Customized design and biomechanical property analysis of 3D-printed tantalum intervertebral cages

Abstract

BACKGROUND:

Intervertebral cages used in clinical applications were often general products with standard specifications, which were challenging to match with the cervical vertebra and prone to cause stress shielding and subsidence.

OBJECTIVE:

To design and fabricate customized tantalum (Ta) intervertebral fusion cages that meets the biomechanical requirements of the cervical segment.

METHODS:

The lattice intervertebral cages were customized designed and fabricated by the selective laser melting. The joint and muscle forces of the cervical segment under different movements were analyzed using reverse dynamics method. The stress characteristics of cage, plate, screws and vertebral endplate were analyzed by finite element analysis. The fluid flow behaviors and permeability of three lattice structures were simulated by computational fluid dynamics. Compression tests were executed to investigate the biomechanical properties of the cages.

RESULTS:

Compared with the solid cages, the lattice-filled structures significantly reduced the stress of cages and anterior fixation system. In comparison to the octahedroid and quaddiametral lattice-filled cages, the bitriangle lattice-filled cage had a lower stress shielding rate, higher permeability, and superior subsidence resistance ability.

CONCLUSION:

The inverse dynamics simulation combined with finite element analysis is an effective method to investigate the biomechanical properties of the cervical vertebra during movements.

Keywords

Biomechanical cervical intervertebral cage lattice structure inverse dynamics simulation finite element analysis

1. Introduction

Cervical intervertebral cages are special bone implants that are used in anterior cervical discectomy and fusion (ACDF) surgeries to treat cervical degenerative disc disease (CDDD) [1]. Intervertebral cages provide fused segments with adequate load-bearing and mechanical stimulations for osseointegration. The geometric characteristics, biomechanical properties, and biocompatibility of intervertebral cages should match those of the spinal segments of patients. However, intervertebral cages used in clinical applications were often general products with standard specifications, which were challenging to match with the cervical vertebra and prone to cause stress shielding and subsidence [2].

Additive manufacturing (AM), also known as three-dimensional (3D) printing, has the advantages of design freedom, low material usage, short processing time, and complex component fabrication capability [3]. Therefore, AM is employed to manufacture customized intervertebral cages that match the anatomical features of the cervical vertebra of patients.

Intervertebral cages can be divided into two categories, non-metallic and metallic cage [4]. Poly-ether-ether-ketone (PEEK) is generally used to fabricate non-metallic intervertebral cages it has an elastic modulus close to cortical bones and good biocompatibility. However, due to the insufficient mechanical strength and osseointegration of PEEK [5,6], researchers are exploring new methods to improve its mechanical properties and bioactivity [7,8]. Ti6Al4V is extensively used to manufacture metallic intervertebral cages because of its outstanding load-bearing ability and biocompatibility. However, because the elastic modulus of Ti6Al4V (110 GPa) is much higher than that of human bones, stress shielding is produced in bone tissues around bioimplants [9,10]. In recent years, tantalum (Ta) has attracted considerable attention in bone tissue engineering due to its excellent biological properties [11,12]. In comparison to Ti6Al4V, Ta has superior bioactivity and corrosion resistance [13–15], while the high density (16.68 g/cm³), high elastic modulus (186 GPa), and low machinability of Ta have limited its further application.

The lattice structure design is an effective method to control the elastic modulus and strength of bulk materials [16]. Selective laser melting (SLM) has the advantages of high energy input and precise molding; thereby, it can be used to fabricate complex Ta lattice structures [17]. The elastic modulus and strength of lattice structures can be tailored close to those of human bones by changing geometrical design parameters, such as relative density and unit cell architecture [18]. Porosity, pore size, and pore shape can also be customized to accelerate cell adsorption, cell proliferation, and bone in growth [19,20]. Therefore, lattice structures provide a new idea for customized intervertebral cage design.

