Biomechanical Analysis of Stress–Strain Distribution in the Lumbar Spine–Sacrum–Pelvis System with Emphasis on Sacroiliac Joint Dysfunction

Abstract

Background: Chronic lumbopelvic pain is often linked to sacroiliac joint dysfunction, where the joint’s complex structure and biomechanics complicate diagnosis and treatment. Variability in load distribution and ligament stabilization within the pelvic ring further contributes to challenges in managing this condition. This study aims to develop a finite element model of the “lumbar spine–sacrum–pelvis” system to analyze the effects of lumbar lordosis, pelvic tilt, and asymmetrical articular gaps on stress and strain in the sacroiliac joint. Methods: A three-dimensional model was constructed using CT and MRI data, including key stabilizing ligaments. Sacral slope angles of 30°, 60°, and 85° were used to simulate varying lordosis, while pelvic tilt was introduced through a 6° lateral rotation. Results: The analysis revealed that sacral slope, ligament integrity, and joint symmetry significantly influence stress distribution. Hyperlordosis led to critical stress levels in interosseous and iliolumbar ligaments, exceeding failure thresholds. Asymmetrical gaps and pelvic tilt further altered the sacral rotation axis, increasing stress on sacroiliac joint ligaments. Conclusions: These findings highlight the importance of maintaining sacroiliac joint symmetry and lumbar–pelvic alignment to minimize stress on stabilizing ligaments, suggesting that treatment should focus on restoring alignment and joint symmetry.

1. Introduction

Chronic lumbopelvic pain, estimated to have mechanical origins in approximately 85% of cases [1,2], is frequently linked to degenerative changes in the sacroiliac joints. Osteoarthritis of the sacroiliac joints can present with both lumbar and pelvic pain, which may mimic or coexist with symptoms of lumbar osteochondrosis, making differential diagnosis challenging [3,4]. Evidence suggests that sacroiliac joints are the source of lower back pain in 53% of patients [5,6] and of lumbosacral pain in 10–27% [7,8]. Unclear diagnostic criteria for sacroiliac osteoarthritis often lead to ineffective treatment, resulting in persistent pain, restricted movement, and altered posture affecting both the trunk and lower limbs [4]. Consequently, sacroiliac joint disorders can lead to prolonged disability, a diminished quality of life, and social adaptation challenges [7,9].

Pelvic alignment is a key factor in the biomechanics of lower limb kinematics, as it directly influences the distribution of forces and the movement patterns within the kinematic chain. Misalignment, such as pelvic tilt or rotation, can result in compensatory changes in the hip, leading to uneven load distribution and increased joint stress. These alterations may contribute to gait abnormalities, overuse injuries, and joint degeneration. Understanding the role of pelvic alignment is, therefore, critical for analyzing its impact on overall biomechanical stability and lower limb functionality.

The clinical presentation of sacroiliac joint osteoarthritis relates to compromised load-bearing capacity [10], which is the joint’s ability to adapt efficiently to loading, facilitated by coordinated muscle contractions and ligament tension that maintain adequate joint compression [11]. Factors impacting the load-bearing capacity of sacroiliac joints include asymmetrical articular gaps, sacral and pelvic tilt in the frontal plane (lateral angularity), sacral rotation, and lower segmental lumbar lordosis [10,12,13]. Studies show that, among adults under 40, articular gaps average around 2.5 mm, whereas in older patients, it decreases to approximately 1.5 mm [14]. Asymmetrical articular gaps are a recognized indicator of sacroiliac joint dysfunction and osteoarthritis [15]. In most adults, a line drawn through the cranial sacral plate in the frontal plane remains horizontal; however, a unilateral shift of even 2 mm can be clinically significant [16,17]. To maintain vertical alignment, the lumbar spine often inclines laterally toward the higher sacral edge and elevated iliac crest.

