Nucleus Disc Replacement: Design and Material Selection FEA Analysis

the original work is properly cited. Study Design . We selected the materials and implant design and performed Finite Element Analysis (FEA) studies. Background . Nucleus disc replacements, implanted since 1960, have undergone continuous evolution in materials and designs, but subsidence, extrusion, and in vivo degradation limit widespread use. Aim . Te aim of this study is to create a new nucleus disc replacement that avoids the abovementioned drawbacks. Material and Methods . We created eighteen designs with varied materials and analyzed them with FEA in compression and shear tests in a lumbar spine model programmed in Ansys Parametric Design Language. Results . Bionate ® 80A had the closest mechanical characteristics to the intact disc nucleus. Monobloc designs bore physiological stresses correctly but sufered signifcant deformations with permanent damage during surgical insertion through the annulus opening. In addition, sandwich designs were too rigid and had an unreliable curing process. Terefore, we chose an oval doughnut-like 5mm wall monobloc Bionate ® 80A nucleus replacement. It minimized implant stress in loading, distributed loads uniformly, and tolerated lateral compression during implantation. Conclusions . Out of the eighteen designs we analyzed with FEA, we found that the monobloc oval doughnut-like Bionate 80A nucleus replacement reproduced best the biomechanics of the natural disc nucleus and had the lowest subsidence risk as it transmits the load to the ring apophysis. Furthermore, implanting it through the annulotomy required to perform a lumbar microdiscectomy should be possible due to its elasticity. Furthermore, due to its elasticity implanting it through the average annulotomy required to perform a lumbar microdiscectomy should be possible.


Introduction
Chronic low back pain keeps being one of the most common human ailments [1]. One of its causes is degenerative disc disease, which can lead to disc herniation. Te standard treatment for these cases is a discectomy, frequently followed by spinal arthrodesis. In both events, the index level undergoes biomechanical changes that cause arthritic changes in this level [2] and adjacent ones [3]. Terefore, the best approach would be to replace the function of the damaged intervertebral discs.
Nucleus replacement (NR) devices aim to substitute the nucleus pulposus with an intact annulus fbrosus. Tis technique is less invasive than spinal fusion or total disc replacement to treat disc herniation or degenerative disc disease.
A nucleus replacement should restore vertebral alignment, physiological curvature, instantaneous center of rotation, and disc height without overstretching spinal ligaments or zygapophyseal joint capsules, allow six degrees of freedom [4] and provide a close ft to the vertebral endplates [4][5][6]. It must be biocompatible, stif, possess viscoelastic behavior and shock absorption capacity similar to the intact nucleus [7], and avoid stress shielding [7,8].
Target mechanical properties for the whole disc after nucleus replacement (intact annulus + nucleus prosthetic device) are compressive strength >6.5 kN, shear strength >3 kN, compressive fatigue strength >2500 N, wear tests 900-1850 N-10 million cycles, shear force fatigue strength >100 N, torsion torque fatigue strength >3.5 Nm, and stifness: 800-2500 N/mm. In addition, it must have a high wear resistance with minimal debris generation, optimal long-term performance (30-100 million cycles), and compatibility with CT and MRI.
Te initial biomechanical evaluation through fnite element analysis (FEA) allows cost saving, design improvement, and product optimization. In addition, it enables implant mechanical behavior reproduction and analysis of surrounding spinal structure response (annulus, ligaments, vertebral endplates, and zygapophyseal joints) [19][20][21][22][23]. Tis information is essential to validate the spinal implant, restore the lumbar spine's biomechanics, and minimize abnormal loading on surrounding anatomical structures [24].
Introduced in the 60', there has been a steady search to fnd a material that reproduces intact disc biomechanics, creating a design that is easy to insert and with a minimal risk of subsidence or extrusion. Silicones, diverse polymers, hydrogels, and polyurethanes (PU) have been tested and ruled out because of cracking [25], subsidence [26], or extrusion [27]. In addition, researchers have improved designs continuously to ease insertion. Researchers have recently introduced new materials like nanofbers [28], providing a scafold for cell ingrowth and revitalization [29]. Leading research groups have tested diferent materials [30], and stem cells [31], both autologous and heterologous, are being used, but none of these new strategies have yet reached clinical application.
Te purpose of our study was to test diferent materials and create diferent designs to reach a specifc implant complying with the requirements mentioned above.

