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1. Introduction

One of the common causes of chronic low back pain is degenerative disc disease, which occurs when the intervertebral discs lose their elasticity and hydration over time and become more prone to damage. One of the possible treatments for this condition is to remove the affected disc and replace it with an artificial disc that mimics the function and structure of the natural disc. This procedure is known as total disc replacement (TDR) and it aims to restore the normal height, alignment and motion of the spinal segment. TDR has been developed since the 1960s and has undergone several improvements in terms of design, materials and biomechanics [1].

However, TDR is not without challenges and complications. One of the major issues is the accurate placement of the artificial disc in the disc space, which requires precise surgical skills and techniques. Any deviation from the optimal position can lead to mechanical failure of the implant, such as loosening, subsidence, migration or fracture. Moreover, the artificial disc may generate wear particles due to friction and loading, which can induce inflammatory and osteolytic reactions in the surrounding tissues and affect the long-term stability and performance of the implant. [2]

Therefore, it is essential to study the biomechanical behavior of TDR systems under various loading and motion conditions, as well as the effects of implant position and orientation on the stress distribution and wear generation. Experimental studies are useful but costly and time-consuming, while clinical studies are limited by ethical and practical constraints.

 

2. Theoretical Background

2.1 Intervertebral disc replacements:

These replacements consist of bearing surfaces designed to accommodate loading without fracture, to reduce friction and wear, and to maintain a longer range of motion. [3]

TDR models can be categorized by design, fixation (contact between the implant and the vertebral endplates), friction pair, location of the center of motion and finally compatibility with MRI capability.

Design: The regular disk contains 6 degrees of freedom(6df), 3 in displacement and 3 in rotation, and thus we distinguish between three types of designs:

Free design (6df) (unconstrained): Like the LTDRESP® (Elastic Spine Pad), these designs do not require perfect centering but impose greater pressure on the posterior joints.

Semi-constrained design (5df) with free core: Such as SBCharité®, Mobidisc®, which are stable designs where the displacement takes place within the core and increases with the radius of the core.

Constrained Design (3df) with Fixed Core:

Such as the Maverick® ProDisc-L®, which requires excellent stability and therefore a perfect fixation.

Fixation: Fixation of the instrument in the short and long term is a must for all prostheses. At the macro level, fixation can be achieved through immediate fusion through a stem, keel, screw, macrostructure or porous surfaces as the surface coating process facilitates osseointegration and may be using hydroxyapatite, tricalcium phosphate, porous titanium or chromium-cobalt.

Friction pair: there are four pairs (metal/PE, ceramic/PE, metal/metal, ceramic/ceramic)

The (metal / PE) bearing is the oldest bearing used in industrial prostheses, and the particles resulting from PE debris are large in size, while the particles resulting from (metal/metal, ceramic/ceramic) bearing debris are very few and smaller in size.

 

2.2 Design considerations:

For a total disc arthroplasty, the basic requirements are to maintain or re-establish functional disc motion while minimizing the wear and failure of the implant. Because the intervertebral disc and surface joints form a three-joint group, maintaining normal mobility requires that the surface joints be effective and that the artificial disc replacement adequately complement their functions. [4]

Bearing materials must allow movement while distributing the load with low friction and high wear resistance. The response to osteolysis such can be directly related to particle size, particle density, surface chemistry and tissue types in contact with the prosthesis. Consideration should also be given to the use of specific bearing surfaces such as articulated joints (MOP) or newer bearing such as MOM to reduce the severity of osteoporosis.

The current categories of materials most used in total disc replacement are (cobalt-chromium alloys- titanium alloys- stainless steel-polyethylene-polyurethane-ceramics).It should be noted here that ultra high molecular weight polyethylene (UHMWPE) is more Polymeric materials commonly used for orthopedic bearing surfaces.

 

2.3 Literature review:

There are costs involved in the failure of medical treatment on the one hand, and resorting to surgical options on the other hand, including spinal fusion surgery, which has been widely accepted as a useful treatment option. [5]

Numerical analysis methods based on finite elements are powerful tools for studying the biomechanics of the spine and the performance of lumbar prostheses. These methods can simulate various loading conditions and geometrical configurations of the prostheses and the surrounding tissues, and provide detailed information on the mechanical response, stress distribution and deformations of the system.

One of the main applications of finite element analysis is to evaluate the effect of lumbar prostheses on the spinal motion and stability. Several studies have used finite element models to investigate the loading state during the natural movements of the spine represented by axial rotation, flexion/extension, lateral bending and axial loading [1] [6], and to compare the biomechanical behavior of different types of prostheses, such as ball-and-socket, sliding-core or constrained designs [7] [8]. These studies have shown that lumbar prostheses can restore or improve the range of motion and flexibility of the spine, but may also alter the load transfer and stress distribution in the adjacent segments and structures, such as the facet joints, ligaments and vertebrae bodies [9]. Another application of finite element analysis is to optimize the design and material properties of lumbar prostheses [10], and to evaluate the effect of different materials on the wear and friction characteristics of the prostheses [11]. These studies have suggested that the geometry and material of the prostheses can influence their durability, compatibility and functionality, and that there is no single optimal solution for all cases.

