPs were analyzed. (LPSL), sacrospinous ligament (SS), interosseous sacroiliac ligament (ISL), and sacrotuberous ligament (ST) complexes were modelled as 3D tension-only truss elements. Te 2.4. Model Validation. Two studies were performed to material properties of each ligament were obtained from the validate this model. For the pelvic model, the distribution of literature [21]. Te attachment regions were chosen the main strain of the pelvis was compared with that Journal of Healthcare Engineering 3 SPSL ASL LPSL SS ST (a) (b) Figure 1: Ventral (a) and dorsal (b) views of the fnite element model. Ligaments are represented in color lines, with red arrows identifying each ligament complex (note the interosseous sacroiliac ligament is not visible in anterior-posterior views). ASL indicates anterior sacroiliac ligament; LPSL, long posterior sacroiliac ligament; SPSL, short posterior sacroiliac ligament; SS, sacrospinous ligament; ST, sacrotuberous ligament. L L L L F3 F1 F4 F2 PA PA PA PA (a) (b) (c) (d) RLRLRL RL F3 F1 F4 F2 (e) (f ) (g) (h) Figure 2: Loading and boundary conditions for four manipulations of oblique pulling. Te yellow triangles represent the fxed sites of the pelvic model. Te superior view (a, b, c, and d) and frontal view (e, f, g, and h) of the pelvis are shown, (a) and (e) manipulation of oblique pulling-F1; (b) and (f ) manipulation of oblique pulling-F2; (c) and (g) manipulation of oblique pulling-F3; (d) and (h) manipulation of oblique pulling-F4. reported in the study of Zhang et al. [23]. In our model, the and superior S2 vertebral endplates were calculated. In this distribution of the main strain of the pelvis was analyzed model, the displacements were investigated under the same loading. 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 3. Results studies [20, 25]. When the bilateral ilia were fxed, fve translational forces (anterior, posterior, superior, inferior, 3.1. Mesh Convergence Study. Te maximum stress and and mediolateral) of 294 N and three moments (fexion, maximum displacement on the left SIJ surface of the sacrum extension, and axial rotation) of 42 Nm were applied to the were analyzed for each of the meshes, under MOP-F1, F2, centre of the sacrum, respectively. Te displacements of F3, and F4, which are shown in Figure 3. Te diferences in a node lying in the midsagittal plane between the inferior S1 maximum stress and maximum displacement between mesh 4 Journal of Healthcare Engineering Table 2: Element and node numbers for four diferent mesh resolutions. Element number Node number Mesh 1 142,007 58,480 Mesh 2 243,492 101,724 Mesh 3 458,867 201,982 Mesh 4 1,051,834 481,435 0.12 0.09 0.06 0.03 2 0.00 0 500000 1000000 1500000 0 500000 1000000 1500000 Number of Mesh Elements Number of Mesh Elements MOP-F1 MOP-F3 MOP-F1 MOP-F3 MOP-F2 MOP-F4 MOP-F2 MOP-F4 (a) (b) Figure 3: (a) Maximum stresses on the left SIJ surface of the sacrum for diferent number of mesh elements, under MOP-F1, F2, F3, and F4. (b) Maximum displacements on the left SIJ surface of the sacrum for diferent number of mesh elements, under MOP-F1, F2, F3, and F4. 3 and mesh 4 under four MOPs were less than 5%, which was pubis, while the stress of the dorsal pelvis was mainly con- considered as reasonably close ranges. According to these centrated on the left iliac crest and the greater sciatic notch. results, mesh 3 with 458,867 elements was selected for Te maximum stress value was 52.6 MPa. Under MOP-F4, further study. the area of stress concentration was roughly the same as that under MOP-F3. Te maximum stress value was 80.0 MPa. Te distributions of stresses on the SIJ surface of the 3.2. Model Validation. Te stresses were located mainly in sacrum are shown in Figure 6. Under four MOPs, the the upper and posterior areas of the acetabulum and extended principal stresses were concentrated on the anterior and to the iliac crest, the incisura ischiadica major, and the rear inferior part of the left SIJ. Higher stress was observed on the acetabulum. Te area of stress concentration and maximum left SIJ for the four MOPs. Among them, MOP-F3 produced value of stress were consistent with those reported in a pre- the highest stress on the left SIJ, at 6.6 MPa, while MOP-F1 vious study [23]. Under eight loading conditions, the dis- produced the lowest stress on the left SIJ, at 5.6 MPa. placements 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. 