Current diagnostic and therapeutic approaches for sacroiliac joint disorders remain inconsistent [18]. Diagnostic unreliability and low treatment efficacy for sacroiliac joint osteoarthritis are partially attributed to the unique anatomical and biomechanical characteristics of the joint [19]. Disagreements persist regarding which parts of the joint bear the most load and which structural elements possess the highest mechanical rigidity [20]. Some studies point to the extra-articular sacrotuberous ligament as a key load-bearing structure [21], while others highlight intra-articular structures, specifically the ventral, dorsal, and interosseous sacroiliac ligaments or the iliolumbar ligament (particularly its iliac-sacral segment), as primary passive stabilizers [22].

Computational modeling techniques have greatly expanded the ability to analyze biomechanical systems, with finite element methods (FEMs) becoming the standard for biomechanical simulation studies [23,24,25]. However, research on sacroiliac joint osteoarthritis and lumbar spine biomechanics varies significantly, often yielding inconsistent results [26].

Table 1. Summary of key computational modeling studies.

Reference	Focus	Key Findings
[27]	Pelvic model with leg length discrepancies	Von Mises stress increased significantly in the sacroiliac joint with a 1 cm discrepancy
[28]	Impact of ligaments on sacroiliac joint stability	Ligament dysfunction increases stress and displacement, affecting pelvic stability.
[29]	Stress in sacroiliac joint ligaments under vertical load	Highest stress values were found in the sacroiliac and iliolumbar ligaments
[30]	Stress in interosseous sacroiliac joint ligaments	Interosseous sacroiliac ligaments experience maximum stress during vertical loading
[31]	Role of ligaments in sacroiliac joint stability	Interosseous, posterior sacroiliac, and iliolumbar ligaments stabilize the pelvic ring under load
[32]	Lumbar spine under six movements	Rotational movements produce the highest stress in intervertebral discs, increasing injury risk
[33]	Finite element models validation for lumbar spine	Comprehensive validation of finite element models under various loading conditions
[34]	Loading conditions in lumbar finite element models	Models validated under pure-moment, pure-compression, and combined-loading scenarios
[35]	Finite element modeling of lumbar spine pathologies	Developed models for disc degeneration and scoliosis analysis
[36]	Degeneration in LIV-LV segment	Early degeneration increases stress; advanced stages shift stress toward the dorsal side
[37]	Lumbar surgical techniques comparison	Stability differences between lateral and transforaminal lumbar interbody fusion techniques
[38]	Fixation approaches in LIV-LV level	Variations in biomechanical behavior between healthy and fixed lumbar spine models

summarizes key studies, their methodologies, and findings, providing a clearer understanding of current knowledge and gaps.

However, much of the existing research is fragmented, with individual studies focusing on isolated factors, making it challenging to comprehensively evaluate the interplay of these variables.

This review highlights the need for a mathematical model of the “lumbar spine–sacrum–pelvis” system that considers key stabilizing ligaments of the sacroiliac joint and vertical body alignment, as well as major factors influencing body weight transfer to the sacrum and pelvis and ground reaction forces. Factors include pelvic and sacral tilt, asymmetrical articular gaps of the sacroiliac joint, and lower segmental lumbar lordosis. The goal of this study is to examine the relationship between these factors and the stress–strain parameters of the elements within the “lumbar spine–sacrum–pelvis” system.

2. Materials and Methods

The model “lumbar spine–sacroiliac joints–pelvis” with major ligaments was constructed on the base of CT and MRI scans. These models were created using Solidworks 2022 software (Dassault Systèmes SolidWorks Corporation, Waltham, MA, USA). To create a geometric model of the sacroiliac joint, geometric models of the vertebrae L_I–L_V, sacrum S_I–S_V with the coccyx, and pelvic wings were previously constructed (Figure 1). For this purpose, the corresponding slices of computer tomograms of real biomechanical systems were used. Disc-shaped elements were placed between the vertebrae and articular processes to mimic the presence of intervertebral discs and articular cartilage.

The following ligaments, which play a key role in the rotational stabilization of the sacroiliac joint and in the position of the lower lumbar segments and sacrum in relation to the pelvis, were taken into account in the simulation: anterior sacroiliac, interosseous sacroiliac, posterior sacroiliac, sacrotuberous, and sacrospinous. Their positions were reproduced based on MRI scans and the layout scheme according to the work in [39,40].