Due to the complexity of clinical trials, it is difficult to verify the reliability of intervertebral cages. Therefore, finite element analysis (FEA) is used to investigate the biomechanical behavior of interbody cages [21,22]. Moreover, FEA can intuitively provide the stress and strain distributions of the vertebra, endplates, and intervertebral cages of patients. Hence, the impacts of design parameters on the biomechanical behavior of customized cages can be studied in detail. However, in most previous studies [23–25], FEA models did not consider cervical spine movement characteristics in everyday human life and simplified loading conditions on fused spinal segments by static analysis; thus, actual situations were not reflected. The inverse dynamics simulation of the AnyBody Modeling System is an effective method to obtain the joint and muscle reaction forces during movements [26,27]. In AnyBody, a musculoskeletal model is first developed, captured motion data are then imported to inverse dynamics simulations, and joint and muscle forces for different motions are used as loading boundaries for FEA [28]. Zairi [29] employed the AnyBody Modeling System to compute the pressures on intervertebral discs when an external traction device was applied. Grujicic [30] used the AnyBody Modeling System to investigate the effects of seat features on the muscle and joint forces of drivers. Ignasiak [31] confirmed that the AnyBody spinal fusion model could predict postural changes after surgeries well.

In this work, three kinds of customized designed Ta intervertebral cages with gradient structures were printed by SLM. The joint and muscle reaction forces and positions of the cervical C5-C6 segment were obtained by performing inverse dynamics simulations in AnyBody Modeling System. The mechanical properties of Ta lattice intervertebral cages and specimens were analyzed by experiments and numerical simulations. The purpose of this study is to design and fabricate customized tantalum (Ta) intervertebral fusion cages that meet the biomechanical requirements of the cervical vertebra of patients.

2. Material and methods

2.1. Design method

According to the computed tomography (CT) scan data of the C5-C6 spinal segments (male; 25 years old; height, 179 cm; weight, 73 kg), a cervical three-dimensional (3D) model for multibody dynamics (MD) simulations and FEA was created (Fig. 1).

Fig. 1.

3D model of the cervical vertebra and initial design framework of the customized cage.

The Ta intervertebral cage designed for this analysis consisted of a solid outer frame, a porous layer, and a graft bone area. According to the anatomical structure of the cervical C5-C6 segment and the size range recommended by Scholz et al. [32], the length and width of the cage were 16.9 mm and 10.2 mm, respectively. The inferior and superior surfaces of the cage were obtained by performing Boolean operations between the C5-C6 segment model and the initial outer frame of the cage (Fig. 1). The porous area was filled with lattice structures. Three types of cages with different types of unit cells were designed - bitriangle (BT), octahedroid (OH), and quaddiametral (QD), and they were named Cage-BT, Cage-OH, and Cage-QD, respectively (Fig. 2). The solid cage was designed as the control group and named as Cage-solid. To match stress distribution on the cage, a porous gradient lattice structure was adopted. The outer ring of the cage was filled with a 50% porous lattice to bear large stress, and the inner circle was filled with a 60% porous lattice to bear minor stress. The porosity gradient design of the lattice structure (outer with 50% and inner with 60%) was to realize the functional biomimetic of human bone. The outer ring with 50% porosity was to play load-bearing function like cortical bone. Furthermore, the outer ring pore size at 500 um was beneficial for cell proliferation. The inner ring with 60% porosity and 600 um pores was able to promote bone tissue growth and transmission of nutrients and oxygen atoms like cancellous bone [33,34]. The detailed design parameters are listed in Table 1.

Fig. 2.

Design parameters of the Ta lattice-filled cages.

Table 1

Design parameters of the Ta compression samples

Cage	Porosity	Unit cell length (mm)	Strut diameter (mm)	Pore size (mm)
Cage-BT outer ring	50%	1.5	0.57	0.52
Cage-BT inner ring	60%	1.5	0.48	0.62
Cage-OH outer ring	50%	1.18	0.58	0.55
Cage-OH inner ring	60%	1.18	0.5	0.65
Cage-QD outer ring	50%	1.55	0.55	0.50
Cage-QD inner ring	60%	1.55	0.48	0.60

To obtain the lattice structure that meets the mechanical performance requirements of the intervertebral fusion cage, equivalent lattice structure specimens with the same cross-sectional areas as the cages were designed, and a quasi-static compression test was conducted to evaluate their mechanical properties. The design parameters of the equivalent lattice structure are presented in Fig. 3.

Fig. 3.

Design parameters of the Ta compression samples.

