Biomechanical evaluation of an osteoporotic anatomical 3D printed posterior lumbar interbody fusion cage with internal lattice design based on weighted topology optimization

Abstract

In this study, we designed and manufactured a posterior lumbar interbody fusion cage for osteoporosis patients using 3D-printing. The cage structure conforms to the anatomical endplate’s curved surface for stress transmission and internal lattice design for bone growth. Finite element (FE) analysis and weight topology optimization under different lumbar spine activity ratios were integrated to design the curved surface (CS-type) cage using the endplate surface morphology statistical results from the osteoporosis patients. The CS-type and plate (P-type) cage biomechanical behaviors under different daily activities were compared by performing non-linear FE analysis. A gyroid lattice with 0.25 spiral wall thickness was then designed in the internal cavity of the CS-type cage. The CS-cage was manufactured using metal 3D printing to conduct in vitro biomechanical tests. The FE analysis result showed that the maximum stress values at the inferior L3 and superior L4 endplates under all daily activities for the P-type cage implantation model were all higher than those for the CS-type cage. Fracture might occur in the P-type cage because the maximum stresses found in the endplates exceeded its ultimate strength (about 10 MPa) under flexion, torsion and bending loads. The yield load and stiffness of our designed CS-type cage fall into the optional acceptance criteria for the ISO 23089 standard under all load conditions. This study approved a posterior lumbar interbody fusion cage designed to have osteoporosis anatomical curved surface with internal lattice that can achieve appropriate structural strength, better stress transmission between the endplate and cage, and biomechanically tested strength that meets the standard requirements for marketed cages.

1. Introduction

Posterior lumbar interbody fusion is a common, effective treatment for spinal degeneration and instability that restores intervertebral height and stabilizes the spinal column[1,2]. However, subsidence is one of the potential clinical complications of interbody cages and a major cause of intervertebral disc height restoration failure. Biomechanically, intervertebral cage subsidence is associated with the stress transfer capability influenced by the endplate/cage interfacial contact area and the stress-shielding effect degree[3].

Although the lumbar cage superior and interior surface morphology has been proposed for redesign with sufficient endplate-cage contact area to improve stress transfer and reduce cage subsidence risk factors[3,4], morphology changes in the lumbar spine and intervertebral discs were found to be more significant for osteoporotic patients[5-7]. Serious endplate concave curved surfaces, that is, intervertebral disc mid heights were higher in the osteoporosis and osteopenia patients compared to those of normal subjects. This is unfavorable for stress transfer through the lumbar cage surfaces. However, in the current posterior cage surface design, no suitable superior/interior surface designs were found based on the endplate morphology for osteoporosis statistical results.

The stress-shielding effect caused by the cage must also be avoided to reduce the subsidence risk factor. Accordingly, many authors have promoted metal-free material with the aim of reducing segmental stiffness, such as polyether ether ketone (PEEK), ceramics, or composite material (COMBO cage composed of metal and PEEK) to prevent obvious stress-shielding effects[3,8]. However, the interbody fusion mechanism of these materials was not found to be more prominent than that of titanium alloys[3]. Making a metal cage with sufficient strength and stress-shielding effect reduction through structural optimization must be improved in the redesign process.

Using metal additive manufacturing (AM, also known as 3D printing) techniques to create a lattice design on the implant surface or internal cavity has been proven in many studies to induce and promote better osseointegration[9-13]. The titanium cage is expected to have appropriate structural strength and bone growth ability when the lattice design concept can be used in the internal cage cavity. However, this complex, high-precision hybrid design must be achieved using the metal AM technique, which has great potential to create a porous (lattice) structure in a dense titanium body[9-13].

In this study, we designed a posterior lumbar interbody fusion cage for the osteoporosis patient with appropriate structural strength and superior/inferior curved surface (CS-type) design for stress transfer as well as internal lattice design for bone ingrowth. The cage structure was generated by integrating finite element (FE) analysis and weight topology optimization (WTO) under different lumbar spine activity ratios. The CS-type cage superior/inferior surfaces were generated based on the statistical results from osteoporosis patient endplate surface morphology. The CS-type biomechanical behaviors and plate (P-type) cages under different daily activities were compared by performing non-linear FE analysis. The lattice was designed in the CS-type cage internal cavity and manufactured using metal 3D printing to conduct in vitro biomechanical tests.