The modeling of the sacroiliac joint with ventral, interosseous, and dorsal sacroiliac ligaments was performed by introducing a geometric element that provides the necessary degrees of freedom of the sacrum relative to the iliac wing, whose shape and structure correspond to the works in [40,41,42] (Figure 2).

In this study, the mechanical properties of biological tissues were characterized using the modulus of elasticity and Poisson’s ratio, which are essential for accurately simulating their behavior under load. Modulus of elasticity (Young’s modulus) represents the stiffness of the material, while Poisson’s ratio describes how a material changes shape in one direction when stretched or compressed in another. The values used for modeling are summarized in

Table 2. Mechanical characteristics of the “lumbar spine–sacroiliac joints–pelvis” system.

Biological Tissues	Modulus of Elasticity, MPa	Poisson’s Ratio
Cancellous bone	690	0.35
Cortical bone	6900	0.32
Intervertebral disc	50	0.35
Cartilages	50	0.35
Ligaments	164	0.48

[43,44].

To model the sacroiliac joint with the lumbar region under various lumbar lordosis conditions, functional shifts were introduced into the geometric model. Three angles of inclination of the cranial sacral plate relative to the horizontal (SS—sacral slope) were set, SS = 30°, SS = 60°, and SS = 85° [40], taking into account the corresponding lumbar lordosis (Figure 3).

The asymmetry of articular gaps of the sacroiliac joint was modeled by doubling the width of the right element. Given that the ventral, interosseous, and dorsal sacroiliac ligaments in the area of the wider joint space are in a state of hyperextension and microtrauma [2], their physical–mathematical properties were modeled by halving Young’s modulus [43,45]. Meanwhile, the physical–mechanical properties of the remaining biological tissues were assumed to be constant.

The tilt of the pelvis (lateral angularity) was modeled by rotating it at an angle of 6° relative to the horizontal line in the frontal plane. This pelvic tilt angle corresponded to a shift of 4.0 to 5.0 cm in the frontal plane (distance h) (Figure 4). At the same time, the vertical axis of the mathematical model of the lumbar spine passed through the center of vertebra L₁ [17].

The model was loaded along the upper vertebra L_I with a compressive vertical force along the spine axis equal to the weight of the body part located above the vertebra L_V (Figure 5). According to the study in [46], the value of this load is 50% of the total body weight. One level of loading on the lumbosacral region was considered for an average human weight (80 kg): 400 N in the cranio–caudal direction. The model was rigidly fixed on the surfaces of the pelvic wings, which excluded their displacement.

The finite element mesh was generated using spatial tetrahedral elements with 10 nodes, as well as 3-node triangular shell elements that account for both bending and membrane properties [47]. An example of the meshed model is shown in Figure 6.

In the studied bone stress state, von Mises equivalent stress was selected as the primary measure to evaluate bone failure or structural integrity. Von Mises stress is a widely used metric in biomechanical models to predict material behavior under complex loading conditions. It helps identify regions in tissues where deformation or failure is most likely to occur, providing critical insights into stress distribution [28,32,35,36].

A mesh convergence analysis was conducted to identify the optimal element size, refining the mesh by reducing element dimensions from 3.0 mm down to 0.05 mm. The mesh was refined until the maximum von Mises equivalent stress converged to within a 5% change threshold across all elements [48].

The process concluded with a final mesh size range between 1.0 mm and 0.05 mm. The total number of finite elements ranged from 5,947,441 to 7,000,652, with node counts between 8,470,111 and 10,695,410. Quality analysis of the finite-element models revealed no critical errors, ensuring the reliability of the mesh.