2.2. Specimen fabrication

The cage samples and the equivalent lattice structure compression specimens were fabricated with pure Ta powder by SLM (Xian Bright Laser Technologies Co. Ltd.) (Figs 3 and 4).

Fig. 4.

Ta Intervertebral cages printed by SLM.

2.3. Musculoskeletal modeling

2.3.1. Motion data collection

The subject (male; 25 years old; height, 179 cm; weight, 73 kg) was required to keep feet static and neck motion uniformly. An optical motion capture system (Vicon Motion System Inc., Oxford, UK) was used to collect the motion data of the subject’s cervical vertebra during upright standing, flexion, extension, rotation, and lateral bending. The Vicon video cameras tracked the trajectories of optical markers stuck on specific human body sites. The data acquisition frequency of the cameras was set to 100 Hz. The recorded trajectories were imported into AnyBody Modeling System to build a musculoskeletal model of the human body.

2.3.2. Customized spinal dynamics model

The AnyMoCap model in the AnyBody Modeling System v.7.1 (AnyBody Technology A/S, Aalborg, Denmark) was used to calculate the joint and muscle forces of the cervical C5-C6 segment. The height and weight of the human body were used to scale the default model. To customize the cervical vertebra model, the C5-C6 segment of the default model was replaced with the 3D model of the C5-C6 segment of the human body (Fig. 5(a–d)). The collected trajectories from the optical markers were used to simulate the motions of the corresponding points on the customized AnyMoCap model (Fig. 5(e–i)). The joint and muscle forces of the C5-C6 segment during upright standing, flexion, extension, rotation, and lateral bending were computed by inverse dynamics analysis, and subsequently, the position and orientation of the C5-C6 segment was exported (Fig. 5(j–n)).

Fig. 5.

Cervical vertebra motion simulation: (a–d) Musculoskeletal multibody dynamics model, (e–i) Inverse dynamics analysis, and (j–n) Position and orientation of the C5-C6 segment.

2.4. Finite element analysis model

The FEA model consisted of the cervical C5-C6 segment, the Ta intervertebral cage, endplates, and an anterior fixation system (Ti plate and screws) (Fig. 6). The 3D model of the Ti anterior fixation plate and screws with appropriate size was established according to the clinical standards of ACDF [35]. Due to the complex geometry of the model, the meshing operation was heavy. In this study, Altair SimSolid2021 (Altair Engineering Inc, Troy, Michigan, USA) software was used to analyse the biomechanical properties of cages. SimSolid could eliminate geometry simplification and meshing, the two most time-consuming and expertise-extensive tasks done in traditional FEA, enabling the analysis of fully-featured CAD assemblies in minutes without meshing [36]. SimSolid has been used to analyse the mechanical behavior of load-bearing lattice bone implants and lattice-infill automotive connecting rods by some researchers [37,38].

Fig. 6.

FEA model of ACDF.

The material properties of different components of the model are listed in Table 2 [39–42]. The cervical vertebra consisted of cortical and cancellous bones, and the thickness of the cortical bone was 0.5 mm. The thickness of the endplates was 0.6 mm. The contact model of the cortical bone, the cancellous bone, and the endplate was created by assigning bonding contacts. The contact model between the endplates and the cage was built by assigning separating contacts with a frictional coefficient of 0.5 [41]. The contact model between the Ti screws and the vertebra was established by adopting separating contacts with a frictional coefficient of 0.95 [25]. The inferior surface of the C6 segment was completely fixed. The joint and muscle reaction forces (Table 3) obtained from the inverse dynamics analysis during upright standing, flexion, extension, rotation, and lateral bending were applied to the superior surface of the C5 segment. Adapt for stress was selected as the default solution settings.

