SIJ pain is a common disease that affects 90% of adults throughout their lives . Manipulations have a good effect on SIJ pain without specific causes. However, the effects of manipulations on the SIJ and the ligaments have not been clear yet. In this study, the three-dimensional finite element model was used to quantitatively analyze the effects of three manipulations on the displacements of SIJ and the strains of surrounding ligaments, which provided a theoretical basis for the indications of manipulations.
The anterior part of the SIJ is the synovium, which can move slightly, and the posterior part is the interosseous ligament, which mainly plays a role in maintaining the stability of the joint. Walker et al.  found that the SIJ had a range of motion of less than 3 mm and a rotation of no more than 2° in a standing or sitting position. Some researchers found that the slip of the SIJ did not even exceed 1 mm . In this study, it was found that the MOP could produce the maximum displacement of the SIJ with the value of 0.962 mm among the three manipulations, while the MLLH could cause the minimum displacement of the SIJ and the value was 0.114 mm. The displacements of SIJ under the three manipulations were all less than 1 mm, which was consistent with the previous studies [34, 35].
In MLLH, neither of the sacrum and iliac bone was fixed directly. As a result, they moved simultaneously during the process. Therefore, the relative displacement of the joint surface was small. The displacement produced by MHKF was also small, the reason might be related to the point of force at the distal femur. The displacement produced by MOP was the largest, considering that the point of force was on the pelvis, and the direction of force was medial-lateral. The MOP could produce the largest displacement in the AP and MI directions, and the MHKF could produce the largest displacement in the SI direction. The biomechanical properties of manipulations can provide a theoretical basis to choose manual therapy.
Ligaments play an important role in maintaining the stability of the pelvis. Sichting et al.  found that ligaments were the mechanical stabilization device of the pelvis. Bohme et al.  observed that the ASL and ST had the greatest load with 80% and 17% of the total load under the anteroposterior compression pelvic injuries and that the SS played an important role in the vertical stability of the pelvis. Eichenseer et al.  considered that ligaments around the SIJ could limit the movement of the SIJ and reduce the stress of the SIJ. In this study, it was found that the three manipulations could cause different degrees of strain on the ligaments around the SIJ. In MOP, the patient's sacrum was fixed relatively and the point of force was on the anterior superior iliac spine and the direction of the force was a MI direction. Therefore, the MOP could cause the largest strain of the ligaments among the three manipulations. The ligament strains produced by MLLH and MHKF were smaller. It might be related to the point and direction of manipulative force as well as the style of pelvic fixation. These results indicated the SS, ASL and ISL had the greatest strains under the three manipulations, which was consistent with the previous studies [12, 31].
In MLLH, the displacement was the smallest, and the ligament strains were also the smallest. In MOP, the displacements and the ligament strains were both the largest. It can be seen that the displacements of SIJ and the ligament strains remain consistent under the three manipulations. These results also prove the reliability and effectiveness of the model.
Szadek et al.  found that there were substance P and calcitonin gene-related peptide positive nerve fibers on the SIJ cartilage and surrounding ligaments, indicating that the pain source of SIJ might come from cartilage and ligament tissues. So, is it possible to reduce the pain by pulling the subluxated SIJ back, or by alleviating the spasm of the surrounding ligaments? Chen et.al  believed that manipulations were unlikely to pull the SIJ back. The clicking sound and the sense of movement during the manipulative process were likely to be due to the movement of attachment of the SIJ or L5/S1 facet joints. Tullberg et al.  argued that manipulations could not change the position of the SIJ, and the cause of pain relief was related to the soft tissues around the joints. Ivanov et al.  also considered that the ligaments around the SIJ contained a lot of nerve tissues, and even if a small strain occurred, it would cause pain. Base on the results of this study, the displacements of the SIJ were all less than 1 mm under the three manipulations. In fact, there are lots of muscles and other soft tissues around the SIJ in human bodies. Hence, it can be estimated that the displacement will be smaller in patients. Therefore, it is considered that manipulations are difficult to pull the SIJ back. However, the manipulations could cause different degrees of strains on the surrounding ligaments. Although the ligament strains were small, it could still relieve the spasm of the surrounding ligaments and reduce pain.
There are some limitations in this study. First, our finite element model is based on the geometry and material properties of individual pelvic bones and ligaments in a single male case. However, it is well known that anatomical structures of the pelvis are very different, which must be considered when drawing conclusions in clinical. Second, although muscles and other soft tissues are most likely to participate in maintaining pelvic stability, the effects of them on the pelvis are not considered in this model. Third, the ligaments’ characteristics are regarded to be linear. Fourth, there is no unified standard for manipulations currently. So, the specific processes of manipulations are simulated and simplified based on plenty of physicians’ experience.