In calculating the biomechanical system, the following primary hypotheses and assumptions were applied:

−

Material properties: all materials were assumed to be homogeneous and isotropic, with known physical and mechanical properties;

−

Modeling framework: the analysis was performed under a physically and geometrically linear framework, assuming small deformations and displacements. This allowed for the application of Hooke’s law to describe material behavior;

−

Lumbosacral spine specificity: a unique aspect of the calculation involved the lumbosacral spine under conditions of increased lordosis. For this degree of lordosis, the joint cartilage in the facet joint contact zones was modeled to function minimally in reducing friction between the bones. As a result, a “bone-on-bone” contact problem was addressed, leading to stress concentration in this region.

This study focused exclusively on the biomechanical effects of lumbar lordosis, pelvic tilt, and asymmetrical articular gaps within the lumbosacral–pelvic system. Degenerative changes in adjacent joints were also excluded to minimize confounding variables and ensure that the observed stress–strain patterns could be directly attributed to the modeled conditions. This methodological approach provides a clearer understanding of the specific factors influencing the biomechanics of the sacroiliac joint and its surrounding structures

3. Results

3.1. The Influence of Lumbar Lordosis

Illustrations of von Mises equivalent stress and strain localization in the model of the lumbosacral region and sacroiliac joint in the presence of ligaments are shown in Figure 7 (the non-deformed state of the model is shown in translucent color).

Analysis of the stress—state of the lumbosacral model and the sacroiliac joint (Figure 8, Figure 9 and Figure 10) showed that the ligaments restrict the rotational mobility of the sacroiliac joint at all degrees of lumbar lordosis, tightening or relaxing, depending on the direction of movement.

Thus, at physiological values of lumbar lordosis and sacral slope (SS = 60°), the maximum stress magnitude in the cartilage zone of the sacroiliac joint reaches 0.55 MPa, which is more than twice as low as in the model without ligaments (1.3 Mpa). Meanwhile, the stress level in the intervertebral discs is maximal in the lumbosacral region and does not exceed 0.5 Mpa, which is half of that in the model without ligaments. In the facet joint zones of the L_II–L_III, L_III–L_IV, and L_IV–L_V segments, stress intensity is higher at 1.6 Mpa; however, this is 12% lower than in the model without ligaments (Figure 11).

The maximum tensile stress in the ligaments is noted in the cranial part of the ventral and dorsal sacroiliac ligaments, reaching 1.1 Mpa, then decreasing to 0.83 Mpa in the iliotransverse ligament, reaching 0.19 Mpa in the sacrospinous ligament, and is distributed fairly evenly across the sacrotuberous and iliolumbar ligaments (

Table 3. Maximum of von Mises equivalent stress of ligaments for different physiological values of lumbar lordosis.

Iliolumbar	Sacrospinous	Sacrotuberous	Ventral Sacroiliac			Iliotransverse	Dorsal Sacroiliac
			Cranially	Medially	Caudally		Cranially	Medially	Caudally
normal physiological value of lumbar lordosis (SS = 60°)
4.25	0.99	0.76	5.00	3.75	3.75	4.17	5.00	3.30	1.65
vertical sacrum and smoothed lordosis (SS = 30°)
0.68	0.65	0.3	3.00	3.00	3.00	2.25	2.25	2.00	1.5
horizontal sacrum and hyperlordosis (SS = 85°)
7.2	1.3	1.5	9.16	5.34	4.5	6.87	9.16	6.11	2.29

).

With a reduction in lumbar lordosis depth and sacral verticalization (SS = 30º), the maximum stresses in the sacroiliac joint cartilage reach 0.3 Mpa, which is twice as low as in the model without ligaments. The stress level in the L_V–S_I disc does not exceed 0.2 Mpa. In the facet joint zones of the L_II–L_III, L_III–L_IV, and L_IV–L_V segments, stress intensity reaches 0.65 Mpa, which is significantly lower than in the physiological lordosis and in the model without ligaments. The maximum tensile stress is noted in the cranial and caudal parts of the ventral sacroiliac ligaments at 0.55 and 0.46 Mpa, respectively. In the iliotransverse ligament, tensile stress reaches 0.34 Mpa. In the remaining ligaments, the tensile stress values are evenly distributed, reaching a maximum of 0.23 Mpa in the caudal part of the dorsal sacroiliac ligaments.