Table 2

Material properties of the FEA model

Components	Young’s modulus (MPa)	Poisson’s ratio	Yield strength (MPa)	Ultimate compressive strength (MPa)
Cortical bone	12000	0.3	125	130
Cancellous bone	100	0.3	5.5	5.9
Endplates	500	0.25	—	—
Capsular ligament	32	0.4	—	—
Nucleus pulposus	1.3	0.5	—	—
Annulus fibrosus	3.4	0.4	—	—
Ti plate	114000	0.34	805	896
Ti screws	114000	0.34	805	896
Ta cage	186000	0.35	362	400

Table 3

Maximum joint and muscle reaction forces during different movements

Motion	Force in the X-axis (N)	Force in the Y-axis (N)	Force in the Z-axis (N)
Stand upright	8	71	−500
Flexion	3.7	157	−136
Extension	1	−82	−389
Rotation	−71	14	−1152
Lateral bending	−247	118	953

2.5. Computational fluid dynamics model

The BT, OH, and QD lattice structure models with the same porosity (60%) and pore size (0.6 mm) were selected for CFD simulations. The density and dynamic viscosity of the fluid were 1000 kg/m³ and 0.001 Pa⋅s, respectively. The inlet and outlet pressures on the fluid domain were 0.1 Pa and 0 Pa, respectively. The boundaries of the fluid domain were non-slip walls (Fig. 7).

Fig. 7.

CFD model boundary conditions.

2.6. Compression experiments

Quasi-static compression experiments were carried out on a 100 KN electronic universal testing machine (ETM105D; Shenzhen, China) with a compression speed of 1 mm/min. The compression load is applied on coordinates (0, 0, Z), which was parallel to the printing direction of the lattice structure samples. Compression experiments were carried out on the compression samples (Fig. 3) and the intervertebral cages (Fig. 4) respectively.

According to the ASTM F2267-04(2018) Standard Test Method for Measuring Load Induced Subsidence of Intervertebral Body Fusion Device Under Static Axial Compression, the subsidence resistance abilities of the printed intervertebral cages were quantitatively evaluated. Polyurethane foam (15 pcf; SAWBONES, Pacific Research Laboratories, Vashon, WA) was used to replace cancellous bones [40]. Two pieces of polyurethane foam were fixed on the upper and lower plates of the testing machine. Each Ta lattice-filled cage sample was placed between the two pieces of polyurethane foam (Fig. 8). The quasi-static compression tests of the cage-polyurethane systems and the lattice-filled cages were executed at the compression speeds of 6 mm/min and 1 mm/min, respectively.

Fig. 8.

Quasi-static compression experiments of Ta cage-polyurethane systems.

3. Results

3.1. Inverse dynamics analysis

The joint and muscle reaction forces of the C5-C6 segment during movements are presented in Fig. 9 and Table 3. The peak forces under flexion and extension were 207 N and 397 N, respectively, and these values were lower than the peak force during upright standing (505 N). The peak forces during rotation and lateral bending increased significantly as compared to those during upright standing, flexion, and extension. Among the five movements, the largest peak force of 1154 N was produced during the rotation of the spine.

Fig. 9.

Joint and muscle reaction forces of the C5-C6 segment during different movements.

3.2. Finite element analysis

3.2.1. Micromotion

Figure 10 shows the displacement distributions of the Cage-BT, Cage-OH, Cage-QD, and Cage-solid samples during different movements, and the maximum displacements between the cages and the endplate are presented in Fig. 11. In comparison to the solid cage, the lattice-filled cages had lower peak displacements. The micromotion of the contact surface between the cages and the endplates was significant under rotation and lateral bending, and the displacements of both the cages and the endplates exceeded 0.05 mm. During upright standing, flexion, and extension, the micromotion displacement was less than 0.034 mm, which noticeably decreased as compared to those under rotation and lateral bending movements. Except for lateral bending, the micromotion of the Cage-OH sample was more extensive than those of Cage-BT and Cage-QD.

Fig. 10.

Displacement distributions of the Cage-BT, Cage-OH, Cage-QD, and Cage-solid models during different movements.

Fig. 11.

Maximum displacements between the cages and the endplates during different movements.

