RESEARCH ARTICLE
Christopher John NASSAU, N. Scott LITOFSKY, Yuyi LIN
Analysis of spinal lumbar interbody fusion cage subsidence
using Taguchi method,
finite element analysis, and artificial
neural network
© Higher Education Press and Springer-Verlag Berlin Heidelberg 2012 Abstract Subsidence, when implant penetration induces failure of the vertebral body, occurs commonly after spinal reconstruction. Anterior lumbar interbody fusion (ALIF) cages may subside into the vertebral body and lead to kyphotic deformity. No previous studies have utilized an artificial neural network (ANN) for the design of a spinal interbody fusion cage. In this study, the neural network was applied after initiation from a TaguchiL18orthogonal design array. Three-dimensional finite element analysis (FEA) was performed to address the resistance to subsidence based on the design changes of the material and cage contact region, including design of the ridges and size of the graft area. The calculated subsidence is derived from the ANN objective function which is defined as the resulting maximum von Mises stress (VMS) on the surface of a simulated bone body after axial compressive loading. The ANN was found to have minimized the bone surface VMS, thereby optimizing the ALIF cage given the design space. Therefore, the Taguchi-FEA-ANN approach can serve as an effective procedure for designing a spinal fusion cage and improving the biomechanical properties. Keywords anterior lumbar interbody fusion (ALIF), artificial neural network (ANN), finite element, interbody cage, lumbar interbody fusion, subsidence, taguchi method
1
Introduction
Cage design for vertebral body or disc reconstruction has continually been of interest since the work of Bagby (1988), in which he used a stainless steel implant with autogenous bone graft in horses to encourage bone growth through the implant, demonstrating to the spine surgery community its potential use in the human spine [1]. Since then, cylindrical, boxed, rectangular, and in more recent years, standalone screw-cage devices have been developed [2–4]. These devices have been made of various materials, including polyetheretherketone (PEEK), carbon-fibre rein-forced PEEK, titanium, and even bioabsorbable polymers like poly-L, D-lactic acid (PLDLA) [5–7]. Cages offer biomechanical advantages of supporting axial load, providing initial segmental stability, and restoring the height of the patient’s disc and anterior vertebral column. Spinal fusion surgery includes posterior lumbar inter-body fusion (PLIF), a procedure where entry is made through the patient’s back, transforaminal lumbar inter-body fusion (TLIF), a refined PLIF from more the side of the spinal canal through a midline incision in the back, and anterior lumbar interbody fusion (ALIF), where entry is from the front of the body, usually through the lower abdomen or side. After the incision, and the muscles and blood vessels have been retracted, the disc material is removed. The surgeon then performs a fusion by inserting bone graft, often within and around a cage, and uses pedical screws, and/or rods for added stability. ALIF is advantageous in that both the back muscles and nerves are not disturbed. Anterior graft placement puts the bones in compression, promoting fusion. Large implants may be used with ALIF, adding initial segmental stability. Typical cages are much smaller for other procedures. PLIF cages are usually boxed, bullet, or cylindrical and TLIF cages are usually in a rounded or “banana” shape [8]. Here the implant curvature follows the anatomic shape of the endplates, aiding in insertion andfinal placement. Received May 10, 2012; accepted July 5, 2012
Christopher John NASSAU, Yuyi LIN (
✉
)Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
E-mail: LinY@missouri.edu N. Scott LITOFSKY
Division of Neurological Surgery, University of Missouri, Columbia, MO 65211, USA
Potential problems with ALIF include vascular injury, retrograde ejaculation, ileus, pseudarthrosis and subsi-dence. Subsidence, penetration of the cage device into the inferior vertebral body with potential collapse of the vertebral body, can lead to fusion failure. Subsidence may stem from the surgical approach, cage design, or the bone mineral density [9–14]. The implant is often designed with ridges, spikes, or threads on its surface to help retard migration or extrusion. Rarely, mechanical failure of the cage may occur. Subsidence failure not only can be very painful, but can cause an overall mechanical instability of the spinal segments. Pearcy et al. (1983) showed that graft surface area of less than 40% of the surface area of the endplate showed a significant increase in subsidence [15]. Zander et al. (2002) found similarly that the increases in bone graft contact surface and bone graft stiffness caused a decrease and increase in vertebral body endplate stress respectively [16].