2. Materials and methods

2.1. Statistical analysis of endplate morphology of elderly osteoporosis patients

The lumbar spine computed tomography (CT; Gold Seal Optimal CT660 scanner, GE Healthcare, Chicago, IL, USA) images from 20 elderly osteoporosis patients over the age of 65 years from August 2018 to December 2018 were collected to measure the endplate morphology[14]. All lumbar spine images were obtained using a human trial program, in accordance with the ethical standards approved by the Institutional Review Board of the Tri-Services General Hospital, Taipei, Taiwan (approval number: 2-107-05-109). The image interval was 0.625 mm to maintain clearer image quality for easy measurement of lumbar endplate morphology.

The lumbar spine mean Hounsfield units (HU) value was measured as the criterion for determining osteoporosis according to the methodology defined by Patel et al.[5]. The HU value range between 70 (about bone density = 0.648 g/cm³) and 120 (about bone density = 0.833 g/cm³) was used as the acceptance criterion for judging osteoporosis in this study. Severe osteoporosis with HU value below 70 was excluded because vertebral interbody fusion surgery was not recommended for patients by the clinician[14]. To ensure lumbar spine image measurement accuracy, older adults who had lumbar fractures with lumbar implantation, vertebroplasty, kyphoplasty, endplate fracture, kyphosis, Kümmell’s disease, or other lumbar surgeries, and who had spinal cancer, cancer with spinal metastasis or bone cortex hyperplasia were excluded from the study[14].

The superior/inferior endplate morphologies were measured from the second (L2) to the fifth (L5) osteoporotic lumbar vertebrae. After the 3D lumbar spine image was reconstructed using reverse engineering software (Creo Parametric v2.0, PTC, Needham, MA, USA), the curved surface endplate position variations were measured at 25%, 50%, and 75% of the endplate length in the coronal and sagittal planes (Figure 1). The amount of each measurement position was counted to obtain the average endplate subsidence morphology for 20 elderly patients with osteoporosis. The endplate morphology statistical results can be exported to modify the following validated FE model.

Figure 1.

The superior/inferior endplate morphologies were measured from the second (L2) to the fifth (L5) osteoporotic lumbar vertebrae, and the positions of the curved surface endplate variation were measured at 25%, 50%, and 75% of the endplate length in the coronal and the sagittal planes.

2.2. FE model generation for osteoporotic endplate morphology

A 70-year-old female patient was selected from the previously mentioned elderly osteoporotic image database as a volunteer to reconstruct a lumbar spine 3D model from L2 to L5. The reconstruction covered cortical bone, cancellous bone, endplates, discs (nucleus and annulus fibrosus), and facet joints (with 1-mm gap) in Creo CAD software. All ligaments relative to the L2 to L5 lumbar spine were constructed according to their anatomical positions and referenced using the result from a study by Chazal et al. (Figure 2)[15]. The FE model was generated with quadratic ten-node tetrahedral structural solid elements and a total of 689,810 elements and 1,022,598 nodes in the FE package (ANSYS Workbench v18.2, ANSYS Inc., PA, USA) for simulation (Figure 1).

Figure 2.

Finite element model generation processes included computed tomography image processing, computer-aided design model generation, mesh generation, model validation, and endplate morphology modification.

Cortical, cancellous bones, endplate, and discs were defined with linear elastic and isotropic properties adopted from the relevant literature[2,16]. The material property of all ligaments was calculated using the hyper-elastic Ogden third-order formula[2,16] (Table 1). Contact elements with friction (friction coefficient as 0.2) were used to simulate the facet joint mechanism. Nodes on the bottom of the L5 endplate were constrained in all directions as the boundary conditions. Besides applying axial loads of 150 N on the upper endplate of L2, flexion (-Rx), extension (+Ry), bending (+Rx), and axial rotation (-Rz) with 10 N-m, 7.5 N-m, 10 N-m, and 10 N-m, respectively, were individually applied as the four different load conditions (Rx, Ry and Rz are shown in Figure 3)[17,18]. The intervertebral range of motion (ROM) for L3-L4 was calculated to validate our FE model[17]. The model reliability was attained due to a variation of about 30% of the average ROM at L2-L3, L3-L4, and L4-L5 when compared to the works by Yamamoto et al.[17] The ROM was defined as the variation in the rotation angle of the adjacent lumbar vertebral bodies. The rotation angle of a single vertebral body was obtained by calculating the dot production of a fixed vector, which was formed by the same two feature points within the vertebral body, before and after simulations[17-19].