With hyperlordosis and sacral horizontalization (SS = 85°), the maximum stress in the sacroiliac joint cartilage was found to be 0.52 Mpa, which is four times lower than in the model without ligaments. The stress level in the L_V–S_I disc does not exceed 0.74 Mpa, which is half the value in the model without ligaments. In the facet joint zones of the L_III–L_IV and L_IV–L_V segments, stress reaches a maximum level of 2.5 Mpa, which is one and a half times lower than in the model without ligaments. The magnitude of linear displacements of the vertebral segments is minimal. The maximum tensile stress in the ligaments is noted in the cranial part of the dorsal sacroiliac ligaments at 1.5 Mpa, in the iliolumbar ligament at 1.3 Mpa, and in the cranial part of the ventral sacroiliac ligaments at 1.13 Mpa. The iliolumbar ligament is loaded more than ten times higher than in the previous cases. The sacrotuberous ligament has a tensile stress magnitude of 0.38 Mpa, which is several times higher than in the other two cases. A similar pattern is observed with the sacrospinous ligament, where the tensile stress is 0.33 Mpa.

3.2. The Influence of Asymmetry of the Width of the Articular Gaps

The obtained patterns of stress and strain distribution in the model with symmetrical articular gaps, as well as with their asymmetry and overstretching of the ventral, interosseous, and dorsal sacroiliac ligaments, indicate a change in the functional behavior of the entire joint. Thus, with symmetrical articular gaps, the rotational axis of the sacroiliac joint mobility passes horizontally through the conditional centers. In this case, the left and right ligaments are loaded evenly (Figure 12).

Asymmetry in the width of the sacroiliac joint articular gaps leads to a change in the position of the conditional axis of sacral rotational mobility; the sacrum additionally rotates relative to the left sacroiliac joint (Figure 13). This causes the conditional axis of sacral rotational mobility to shift forward and downward on the right relative to the pelvis, and backward and upward on the left. This, in turn, leads to a significant redistribution of stresses and strains between the left and right joints and ligament bundles. Figure 14 shows the displacement of the axis of sacral rotational mobility in symmetrical and asymmetrical articular gaps.

The results of calculations with asymmetry in the width of articular gaps are presented in Figure 15 and

Table 4. Maximum of von Mises equivalent stress (σ) and equivalent strain (ε) in the sacroiliac joint with ligaments under symmetrical and asymmetrical articular gaps.

ligaments of the sacroiliac joints

symmetrical articular gaps

ventral

dorsal

iliotransverse

interosseous

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

1.22

0.50

1.36

1.30

0.95

0.5

1.09

0.7

cartilages of sacroiliac joints

iliolumbar ligament

sacrospinous

sacrotuberous

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

0.63

2.2

1.28

0.65

0.37

0.18

0.27

0.13

asymmetrical articular gaps

ventral

dorsal

iliotransverse

interosseous

left

right

left

right

left

right

left

right

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

1.32

0.9

1.09

1.2

1.82

0.90

1.46

1.5

1.3

0.9

0.73

1.00

1.14

06

1.27

1.1

cartilages of sacroiliac joints

iliolumbar ligament

sacrospinous

sacrotuberous

left

right

left

right

left

right

left

right

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

0.64

3.00

0.62

1.5

1.24

0.6

1.82

1.00

0.39

0.2

0.52

0.35

0.24

0.12

0.43

0.20

.

Analysis of the obtained results showed that with asymmetrical articular gaps, an increase in stress magnitude was observed on the left side in the ventral sacroiliac ligaments of up to 1.32 Mpa, dorsal ligaments up to 1.82 Mpa, interosseous ligaments up to 1.14 Mpa, and in the iliotransverse ligament up to 1.3 Mpa. In the hyaline cartilage of the sacroiliac joint, stress values remained virtually unchanged at around 0.63 Mpa on both sides. The stress magnitude increased in the right iliolumbar ligament up to 1.82 Mpa and in the right sacrospinous and sacrotuberous ligaments up to 0.52 Mpa and 0.43 Mpa, respectively.