Spinal biomechanics withfinite element analysis (FEA) is in its infancy. Belytschko et al. (1973) made an early mathematical model for force analysis of the human vertebral column [17]. FEA can also be used to study compressive forces on intervertebral discs and vertebral bodies [18–21]. With advancement in computer technol-ogy, FEA has been used with increasing frequency for evaluation, complementing experimental design methods. Therefore, FEA may be used for the design of an interbody fusion cage. Because small design input changes make large output differences in FEA, process control para-meters should be evaluated with known methodologies to aid in optimization.
Taguchi statistical methods were developed by Genichi Taguchi to improve the quality of manufactured goods by robustly designing them, which came about in the 1950s and after [22,23]. Traditional statistical experiments consisted of changing one variable in an experiment, while keeping the other variables at predetermined levels to get results for a single change made. Taguchi methods utilize two-, three-, as well as combination-level fractional factorial designs. The advantage of a fractional factorial design in general is that it can minimize the number of experimental runs. Taguchi expanded on the methodology of previously known statistical methods with the goals to
control the quality and cost of manufacturing design. The result was making the designs less sensitive to outside and uncontrollable noise versus other methods. There are a variety of orthogonal array choices from Taguchi methods based on the particular analysis being done, ranging from few to many variables. Taguchi methods have been used with FEA to help simplify the design process [24], and recently have been applied to musculoskeletal devices [25– 34].
Much like a biological network, an artificial neural network (ANN) utilizes a network of neurons, which could be implemented by hardware or software only, to perform a specific function or task. However the difference in an ANN is that the function of artificial neurons is to perform the desired task as well as estimate a cost. ANNs can be used to gain an understanding of geometric designs without the need to create an enormous amount of models, a tedious and arduous process. In addition, ANNs can reduce the time and effort spent in model development and computation time. In order to properly utilize the benefits of an ANN, the program must be taught, as learning in the program is done through finding connections, which in turn minimize the cost of each path. Also, there are three main types of learning developed for ANNs: supervised, unsupervised, and reinforced learning [35]. Generally, supervised learning is used when inputs and labels, or outputs, are explicitly present and the goal is to find the path to the desired label, while unsupervised learning is concerned with how an agent might hope to reach a particular output given an environment, in order to maximize reward.
In this study, we address ALIF cage design, considering the impact of FEA, Taguchi methodology, and ANN. Cages should be designed multiobjectively, to resist both subsidence and migration, but subsidence resistance only will be considered in this study to simplify the process. Hsu et al. (2010) analyzed a cylindrical vertebral body replacement device to ovoid penetration into the bone [32], but addressed a spike design, and did not utilize a neural network, which has been used for designing spinal pedical screws [26]. Yang et al. found with Taguchi and FEA that an increase in endplate von Mises stress (VMS) was linked strongly to a smaller contact region between the inner and
outer diameter of a cervical ring cage [34], thereby increasing the likelihood for subsidence. We hypothesize that anterior fusion cage design can be optimized to resist subsidence with FEA in conjunction with ANNs and the Taguchi method. Supervised learning will be used, as the inputs are known explicitly from the array, as well as their resulting FEA responses for each trial.
First, the important device parameters are identified and arranged in a Taguchi matrix to unbiasedly organize the variables. Next, each run will encompass different parameter sets which correspond to trials, where each trial yields a response from the compressive loading. The matrix and responses are then entered into the ANN and observed. After that, retraining of the ANN occurs with randomly generated models, and it is checked that FEA can replace the ANN. Finally, the objective function is obtained for minimizing the maximal bone surface VMS.
2
Materials and methods
2.1 Finite element analysis
The program SolidWorks 2011 (Dassault Systèmes Solid-Works Corporation, Waltham, MA, USA) was used for the solid modeling of the cage models and bone body. The models were next imported into Abaqus/CAE 6.9 (SIMULIA, Providence, RI, USA). The bone body was assumed to simulate the inferior vertebral body with osteopenia. The superior vertebral body was removed as the fusion case was not considered, thus the bone could not transfer the load to the implant. The top half of the implant was removed, and it was assumed that a 1200 N uniform axial compressive load had transferred onto the implant [11]. The upper part of the inferior bone body and ridges
were finely meshed. Surface-to-surface contact elements were used for the interface between the spinal fusion cage and the surrounding bone with frictionless contact. Boundaries were added to the bottom surface of the bone body and around the device in the y-direction, as slip distance/micromotion was not considered. The Poisson’s ratio of the underlying cancellous bone, cortical bone, and implant were set to 0.3. The elastic modulus of the bone body and the partitioned 0.5 mm cortical bone surface were 137.5 MPa and 12.0 GPa respectively, while the implant ranged from 3.6 to 110.0 GPa to represent PEEK and Ti6Al4V. The implant height not including ridges was kept
constant, and would be 6 mm for thefinal device. The bone dimensions were set at 40 mm 40 mm 50 mm and the outer implant dimensions set at 34 mm 26 mm. The dimensions for the graft had been determined by changing the width between the outer and inner dimensions of the two spaces from 6, 4.75, and 3.5 mm for the corresponding smallest to largest graft dimensions.
