Introduction

The human body uses an ingenious 3-D framework of bones, joints, muscles, and ligaments for posture and movement. In upright posture, the trunk load passes the sacroiliac joints (SIJ). The orientation of the SIJ surfaces, however, is more or less in line with the direction of loading, which induces high shear forces between sacrum and coxal bones.34 The SIJ have a strong passive, viscoelastic ligamentous system for providing stability. These ligaments are vulnerable for creep during constant trunk load and need to be protected against high SIJ shear forces.19 From a biomechanical point of view, an active muscle corset that increases the compression force between the coxal bones and the sacrum could protect the ligamentous system and support the transfer of trunk load to the legs and vice versa. Interlocking of the SIJ may be promoted by transversely oriented muscles, e.g., M. transversus abdominis, M. piriformis, M. gluteus maximus, M. obliquus externus abdominis, and M. obliquus internus abdominis, which has been described as self-bracing.3335 However, due to the complex lines of action of (counteracting) muscles and ligaments in the pelvic region, it is difficult to demonstrate the contribution of transversely oriented muscles to SIJ stability, in vitro as well as in vivo.

In the past, a number of biomechanical models of the lumbosacral region (spine and pelvis) have been developed to study the aetiology of low back pain (LBP) in relation to (over)loading of the lumbar spine1, 9, 11, 36 and the pelvis.10,27 Most of these models dealt with mechanical stability in terms of muscle3,4,18 and compression forces between (lumbar) vertebrae.2,8,12,20,22, 28 A different approach is to relate LBP to overloading of SIJ and nearby ligaments, for example the iliolumbar ligaments.24,30 The load transfer through the SIJ was studied using a static, 3-D biomechanical simulation model based on the musculoskeletal anatomy of the trunk, pelvis, and upper legs.15 This simulation model calculates forces in muscles, ligaments, and joints that are needed to counterbalance trunk weight and other external forces. It was shown that this simulation model underestimated antagonistic muscle activity, but a good agreement was found for agonist muscle activity. The number of passive structures in the model was small, for example no joint capsules were incorporated. Therefore, the model was only valid for postures in which none of the joints were near an end position. The aim of the present study was to determine which muscles have to become active in the 3-D pelvic simulation model when there is an imposed reduction of the vertical SIJ shear force.

Materials and Methods

The 3-D Simulation Model

The present study was performed using the validated, 3-D simulation model as described by Hoek van Dijke et al. 15 The model is based on the musculoskeletal anatomy of the trunk, pelvis, and upper legs, including muscle and ligament attachment sites, cross-sectional areas of muscles and the direction of muscle, ligament, and joint reaction forces. The geometry of this model was based on structures extracted from MRI slices and from previously published data on lumbar spine8 and upper leg4,17 geometry. Figure 1a illustrates, in frontal and median view, the bones on which muscle and ligament forces act in the simulation model. These are the lowest thoracic vertebra, five lumbar vertebrae, the sacrum, the left and right coxal bones and the left and right femurs. The vertebrae are treated as a single structure. The arrangement of the bones depends on the static posture for which muscle forces are calculated, for example standing with or without trunk flexion. A description of the model equilibrium, its optimization scheme and validation of some of the parameters is presented in the Appendix. In the present study, we focus on the compression and shear forces in the SIJ. These forces are represented as perpendicular vectors. The normal vector of the SIJ surface has an oblique direction (xyz = 0.365, ±0.924, 0.114). Compression force is defined along this normal vector and can only vary in magnitude. One of the two components of the SIJ shear force was defined in the YZ-plane (xyz = 0, ±0.123, 0.992). This force is denoted as the vertical SIJ shear force. Directions of the SIJ compression force and the SIJ vertical shear force in the YZ-plane are shown in Fig. 1a, left panel. Figure 1b shows the vectors representing the most important muscle and ligament forces in the pelvic region superimposed on the bones. Bone shapes are for illustration purpose only; they are not part of the simulation model. In total, the model contains 100 vectors for muscle forces, 8 vectors for ligament forces, and 22 vectors for joint forces; see Table 1 for a list of all the structures.