Relative strains were distributed differently. In the case of asymmetrical articular gaps, an increase in relative strains was observed in the right ventral (from 0.5 to 1.2%), dorsal (from 1.3 to 1.5%), and interosseous (from 0.7 to 1.1%) sacroiliac ligaments. The iliotransverse ligaments were strained on both sides.

The hyaline cartilage of the sacroiliac joint was more deformed on the left, up to 3.0% compared to 2.2% in the normal state. The iliolumbar ligaments were more deformed on the left, reaching 1.0% versus 0.65% in the normal state.

The sacrospinous and sacrotuberous ligaments were more deformed on the right, 0.35% compared to 0.13% in the normal state and 0.02% compared to 0.13%, respectively.

Such an asymmetrical increase in stress and strain values may not play a significant role with a single load application. However, if loading cycles are repeated multiple times, for instance during running, walking, or jumping, this may lead to ligament microtrauma and functional disorders. According to the authors of [2], biological structures can be damaged not only by a single application of a large external force but also by the repeated application of significantly smaller forces. The effect of small external forces can cause microscopic damage, such as microcracks or minor plastic deformations, which may go unnoticed. However, after many cycles, microscopic damage can accumulate until the weakened structure fails. These are so-called “fatigue injuries”, which can occur after repeated loading cycles with forces less than 30% of the strength limit. According to the authors of [44], the strength limit of ligaments is 25 Mpa. Therefore, ligaments with stress values reaching 7.5 Mpa or higher are at risk of damage.

The obtained results of the unilateral displacement of the conditional axis of sacral rotational mobility with asymmetry in the width of the joint spaces align with the hypotheses of Don Tigny [49,50] and Gracovetsky [51] that, under certain conditions, the axis of sacral rotational mobility may shift forward and downward on one side, fixing at the S_III level, and backward and upward on the other side, fixing at the S_I level.

According to the authors of [51], such a shift forms a functional deformation of the pelvis, known as a “twisted pelvis”. According to the authors of [49], the shift in the conditional axis of sacral rotational mobility will alter load transfer not only in the “lumbar spine–sacrum–pelvis” system but also in the “sacrum–pelvis–lower limbs” system. These changes will intensify during walking and running.

3.3. The Influence of Pelvic Tilt (Lateral Angularity)

Pelvic tilt (lateral angularity) leads to a significant redistribution of stresses and strains between the left and right sacroiliac joints and ligament bundles. During loading, the sacrum undergoes an additional rotation. This causes the conditional axis of sacral rotational mobility to shift relative to the pelvis, forward and downward on one side and backward and upward on the other. Thus, the pelvic tilt results in additional compression of the lower-positioned left sacroiliac joint (Figure 16).

Figure 17 shows the displacement of the axis of sacral rotational mobility with the tilt of the pelvis (lateral angularity). It is evident that the conditional center of rotation shifts beyond the hyaline cartilage of the sacroiliac joint. At the same time, an increase in compressive strain is observed in the lower-positioned left sacroiliac joint.

The results of calculations with the tilt of the pelvis (lateral angularity) are presented in Figure 18 and

Table 5. Maximum of von Mises equivalent stress (σ) and equivalent strain (ε) in the sacroiliac joint with the tilt of the pelvis (lateral angularity).

ligaments of the sacroiliac joints

the normal state of the sacroiliac joint

ventral

dorsal

iliotransverse

interosseous

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

0.95

0.50

1.22

1.10

0.41

0.5

0.55

0.7

cartilages of sacroiliac joints

iliolumbar ligament

sacrospinous

sacrotuberous

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

0.63

2.2

1.28

0.65

0.37

0.18

0.27

0.13

with with with the tilt of the pelvis (lateral angularity)

ventral

dorsal

iliotransverse

interosseous

left

right

left

right

left

right

left

right

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

1.26

0.7

0.77

1.7

1.54

1.10

0.77

3.00

1.0

0.7

0.60

1.40

0.98

0.7

0.77

2.4

cartilages of sacroiliac joints

iliolumbar ligament

sacrospinous

sacrotuberous

left

right

left

right

left

right

left

right

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

σ, Mpa

ε, %

0.71

2.00

0.56

4.1

3.23

1.0

2.44

1.00

0.45

0.18

0.31

0.16

0.41

0.14

0.23

0.097

.