Material and Methods
Finite element analysis (FEA) helps in implant mechanical behavior reproduction and surrounding spinal structure response evaluation (annulus, ligaments, vertebral endplates, and zygapophyseal joints). Tis information is crucial to validate any spinal implant before undertaking further steps. It allows cost saving, design improvement, and product optimization [21].
First, we created the fnite element analysis (FEA) model using data from cadaveric human lumbosacral spines that we reported in a previous publication [32]. In short, we used twelve lumbosacral spine specimens from fresh, cold, preserved cadavers, ruling out osteoporosis with dual energy X-ray Absorptiometry (DEXA) scan studies. We removed all soft tissues, kept the ligaments and intervertebral discs, and sectioned the spines at the T 12 -L 1 disc and the sacroiliac joints. We performed CT scan studies (GE Healthcare, Milwaukee, Wi, USA) with 0.625 mm section images. We examined these section images with a 1.25 mm collimation and a pitch of 3 (0.75 mm/rotation) from L 1 to the coccyx, reconstructing them in 3D with an x-y matrix of 512 × 512, an isotropic voxel of 1 × 1 × 1 mm, and a 0.5 mm slice spacing. We transferred the CT scan images to digital imaging and communications in medicine (DICOM). We measured each vertebra and intervertebral disc size and dimensions. We performed the MRI studies with a 1.5 Tesla GE MRI scan (GE Healthcare, Milwaukee, Wi, USA), looking for disc degeneration and zygapophyseal joint osteoarthritis.
We analyzed CT and MRI scan images with the NETEOUS program, developed at the Biomechanics Institute of Valencia in collaboration with INGECOT (University of Oviedo, Asturias, Spain).
We obtained morphological data about geometry, morphometry, and dimensions of each lumbar and sacral vertebra and the intervertebral discs. In addition, we calculated anteroposterior (AP) and lateral (L) vertebral endplate dimensions, as well as the height and angulation of each intervertebral disc. Tis lumbar spine model is a parametric model programmed in APDL ("Ansys Parametric Design Language"). Te model can draw any section of the lumbar spine starting from sagittal plane radiography. We can change the diferent parameters in the model, the geometry of the vertebrae, the model mesh, and the material's mechanical properties. For each vertebra, the coordinates of four points are necessary to reproduce its geometry and position in the lumbar spine model. We calculated the rest of the parameters to build the model using formulas derived from the study by Panjabi et al. [33].
We can change the parameters of the mesh. We obtain the mesh by dividing the vertebra into diferent regions. One or more combined parameters control the mesh density of other areas. Te higher the mesh density, the higher the accuracy of calculations and the computation time.
In the model, the vertebra is composed of three diferent elements. First, the vertebral body consists of cancellous bone and an outer layer of cortical bone. We modelled the posterior arch with a specifc material for that area.
Te intervertebral discs are composed of three elements: fbrous annulus, nucleus, and annulus fbers. We oriented the fbers as in an intact disc.
We included all the ligaments of the lumbar spine in the model. Te ligaments have a nonlinear behavior. With small deformations, the ligaments have a low elastic modulus, but with a specifc strain, the elastic modulus increases. Each ligament is modelled with two parallel links of two diferent materials to simulate the nonlinear behavior.
Apart from the intervertebral disc, each vertebra articulates with the adjacent vertebra through the upper and lower zygapophyseal joints. Tese joints are responsible for the transmission of a large portion of loads between the vertebrae. We modelled the contacts in the zygapophyseal joints with particular contact elements. Te material properties in zygapophyseal joint contacts are specifc.
Once we had obtained its fnal 3D geometry with CAD software for the biomechanical evaluation of a new nucleus implant, we imported it into Ansys for fnite element modelling. Ten, we assigned mesh properties and materials' mechanical properties to the implant and used four-node solid elements for the mesh.
Tis simple geometry represents the frst approach for the biomechanical evaluation of a nucleus implant.
We evaluated two design groups, monobloc and sandwich-type. First, we selected the materials for each design type. Ten, we evaluated each design with FEA. Finally, we evaluated eighteen original designs to fnd the one that is the most suitable for the particular characteristics needed for a nucleus disc replacement.