3.4. Displacement of SIJ. In MOP-F1, the displacements of the left SIJ were 1.088, 0.305, and 0.033 mm in the anterior- posterior (AP), superior-inferior (SI) and medial-lateral 3.3. Stress of the Pelvis and SIJ. Te stress distributions of the (MI) direction, respectively. In MOP-F2, the displace- pelvis under four MOPs are shown in Figure 5. Under MOP- ments were 1.211, 0.186, and 0.064 mm in the AP, SI, and MI F1, the stress of the ventral pelvis was mainly concentrated on direction, respectively. In MOP-F3, the displacements were the left SIJ, extended to the arcuate line, the right SIJ, the right 0.962, 0.048, and 0.117 mm in the AP, SI, and MI direction, anterior-inferior iliac spine, the upper part of the right ac- respectively. In MOP-F4, the displacements were 1.105, etabulum, and the outer upper edge of the right pubis. While 0.064, and 0.094 mm in the AP, SI, and MI direction, re- the stress of the dorsal pelvis was mainly concentrated around spectively. Te four MOPs mainly produced anterior- the left posterior inferior iliac spine and the greater ischial posterior displacement. Te displacement of the left SIJ notch. Te maximum stress value was 76.9 MPa. Under under four MOPs are shown in Figure 7. MOP-F2, the area of stress concentration was roughly the same as that under MOP-F1, but the maximum stress value was higher, at 85.0 MPa. Under MOP-F3, the stress of the 3.5. Strain of Ligaments. Te strains of six ligaments under four MOPs are shown in Figure 8. For most of the ligaments, ventral pelvis was mainly concentrated on the left iliac crest, the left SIJ, the arcuate line, and the superior ramus of the the strain of the left ligament was greater than that of the Max stress (MPa) Max Displacement (mm) Journal of Healthcare Engineering 5 Superior Inferior Anterior Posterior Mediolateral Flexion Extension Axial rotation (mm) (mm) (mm) (mm) (mm) (degree) (degree) (degree) Present model (computational) Eichenseer et al. (computational) Miller et al. (experimental) Kim et al. (computational) Figure 4: Comparison of sacral displacements under eight loadings comparable to those in previous experimental and computational studies. right ligament under four MOPs. In MOP-F1, the left SS, greater stress on the right hemi-pelvis. Terefore, MOP-F2 ASL, and ISL had a higher strain value, which were 3.71, 1.41, and F4 produced greater stress on the left and right pelvis and 1.36%, respectively. In MOP-F2, the left SS, ST, and ASL than MOP-F1 and F3. had a higher strain value, which were 4.29, 1.51, and 1.28%, 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 respectively. In MOP-F3, the left SS, ASL, and ST had a higher strain value, which were 3.05, 1.61, and 1.09%, interosseous ligaments [30], so the motion of SIJ is mainly undertaken by the lower 1/3 part of SIJ. Te stresses on SIJ respectively. In MOP-F4, the left SS, SPSL, and ASL had a higher strain value, which were 2.85, 1.90, and 1.04%, surfaces of the sacra produced by four MOPs mainly dis- respectively. tributed 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 4. Discussion observed on the left SIJ surfaces under four MOPs. Com- SIJ subluxation is a common clinical disease [26, 27]. Te pared with MOP-F2, MOP-F1 produced a smaller maximum main cause of the disease is the minor displacement of SIJ or stress on the left SIJ surface, which was connected to the the injury of surrounding ligaments. According to many direction of MOP-F1 parallel to the SIJ surface. Compared with MOP-F4, MOP-F3 produced a greater maximum stress clinical reports [17, 28, 29], MOP could achieve good results in the treatment of SIJ subluxation. However, MOP has had on the left SIJ surface. Tis phenomenon suggested that the SIJ surface was compressed and the motion forms of SIJ no uniform standard for force point and direction. In this study, we established a three-dimensional fnite element included translation and rotation. model