Analysis of the stress–strain state of the sacroiliac joint with the lumbar spine under a load of 400 N along the spine showed that, with pelvic tilt compared to horizontal alignment, there is an increase in stress values in the left ventral sacroiliac joint ligaments from 0.95 to 1.26 Mpa, dorsal from 1.22 to 1.54 Mpa, interosseous from 0.55 to 0.98 Mpa (almost double), iliotransverse from 0.41 to 1.0 Mpa (more than double), iliolumbar from 1.28 to 3.23 Mpa, sacrospinous from 0.37 to 0.45 Mpa, and sacrotuberous from 0.27 to 0.41 Mpa. An increase in stress was noted in the left hyaline cartilage of the sacroiliac joint from 0.63 to 0.71 Mpa.

A different pattern is observed in the distribution of strains. A significant increase in relative tensile strain is observed in the right ventral sacroiliac joint ligaments, from 0.5 to 1.7% (more than threefold), dorsal from 1.1 to 3.0% (almost threefold), interosseous from 0.7 to 2.4% (more than threefold), iliotransverse from 0.5 to 1.4% (almost threefold), and iliolumbar from 0.65 to 1.0%.

In the sacrospinous and sacrotuberous ligaments, strain values remained the same and were distributed relatively evenly on the left and right. An increase in relative compressive strain was noted on the left in the hyaline cartilage, as well as in the ventral, interosseous, and dorsal sacroiliac joint ligaments.

As in the models in [27], the sacroiliac joint region in our pelvic ring model with primary ligaments was found to be the most stressed. This is due to the anatomical structure of the sacroiliac joint, which is designed to absorb and distribute large vertical loads (the weight of the upper body) to the pelvis and then to the lower limbs while allowing minimal movement [52].

The obtained results regarding the displacement of the sacral rotational axis relative to the pelvis—forward and downward on one side and upward and backward on the other—confirm Don Tigny’s hypothesis [49,50]. According to him, the normal rotational axis of the sacrum relative to the pelvis is positioned symmetrically at the S_II level on both sides. With certain functional changes, the sacral rotational axis may shift forward and downward to the S_III level on one side and upward and backward to the S_I level on the other. In this case, the rotational axis may extend beyond the sacroiliac joint cavity and project into the area of its interosseous ligaments. This results in additional microtrauma to these ligaments. This occurs because sacral rotation is not around the anatomical region covered by hyaline cartilage, but rather around an anatomical structure covered by interosseous ligaments. This changes the friction force and the nature of the forces acting on the ligaments. Such displacement leads to the formation of a functional deformation of the pelvic ring, known as a “twisted pelvis”. This deformation disrupts load transfer within the kinematic chain of the “sacrum–pelvis”, and subsequently, according to Don Tigny, within the kinematic chain of the “sacrum–pelvis–hip joints”. On the other hand, according to Gracovetsky [51], load distribution disruption in the “sacrum–pelvis” kinematic chain induces negative changes in the “sacrum–lumbar spine” kinematic chain.

4. Discussion

The results of this study provide important insights into the biomechanics of the lumbar spine–sacrum–pelvis system, with particular relevance to sacroiliac joint dysfunction. The identified stress–strain distributions under varying conditions of lumbar lordosis, pelvic tilt, and asymmetrical articular gaps underscore the critical role of joint symmetry and alignment in minimizing ligament stress. These findings have potential clinical implications, particularly in guiding rehabilitation strategies aimed at correcting pelvic misalignments and improving lumbar stability. For instance, the results support early interventions to address hyperlordosis or pelvic tilt, which may help reduce chronic ligament overloading and associated pain.

The modeling results reveal that hyperlordosis leads to stress concentrations in the interosseous and iliolumbar ligaments, often exceeding failure thresholds. Such findings underscore the importance of early detection and management of hyperlordosis to prevent ligament damage and joint instability.