A third application of finite element analysis is to validate and predict the outcomes of lumbar prosthesis implantation. Some studies have used finite element models to compare the preoperative and postoperative conditions of patients who underwent total disc replacement surgery [12], and to assess the agreement between the model predictions and the clinical measurements [13]. These studies have demonstrated that finite element analysis can provide useful insights into the surgical planning and evaluation of lumbar prosthesis implantation, but also highlighted some challenges and uncertainties in modeling the complex interactions between the prostheses and the biological environment.

 

2.3 Importance and aims

In this paper, we present a contribution in to the evaluation of the performance of artificial discs for the lumbar spine using three-dimensional computer evaluation. Th presented approach combines the mechanical design data from computerized tomography (CT) scans and three-dimensional mechanical design software to create a realistic model of the disc and the surrounding bone structure. We then suggest the use of the 3D finite element method to simulate the mechanical behavior of the disc and the bone under different loading conditions, taking into account the material properties of the disc and the bone. This allows us to assess the implantation process and the biomechanics of the artificial disc in the biological environment, and to optimize its design and functionality.

 

 

 

 

3. Materials and Methods

3.1 Study sample:

The study sample includes patients with low back pain and different degrees of uniplane disc degeneration. A (38) year old man was chosen as a model for the study, who has slight disc degeneration with decreasing height in the position (L3-L4).

The sample had normal vertebral bodies, did not suffer from advanced spinal diseases (slipped vertebrae-osteoporosis - disc collapse) and did not undergo previous spinal surgery.

Based on a series of CT scans applied to the selected sample imported into DICOM file format in Materialize MIMICS software, the (L3-L4) model is ready to be imported into STEP file format into Solidworks CAD 2019 on which the finished element model is prepared for the studied case.

 

3.2 finite element models:

3.2.1 Biomodel before replacement(L3-L4):

A model of the (L3-L4) level was built, where the natural disc model included both the central nucleus pulposus (NP ) and the annulus fibrosus (AF). The nucleus pulposus constituted about 44.8% of the total disc volume, and this percentage is acceptable as it falls within the normal range of volume formed by the nucleus of the disc, which is(30-50%), mentioned in previous studies [11]. While the fibrous ring surrounds this nucleus, it is a series of peripheral fibrous bundles, which were represented by 6 lateral layers connected to each other as shown in Figure(1), taking into account their cross-sectional areas as mentioned in previous studies [14].

 

Figure (1):3D model of the lumbar intervertebral disc according to the sagittal plane

 

Figure (2): 3D model of the lumbar vertebrae according to the sagittal plane

The following regions were assigned to the vertebrae (the upper and lower endplates- the cancellous bone- the cortical bone- the posterior bone) as shown in Figure (2).

The studied model also includes seven types of main ligaments that connect the vertebral bodies, namely: the anterior longitudinal ligament(ALL), the posterior longitudinal ligament(PLL), the ligament (LF), the capsular ligament(CL), the supraspinal ligament(SS), and the Interspinous ligament (IS), transverse ligament (TL) which are established by their characteristics in their anatomical locations [14]. This final, representative model was exported to ANSYS^TM19.2 software to perform a finite element analysis (FEA).

The number of elements has been determined following a prior convergence study that has been performed on the models to achieve a compromise between the elements number and the numerical cost. Accordingly, a mesh with tetrahedral elements was used for bony structures and the nucleus of the intervertebral disc, while the main spinal ligaments were used as tension-only nonlinear springs [15]. The mixed elements technique was used to facilitate the construction of the annulus fibrosus of the natural disc, where the six layers were modeled as quadric elements as a primary stage and then as pyramided elements as a secondary stage [14]. Obtaining direction-dependent stiffness and tensile-related load absorption, these elements were applied at an angle (30°). Table (1) shows the number of elements and nodes of this mesh for each component of the models included in this study.

 

Table (1): The number of elements and nodes of mesh for each of the components included in the model validation study

 

3.2.2 Total disc Replacement model

The ball-on-socket designs approved by the Food and Drug Administration were selected with the appropriate measurements, and their 3D models were designed and created to fit the intervertebral space in the position(L3-L4) using(SolidWorks2019) software, according to the dimensions of both the anteroposterior diameter(AP) and the mediolateral diameter (ML). for the endplates of the studied model. As in figure (3)  

 

 

 

 

Figure (3): The 3D model of the artificial discs.