Monobloc Designs.
Traditionally, monobloc designs have a single interface-free elastomeric material (hydrogel, PU, silicone). Teir advantages are wearing and mechanical properties like the intact disc, and their drawback is the extrusion risk. In addition, the compression required to insert these designs could lead to damage and accelerated degradation. Figure 1 shows the monobloc designs evaluated in this study.

Sandwich
Designs. Tey consist of two diferent materials, one for the outer component, which encloses an inner one. Te outer material is usually stif PEEK (Polyetheretherketone), Polyethylene (PE). Te inner is viscoelastic (PU, silicone, hydrogel) or a shape memory material (PU). Te sandwich designs' advantages are their viscoelastic and tissue integration properties, which minimize migration and extrusion, and the disadvantage is their low compressibility, usually requiring a bigger annulotomy for its insertion. Figure 2 shows the disc nucleus sandwich designs analyzed in this study. Figures 2(a)-2(c) show a rigid outer shell (PEEK) and a hydrogel or viscoelastic shock-absorbing core. Figures 2(d)-2(f ) show dampening designs, while Figures 2(g) and 2(h) show shape-memory models with two PEEK shells containing a shape-memory polymer (PU). Figure 2(i) shows a hard outer shell and a softer viscoelastic core. Finally, Figure 2(j) shows an external bag flled with viscoelastic materials.

Sandwich Design Material Selection.
We evaluated propylene, polyethylene terephthalate + dimethyl siloxane, polyamide 6,6 plus polyethylene terephthalate for the bag, hydrogel, ultrahigh molecular weight polyethylene (UHMWPE), PEEK, PU that cures at body temperature, and elastomeric microspheres for the core.

Selection Criteria.
We were interested in a nucleus replacement that was easy to insert through a minimal annulectomy, mechanical behavior like the natural nucleus, and minimal wear and tear.

Design Analysis.
We performed design analysis by simulation with FEA under physiological loading conditions, analyzing stresses, and deformations in compression and shear.

Compression Test.
We applied a compressive force to a standard cylinder (a diameter of 29 mm ± 0.5 mm and a height of 12.5 mm ± 0.5 mm), obtaining force/deformation curves. We performed four compression cycles, considering the fourth at 10% and 20% deformation. We evaluated the implant under diferent physiological load cases [10]: axial compression of 1000 N (compression load on the lumbar spine during walking), axial compression of 1000 N and anterior-posterior shear of 300 N (normal load combination typical of walking activity), axial compression of 1000 N, fexion moment of 8 Nm in the sagittal plane, and axial rotation torque of 8 Nm (representative of a worst-case scenario, with a high potential for producing disc herniation).
We considered fxing the displacements and rotations of nodes below the lower vertebra to apply loads. We joined the nodes in the upper vertebra's upper edge to the upper vertebra's superior central node with links elements. Ten, we merged the nodes of the spinous process with the previous structure with link elements. Next, we spread the load evenly with this structure. Finally, we placed the loads in the top central node of the upper vertebra; this node is the central node of the structure described above.