Table 1.

Materials properties used in FE analysis

Materials	Young’s modulus (MPa)	Poission’s ratio
Cortical bone	12000	0.3
Cancellous	100	0.2
Endplate	24	0.25
Core	1	0.499
Annulus fibrosus	4.2	0.45
Ti6Al4V	110000	0.3

FE: Finite element

Figure 3.

The weight topology optimization (WTO) analysis included the lumbar spine subjected to 21.5% for flexion/extension, 33% for bending, and 24% for axial rotation in the individual topology poetization (middle part). Top right part shows the reserved element after of WTO analysis. Bottom right part shows that the shape of a single posterior cage can be projected from the contours of half of the transverse cross-section plane and the sagittal plane.

To simulate the endplate morphologies in the elderly osteoporotic model, refer to the previous statistical result for the average endplate subsidence of 20 elderly patients with osteoporosis from L2 to L5. The endplate subsidence at 25%, 50%, and 75% of the endplate length in the coronal and sagittal planes were counted (Figure 2). All model endplates were modified based on the previous FE model according to the measured data to present the subsidence characteristics.

2.3. Osteoporotic cage design with weighted topology optimization

Standard topological optimization (STO) analysis provided in ANSYS is a technique for optimizing designs for structural objects with prescribed loads and boundary conditions. This method suggests the best material distribution to achieve the desired properties while satisfying the prescribed constraints. The optimization process removed elements with stress constraints to find the objective function for minimizing the cage volume. Elements were set up with an initial density. The L3 – L4 intervertebral disc under flexion (-Ry), extension (+Ry), bending (Rx), and axial rotation (-Rz) load condition performed STO individually to calculate if the intervertebral disc could be preserved to maintain sufficient strength (Figure 3 for Rx, Ry, Rz).

However, these individual simulations cannot reflect optimal structures for daily actives with multi-directional loads because in these four simulations, only a single load at the single simulated time was considered. Therefore, the WTO method was then performed for four different load cases with associated weights to recalculate the lightweight and maximum structural strengthening characteristics for an L3 – L4 disc. The WTO objective was to minimize compliance for different load cases and their associated weights[20]. The final WTO result summed the model compliance for all load cases. To simulate active lumbar spine movement during daily activities, we assumed that the lumbar spine would be subjected to 21.5% for flexion and extension, 33% for bending, and 24% for axial rotation[21]. The intervertebral disc structure was then obtained through the WTO result, and each element density was recalculated by summing each of the element densities under different loads by multiplying their corresponding weight coefficients, that is, Ei density = (Ei dflexion × 0.215) + (Ei dextension × 0.215) + (Ei dbending × 0.33) + (Ei dtorsion × 0.24) (Figure 3).

Where i is the element number, and Ei dflexion, Ei dextension, Ei dbending and Ei dtorsion, represent the density of the i element under flexion, extension, bending, and torsion, respectively.

The posterior cage top and side profiles were contoured based on the triangular mesh in the transverse and sagittal planes as suggested by the WTO analysis results to ensure that the vertebral cage maintained sufficient strength under physiological loads. The cage was simplified into a “banana” 25 mm in length, 16 mm in width, and 16.2 mm/12 mm in anterior/posterior height (Figures 3 and 4). Two CS-type and P-type forms were designed for the cage superior/inferior surface with respect to facilitating the follow-up biomechanical FE analysis. The CS-type cage curved surface feature was designed according to the previously obtained endplate morphology (Figure 4).

Figure 4.

Two CS-type and P-type forms were designed for implant between L3 and L4 spine body. Top right part shows the dimension of cage, that is, 25 mm in length, 16 mm in width, and 16.2 mm/12 mm in anterior/posterior height. Bottom right part shows the solid and mesh models of CS-type and P-type cages.