 

3.2.3 Model (L3-L4) after virtual replacement

Grooves were created on the surfaces of each of the lower endplates of the vertebrae (L3)and the upper endplate of the vertebrae(L4)along the mid-sagittal line, and the disc was replaced at the site(L3-L4) with the replacement disc (ProDisc-L) with a posterior site of (4mm) as in the figure(4-a), as for the (CHARITE') disc, it was inserted in an anterior position where the teeth were removed to facilitate the application of the implant and simplify the simulation as in Figure(4-b) and both the anterior and posterior longitudinal ligaments were removed to simulate the procedure followed in the implantation of the replacement disc [15].

The upper and lower endplates of the discs (ProDisc-L) and (CHARITE') were modeled as rigid bodies [16]. The mesh was constructed as hexahedral elements, while the mesh of the core was of quadruple elements [15]. As in Figure (4) and Tables (2) and (3).

 

 

 

 

 

 

Table(2):Number of elements and nodes (ProDisc-L)

 

 

Table (3): Number of elements and nodes (Charite').

 

 

3.3 Boundary conditions

3.3.1 Model Validation

An analysis was performed using ANSYS^TM19.2 software to validate the pre-replacement biomodel by applying a compressive load of 1000[N] that is representative of the load applied to the spine.

Material behaviors were considered linear, and the contact were in the interfaces of each of (cortical bone- cancellous bone), (cortical bone- posterior bone), (nucleus pulposus- the six fibrous layers) and (intervertebral disc- upper endplates). And the) and (the endplates- the bodies of the vertebrae) are all fully linked (Bonded), and the studied model was fully fixed at the lower endplate of the vertebra (L4) as shown in Figure (5).

 

 

 

 

 

 

Figure (5): partially boundary conditions for model (L3-L4)

 

3.3.2 Dynamical testing 

A compressive load of 500N was applied to the upper endplate of the vertebra (L3) to simulate compressive physiological loading, the lower endplate of the vertebra (L4) was fully fixed, and a moment of 7.5 N. m was applied in the three anatomical planes to simulate each of the movements of flexion, extension, lateral bending, and axial rotation.

 

3.4 Materials properties

It was considered that the materials of the bone structures and the materials of the alternative discs for the studied components are isotropic linear elastic and homogenous [17][18].

Tables (4), (5) and (6) show the properties of the materials of the components included in this study, which were obtained as reference values from previous studies. [16] [14] [19] [20]

 

Table(4): properties of vertebrae  materials

 

 

Table (5): properties of the total replacement discs materials

 

 

Table (6): properties of ligament and annulus fibrous layers materials

 

 

4. Results and discussion

4.1 biomodel validation

The initial strains of the endplates and cortical bone of the FEM results were compared with previously published experimental data at different locations shown in Figure (6) when applying the analysis used to validate the model (L3-L4) to simulate a previous study using tested samples [21].

The results of the model validation analysis indicated that there is a good agreement between the results of FEM and the experimental results with the trends shown by the optimal values mentioned in the study [21] as in the graph in Figure (6).

 

Figure (6): Scheme of primary initial strains at different sites for each of the previously published experimental results and the FEM results of the studied model.

 

The difference in some values may be due to several reasons, including the ease of controlling the direction of the compressive load on the model studied in the experimental tests, and the difference of the studied samples between the subjects.

Also, the FEM model predicted a disc pressure value of (0.73 MPa) and a total vertical displacement of the L3 vertebra of (1.2 mm), and these values were within the range of values reported experimentally in the study [21] as in Table (7).

 

 

Table (7): Experimental values of normal disc pressure and total vertical displacement of the L3 vertebra.[21]

 

 

4.2 Range of motion:

The term range of motion (ROM) was defined as the total angular rotation of the vertebra (L3), where the studied model predicted in the case of the two prosthetic discs (ProDisc-L) and (CHARITE') a total range of motion in the movements (flexion/extension, lateral bending, and axial rotation). as shown in the following chart in Figure (7).

 

 

Figure (7): A graph representing the comparison of the angular range of motion between the FEM and the value of the experimental data with the value of its standard deviation.

 

The results of the analysis indicate that there is a good agreement between the results of (FEM)and the experimental results of a previous reference study that included the normal state of lumbar movement [22],where the range of motion of the studied model was maintained in all three main levels in general, and this indicates the ability of the ball-on-socket design of the two alternatives   (ProDisc-L) and (CHARITE') on motion recovery.

For the ProDisc-L, the model showed the largest rate increase in range of motion (1.8°) compared to the normal range (by 1.5 times) in axial rotation movement, and this increase may be due to the lack of initial movement segment constraints when loading in axial rotation [23] As in the case of keeping part of the annulus fibrous  of the damaged disc or keeping the anterior longitudinal ligaments, which affect the stability of the axial rotation of the prosthesis.