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Shear test. We used four identical parallelepiped pieces, 4 mm ± 1 mm thick, 20 mm ± 5 mm wide, and 25 mm ± 5 mm long, bonded with a high modulus adhesive on their two largest opposite faces to 4 rigid plates of the same width and length on a sandwich arrangement. We obtained a force/ deformation curve, calculating the shear modulus at a 25% shear stress using the formula c � d/2c, where d is the test piece deformation and c is the tested element thickness, both in millimeters. First, we calculated the 25% shear stress using τ 25 � F 25 /2A (F force in Newtons and A test pieces' bonded area in mm 2 ). Next, we calculated the shear modulus G (N·mm −2 ) using G � τ 25 /c 25 � τ 25 /0.25. Finally, we repeated the test three times, obtaining a mean value.

Anatomical Data.
We obtained these data from plain lumbar spine sagittal radiography and 1.5 Tesla Magnetic Resonance Images of human spine specimens and processed them with Materialise's software Mimics v.11, building threedimensional images. We calculated the intervertebral nucleus's volume and shape (length, size, and width) and transformed them into a CAD (computer-aided design) fle. We validated the implant biomechanical geometry with fnite element analysis (FEA) using the image analysis data and the lumbar spine model programmed in APDL ("Ansys Parametric Design Language") ( Figure 3). We used the data from our previous studies [32]. In addition, we obtained data from the literature [34] the spinal elements' mechanical properties. Figure 1: Monobloc designs evaluated in our study that aimed to optimize insertion and mechanical properties. We spread the load evenly within this structure and placed it in the upper vertebra's top central node. We performed all simulations with the implant located at the lumbar segment L 4 -L 5 . After implant insertion, we did not close the 8 mm annulus defect necessary to insert the implants.

Results
Te selected monobloc elastomeric design bore physiological stresses correctly in FEA studies (Figure 4(a)) but suffered signifcant deformations during insertion (Figure 4(c)). Terefore, we used reinforced polyurethane (a composite) or polyurethane carbonate (PCU) and ruled out PEEK and rigid polymers.
FEA studies of sandwich designs showed that those with a hard inner core (PEEK) and a softer outer component were too stif (Figure 5(b)). Although they had acceptable lateral compressibility for the introduction (Figure 5(a)), their insertion required an annulotomy of at least 18 mm in length. Others had excessive wear. Furthermore, sandwich Figure 2: Sandwich designs that we evaluated in this study. We can group them into shock absorbing (a-c), dampening (d-f ), shape memory (g-i), and balloon type (j).
designs with a stif core and small endplate contact area had a high subsidence risk (Figures 4(c) and 4(d)).
After the study, we chose an oval doughnut-like hollow compressible monobloc elastomeric design with a 5 mm wall (Figures 5(a) and 5(b)). In FEA analysis, it minimized implant stress under loading conditions, distributed strains uniformly, and tolerated the lateral compression during implantation.

Nucleus Replacement Biomechanical Results.
Comparing the three types of Bionate ® selected for our design, 80A has the lowest Z-axis displacement and stresses under the 1000 N axial load, even when combined with 300 N anteroposterior shear and 8 Nm rotation torque, favoring fatigue endurance. Implant stresses increase with material hardness for all axes and are higher for 90A than 80A, with no signifcant diference between 90A and 55D (Table 1 and Figure 6). Te maximum stresses happen on the Z-axis.

Annulus Stresses.
Under 1000 N axial compression, all three Bionate ® types induced similar annulus stresses, being maximum on the Z-axis. Adding 300 N anteroposterior shear Bionate ® 80A made the annulus bear more load than 90A and 55D. Te maximum stress also happened on the Zaxis. When adding 8 Nm rotation torque, the annulus supported the highest stresses with Bionate 80A. Again, 80A shared more load with the annulus than 90A and 55D, which had a similar behavior (