3.2.2. Stress distribution on endplates

The stress distributions on the endplate in the Cage-BT, Cage-OH, and Cage-QD models under different movements are shown in Figs 12 and 13. High-stress concentration occurred in the peripheral region of the endplates. Among the five motions, the minimum stress on the endplate occurred under flexion, and stresses during rotation and lateral bending were noticeably higher than those under the other movements. The area of high-stress concentration on the C5 segment inferior endplate in the Cage-BT model was smaller than those in the Cage-OH and Cage-QD models, especially during lateral bending. In comparison to Cage-BT, the Cage-OH sample has higher peak Von-Mises stresses on the C5 segment inferior endplate during extension. The difference between peak stresses can reach 6.8 MPa, higher than the yield strength of cancellous bone (5.5 MPa). It indicated that the Cage-OH was prone to local subsidence. Under rotation, the maximum Von-Mises stress on the C5 segment inferior endplate in the Cage-QD model (29 MPa) was much higher than those in Cage-BT (20.1 MPa) and Cage-OH (18.3 MPa). In comparison to the C5 segment inferior endplate, the C6 segment superior endplate had more small stress concentration areas, which primarily appeared in the contact region between struts of the lattice structure and the endplate, indicating that the C6 segment superior endplate was prone to local subsidence. According to the maximum Von-Mises stresses shown in Fig. 14, it can be inferred that the sum of stresses induced by Cage-BT on the endplate of the C5-C6 segment was smaller than those for Cage-OH and Cage-QD.

Fig. 12.

Stress distributions on the C5 segment inferior endplate.

Fig. 13.

Stress distributions on the C6 segment superior endplate.

Fig. 14.

Peak stresses on the endplate during different movements.

The stress shielding rate was determined as [43] $\begin{eqnarray}\displaystyle {\varphi}=\left(1-{\displaystyle \frac{{\sigma}_{p}}{{\sigma}_{0}}}\right)\times 100\%, & & \displaystyle\end{eqnarray}$ (1) where 𝜎_p and 𝜎₀ are the stresses on the endplate after and before cage implantation, respectively.

The average stresses on the C6 segment superior endplate during different movements are listed in Table 4. The average stress shielding rates of the Cage-BT, Cage-OH, Cage-QD, and Cage-solid samples during upright standing, flexion, extension, rotation, and lateral bending were calculated by Eq. (1). The average stress shielding rate of the solid cage was much higher than those of the lattice-filled cages (Fig. 15), indicating that the lattice-filled structures significantly reduced stress shielding. The average stress shielding rates of Cage-BT, Cage-OH, and Cage-QD were 65%, 73.8%, and 65.3%, respectively (Table 5). Moreover, the Cage-OH sample had the highest stress shielding rate, and the stress shielding rates of Cage-BT and Cage-QD were similar. These results imply that the ability of Cage-BT and Cage-QD to relieve stress shielding was notably superior to that of Cage-OH.

Table 4

Average stresses on the C6 segment superior endplate under different movements

Part	Upright standing (MPa)	Flexion (MPa)	Extension (MPa)	Rotation (MPa)	Lateral bending (MPa)
Cage-BT	0.312	0.177	0.321	0.802	0.796
Cage-OH	0.247	0.114	0.243	0.65	0.624
Cage-QD	0.277	0.184	0.293	0.852	0.825
Cage-solid	0.213	0.098	0.225	0.533	0.55
Before implantation	1.11	0.376	0.835	2.66	2.54

Fig. 15.

Average stress shielding rates of the cages under different movements.

Table 5

Average stress shielding rates of the printed cages under different movements

Part	Upright standing	Flexion	Extension	Rotation	Lateral bending
Cage-BT	71.9%	52.9%	61.6%	69.8%	68.7%
Cage-OH	77.7%	69.6%	70.9%	75.6%	75.4%
Cage-QD	75%	51.1%	64.9%	68%	67.5%
Cage-solid	80.8%	73.9%	73.1%	80%	78.3%