2.4. Biomechanical FE analysis

CS- and P-type cages were implanted along the L3 – L4 disc according to the posterior lumbar interbody fusion approach to perform the FE simulations. Two CS- and P-type cage models were also meshed using quadratic ten-node tetrahedral structural solid elements, and Ti6Al4V was assigned as the material property for the cage (Figure 4 and Table 1). Other material properties, load, and boundary conditions were the same as in the previous FE model generation and validation sections. Maximum von Mises stresses and stress distribution on the L3 interior endplate and L4 superior endplate were recorded for comparison to understand the mechanical responses between different implant combinations (Figure 4).

2.5. Lattice design, AM fabrication, and in vitro functional test

The CS-type cage internal cavity was filled with an array arranged in a gyroid lattice provided in Creo CAD software, designed as a spiral structure with 0.25 mm wall thickness for accepting cell clustering in a 4 mm³ unit cube. The lattice structure was found to stick together after printing because the hole size within the unit lattice was smaller than 4 mm³ (a limitation of the metal 3D printer). The cage was fabricated by a metal 3D printer (AM400, Renishaw, Gloucestershire, UK) using titanium alloy powder (Ti6Al4V powder with average grain size of 30 μm)[20] (Figure 5A). The 3D printing machine was operated with a laser power of 400 W, a scanning rate of 0.6 m/s, and an exposure time of 125 s. Completed cages were acid-etched to remove residual sandblast particles and then cleaned using ultrasonic oscillations (Figure 5A)[20].

Figure 5.

(A) 3D-printed CS-type cage. (B-D) The clamping device of in vitro tests under compression, compression-shear and torsion, respectively.

Static compressive, compressive-shear, and torsion tests conformity with the ASTM F2077-14 standard were performed to evaluate the CS-type cage mechanical resistance and judge whether compliance with FDA-recommended values was attained. The superior and inferior of each three AM cages were clamped using the specific jigs on the material test machine according to the ASTM F2077 for all test groups.

For the static compression/compressive-shear tests, a 500 N preload was applied and a crosshead speed of 6 mm/min was applied until achieving ultimate strength, that is, cage cracked/fractured or force decreased to below 20% of the maximum load (UH-F500 KNI, Shimadzu Corp., Kyoto, Japan) (Figure 5B and C). The yielding load, stiffness, and fracture pattern were recorded. The torsion was tested at a rate of 60°/min with a downward preload of 500 N until the cage was destroyed or the maximum torque value was reduced by 20% (Figure 5D). The yielding torque, stiffness, and damage were also recorded.

3. Results

Table 2 shows the average subsidence for L2 – L5 superior and inferior endplates at 25%, 50%, and 75% of the length at the coronal and sagittal planes, respectively, for a total of 20 osteoporosis patients with HU values between 70 and 120. The constructed FE model was designed to simplify the sagittal plane into a symmetrical plane. Subsidence of 25% and 75% of the length at the coronal plane were presented with the same value. Relevant data were input to reconstruct the FE model endplate. At the L3/L4 disk where the cage was placed, subsidence of 50% in the coronal and sagittal planes was 2.33 mm for L3 inferior endplate and 1.70 mm for L4 superior endplate (Figures 1 and 2, Table 2).

Table 2.

The average subsidence for L2 – L5 superior and inferior endplates at 25%, 50%, and 75% of the length at the coronal and sagittal planes, respectively

Endplate	Coronal plane (mm)			Sagittal plane (mm)
	25%	50%	75%	25%	50%	75%
L2 superior	1.30	1.85	1.30	2.12	1.85	1.79
L2 inferior	1.71	1.83	1.71	1.58	1.83	1.94
L3 superior	1.17	1.45	1.17	1.43	1.45	1.59
L3 inferior	2.21	2.33	2.21	1.84	2.33	2.09
L4 superior	1.60	1.70	1.60	1.61	1.70	1.76
L4 inferior	3.18	3.20	3.18	1.55	3.20	1.97
L5 superior	1.54	1.47	1.54	1.08	1.47	1.77
L5 inferior	2.97	2.99	2.97	1.59	2.99	2.30

The middle part of Figure 3 shows the analysis results from the L3/L4 intervertebral disc topology optimization under a single load. The gray triangular grid position is the place where the structure must be reserved. The bottom right part of Figure 3 shows that the shape of a single posterior cage can be projected from the contours of half of the transverse cross-section plane and the sagittal plane. Figure 4 shows the size and implantation positions for the CS- and P-type cages designed in this study. The bottom right part of this figure also shows the FE mesh models for these two cages.