In addition, the (ProDisc-L) prosthesis showed an increase in the range of motion in the extension movement (2.7°) compared to the normal range (by 1.125 times), and this may be due to the removal of the entire disc with the anterior and posterior longitudinal ligaments before inserting the prosthesis, which is of the main structures are supposed to counteract the extension moments, which makes the extension movement in the implant plane more flexible.

 

4.3 Equivalent (Von-Mises) stress

As in Figures (8)and (9) shows the depth at which the greatest stresses occurred within the structure of the core material.

 

Extension 2mm + base core	Flexion 3.4mm (approximately the middle of the core)
axial rotation 2 mm	lateral bending 1.5 mm

 

 

 

 

 

 

 

Figure (8): Distribution of Von-Mises stresses on the bearing surface of a (UHMWPE) core of (ProDisc-L) during flexion, extension, lateral bending, and axial rotation.

 

Extension 0.1mm	Flexion 0.04 mm
axial rotation 0.01 mm	lateral bending 0.3 mm

 

 

 

 

 

 

Figure(9): Distribution of Von-Mises stresses on the bearing surface of a (UHMWPE) core of (CHARITE^') during flexion, extension, lateral bending, and axial rotation.

 

 

For the disc (ProDisc-L), most of the forward loads seem to be transferred evenly at flexion through the large contact area, as the upper surface of the replacement disc rotates smoothly above the bearing surface of the core and closer to the pole region, and in extension movements, the upper surface of the disc tends to rotate opposite the center of the originally fixed rotation of the disc (ProDisc-L) where the contact area changes.

For the disk (CHARITE'), the maximum stress values appear at the circumferential edge of the disc core at all movements. The outer circumferential edge of the core (area of local minimum thickness) of the TDR design has been identified as the most vulnerable site based on the analysis of the core in the retrieval study[24].

 

Regarding the maximum results on a UHMWPE core bearing surface, Figure(10) shows a plot of the maximum Von-Mises stress values for both replacement discs.

 

 

Figure(10): Diagram of the maximum (Von-Mises) stress values on the surface of the bearing core (UHMWPE) for both (ProDisc-L) and (CHARITE') during the physiological movements of the studied section.

 

The maximum value of (Von-Mises) stress on the surface of a core bearing (UHMWPE) was the value (68MPa) in the case of the disc (CHARITE') at a depth of (0.01mm) at the axial rotation, and that this may expose the disc to damage under the conditions of loading applied as research reported in the previous report on the yield stress value of high molecular weight polyethylene corresponds to (21MPa) [25], As for the (ProDisc-L)core, all FEM results were less than the previously mentioned yield stress value for (UHMWPE) reported, as the maximum value for(Von-Mises) stress was (15.6 MPa) at flexion, which means that The core will not deform, unlike the (CHARITE') disc core, which allowed segmental movement at all levels, but with stress concentrated at specific points on its perimeter, but at depths within the material structure of less than (0.5 mm). This can be avoided by increasing the thickness of this region.

 

4.4 Bone behavior study:

The Von-Mises yield criterion is also commonly used to predict the yield point of bone.[26]

This criterion based on the distortion energy theory is applied to investigate the stresses that occur on the cortical side of the bone based on the mechanical properties of the bone, which behave as a ductile material.[27]

The graphic representation of the equivalent (Von-Mises) stress values for both models is shown in Figure (11).

The value of yield stress for bone material when tested by compression (131 ~ 106 MPa), while for cortical bone (224 ~ 131 MPa), and all the previous and resulting values in the biological analyzes that included the two alternatives (ProDisc-L) and (Charite) are less than the minimum stress field Subject to the bone in general and cortical bone in particular. Accordingly, the bone material of both vertebrae in the studied models does not deform plastically in all motion tests. [28]

 Figure(11): Chart of (Von-Mises) stress values equivalent to the cortical bone for the studied models that included both (ProDisc-L) and (CHARITE') during physiological movements.

 

 

5. Conclusion

 

In this paper, we proposed a contribution to the design of personalized 3D models for patients with disc degeneration in the lumbar spine, based on finite element analysis techniques and 3D design and analysis software. We used 3D design and analysis software to create customized prosthetic models that fit the specific case of the patient and reduce the maximum stresses on the artificial disc. This can improve the longevity and functionality of the implant by preventing the failure of the replacement disc and damaging the surrounding tissues.

We also use finite element analysis techniques to study the effect of different materials and designs on the stability and performance of the bioprosthetic disc under various loads and stresses. This can help us identify the weak points and possible improvement plans of the proposed model and modify the materials accordingly.

We suggest that this method can be used to design and evaluate numerical bioprosthetic models before manufacturing and implantation. We also show that this method has several advantages over traditional methods, such as high spatial accuracy, time and material efficiency, and ease of modification. We demonstrated the effectiveness of our method by presenting numerical results and comparisons with the referential methods.

 

 

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