3.2.3. Stress distribution in the anterior fixation system

The stress distributions of the vertebral screw holes are shown in Figs 16 and 17, and those of the Ti plate and screws are presented in Figs 18 and 19, respectively. In comparison to the lattice-filled cage models, the solid cage model had a higher stress level for the vertebral screw holes, the Ti plate, and the Ti screws. Especially, during rotation, the peak stress difference of Ti screws between Cage-BT and Cage-solid models can reach 347.2 MPa. Among the three lattice-filled cage models, Cage-OH had the highest stress level and experienced stress concentrations on the vertebral screw holes, the Ti plate, and the Ti screws. Under flexion, the peak stresses on the C6 vertebral screw holes of Cage-OH (11.5 MPa) and Cage-solid (12.2 MPa) were even very close. Due to good stability of the lattice structure under compression, the stresses on the vertebral screw holes, the Ti plate, and the Ti screws of the Cage-BT and Cage-QD models were smaller than those of the Cage-OH and Cage-solid models. Among the five motions, the stress concentration levels on the vertebral screw holes, the Ti plate, and the Ti screws during rotation and lateral bending were noticeably higher than those under the other movements. For example, the peak stress on the vertebral screw holes and Ti screws of the Cage-BT model during lateral bending were 28.1 MPa and 265.5 MPa larger than during flexion, respectively. High-stress concentration occurred on the upper edge of the C5 vertebral screw holes and the lower edge of the C6 vertebral screw holes. The stress on the head of the Ti screws was significantly higher than those on the tail of the Ti screws. The high-stress concentration positions on the contact interface between the bone, Ti plate, and Ti screws have a high risk of loosening and were the critical factors for the lifetime of the anterior fixation system.

Fig. 16.

Stress distributions of the C5 vertebral screw holes.

Fig. 17.

Stress distributions of the C6 vertebral screw holes.

Fig. 18.

Maximum stresses of the vertebral screw holes. (a) C5 screw hole and (b) C6 screw hole.

Fig. 19.

Stress distributions of the Ti plate and screws.

3.3. CFD analysis

In this section, the fluid flow behaviors in the BT, OH, and QD lattice structures are simulated and their permeability is calculated. According to Darcy’s law, permeability (k) can be calculated as [44]: $\begin{eqnarray}\displaystyle k={\displaystyle \frac{{\mu}qL}{A\cdot {\Delta}_{p}}}, & & \displaystyle\end{eqnarray}$ (2) where 𝜇, q, L, A, and Δ_p represent the fluid dynamic viscosity (Pa⋅s), the volume flow rate (mm³/s), the length of the fluid domain (mm), the cross-sectional area of the fluid domain (mm²), and the pressure drop (Pa), respectively.

Table 6 lists the permeability of the three types of lattice structures. The permeability of the BT, OH, and QD lattices was within the range of human trabecular bone permeability (1.5 × 10⁻⁹ −12.1 × 10⁻⁹ m²) [45]. The permeability of BT was 28% higher than those of OH and QD, indicating that the BT lattice was beneficial to cell growth.

Table 6

Permeability of different lattice structures

Sample	Permeability (m²)
Lattice-BT	8.367 × 10 ⁻⁹
Lattice-OH	6.48 × 10⁻⁹
Lattice-QD	6.563 × 10⁻⁹

3.4. Mechanical properties

3.4.1. Ta-equivalent lattice structures

The stress-strain curves of the equivalent lattice structures are exhibited in Fig. 21. The yield strengths of the BT, OH, and QD lattice structures were 43.8 MPa, 67.5 MPa, and 39.5 MPa, respectively, and their elastic moduli were 0.83 GPa, 1.56 GPa, and 0.92 GPa, respectively. Higher porosity is beneficial to bone growth; however, the mechanical strength of lattice structures is weakened. The elastic moduli of the BT, OH, and QD Ta lattice structures were within the range of human cancellous bone modulus (0.76–18.2 GPa) [46]. The BT lattice structure had the minimum elastic modulus and could reduce the risk of stress shielding.

Fig. 20.

Fluid flow velocities in the cross-section of different lattice structures. (a) xy cross-section and (b) yz cross-section.

Fig. 21.

Stress-strain curves of different Ta lattice structures.

3.4.2. Ta intervertebral cages

According to the ASTM F2267-04(2018) standard, the stiffness of the polyurethane foam test block (K _p) was calculated as $\begin{eqnarray}\displaystyle K_{p}={\displaystyle \frac{K_{s}K_{d}}{K_{d}-K_{s}}}, & & \displaystyle\end{eqnarray}$ (3) where K _d is the stiffness of the intervertebral cage and K _s is the stiffness of the system.

The load-displacement curves of different cage-polyurethane systems are presented in Fig. 22(a). The K _s values of the BT, OH, and QD lattice-filled cage-polyurethane systems were 431 N/mm, 332 N/mm, and 407 N/mm, respectively (calculated by the slopes of the initial linear stage in the load-displacement curves).