The biomechanical FE analysis result showed that the maximum stress values at the L3 inferior and L4 superior endplates under flexion, extension, lateral bending, and torsion for the P-type cage implantation model were all higher than those for the CS-type cage (Figure 6). Fracture or cracking might occur for the P-type cage implantation because the maximum stresses found in the endplates exceeded the ultimate strength value when the inferior part of L3 was subjected to flexion and torsion loads, and the superior part of L4 was subjected to flexion and bending loads. Figure 7 showed the stress distribution for the L3 inferior and L4 superior endplates under all load conditions for the CS-type and P-type cage implantations.

Figure 6.

The maximum stress values of CS-type and P-type cages at the L3 inferior (A) and L4 superior (B) endplates under flexion, extension, lateral bending, and torsion.

Figure 7.

The von Mises stress distributions of L3 inferior and L4 superior endplates for CS-type and P-type cages under all load conditions.

Table 3 lists the yielding load and stiffness of our designed CS-type cage and the optional ISO 23089 standard acceptance criteria under compression, compression-shear, and torsion. Figure 8 shows the corresponding fracture types under three load conditions.

Table 3.

The biomechanical in vitro test result of the yielding load and stiffness of our designed CS-type cage and the ISO 23089 standard acceptance criteria under compression, compression-shear and torsion

Test model	Comparative parameter	ISO 23089	CS-type cage	Safety factor (CS-type/ISO23089)
Static axial compression	Yield load (N)	6317	134643	21.3
	Stiffness (N/mm)	5914	70080	11.8
Static compression-shear	Yield load (N)	1996	23904	12.0
	Stiffness (N/mm)	1435	19841	13.8
Static torsion	Yield load (N-m)	7	19.8	2.8
	Stiffness (N-mm/degree)	1	3.5	3.5

Figure 8.

The CS-type cage fracture pattern after in vitro test: (A) ISO view and (B) back view.

4. Discussion

The FE analysis result found that the maximum stresses in the superior and inferior endplates using the P-type cage were relatively high regardless of the type of load conditions, and the stress concentration was also relatively serious. Figure 9 shows the contact status of the two cages and endplates, which can explains why the P-type cage and endplate can easily cause point contact that obviously generates stress concentration. The CS-type cage and endplate were in surface contact with a larger contact area, enabling the stress to be transmitted more uniformly. These results were consistent with the literature and can be explained by the maximum stress location under four different loads, as shown in Figure 7[22,23]. Figure 7 shows that the stress concentration and maximum stress positions of the endplate using the P-type cage can be found in the contact point (star symbol) between the endplate and the cage regardless of the type of applied loads. The maximum stress value for the P-type cage was significantly higher than that for the CS-type cage. The endplate stress concentration using the CS-type cage was less obvious, and it was in a position with larger contact area under different applied loads, that is, at the anterior side under flexion, at the posterior side under extension, and at the lateral side under bending and torsion.

Figure 9.

Status of contact areas between cage and endplate for CS-type and P-type cages under all load condition simulations. Red ovals/circles indicate the positions of fractures or damages. Bottom left: two red oval regions show the possibility superior/inferior contact areas of the CS-type cage; bottom right: four red circle regions show the possibility of superior/inferior contact points of the P-type cage.

This study screened elderly osteoporosis patients to obtain the endplate curved surface characteristics, which are more in line with the fit of the general population of osteoporosis patients for the cage and the endplate. Although the curved surface design of our CS-type cage may not be able to achieve 100% endplate-conformation for each patient, that is, patient-specific endplate morphology can match compatibility. However, a CS-type cage with enhanced load-bearing surfaces can be applied in clinical practice for design and manufacture purposes. The cage complex surface can be manufactured using traditional machining or 3D printing fabrication if the internal lattice design is not considered. According to the Food and Drug Administration (FDA) regulations, a spine cage must pass 5 million fatigue functional tests, such as compression, compression-shear, and torsion, before it can be marketed. A patient-specific design is unlikely to perform relevant mechanical tests alone due to excessive variation in the geometric size. Conversely, our CS-type cage is likely to be standardized and defined as the worst cage (usually the smallest cage) to perform the mechanical tests required by the FDA.

