Stress evaluation along the posterior annular circumferential tears on the L5-S1 spinal unit as an index of tear progression

Vinyas; Subraya Krishna Bhat; Hiroshi Yamada; Nitesh Kumar; Raviraja Adhikari; Shyamasunder Bhat N

doi:10.1016/j.jor.2025.01.026

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67 (); 148-164

doi:

10.1016/j.jor.2025.01.026

Stress evaluation along the posterior annular circumferential tears on the L5-S1 spinal unit as an index of tear progression

Vinyas^a, Subraya Krishna Bhat^a,, Hiroshi Yamada^b, Nitesh Kumar^a, Raviraja Adhikari^a, Shyamasunder Bhat N^c

a Department of Mechanical and Industrial Engineering, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Udupi, 576104, Karnataka, India

b Department of Biological Functions Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196, Japan

c Department of Orthopaedics, Kasturba Medical College, Manipal Academy of Higher Education, Manipal, Udupi, 576104, Karnataka, India

⁎Corresponding author: Subraya Krishna Bhat. sk.bhat@manipal.edu

Received: 2024-12-23, Accepted: 2025-1-19, Published: 2025-1-21

The Authors

Disclaimer:
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.

Abstract

Low back pain is a critical health issue related to the formation and growth of tears (or lesions), along with degenerative changes, which is commonly observed in the posterior regions of intervertebral discs (IVD) in the lower spine segments. Early and accurate prediction of growth of these tears is a challenging task with immense clinical significance. Finite element method is a promising technique in this direction, however, the combined effects of tears and degeneration in the posterior region of annulus has not been studied. The present work focuses on a numerical evaluation of the contribution of annulus material degeneration, the position of tear and regular physiological movements (extension, flexion, left and right lateral bending) on the growth of the posterior circumferential tear in the annulus of the L5-S1 spinal unit. The material models developed previously to describe degeneration effects were adopted for defining the annulus material. The tear is modelled by altering the mesh to determine its effects in the presence of degeneration in the annulus. Degeneration, which is a loss of functional ability due to age-related effects, influenced the stress response significantly across all types of movements. Flexion movement is found to have the most predominant damaging effect on the tears, evident by the higher stresses along the tear boundary. Tears near the outer periphery of the annulus were likely to experience higher magnitudes of stress for an applied load and, hence, were suggested to be more critical. Extension movement seemed to aid in the recovery of the tear, supporting the results of clinical studies. This study highlights the complex interaction between physiological movements and the progression of posterior circumferential tears under different stages of degeneration, which can enable clinicians to develop and implement suitable patient-specific treatment modalities.

Keywords

L5-S1

Posterior circumferential tear

Degeneration

IVD

Finite element method

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1 Introduction

Low back pain has become a common problem in majority of the people worldwide.¹^,² Patients dealing with this condition often find it difficult to carry out their daily tasks. Various factors, such as ageing, intense physical work, and poor posture, are responsible for this problem.³ Ageing leads to disc degeneration, making the annulus brittle and prone to tearing.⁴ The rate of degeneration is reported to be highest in the L5-S1 spinal unit.⁵ Mechanical overloading is a leading factor in the occurrence of tears.⁶

The issue of low back pain is frequently associated with discogenic pain caused by internal disc disruptions or annular tears.⁷^,⁸ Early diagnosis and treatment of these tears is believed to be an effective way to prevent the recurrence of pain ⁸. Despite the clinical importance of annular tears, computational research on their impact on spinal biomechanics is scarce.

Circumferential tear is considered in this study as it is commonly found in the lower region of the spine due to degeneration with ageing.⁴ It has been established in previous research that these tears are found in the anterior and posterior regions of the annulus in the lumbar region of spine. The tears were found to be located at the posterior in larger numbers, particularly in the L5-S1 spinal unit.⁹ Circumferential tears can coagulate to develop into radial tears¹⁰ which is illustrated sequentially in Fig. 1. They create a pathway for the nucleus material to reach the outer third of the annulus which is highly innervated.¹¹ Additionally, the tears may extend beyond the annulus, causing conditions like herniation and sciatica. Considering the higher possibility of critical damage caused by the growth of these tears located in the posterior makes it even more crucial to understand the biomechanical behaviour of the spinal unit in the presence of such tears.