of the pelvis to explore the efects of MOP with Te displacement of the left SIJ was greater than that of diferent force points and directions on SIJ. the right side under four MOPs. Te displacement of the MOP-F1 and F2 were applied at the anterior-inferior left SIJ was 0.96∼1.21 mm in AP direction, 0.03∼0.12 mm in iliac spine, while MOP-F3 and F4 were applied at the MI direction, and 0.05∼0.31 mm in SI direction. Te values anterior-superior iliac spine. Te force direction of F1 and were all within 3 mm, which was consistent with previous F3 were roughly parallel to the SIJ surface, and the force research results [31, 32]. Under four MOPs, the displace- direction of F2 and F4 were parallel to the sagittal plane of ment in the AP direction was the largest in the three di- rections, which might be related to the fact that MOP could the pelvis. Anatomically, the anterior-inferior iliac spine is located inside and below the anterior-superior iliac spine, turn the pelvis outward. In the AP direction, MOP-F2 and F4 produced the largest displacement of the left SIJ. Te closer to the SIJ surface. Terefore, under the same direction of manipulation, MOP-F1 and F2 could produce greater directions of forces applied by MOP-F2 and F4 were maximum stress on the left hemi-pelvis than MOP-F3 and parallel to the sagittal plane, which was more likely to cause F4. In addition, since the anterior-superior iliac spine was SIJ movement in the AP direction than the directions of the closer to the iliac crest region, MOP-F3 and F4 also caused force parallel to the SIJ surface. In the MI direction, greater stress on the left iliac crest region than MOP-F1 and MOP-F3 and F4 produced the largest displacements. Te F2. From the perspective of the mechanical mechanism, the force points of the two manipulations were at the anterior- direction of manipulation parallel to the sagittal plane is superior iliac spine, which were far from the SIJ surface. more likely to produce greater stress on the left hemi-pelvis Tus, the force arm was longer, which was easier to produce displacement in the MI direction. Te sacrum is broad at than that parallel to the SIJ surface. Furthermore, the torque on the right hemi-pelvis was also greater, which could lead to the top and narrow at the bottom. It is wedge-shaped and Displacement (mm or degree) 6 Journal of Healthcare Engineering S, Mises SNEG, (fraction = -1.0) ( : 75%) +7.687e+01 +7.046e+01 +6.406e+01 +5.765e+01 +5.125e+01 +4.484e+01 +3.843e+01 +3.203e+01 +2.562e+01 +1.922e+01 +1.281e+01 +6.406e+00 +0.000e+00 MOP-F1 S, Mises SNEG, (fraction = -1.0) ( : 75%) +8.504e+01 +7.795e+01 +7.087e+01 +6.378e+01 +5.669e+01 +4.961e+01 +4.252e+01 +3.543e+01 +2.835e+01 +2.126e+01 +1.417e+01 +7.087e+00 +0.000e+00 MOP-F2 S, Mises SNEG, (fraction = -1.0) ( : 75%) +5.261e+01 +4.823e+01 +4.384e+01 +3.946e+01 +3.507e+01 +3.069e+01 +2.631e+01 +2.192e+01 +1.754e+01 +1.315e+01 +8.768e+00 +4.384e+00 +0.000e+00 MOP-F3 S, Mises SNEG, (fraction = -1.0) ( : 75%) +8.010e+01 +7.342e+01 +6.675e+01 +6.007e+01 +5.340e+01 +4.672e+01 +4.005e+01 +3.337e+01 +2.670e+01 +2.002e+01 +1.335e+01 +6.675e+00 +0.000e+00 MOP-F4 General view Local view Local view General view Ventral Dorsal Figure 5: Distribution of compressive stresses on the cortical bone of the pelvis under MOP-F1, F2, F3, and F4. Te images of the local view are enlarged images in the red box of the general view. Journal of Healthcare Engineering 7 S, Mises S, Mises SNEG, (fraction = -1.0) SNEG, (fraction = -1.0) ( : 75%) ( : 75%) +5.602e+00 +6.550e+00 +4.500e+00 +5.000e+00 +4.125e+00 +4.583e+00 +3.750e+00 +4.167e+00 +3.375e+00 +3.750e+00 +3.000e+00 +3.333e+00 +2.625e+00 +2.917e+00 +2.250e+00 +2.500e+00 +1.875e+00 +2.083e+00 +1.500e+00 +1.667e+00 +1.125e+00 +1.250e+00 +7.500e-01 +8.333e-01 +3.750e-01 +4.167e-01 +0.000e+00 +0.000e+00 Right Lef Right Lef MOP-F1 MOP-F3 S, Mises S, Mises SNEG, (fraction = -1.0) SNEG, (fraction = -1.0) ( : 75%) ( : 75%) +5.862e+00 +5.960e+00 +4.500e+00 +4.500e+00 +4.125e+00 +4.125e+00 +3.750e+00 +3.750e+00 +3.375e+00 +3.375e+00 +3.000e+00 +3.000e+00 +2.625e+00 +2.625e+00 +2.250e+00 +2.250e+00 +1.875e+00 +1.875e+00 +1.500e+00 +1.500e+00 +1.125e+00 +1.125e+00 +7.500e-01 +7.500e-01 +3.750e-01 +3.750e-01 +0.000e+00 +0.000e+00 Right Lef Right Lef MOP-F2 MOP-F4 Figure 6: Distribution of compressive stresses on the SIJ surface of the sacrum under MOP-F1, F2, F3, and F4. 