Figure 1
figure 1

Panel (a) shows the bones on which the muscles, ligaments and joint reaction forces act in the frontal plane (left) and the median plane (right): the lowest thoracic vertebra, five lumbar vertebrae, the sacrum, the left and right coxal bones, and the left and right femurs. The coordinate system is defined with the origin halfway between the rotation centers of the hip joints. Axes: x posterior, y left, z vertical. Panel (b) shows, superimposed on the bones, the vectors representing the most important force components in the frontal plane (left) and the median plane (right), see also Table 1. The labels in this panel refer to a selection of the muscle structures listed in Table 1

Table 1 List of muscles, ligaments, and joints and the number of vectors describing the forces used in the simulation model on transferring trunk load from lumbar spine via the pelvis to the upper legs (unilateral), see also Fig. 1

Simulations and Data Analyses

A first simulation, with the model in standing posture and a trunk weight of 500 N, showed that the vertical shear SIJ force was 563 N on each side of the sacrum. To find the muscles that promote sacroiliac joint stability, the maximum value for the vertical SIJ shear force was decreased in steps of 30 N (∼5% of the initial vertical SIJ shear force). Theoretically, lowering of the imposed vertical SIJ shear force to 0 N could induce a non-physiological equilibrium between muscle, ligament, and joint forces. In addition, when the model was set in 30° flexion, the force in the iliolumbar, the sacrotuberal, and the posterior sacroiliac ligaments was 250 N. This value was set as a maximum physiological ligament force in the simulation model in the upright position to prevent overloading of the pelvic ligaments that were implemented in the model. The following criteria were defined to warrant a physiological solution for muscle and ligament forces.

  1. 1.

    Muscle tension must not exceed 240 kPa16;

  2. 2.

    Lowering of the maximum vertical SIJ shear force must result in reduction of the total SIJ shear force (combination of vertical and horizontal shear);

  3. 3.

    Ligament force must not exceed 250 N.

A muscle was included for further analysis when it produced at least 15% of the maximum muscle stress during the simulation. For all muscles, the maximum muscle stress depended on the calculated minimum muscle stress (see optimization criterion 1 in the Appendix). Two muscle groups were analyzed separately: (1) the muscles that increased at least 80% in force after the first simulation step and (2) the muscles that increased at least 10 times in force after completion of the simulation series.

Results

Table 2 summarizes the muscle (de)activation pattern when the maximum vertical SIJ shear force was stepwise decreased. Initially, vertical SIJ shear force was 563 N (on each side of the sacrum) at a trunk load of 500 N. The angle between the normal direction of the SIJ surface and the direction of the total SIJ reaction force was 81°, indicating that mainly vertical shear force acted through the SIJ, see Fig. 2a. Force equilibrium was mainly achieved by activation of M. abdominal oblique (internus and externus), M. iliacus, M. psoas, M. rectus abdominis, M. rectus femoris, M. tensor fasciae latae, and loading of the sacrotuberous ligament.

Table 2 Summary of the structures that stabilize the sacroiliac joints in terms of lowered shear
Figure 2
figure 2

Directions of the force in the frontal plane exerted by the right ilium through the SIJ on the sacrum as a reaction to trunk load, Ftrunk. Panel (a): initial loading condition without limitation of the vertical shear component (563 N, see under “initial” in Table 2). This condition led to loading of the sacrotuberal ligaments, Fsacrotuberal lig. (solid thick line). Panel (b): loading condition with the vertical shear component preset at a 120 N lower level than the initial value (see under 443 N in Table 2). This condition led to loading of the sacrospinal ligaments, Fsacrospinal lig. (solid thick line). Panel (c): loading condition with the vertical shear component preset at a 240 N lower level than the initial value (see under 323 N in Table 2). In this situation, SIJ compression force increased by ∼400%, mainly by M. transversus abdominis, Ftransversus abdominis, and the pelvic floor, Fpelvic floor, muscle forces. The location of these muscles is schematically drawn by the thick solid lines, including the M. pubococcygeus, the M. iliococcygeus and the M. coccygeus (as drawn from the mid to the lateral position). It also led to loading of the iliolumbar ligaments to the maximum allowed force Filiolumbar lig. of 250 N, (solid thick line). 3-D images copyright of Primal Pictures Ltd. http://www.primalpictures.com

When the maximum vertical SIJ shear force was decreased from 563 to 443 N in steps of 30 N, the SIJ compression force increased by about 70%. Force equilibrium was obtained, amongst others, by activation of some of the muscles with a hip flexion component (M. adductor longus, M. iliacus, M. pectineus, and M. sartorius, M. rectus femoris) and some of the counteracting hip extensors (MM. gluteus medius and minimus and M. piriformis). Most of these muscles became (more) active after we lowered the maximum vertical SIJ shear force by 30 N. This led to unloading of the sacrotuberous ligaments and loading of the sacrospinal ligaments. The angle between the normal direction of the SIJ surface and the direction of the total SIJ reaction force was reduced to 72°, indicating that a combination of reduced vertical SIJ shear and increased SIJ compression could balance the trunk load on the sacrum, see Fig. 2b.

