Relationship between limb length discrepancy and load distribution across the sacroiliac joint—a finite element study

Authors

  • Ali Kiapour,

    1. Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopedic Surgery, Colleges of Engineering and Medicine, University of Toledo, Toledo, Ohio
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  • Amr A. Abdelgawad,

    Corresponding author
    1. Orthopedic Surgery & Rehabilitation, Paul L. Foster School of Medicine, Texas Tech University Health Science Center at El Paso, 4801 Alberta Ave, El Paso, Texas 79905
    • Orthopedic Surgery & Rehabilitation, Paul L. Foster School of Medicine, Texas Tech University Health Science Center at El Paso, 4801 Alberta Ave, El Paso, Texas 79905. T: 915-545-6750; F: 915-545-6704
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  • Vijay K. Goel,

    1. Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopedic Surgery, Colleges of Engineering and Medicine, University of Toledo, Toledo, Ohio
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  • Adham Souccar,

    1. Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopedic Surgery, Colleges of Engineering and Medicine, University of Toledo, Toledo, Ohio
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  • Tomoya Terai,

    1. Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopedic Surgery, Colleges of Engineering and Medicine, University of Toledo, Toledo, Ohio
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  • Nabil A. Ebraheim

    1. Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopedic Surgery, Colleges of Engineering and Medicine, University of Toledo, Toledo, Ohio
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Abstract

We assessed the relationship between leg length discrepancy (LLD) and the load distribution across the sacro-iliac joint (SIJ). A finite element model of the spine–pelvis was developed with different amounts of LLD by increasing the length of the right femur in the model. Peak stresses and contact loads across the SIJ were computed for different amounts of LLD (1, 2, and 3 cm). The load and the peak stresses across the SIJ articular surfaces progressively increased with the increase in the LLD. Trying to offset the LLD surgically by lengthening of the short side, shortening or stunting the growth (epiphysiodesis) of the long side, or by shoe lifts should decrease the load across the SIJ and should theoretically decrease SIJ pain. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 30:1577–1580, 2012

Leg length discrepancy (LLD) has been associated with low-back pain (LBP).1–7 The mechanism by which LLD leads to LBP is unknown. Previous authors have attributed LBP with LLD to sacro-iliac joint (SIJ) dysfunction.7–9 LLD results in pelvic obliquity that leads to abnormal mechanical alignment of the SIJ of both sides resulting in high loads passing through the joint.7–9 To date, no study has quantified the amount of changes in loads and stresses across the SIJ as a result of LLD. Also, the relationship between the contact load at the SIJ and the amount of LLD is not fully understood. To understand the biomechanical effects of LLD, it is crucial to evaluate the changes in distribution of load at the SIJ for different amounts of LLD.

It is impractical to measure the loading across the SIJ in living subjects due to the small clearance between the joint surfaces and other ethical concerns. Challenges exist for such a lab study on cadavers as well. Thus, finite element (FE) analysis is an excellent modality to study the load distribution across the SIJ. We hypothesized that the LLD will result in an increase in loads across the SIJ and that the magnitude of this increase is related to the amount of LLD.

MATERIALS

An FE was conducted using an existing 3D, nonlinear, experimentally validated model of a ligamentous lumbar spine–pelvis segment.10 The FE model of the pelvis included 32,586 elements and 44,594 nodes (Fig. 1). This model was constructed using a CT scan of a young, healthy male pelvis.10 The transverse CT images were taken at 2-mm increments and were transferred into Image J software (http://rsb.info.nih.gov//ij). Datum nodes were superimposed at the outer boundaries of the bone at each transverse slide. The nodes were then imported into ABAQUS FE element package (Simulia, Providence, RI). Following development of the bony structures, the ligaments were added with the insertion points and thicknesses derived from literature, as explained previously.10 The cartilaginous layer between the contact surfaces of the SIJ was also simulated using a contact formulation with exponential behavior, which adjusted the force transfer across the joint depending on the size of the gap exponentially.

Figure 1.

Finite element model of the lumbo-pelvis segment. The model was developed using validated models of L3–S1 spine and pelvis segment.

The hip joint in the model consisted of part of the femur including the femoral head and the acetabulum. The head was fixed to the acetabulum to prevent any rotation or displacement of the pelvis with respect to the femur.

The spine part of the model was adapted from a nonlinear finite model of intact L3–S1 segments.10, 11 This model was also created previously using CT images of a healthy ligamentous spine tissue with the same methodology as used for the pelvis FE model. The FE spine model included all main physiological features including bone, intervertebral disk, and major ligaments. The ligaments were assigned nonlinear properties with increasing stiffness at higher strains. The disk was modeled as a composite including nucleus pulposus and annulus fibrosus components. The nucleus was given the property of an incompressible fluid; the annulus was modeled as a ground substance reinforced with embedded fiber layers. The nonlinear property of ligaments and the disks along with the posterior facet joints provided nonlinear kinematics to the spine model. The spine and pelvis parts (both innominate bones and sacrum) were combined to generate the lumbo-pelvis model, as described previously.10, 11

The intact model was then used to create LLD disorders of different amounts (1, 2, and 3 cm) with the right side being the longer side (Fig. 2). To simulate LLD, the left femur was fixed, and the right femur was elevated by the proposed amount; both femurs were then fixed in all degrees of freedom. Following simulation of LLD, physiological loads were applied to the models. The loading included a compressive follower pre-load of 400 N, plus a 10-Nm bending moment applied at the superior surface of the L3 vertebra of the intact and LLD models to simulate flexion (Flex), extension (Ext), left and right bending (LB & RB), and left and right axial rotation (LR & RR). The peak stresses across the SIJ along with the resultant load across the joint were computed for all LLD cases at each physiological loading. The data for the LLD cases were compared against those of the intact model; ratios were computed to predict the maximum values and the corresponding loading case.