2.2 Taguchi method
The Taguchi method has been used to arrange the variables for analysis, reduce the number of experimental runs, and serve as training for the ANN. In this study, six design variables of the ALIF cage were considered, including the cage material (CM), ridge height (RH), ridge width (RW), ridge oblique (RO), ridge rows (RR), and graft area (GA). The design space for the RH was made in the general range of interface heights for commercially available devices, as well as the outer cage dimensions. The CM ranges are chosen from two readily available material options for interbody devices. The RR values are evenly spaced across each model, where the ends of the cage width touch the ends of the ridge base.
2.3 Artificial neural network
Supervised learning is used in the employment of the ANN, more specifically the method of back propagation, where the cost of a function is already known or can be computed and is utilized for the design. Using this method the ANN is taught employing the set of variable changes. The cost or outputs, which are used as learning, are the outputs from each of the runs for the maximal VMS on the simulated bone body. In this method the weights of the connections are updated at each iteration of the training set to more accurately predict the cost of each function set.
The architecture in this program is triple layer with six input neurons, the CM, RH, RW, RO, RR, and the GA and one output neuron, the maximal bone VMS. The hidden layer uses three neurons where a sigmoid function serves as the activation function [36]. The number of learning iterations used is 10,000 and the learning rate is 0.5 in order to control the learning of the ANN and reduce the probability for the program to be over trained or stuck in a local minimum or maximum. The momentum for learning of the ANN is set to 0.5, which can provide a faster
convergence in the training set. Validation of the ANN is done by removing two of the function sets with cost and testing the ANN with this data to determine if the error is too large. In addition to the created sets, 9 randomly selected additional designs were used to further train and check the ANN. To validate the ANN, after the 9 sets were run in FEA, the values were entered and checked in the ANN. Thus, the FEA was able to replace the ANN in the intermediate analysis stages. From the total 27 sets, an optimal design is generated using a gradient search. Coding of the ANN is accomplished through Python 2.7 (Python Software Foundation).
3
Results
3.1 Finite element analysis
Based on the original Taguchi L18 array, models were
designed and the FEA studies were performed. After that, running the ANN gave output values, which were randomly selected, and reentered back into the program Fig. 3 The six design parameters for the interbody cage, with increasing levels in order from top to bottom for the cage material and clockwise for the other variables
as training information. From there, an optimum O3 was found, and two additional models changing the graft area were developed. The solution time averaged 30 to 45 minutes for each model. Subsidence of the interbody device was calculated from the largest value of VMS on the bone. After optimization, the FEA models showed improvements of 16.0%, 5.7%, and 55.9% over the original L18, the additional training runs and the worst
initial design, respectively. 3.2 Artificial neural network
The ANN was used to predict the objective function of resulting subsidence on the simulated bone body. Calcula-tion errors from the ANN output ranged from 0.6%–1.0%. The predictions made for implant subsidence by the ANN were closely related to that of the FEA models, where average errors of 2.24%, 4.27% and 4.34% were found of the original L18, additional models, and optimum
para-meters while varying GA respectively. When the ANN is fully trained, runtime is approximately 10 min.
The solution with the lowest bone VMS was found to be O3 at approximately 24.86 MPa. Because a larger graft-to-host bone contact is desired to promote healing, it was sought also to have the ANN predict additional solutions, O1 and O2, which used the same parameter values as O3 except for GA. It was found that O1 (highest GA) and O2 (middle GA) had bone body surface VMS values of 29.70 and 26.97 MPa respectively. Increasing the GA by approximately 49.8% and 31.3% corresponded to the likelihood of subsidence increasing by 16.3% and 7.8% for O1 and O2 respectively versus O3.