(a) Illustration of the IVD with circumferential tears in the posterior of annulus, (b) Close-up view of the tear region, (c) Growth of tears, (d) Tears coalesce to form radial tears, (e) Radial tear reaching the periphery of the annulus12.

In-silico studies can provide information about the stress state of the IVD at any specific location of interest which is useful for understanding the biomechanical response in different loading scenarios. Computational study of the spine and its associated ailments has been popular ever since the possibility of using it for this purpose was realised^13–15 Evaluating the effects of degeneration of the disc has been of interest to many researchers.¹³ However, generic models based on anthropometric data were used in these works with a focus on the region above the L5 vertebra of the spine. The work by Little et al.¹⁶ serves as a predecessor to the current work in which the effects of tears and degenerate nucleus in the L4-L5 level were presented. However, the study excluded vertebra and ignored the degeneration of the annulus.

Our previous studies employed subject-specific 3D model with the representation of the annulus by the Gasser-Ogden-Holzapfel (GOH) material model.¹²^,¹⁴^,¹⁷ The degeneration effect on the material property of the intervertebral disc was achieved by varying the parameters of the GOH model corresponding to the initial tangent modulus for the annulus and increasing the elastic modulus for the nucleus. Sagittal and lateral movements were simulated on the spinal unit for varying degenerative levels in the presence of anterior circumferential tear in the annulus of the IVD. The current study intends to assess the possibility of the growth of a tear in three degenerative levels for sagittal and lateral movements, by evaluating the stresses near the site of the circumferential tear at the posterior.

2 Method

2.1

2.1 Finite element modelling

The FE model of a previously validated intact L5-S1 spinal unit (refer Fig. 2) was utilized in this study for introducing tears in the annulus fibrosus. The earlier work contains the modelling details for the components other than the modifications made in the annulus.¹⁴ Since the annulus is the prime focus of the current investigation, its key information has been reiterated. The definition of the fibre orientation embedded in the matrix material of the annulus in the finite element.¹² The annulus was modelled using the 8-noded hybrid solid components (C3D8H) available in ABAQUS CAE® (Dassault Systemes). The mesh in the annulus is made of 8 × 8 elements, that is, 8 elements each along the longitudinal and radial directions was chosen according to the optimum size identified from mesh independence test.¹⁴

FE model of L5-S1 spinal unit: (a) front and (b) rear isometric views12,17.

The degeneration-related decrease in disc height¹⁸ is neglected here. Hypermesh (Hyperworks, Inc.) software was used to incorporate the tear in the annulus by morphing the elements to the desired position while maintaining its original shape. The tears taken into consideration for the current investigation are shown in Fig. 3, with Fig. 3a providing information on the overall dimension of the model. Tears were modelled at three locations in the annulus by varying the distance of the tear from the nucleus along the radial direction as shown in Fig. 3(b), (c) and 3(d), spanning 5 elements (i.e., approximately 7 mm) in length. The length of the tear was adjusted to 75 % of the total radial width of the annulus. Fig. 4 is provided for better visualization of the annulus model with tear.

a) Scale bar shown on top view of annulus with element dimensions of x = 1.44 mm and y = 0.49 mm. Top view of posterior circumferential tear in the annulus at, b) 2 layers from the centre layer, c) centre layer, d) 2 layers outside the centre layer.

Isometric view of the annulus with tear.

2.2

2.2 Material model and boundary conditions

The evaluation of the material model for the annulus was significant for this study. The Gasser-Ogden-Holzapfel (GOH) material model was assigned for the annulus.¹²^,¹⁴ The stiffening effect due to degeneration of annulus was modelled as described in our previously published study.¹² The material properties of the associated parts in the spinal unit are provided in Table 1. The boundary conditions to simulate the physiological movements involved a pure moment load of 4 Nm applied on the central node of the upper endplate of the L5 vertebra and fixing the centroid of the sacrum.¹²^,¹⁴

Table 1 Material properties and element types used in the in-silico model.