Further stepwise reduction of the vertical SIJ shear force resulted in a sharp rise of the maximum muscle stress. The simulation series ended with exceeding the maximum physiological muscle stress when the vertical SIJ shear force was decreased to about 60% of its initial value. Surprisingly, activation of some of the hip flexors and extensors had decreased or even disappeared. This was not the case for the MM. gluteus medius and minimus. In this simulation, force equilibrium was obtained by activation of the transversely oriented M. transversus abdominis (ventral to the SIJ) and the pelvic floor muscles, i.e., the M. coccygeus, the M. iliococcygeus, and the M. pubococcygeus (caudal to the SIJ). This resulted in further reduction of the angle between the normal direction of the SIJ surface and the direction of the total SIJ reaction force to 35°, see Fig. 2c. This indicates that the SIJ compression force, which increased by about 400% and the reduced vertical SIJ shear force, now clamped the sacrum between the coxal bones, see Fig. 2c. The MM. gluteus medius and minimus contributed to some extent to this increased compression due to a distinct force component in the transverse direction. To maintain force equilibrium, increased SIJ compression led to loading of the iliolumbar and posterior sacroiliac ligaments to the preset maximum value of 250 N.

Discussion

In the present study, the simulation model predicted muscle and ligament forces in the pelvic region when there was an imposed reduction of the vertical SIJ shear force. Initially, the forces acting through the SIJ were mainly vertical shear forces, see Fig. 2a. These forces were not only caused by trunk load, but also by muscles that acted in the longitudinal direction of the spine, for example the M. psoas and M. rectus abdominis. As a result of the forward bending moment, the sacrotuberous ligament was loaded. This large ligament protects the SIJ against excessive flexion of the sacrum relative to the coxal bones. The controlled reduction of the vertical SIJ shear force with 30 N forced some muscles that act as hip flexors and hip extensors to become active. Due to their transverse orientation, especially the MM. gluteus medius and minimus and M. piriformis contributed to the increased compression force between the coxal bones and the sacrum. However, these muscles did not contribute enough to self-bracing of the SIJ, because the total force through the SIJ still mainly acted in vertical direction. When the vertical SIJ shear was further reduced to about 60% of its initial value, the simulation model predicted that self-bracing mainly resulted from the transverse muscles ventrally (M. transversus abdominis) and caudally (pelvic floor) to the SIJ. In this situation, some of the hip flexors and extensors reduced in activity, for example the M. piriformis. Although the M. piriformis has a transverse orientation and crosses the SIJ, its contribution was minimized by the simulation program because this muscle also induces vertical SIJ shear force. The pelvic floor muscles, the M. coccygeus and M. pubo-, and iliococcygeus, contribute to the stabilization with respect to the sacrum. It has been suggested that this stabilization by force closure has an analogy with a classical stone arc.33 When sideways displacement of both ends of the arc is opposed, mechanical equilibrium of the stones is achieved by compression forces and not by shear forces. In the pelvis, the pelvic floor muscles may help the coxal bones to support the sacrum by compression forces, while shear forces between sacrum and coxal bones are minimized, see Fig. 3. Note that the SI compression force is defined as the force acting perpendicular to the SIJ surface. Therefore, decreasing or increasing this force will not alter the shear forces. The articular surfaces of the SIJ are irregular which results in bony interdigitation in the SI joint space. SIJ shear force calculated in the simulation model thus reflects the combination of real joint friction and friction due to this intermingling of bones. The real joint friction forces may be extremely small considering the extremely low coefficients of friction between the articular surfaces. The majority of the shear force is effectuated as normal contact pressures due to the bony interdigitation in the SI joint space. It was not possible to calculate the percentage of shear in terms of joint friction force. This requires a more detailed description of the SIJ surfaces.

Figure 3
figure 3

Analogy of pelvic bones supporting the trunk with a classical stone arc. The M. transversus abdominis and the pelvic floor muscles caudal to the SIJ mainly oppose lateral movement of the coxal bones. Spinal loading is transferred mainly by compression forces through the SIJ to the coxal bones and further down to the legs. 3-D images copyright of Primal Pictures Ltd. http://www.primalpictures.com