In general, STO can only calculate the structural optimization under a single load. However, WTO needed to be applied in this study to solve multi-directional spine load conditions in daily life. The WTO is represented by values between 0 and 1 for each condition, corresponding with proportions of different load conditions. In the present study, 21.5% for flexion and extension, 33% for bending, and 24% for axial rotation correspond to values of 0.215, 0.33, and 0.24 of weight coefficient for each element, respectively[20,21]. Therefore, our designed cage structure (gray mesh found in Figure 2) was calculated by multiplying the respective weight coefficients of different loads to the corresponding STO result (Figure 2). This kind of protocol using WTO considering different load percentages can also be a new mode for designing other cages, such as anterior lumbar interbody fusion (ALIF) and transforaminal lumbar interbody fusion (TLIF).

The combination of internal cavity lattice design in the cage structure has been proven to increase the ingrowth capability of bone cells with strong stabilization. However, there are many lattice design parameters, such as porosity, pore size, and unit size, that still cannot be confirmed to integrate with implant design[9-13]. At present, we only considered the spiral lattice provided by the CAD software. Other lattice design parameters can be further considered in the future. However, the complex contour surface combined with the internal cage cavity lattice design cannot be manufactured by traditional mechanical cutting. Three-dimensional printing techniques are well established for building complex 3D constructions from CAD models. 3D printing techniques have great potential to solve the problems of creating a porous (lattice) surface coating on dense titanium and porous titanium body[9-13]. Therefore, this study utilized metal 3D printing to fabricate our designed CS-type cage to perform the following functional tests. Our 3D printer laboratory was approved by ISO13485 quality management system (Certificate Number: 1760.190828) to ensure that implants manufactured by 3D printing can provide a practical foundation to meet the regulations as well as demonstrate a commitment to safety and quality.

Although the current in vitro mechanical experiment in this study only considers the static state, the results found that the yielding load and stiffness under all load conditions were much higher than the recommended ISO 23089 values[24]. This document specifies requirements for the mechanical assessment of spinal intervertebral body fusion devices (IBFDs) used in spinal arthrodesis procedures. Table 3 presents optional acceptance criteria for yielding load and stiffness for all loads derived from aggregated mechanical test data from IBFDs previously cleared by the U.S. FDA through the 510(k) process. The values in Table 3 represent the 5^th percentile of the range of devices surveyed. This document was also encouraged to incorporate a safety factor to define acceptance criteria. We found that the safety factors in our cage were relatively small under torsion conditions, and the largest under compression conditions. The fracture pattern of our newly designed cage with applied loads reached ultimate strength. No damage was visually found under the static compressive test. The pillar in the middle of the cage was obliquely fractured due to the shear force under the compressive-shear test. Minor wear was found on the corners, possibly caused by friction between the cage and the fixture under torsion (Figure 8).

5. Conclusion

This study integrated WTO and FE analysis to design a posterior lumbar interbody fusion cage with appropriate structural strength and anatomically curved surface for stress transfer and internal lattice design for bone ingrowth based on the osteoporotic endplate morphology. The FE analysis result showed that the maximum endplate stress values under all daily activities for the plate P-type cage with point contact implantation model were all higher than those for the anatomically CS-type cage with surface contact. The newly designed osteoporotic anatomical cage needed to be manufactured using 3D printing technique. The in vitro biomechanical functional test confirmed that the designed cage met 95% of the standard requirements for ISO 23089 standard listing.

Funding

This study is supported in part by MOST project 109-2622-B-010 -005 and 110-2221-E-075-004, Taiwan.

Conflict of interest

The authors declare that they have no conflict of interest.

Author contributions

Conceptualization: Chi-Yang Liao, Chum-Li Lin

Investigation: Shao-Fu Huang, Chi-Yang Liao

Methodology: Shao-Fu Huang, Yi-Ting Chan, Zi-Yi Li

Resources: Chun-Ming Chang, Chun-Li Lin

Writing – original draft: Chun-Li Lin

Writing – review & editing: Shao-Fu Huang, Chi-Yang Liao, Chun-Li Lin

Consent for publication

Not applicable.

Availability of data

Not applicable.