Discussion
After carrying out all the designs and tests of diferent materials, the PCU material imitates intact nucleus characteristics, particularly Bionate ® . Although manufacturers can provide it with diferent hardness, Bionate ® 80A is best suited for nucleus replacements as its properties are the closest to the intact nucleus [38]. On the other hand, more rigid types (55D, 75D, 90A) deform more and distribute loads more unevenly, inducing a higher subsidence risk [37]. Te nucleus replacements need an intact annulus fbrosus to contain the implant in its place. Terefore, this always requires an annulotomy. However, the minimally invasive approach severely limits implant materials and designs. Bionate ® 80A is elastic enough to tolerate compression during insertion, [38] facilitating a smaller annulotomy. An alternative is to perform an annulus repair [30].
Te  and Poisson's ratio was 0.49 (39). Bionate 75D Young's modulus increased from 131.1 MPa to 327.6 MPa, and Poisson's ratio decreased from 0.43 to 0.38 [38]. Tese data confrm that Bionate ® 80A has the best mechanical properties for a nucleus replacement. PCU particles cause a lesser infammatory reaction in implant wear than metal or UHMWPE [43]. In addition, our group saw that Bionate 80A particles induce no local or distant tissue adverse reactions [44]. Terefore, we recommend using best long-term endurance PCU, Bionate ® 80A.
Te design is crucial as the shape and size of the nucleus replacement decisively infuence the annulotomy size. An injectable material curing in situ after the discectomy would be ideal, but achieving it regularly and reliably is challenging. Te reagent mix, temperature, and curing time require strict control for steady results. Additionally, polymerizing agents are cytotoxic, so excess or leaching might have negative consequences. An option is to use a bag subsequently flled with elastomeric self-curing liquid. Tese bags, usually made of porous materials to ease nearby bone and annulus fxation, allow toxic reagent mix difusion. A smooth nonpermeable bag would not adhere to nearby tissues, facilitating extrusion, a critical complication of nucleus replacement devices. As a result, the devices that have reached clinical application [45] have limited use.
Monobloc designs are simpler to manufacture with regular results and more straightforward to customize. However, these nucleus replacements often require a larger annulotomy, increasing the extrusion risk unless we can deform and compress them when inserted. Tat is why Bionate ® 80A is particularly suited for nucleus replacements, and our design fulfls this requirement. We found that the implant manufactured with Bionate ® 80A has a stifness ( Table 1) of 862.81 N/mm, and stifness is between the value of 667 N/mm on average for the L 1 -L 5 discs and 1000 N/mm for the whole L 5 -S 1 segment, which is in the range of the studies carried out by White and Panjabi (1990) (12).
A fnal consideration is that the strongest endplate area is the so-called ring apophysis, a solid cortical bone hoop at its periphery [46]. Terefore, any implant transmitting the load mainly to this apophysis has the lowest subsidence risk. Te rationale behind our nucleus replacement design is to maximize the load transmission to the ring apophysis and minimize it to the rest of the vertebral endplate.
Te most signifcant limitation of our study is that we took from the literature the properties needed to reproduce those of an intact disc nucleus which we should customize for any specifc patient needing this procedure. Furthermore, the evaluation of joint implants with FEA or FEM,           besides being patient-specifc, is also very time consuming. Meshing bones and soft tissues is complicated. In addition, we need to study if the material sufers deterioration and cracking under long-term use.
We have performed an FEA of several designs and materials and found the best to replace the nucleus pulposus. In addition, we have developed a lumbar spine model with the patient's radiological images (plain X-ray and MRI). Tis model allows nucleus replacement customization.

Conclusions
Of all materials we analyzed, Bionate ® 80A has mechanical characteristics closest to the natural nucleus and is the most suitable for the nucleus replacement.
Bionate ® 80A yields the lowest implant stress due to compressive forces (favoring fatigue endurance), produces the highest stress level in the annulus (closest to the natural nucleus), and has the lowest subsidence risk. Unfortunately, all these features worsen directly proportional to material hardness.
Out of the eighteen designs we analyzed with FEA, we found that the monobloc oval doughnut-like Bionate 80A nucleus replacement reproduced the best biomechanics of the natural disc nucleus and had the lowest subsidence risk as it transmits the load to the ring apophysis. Furthermore, implanting it through the annulotomy required to perform a lumbar microdiscectomy should be possible due to its elasticity.

Data Availability
Data are available on request from the corresponding author.

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