The simulation model predicts that simultaneous contraction of the M. transversus abdominis and pelvic floor muscles, i.e., the M. coccygeus, the M. iliococcygeus, and the M. pubococcygeus, contribute to lowering of the vertical SIJ shear forces, increasing of the SIJ compression and hence increasing of the SIJ stability. We emphasize that this simulation model was set up to estimate the forces acting in the pelvic region under static conditions and that the outcome of the simulations must be interpreted with caution.5 Nevertheless, in a previous study co-contraction was shown of pelvic muscles and M. transversus abdominis.26 This result and the prediction of our simulation model suggest that a protective mechanism against high SIJ shear forces may exist in humans. This mechanism has been investigated in vivo and in vitro. The contribution of the M. transversus abdominis to SIJ stability was shown in an in vivo study in patients with LBP.25 An in vitro study in embalmed human pelvises showed that simulated pelvic floor tension increased the stiffness of the pelvic ring in female pelvises.23 It is worthwhile to further investigate the contribution of both muscle groups simultaneously, not only during stiffness measurements of the SIJ but also during lumbo-pelvic stability tests based on increased intra-abdominal pressure (IAP). It was shown that the pelvic floor muscles, in combination with abdominal muscles and the diaphragm, may control and/or sustain IAP to increase lumbar spine stability as well.7,14

In the present study, the ligament forces were not allowed to exceed 250 N. The distribution between muscle and ligament forces depended on the maximum muscle stress as formulated in the first optimization scheme as presented in the Appendix. Increasing the maximum ligament forces might result in a lower maximum muscle stress, which could lead to a different muscle activation pattern to stabilize the SIJ. A small sensitivity test, however, showed that when the ligament forces were allowed to exceed the 250 N up to 500 N and in a next step up to 750 N, the model calculated a similar muscle activation pattern. The outcome of the present study also depended on the choice of optimization criteria and the magnitude of the cross-sectional areas of the muscles. The influence of different criteria was previously investigated for muscle forces in the leg.21 Indeed, various choices led to different calculated forces, but the obtained solutions were qualitatively similar, as was the case in our model. When we developed the model, other optimization criteria were also tested, for example minimization of the sum of muscle forces. However, minimization of the sum of squared muscle stresses yielded the most plausible solutions. The model cannot account for anatomical variations or detailed variation in muscle attachment sites. Obviously, direct comparison between the model predictions and the outcome of in vivo force measurements in the SIJ are not available, so there is no data to confirm the outcome of the present study. Nevertheless, EMG recordings of (superficial) abdominal and back muscles in various postures showed higher M. abdominal oblique internus activity when standing upright than resting on one leg and tilting the pelvic backwards.33 This muscle is considered as one of the self-bracing muscles of the SIJ. It was hypothesized that when standing on one leg, the shear load on the contralateral SIJ is diminished. Posterior tilt of the pelvis with less lumbar lordosis may than lead to less M. psoas major muscle load on the spine meaning less shear load on the SIJ. These findings indirectly support our findings that transversely oriented muscles reduce SIJ shear forces. We emphasize that the present model served as a tool to investigate the general relations between muscle and ligament forces in the pelvic region. The present simulations results may lead to the development of a new SIJ stabilizing training-program to reduce pain induced by high SIJ shear forces. The effectiveness of such a program, however, can only be tested with an intervention study.

The simulation model predicted unloading of the sacrotuberous and loading of the iliolumbar and posterior sacroiliac ligaments when the vertical SIJ shear was forced to reduce. This loading of the dorsal ligaments resulted from the absence of transversely oriented muscles at the dorsal side of the SIJ to counterbalance activation of the M. transverse abdominis at the ventral side of the SIJ. Loading of the iliolumbar ligament has been related to LBP.24 It was shown that in sitting position, the stepwise backward movement of an erect trunk (from upright position into a slouch) resulted in forward flexion of the spine combined with backward tilt of the sacrum relative to the pelvis.32 It was shown, that this movement into a sudden or sustained slouch might cause loading of the well-innervated iliolumbar ligaments near failure load.31 The co-contraction that exists between the deep abdominal M. transversus abdominis and the deep back extensor M. multifidus presumably retains lumbo-pelvic stability.13 In the future, we intend to extend the model with co-contraction between the M. transversus abdominis, the M. multifidus, and the pelvic floor muscles to study prevention of (over)loading of pelvic ligaments at different static postures.

Conclusions

Effective stabilization of the SIJ is essential in transferring spinal load via the SIJ to the coxal bones and the legs. A biomechanical analysis of the upright standing posture showed that activation of transversely oriented abdominal M. transversus abdominis and pelvic floor, i.e., M. coccygeus and M. pubo- and iliococcygeus muscles would be an effective strategy to reduce vertical SIJ shear force and thus to increase SIJ stability. The force equilibrium in this situation induced loading of the iliolumbar and posterior sacroiliac ligaments. The M. transversus abdominis crosses the SIJ and clamps the sacrum between the coxal bones. Moreover, the pelvic floor muscles oppose lateral movement of the coxal bones, which stabilizes the position of the sacrum (the pelvic arc).