Part name	Element type	Young's Modulus (MPa) [degree of degeneration]	Poisson's ratio
Cortical¹⁹	C3D4	12000	0.3
Cancellous¹⁹	C3D4	200	0.3
Nucleus²⁰^,⁸	C3D8H	1 [Healthy]	0.499
		2 [Mild]	0.499
		3 [Moderate]	0.499
Annulus⁸		C1 = 0.4323 MPa, k1 = 2.1638 MPa, k2 = 200 [Healthy]
		C1 = 0.75 MPa, k1 = 3.5 MPa, k2 = 300 [Mild]
		C1 = 1 MPa, k1 = 5 MPa, k2 = 400 [Moderate]
Ligaments²¹	3D Truss	Hypoelastic constitutive law (Tension only),Incremental elastic modulus in MPa (Strain %)
Anterior Longitudinal Ligament		7.8 (ε<12%), 20 (ε>12%)
Posterior Longitudinal Ligament		10 (ε<10%), 20 (ε>10%)
Ligamentum Flava		15 (ε<6%), 19.5 (ε>6%)
Interspinous Ligament		10 (ε<15%), 11.6 (ε>15%)
Supraspinous Ligament		8 (ε<20%), 15 (ε>20%)
Capsular Ligament		7.5 (ε<25%), 30(ε>25%)

3 Results

The information about the location of stress concentration can assist in identifying the site of discogenic pain 22. The maximum shear stress failure criteria (Tresca criterion) was used in its evaluation as shearing has a significant contribution to causing damage.¹⁴^,²³^,²⁴ The mid-plane of the annulus represented as opaque in Fig. 5, was used to avoid numerical errors resulting from the sharp difference at the interface of the vertebra and the disc.²⁵ This section presents the effect of degeneration and tears considered in the current study on the mid-plane Tresca stress response for flexion, extension and lateral bending. Also, the visualization of the deformation of the tears is further enhanced with close-up views of the tear.

The midplane of the annulus represented with opacity.

3.1

3.1 Effect of degeneration on the midplane stress in the annulus and the boundary of tear

It can be observed in the stress contour plots from Figs. 6–8 that the degeneration has a strong influence on the maximum Tresca stress. In the case of flexion and extension, the colour map for high stress is observed with increasing degeneration levels on the contour plot for the midplane of the annulus. The trend is reversed in the case of left and right lateral bending where the healthy model of annulus has high stress compared to the degenerate models. This behaviour is a consequence of the decrease in range of motion (ROM) and is discussed in a previously published paper. During extension movement, the tears tend to close irrespective of the position or degeneration levels. However, during flexion, only the inner tear in a healthy annulus tends to close. In the rest of the cases, the tears were either unaltered or tending to open.

Mid-plane Tresca stress (MPa) for (a) Extension, (b) Flexion, (c) Left Lateral, (d) Right Lateral movements in annulus with Inner tear.

Mid-plane Tresca stress (MPa) for (a) Extension, (b) Flexion, (c) Left Lateral, (d) Right Lateral movements in annulus with central tear.

Mid-plane Tresca stress (MPa) for (a) Extension, (b) Flexion, (c) Left Lateral, (d) Right Lateral movements in annulus with Outer tear.

3.2

3.2 Polar plots to indicate variation of stress at the tear boundary

The variation of stress along the boundary nodes of the tear is reported using polar plots and discussed in detail for the following factors- (a) levels of degeneration, (b) locations along the radial direction and (c) movements. A sample showing the correspondence between the nodes in the tear boundary and the points on the plot is illustrated in Fig. 9. The same principle of correspondence was used for the rest of the tears as well.

Sample figure showing one-to-one correspondence between the nodes at the boundary of tear and the data points on the polar plot for Tresca Stress (MPa).

3.3

3.3 Effects of degeneration on Tresca stress in the tear boundary

The polar plots shown in Figs. 10–12 provided insightful information on the stress at the tear boundary which is not evident in contour plots of the midplane of annulus. The influence of sagittal movements (i.e. flexion and extension) is distinctly clear, with relatively larger differences in stress values between each degeneration level all around the tear compared to the stresses for lateral movements. The almost concentric nature of plots indicates similar stress distribution in the chosen nodal points location of the tear boundary for the different degeneration levels in all three cases of tear. The effect of lateral movements on the stress at the tear boundary was observed to be negligible for the considered degenerative cases.

Polar plot of Tresca stress [MPa] for various degeneration levels in different movements at the boundary of the inner tear.