Pelvic tilt and asymmetrical articular gaps alter the rotational axis of the sacrum, creating uneven stress distributions across the sacroiliac ligaments. These asymmetries may contribute to ligament microtrauma and functional instability, especially under repetitive loading conditions such as walking or running. Clinicians should prioritize pelvic alignment in rehabilitation strategies to mitigate these risks.

This study extends the existing biomechanical understanding of sacroiliac joint function by modeling the combined effects of lumbar lordosis, pelvic tilt, and asymmetrical articular gaps. Unlike prior studies, which often focused on isolated factors, this analysis provides a holistic view of the biomechanical interplay between these variables.

The findings of this study highlight the significant impact of asymmetrical strain on the biomechanics of the sacroiliac joint and surrounding structures. Asymmetrical strain can lead to uneven stress distribution, potentially resulting in microtrauma, ligamentous overloading, and functional instability. These biomechanical alterations emphasize the need for targeted rehabilitation strategies that address asymmetry in joint mobility and muscle strength.

While the finite element model presented in this study advances the understanding of sacroiliac joint biomechanics, several limitations must be acknowledged.

The model employs homogeneous, isotropic material properties for biological tissues. Although this approach is standard, it does not fully capture the anisotropic behavior of ligaments and cartilage, particularly in pathological conditions.

The isotropic assumptions for the material properties of biological tissues were based on an extensive literature review. Most of these studies have demonstrated that isotropic models can reliably approximate the behavior of tissues under static and quasi-static loading conditions. Additionally, mesh convergence tests and sensitivity analyses were conducted to ensure that the isotropic material assumptions provided consistent and realistic stress–strain patterns in the finite element simulations. While anisotropy is known to exist in certain tissues, the isotropic approximation was deemed sufficient for the scope of this study, focusing primarily on global biomechanical trends rather than localized anisotropic effects. The mechanical properties used in this study, including the elastic modulus and Poisson’s ratio for biological tissues, were derived from biomechanical literature. These parameters represent average values for healthy tissues and have been validated in similar finite element analyses to simulate biomechanical behavior under static and quasi-static loading conditions. However, it is important to acknowledge that these properties can vary significantly between individuals and are influenced by factors such as age, sex, and pathological conditions (e.g., degeneration and inflammation). For example, the elastic modulus of cartilage or ligaments may decrease in individuals with osteoarthritis or other degenerative changes, potentially altering stress–strain distributions. To address this variability, sensitivity analyses were conducted to examine the impact of changes in the elastic modulus and Poisson’s ratio on the model’s outputs. These analyses revealed that while variations in these parameters affect absolute stress and strain values, the overall trends and relative comparisons between different conditions (e.g., lumbar lordosis, pelvic tilt, and asymmetrical articular gaps) remain consistent.

The analysis was conducted under static and quasi-static loading conditions, limiting its applicability to dynamic situations such as gait or repetitive mechanical loading during physical activity.

The model is based on averaged anatomical and mechanical properties derived from healthy individuals. Incorporating patient-specific data could enhance the precision and clinical relevance of the findings.

Degenerative changes were not modeled. Degenerative changes, such as cartilage thinning, osteophyte formation, or ligament laxity, may alter stress–strain distributions and joint stability in ways not captured by the current isotropic assumptions. While this choice minimizes confounding factors, it limits the applicability of the results to populations with advanced joint degeneration.

Future studies should incorporate patient-specific data obtained from imaging techniques or mechanical testing to refine input parameters. Additionally, integrating models of pathological tissues with altered mechanical properties could further enhance the clinical relevance of these simulations.

5. Conclusions

This study highlights the complex interplay of lumbar lordosis, pelvic tilt, and asymmetrical articular gaps in influencing sacroiliac joint biomechanics. The findings contribute to a deeper understanding of the mechanical factors underlying sacroiliac joint dysfunction and provide a foundation for developing targeted diagnostic and therapeutic approaches.