Fig. 22.

Load-displacement curves of different (a) cage-polyurethane systems and (b) lattice-filled cages.

The load-displacement curves of the Cage-BT, Cage-OH, and Cage-QD are shown in Fig. 22(b). The K _d values of the BT, OH, and QD lattice-filled cages were 3601 N/mm, 4252 N/mm, and 3134 N/mm, respectively. The value of K _p was inversely proportional to the displacement amplitude of polyurethane foam. The larger the K _p value, the stronger the subsidence resistance ability of the cages. The K _p values of Cage-BT, Cage-OH, and Cage-QD are listed in Table 7, where it can be seen that the Cage-BT sample had the best anti-subsidence ability followed by Cage-QD and Cage-OH.

Table 7

Polyurethane foam stiffness of different cage samples

Sample	Polyurethane foam stiffness (N/mm)
Cage-BT	490
Cage-OH	306
Cage-QD	468

4. Discussion

In previous studies [23–25], the FEA models of intervertebral cage have mainly used the head weight in static conditions as the mechanical boundary condition of the cervical vertebra. However, the inverse dynamics simulations revealed a significant discrepancy between the mechanical conditions of the cervical vertebra in motion and the static state. It was because the muscles, ligaments, and joints during different movements of spinal segments have different resistance for compression and shear loading and different constraint for a range of motion. The joint and muscle reaction forces obtained from the inverse dynamics analysis during different movements could reflect cervical spine movement characteristics in everyday human life.

Due to the mismatch of the geometry and biomechanical properties between intervertebral cages and the cervical vertebra of patients, risks of stress shielding, subsidence, and migration increase after cage implantation. Stress shielding may cause the dissolution of bone tissues around prosthetics [47]. The loss of intervertebral height may occur due to cage subsidence [48]. Cage migration may lead to the loss of cervical lordosis [41,49]. All these factors may reduce the fusion rate and lead to a cage failure revision surgery.

In this study, the stress shielding levels of the cages were quantitatively estimated by calculating their stress shielding rates [43]. The micromotion displacement and the stress distribution on the endplate were used to evaluate the anti-migration and anti-subsidence abilities of the cages [41,50]. The results shown that the lattice-filled structure significantly reduced the micromotion of the solid cage due to it produced greater friction on the endplate. In comparison to Cage-BT and Cage-QD, the Cage-OH sample has higher peak displacements of micromotion, which can be attributed to the fewer contact points between Cage-OH and the endplate per unit area and the smaller frictional force. The unit cell structure of lattice has a significant effect on the stress distribution on endplates. The Cage-OH sample had a stretching-dominant lattice structure (OH), which provided higher compressive strength than the bending-dominant lattice structures (BT and QD). However, the number of contact nodes between the OH lattice and the endplate was lower than those for the BT and QD lattices; thus, higher stress was produced at each contact node between the OH lattice and the endplate. It indicated that the Cage-OH was prone to local subsidence, which the results of the stress shielding rate can further confirm. Among the three lattice-filled cage models, Cage-BT has the minimum stress concentration level and stress shielding rate, which indicates that it has a superior ability to resist stress shielding. Anterior fixation systems can provide immediate stability to the cervical vertebra after ACDF surgeries and promote the process of spinal fusion [51]. It can be propounded that the structural design of the cages significantly influenced the stress levels of the vertebral screw holes and the anterior fixation system. The discrepancy in the peak stress level and stress distribution of the cages occurred because the Cage-solid and Cage-OH samples had larger micromotion displacements; thus, more loads were transferred to the anterior fixation system.

Fluid flow behaviors in lattice structure pores significantly affect cell adsorption, cell proliferation, tissue differentiation, and bone regeneration [52]. During tissue differentiation, the delivery of nutrients and the excretion of metabolic wastes depend on the permeability of lattice structures [53,54]. The fluid flow velocities in the cross-section of different lattice structures are presented in Fig. 20. The fluid in the BT lattice structure had a pronounced velocity gradient between the center, edge, and inlet of the fluid domain; thus, accelerating the mass transfer rates of nutrients, oxygen atoms, and metabolic wastes between lattice pores and facilitating cell migration and proliferation. Moreover, the BT lattice structure had the highest permeability, indicating that it was more favorable to cell growth.