Polar plot of Tresca stress [MPa] for various degeneration levels in different movements at the boundary of the central tear.

Polar plot of Tresca stress [MPa] for various degeneration levels in different movements at the boundary of the outer tear.

3.4

3.4 Effects of positions of tears on Tresca stress in the tear boundary of the annulus

The polar plots from Figs. 13–15 indicate that the Tresca stress magnitudes increased from the inner tear with the lowest magnitude to the outer tear with the highest magnitude for flexion and extension in all the degeneration levels. The stress is relatively higher towards the anterior side and the tips of the tear in the inner tear, towards the tip of the tear for the central tear and towards the posterior of the tear in the case of the outer tear during extension movement. In all the positions of tears, the posterior side of the tear is subjected to a higher stress compared to the other regions of the tear for flexion.

Tresca stress polar plots at the tear boundary of the healthy annulus with varying location of tears for (a) Extension, (b) Flexion, (c) Left lateral, (d) Right lateral movements.

Tresca stress polar plots at the tear boundary of the mildly degenerated annulus with varying location of tears for (a) Extension, (b) Flexion, (c) Left lateral, (d) Right lateral movements.

Tresca stress polar plots at the tear boundary of the moderately degenerated annulus with varying location of tears for (a) Extension, (b) Flexion, (c) Left lateral, (d) Right lateral movements.

In the case of lateral bending the stress was concentrated either at the tear tip or close by it. Accumulation of high stress near the tear tip on the right indicates the possibility for the growth of the tear laterally.

3.5

3.5 Effects of movements on Tresca stress in the tear boundary of the annulus

In Figs. 16–18 the peak stresses are observed for right lateral movement and flexion in the case of an inner tear in the healthy model of the annulus. The stress due to flexion increases for mild degeneration and finally exceeds the stress due to lateral bending marginally in the case of moderately degenerate annulus with inner tear. Except for extension movement for the annulus with central and outer tear, the remaining movements produced higher stress largely towards the posterior side of the tear.

Polar plot for effects of movements on the boundary of (a) Inner tear, (b) Central tear, (c) Outer tear in healthy annulus.

Polar plot for effects of movements on the boundary of (a) Inner tear, (b) Central tear, (c) Outer tear in mild degenerated annulus.

Polar plot for effects of movements on the boundary of (a) Inner tear, (b) Central tear, (c) Outer tear in moderately degenerated annulus.

The plots clearly indicate the dominant role of flexion movement in causing relatively higher stress concentration compared to other movements in the remaining tear positions.

4 Discussions

4.1

4.1 Clinical relevance of the results

The high-stress state around the tear is conducive for the tears to grow. Considering this, flexion was the most harmful movement for posterior circumferential tear. The results of this study indicate that the impact of flexion increases on the tears located radially outward from the nucleus and it is supplemented by increased degeneration. Although some of the findings from animal studies suggest that the tears in the outer extremities are more likely to heal due to the rich blood supply and nutrition,²⁶^,²⁷ the current study highlights the role of the type of movement in determining the state of the tear at a particular location.

Repeated injury of the tears hinders the healing mechanism of the tears.²⁶ Since flexion movement indicates a tendency to cause injury in patients diagnosed with posterior circumferential tears, they may be advised to minimize or avoid it. The findings are supportive evidence for the results obtained in clinical trials.²⁶^,²⁸ People diagnosed with tears closer to the nucleus should also avoid lateral movements due to their damaging effects shown at the tear boundary. Their considerable impact on the tip of the tear is of high concern as the tips are more likely to act as gateways to delamination, leading to further growth and damage. Clinical studies have also proven that lateral movements can also cause low back pain issues.²⁹

However, extension movement can be promoted for physiotherapy to the concerned patients as it is helpful for the recovery or healing of tears by causing the tears to close.²⁶^,²⁷^,³⁰^,³¹ The effect of extension in serving as a beneficial movement for relaxing the load in the posterior has also been observed in clinical studies.³²

4.2

4.2 Limitations and future scope

The generalizability of the result is constrained by the sample size used for this investigation. However, the preliminary assessment is in good agreement with the clinical studies. More samples will be considered for the study to improve the generalizability of the results. The time-dependent behaviour of the disc is intended to be obtained by including porous and viscoelastic properties in future analyses.^33–39 Nevertheless, the detailed investigation of the state of stress at the midplane and the tear boundary has provided insights which are aligned with the findings of clinical studies justifying the simplifications and affirming the efficacy of this study.