Figure 2.

Finite element model of limb length discrepancy (right side longer) as seen from the back. Note the elevation of the right side femur compared to the left side.

RESULTS

In the intact model, both the minimum (79 N) and maximum (140 N) loads occurred in lateral bending (the minimum load in the contra lateral side and maximum load in the ipsilateral side, Fig. 3). The peak joint load increased to 381, 719, and 1,000 N at 1, 2, and 3 cm of LLD, respectively. The peak loads were always higher at the longer leg side. The loads were also higher (340, 682, and 917 N) at the short leg side, compared to intact model.

Figure 3.

The predicted loads (N) across the left and right SIJs for different amounts of leg length discrepancies (LLDs) for different physiological motions. The intact SIJ loads are shown for comparison. The data are for a 400 N follower load and a 10 Nm moment.

Different motions (Flex, Ext, lateral bending, and axial rotation) were associated with higher stresses across the SIJ in the models with LLD, compared to the intact model (Table 1) with equal extremity length. In the intact joint, the peak stress was 7 MPa compared to 53, 84, and 120 MPa in 1, 2, and 3 cm of LLD, respectively. The stresses were also higher on the longer side in LLD cases and increased with increasing LLD. With 3-cm LLD, Flex led to >20 times increase in the stresses in the SIJ of the long extremity side and about 9 times increase in the short side, compared to the stresses in the SIJs with equal extremity length (Table 1).

Table 1. The Predicted Loads (N) across the Left and Right SIJs for Different Amount of Leg Length Discrepancies (LLDs) for Different Physiological Motions
Stress (MPa)Intact1 cm LLD2 cm LLD3 cm LLD
LeftRightLeftRightLeftRightLeftRight
  1. The intact SIJ loads are shown for comparison. The data are for a 400 N follower load and a 10 Nm moment.

Flex5.75.716.533.928.958.154.1119.0
Ext6.56.44.533.834.360.052.494.7
LB6.93.622.226.440.239.556.558.0
RB3.66.99.453.124.783.547.9116.7
LR5.66.131.132.838.367.580.896.0
RR6.15.65.137.326.454.959.5112.9

DISCUSSION

LBP is a major health problem with profound socioeconomic impact. About 75% of people will experience LBP at some time.12 LLD is a possible cause of LBP.1–7 The pathophysiology of LBP due to LDD is not fully understood. With LLD, pelvis obliquity will result in increased stress at the SIJ.7–9 However, the load distribution at the SIJ had not been quantified. We conducted an FE analysis using our validated spine–pelvis model to quantify these biomechanical parameters for different LLDs. This FE model was utilized in our earlier study to assess the effects of lumbar fusion on sacral movements and sacral stresses.10, 11 In those studies, we compared the FE results with experimental data13–16 and found good agreement with the literature under similar surgical/loading scenarios.10 The present study is the first report of which we are aware that quantifies the load distribution across the SIJ as a result of LLD.

We utilized two biomechanical parameters, the overall load at the contact area and the load distribution (stress) over the contact area for evaluating the effects of LLD. The contact load predicts how much load passes through the joint, whereas the stress estimates the concentration or distribution of such load at various points across the contact interface. Although an increase in load usually leads to an increase in stress, the high peak stress is not always an indicator of higher load as the stress also depends on the area of the contact surface at the interface.

We concluded that LLD can significantly increase the load and stress at the SIJ. The peak load also increased notably as discrepancy increased. LLD increases the joint load on both short and long leg sides; however, this increase was higher on the longer side. As little as 1 cm of LLD can increase the load across SIJ to almost 5 times that of intact (shorter side, in LB). This increase can reach almost 12 times of intact at 3 cm discrepancy (RB and LB loadings). Joint loads are maximum in Flex and lateral bending. These observations can help the physician to advice their patients about which positions and movements to avoid.

Finally, we used load and stress parameters as factors to evaluate the effect of LLD on the biomechanics of the SIJ, but that does not necessarily mean that the loading and pain at the SIJ are in a direct correlation. Despite that, increase in the stresses and loads across the SIJ would most likely increase the possibility of a having painful SIJ or to its degeneration.

In conclusion, our FE-based study showed that increased LLD will result in significantly higher loads and peak stresses at contact surfaces of the SI joint. This may potentially cause LBP. Trying to offset the LLD surgically by lengthening the short side, shortening the long side, or by using shoe lifts should decrease the load at the SIJ, and consequently reduce the pain at the joint.

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