The lattice-filled structure significantly reduced the elastic modulus of the solid cage. The mechanical properties of the lattice depend on its structural design parameters, such as relative density and unit cell architecture. In comparison to BT and QD, the OH lattice had higher yield strength and elastic modulus at the same relative density and pore size; thus, it had stronger deformation resistance. The vertical struts of the OH lattice structure were the main load-bearing components and were less prone to deformation than the inclined struts in the BT and QD lattice structures under compression [55,56]. The BT lattice structure had the minimum elastic modulus and could reduce the risk of stress shielding. In subsidence testing, the polyurethane foam test block stiffness (K _p) for the Cage-BT, Cage-OH, and Cage-QD were 490 N/mm, 306 N/mm, and 468 N/mm, respectively. The median block stiffness (K _p) of FDA-cleared cervical intervertebral body fusion devices (IBFDs) was 424 N/mm reported by Peck et al. [57]. It indicates the subsidence resistance ability of the Cage-BT, Cage-OH, and Cage-QD was similar to that of FDA-cleared single-piece cervical IBFDs. The median compression stiffness of FDA-cleared IBFDs was 10108 N/mm, significantly higher than that of the Cage-BT, Cage-OH, and Cage-QD (3601 N/mm, 4252 N/mm, and 3134 N/mm, respectively). It demonstrates the lattice-filled structure significantly reduced the elastic modulus of the solid metallic cage. The detailed comparison of mechanical testing data between as-designed intervertebral cages and FDA-cleared IBFDs was listed in Table 8. The subsidence test results of Ta intervertebral cages revealed that the Cage-BT sample had the largest polyurethane foam stiffness, indicating that it had the optimum subsidence resistance ability. It was consistent with the results obtained from FEA.

Table 8
The comparison of mechanical testing data between as-designed intervertebral cages and FDA-cleared IBFDs

Mechanical testing data Our work Peck et al. [57]

Cage-BT Cage-OH Cage-QD 5th Percentile 25th Percentile 50th Percentile 75th Percentile 95th Percentile

Polyurethane foam test block stiffness (K _p) (N/mm) 490 306 468 257 324 424 522 791

Stiffness of intervertebral cage (K _d) (N/mm) 3601 4252 3134 5097 7984 10108 13300 19203

Mechanical testing data	Our work	Peck et al. [57]
Polyurethane foam test block stiffness (K _p) (N/mm)	490	306	468	257	324	424	522	791
Stiffness of intervertebral cage (K _d) (N/mm)	3601	4252	3134	5097	7984	10108	13300	19203

The degeneration of adjacent cervical segment is closely related to the mechanical properties of cage. The effect of the mechanical properties of the cages on the degeneration of adjacent segments is our essential work in the future.

5. Conclusions

Three kinds of tantalum (Ta) lattice intervertebral cages with gradient structure were customized designed and printed by SLM process. Reverse dynamics, FEA, CFD and compression tests were executed to investigate the biomechanical properties of the as-designed intervertebral cages. The main findings of this work are presented below.

The inverse dynamics simulations revealed a significant discrepancy between the mechanical conditions of the cervical vertebra in motion and the static state. The peak forces under rotation and lateral bending were significantly higher than those under upright standing, flexion, and extension.

The FEA results indicated that the lattice-filled structure significantly reduced the micromotion displacement and anterior fixation system stress of the solid cage. In comparison to the Cage-OH and Cage-QD, Cage-BT had lower endplate stress concentration, stress shielding rate, and higher permeability.

In subsidence testing, the Cage-BT sample had the largest polyurethane foam stiffness, indicating that it had the optimum subsidence resistance ability.

Footnotes

Acknowledgements

This work was supported by the Universities Scientific Research Project of Xinjiang, China (grant number: XJEDU2021I008) and the Natural Science Foundation of Xinjiang Uygur Autonomous Region, China (grant number: 2023D01A86).

Conflict of interest

The authors declare that they have no conflict of interest.

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