5 Conclusion

A parametric study of the effect of posterior circumferential tear in combination with the degeneration effect is simulated for four physiological movements at the L5-S1 spinal unit model. The position of the tear significantly contributes, along with the degeneration and type of movements to the stress state around the tear. In general, the magnitude of stress was observed to increase with the increase in degeneration and the distance of the tear from the nucleus for all the considered movements. Flexion movement caused the greatest damage by significantly increasing the stress levels in the proximity of the tear and opening it in almost all cases. Extension movement was found to close the tears with the least stress levels, suggesting the possibility of healing, especially in the case of outer and central tears. This study improves the understanding of the state of the tear in the presence of degenerative effects for different movements, which can assist occupational therapists and spine or neurosurgeons in providing clinical advice and choosing the appropriate treatment modality.

CRediT authorship contribution statement

Vinyas: Conceptualization, Methodology, Software, Visualization, Investigation, Writing – original draft, Writing – review & editing, Validation. Subraya Krishna Bhat: Conceptualization, Methodology, Visualization, Writing – review & editing. Hiroshi Yamada: Conceptualization, Methodology, Visualization, Supervision, Writing – review & editing. Nitesh Kumar: Conceptualization, Methodology, Writing – review & editing. Raviraja Adhikari: Conceptualization, Supervision, Resources. Shyamasunder Bhat N: Conceptualization, Supervision, Data curation, Writing – review & editing.

Ethical approval

An institutional ethical clearance has been obtained from Kasturba Medical College and Kasturba Hospital's institutional ethical committee. [IEC Project No.IEC:931/2018].

Funding statement

No funding was received for this work.

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Show Sections

[1] Yan W., et al . Research relating to low back pain and physical activity reported over the period of 2000–2020. J Pain Res. 2021;14(March):2513-2528.
[Google Scholar]

[2] The global epidemic of low back pain. Lancet Rheumatol. Jun. 2023;5(6):e305.
[Google Scholar]

[3] Natarajan R.N., . Modeling changes in intervertebral disc mechanics with degeneration. J. Bone Jt. Surg.. Apr. 2006;88(suppl_2):36.
[Google Scholar]

[4] Adams M.A., Lama P., Zehra U., Dolan P., . Why do some intervertebral discs degenerate, when others (in the same spine) do not? Clin Anat. 2015;28(2):195-204.
[Google Scholar]

[5] Siemionow K., An H., Masuda K., Andersson G., Cs-Szabo G., . “The effects of age, gender, ethnicity, and spinal level on the rate of intervertebral disc degeneration. A review of 1712 intervertebral discs,”. Spine (Phila. Pa. 1976). 2011;36(17):1333-1339.
[Google Scholar]

[6] Pan J., Pendharkar A.V., Park J., . Spinal biomechanics. Intervertebral Disc Degener. Prevalence, Risk Factors Treat.. 2016;115:37-62.
[Google Scholar]

[7] Schwarzer A.C., Aprill C.N., Derby R., Fortin J., Kine G., Bogduk N., . The prevalence and clinical features of internal disc disruption in patients with chronic low back pain. Spine (Phila. Pa. 1976). 1995;20(17):1878-1883.
[Google Scholar]

[8] Sehgal N., Fortin J.D., . Review Article Internal Disc Disruption and Low Back Pain. . 2000;3(2):143-157.
[Google Scholar]

[9] Osti O.L., Vernon-Roberts B., Fraser R.D., . Volvo award in experimental studies: anulus tears and intervertebral disc degeneration: an experimental study using an animal model. Spine (Phila. Pa. 1976). 1990;15(8):762-767.
[Google Scholar]

[10] Kirkaldy-Willis W.H., Wedge J.H., Yong-Hing K., Reilly J., . Pathology and pathogenesis of lumbar spondylosis and stenosis. Spine (Phila. Pa. 1976). Dec. 1978;3(4):319-328.
[Google Scholar]

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Stress evaluation along the posterior annular circumferential tears on the L5-S1 spinal unit as an index of tear progression

Abstract