1.5 1.0 0.5 0.0 MOP-F1 MOP-F2 MOP-F3 MOP-F4 MOP-F1 MOP-F3 MOP-F2 MOP-F4 AP SI Figure 8: Ligament strains under MOP-F1, F2, F3, and F4. L: left; MI R: right; ASL: anterior sacroiliac ligament; ISL: interosseous sa- Figure 7: Te displacements of the left SIJ under MOP-F1, F2, F3, croiliac ligament; SS: sacrospinous ligament; ST: sacrotuberous and F4. AP: anterior-posterior direction; SI: superior-inferior di- ligament; LPSL: long posterior sacroiliac ligament; SPSL: short rection; MI: medial-lateral direction. posterior sacroiliac ligament. Displacement (mm) Strain (%) ASL (L) ASL(R) ISL (L) ISL (R) SS (L) SS (R) ST (L) ST (R) LPSL (L) LPSL (R) SPSL (L) SPSL (R) 8 Journal of Healthcare Engineering lies between the iliac bones on both sides forming SIJ [33]. 5. Conclusions Tis special structure makes the SIJ move up easily, but In this study, a three-dimensional fnite element model of move down difcultly. Te anterior-inferior iliac spine is the pelvis was established, and four manipulations with located inside and below the anterior-superior iliac spine. diferent force points and diferent directions were studied. Tus, MOP-F1 and F2 applied at the anterior-inferior iliac Te results showed that MOP-F3 and F4 caused greater spine could produce a larger upward displacement in the SI stresses on the SIJ surface. Te four MOPs all produced small direction. displacements of the SIJ and diferent degrees of ligament Ligaments play an important role in maintaining pelvis strain. Among them, MOP-F2 and F4 could produce greater stability. Abdelfattah and Moed [34] found that the pubic displacements of SIJ and ligament strains. MOP-F1 and F2 symphysis and the anterior sacroiliac ligament played a key applied on the anterior-inferior iliac spine mainly produced part in maintaining pelvis stability when the pelvis sufered the displacement in AP and SI directions, while F3 and F4 “book-turning” violence. Sichting et al. [35] considered that applied on the anterior-superior iliac spine mainly produced the ligaments around SIJ not only played a role in main- the displacement in AP and MI directions. taining mechanical stability of SIJ, but also acted as a neuromuscular feedback mechanism. Eichenseer et al. [25] through a fnite element model, demonstrated that Data Availability with the decrease of ligament stifness, the stress and Te data used to support the fndings of this study are movement of SIJ would increase. Bohme et al. [36] found available from the corresponding authors upon request. that the anterior sacroiliac ligament and the sacrotuberous ligament bore the largest load in the case of anterior and Conflicts of Interest posterior compression fractures of the pelvis, accounting for 80% and 17% of the total load, respectively. Te sac- Te authors declare that they have no conficts of interest. rospinous ligament played an important role in main- taining vertical stability of the pelvis. Our results indicated Acknowledgments that the strains of the sacrospinous ligament, the anterior sacroiliac ligament, and the interosseous ligament were Tis work is supported by the Natural Science Foundation of larger than the other three ligaments in most cases under Hunan Province (grant no. 2022JJ40403), the National four MOPs. Among them, the strain of sacrospinous lig- Natural Science Foundation of China (grant no. 81904316), ament caused by MOP-F2 was the largest, at 4.29%. Under and the Key Laboratory Project of Orthopaedic Plant Re- MOP-F2, the displacement of SIJ was the largest, which led search and Development of Hengyang City (grant no. to the largest ligament strain. Te anterior sacroiliac lig- 2018KJ115). Te authors would like to thank all their col- ament is a broad and thin ligament located in the front of leagues for their support on this project. Te authors really SIJ. 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Published: Jan 3, 2023

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