4
Discussion
For proper spinal implant design evaluation, large differences in design comparison, such as a cylindrical versus a boxed cage, or a cage with dynamic interface differences (large spikes or notches versus continuous ridges) should be avoided. Side-by-side comparisons of vastly different designs may lead to inconsistent conclu-sions about device design variables in relation to performance. The use of numerical methods for implant design has been widely used. However, application of an ANN to the design of a spinal fusion cage has not been previously described. Our hypothesis was supported in that we were able to optimize an anterior fusion cage design to resist subsidence with FEA in conjunction with ANNs and the Taguchi method. Design O3 yielded much lower bone stress than initial designs. We also found that designs O1 and O2 were approximately the same or better respectively than the best initial designs.
FEA is a useful tool, which allows seemingly similar designs to be evaluated, where slight changes can make large output differences, such as local VMS. In spite of its utility, FEA is very time consuming, and making minute changes in a design to isolate variables would equate to a lack of an efficient use of time. With Taguchi, ANN, and FEA, the ANN yielded the geometric values to produce the lowest stress on the bone body given the values. Chao et al. found that spinal pedical screws had a higher bending and pullout strength when compared to commercial devices with the same geometric limits [26]. For cage design, it may be of interest to compare available devices with an optimized cage given similar interfacial pattern and space. Fig. 4 Architecture of the ANN with six input parameters, three hidden layers, and one objective of the resulting subsidence, where minimizing the maximal VMS corresponds to improving subsidence resistance
Commercial ALIF devices are most often designed with ridge or spike profiles, but sometimes contain hooks or screws. Careful scrutiny should be used when evaluating biomechanical results from comparisons of devices of greatly differing shape, cage material, footprint, and interface, and the suggested clinical implications.
Methodical device optimization takes a long time tofind the best design. Therefore, ANN was utilized to develop a model to reach the desired objective. Although FEA is sophisticated in evaluating designs, it is not convenient for device optimization, especially for large degree of freedom models. Design of a musculoskeletal device requires many numerical calculations. A simple additive model would not
be suitable as a predictor, and may or may notfind the best solution. ANN is versatile, efficient, and may lean towards continuous solutions. As in this case though, the boundaries set forth resulted in the best solution coming from minimizing or maximizing respective parameter values. If the same time is spent on design between ANN and a less sophisticated method, most likely the ANN will yield a biomechanically superior design, especially when model complexity increases and addi-tional loads are taken into account [30].
Several limitations exist with this study. First, since ANN accuracy is dependent on the amount of training data, if more accuracy is desired, a significant amount of time Table 1 The design variations of the ALIF cages for the Taguchi array learning process, T1–T18, the additional runs which replaced the ANN and served as more training, A1–A9, and the optimum parameters while varying GA, O1–O3
Run Cage material/GPa Ridge height/mm Ridge width/mm Ridge oblique/(°) Ridge rows Graft area/mm2
T1 3.600 0.700 1.000 90.000 7 224.000 T2 3.600 0.700 1.450 97.000 9 325.875 T3 3.600 0.700 1.900 104.000 11 446.500 T4 3.600 1.050 1.000 90.000 9 325.875 T5 3.600 1.050 1.450 97.000 11 446.500 T6 3.600 1.050 1.900 104.000 7 224.000 T7 3.600 1.400 1.000 97.000 7 446.500 T8 3.600 1.400 1.450 104.000 9 224.000 T9 3.600 1.400 1.900 90.000 11 325.875 T10 110.000 0.700 1.000 104.000 11 325.875 T11 110.000 0.700 1.450 90.000 7 446.500 T12 110.000 0.700 1.900 97.000 9 224.000 T13 110.000 1.050 1.000 97.000 11 224.000 T14 110.000 1.050 1.450 104.000 7 325.875 T15 110.000 1.050 1.900 90.000 9 446.500 T16 110.000 1.400 1.000 104.000 9 446.500 T17 110.000 1.400 1.450 90.000 11 224.000 T18 110.000 1.400 1.900 97.000 7 325.875 A1 5.142 1.385 1.007 93.316 11 243.085 A2 4.697 1.399 1.040 90.524 11 236.253 A3 5.066 1.391 1.002 90.003 11 240.383 A4 3.678 1.381 1.006 93.699 11 399.683 A5 4.082 1.396 1.003 95.104 11 227.466 A6 5.007 0.714 1.003 92.645 11 418.706 A7 3.600 0.700 1.900 104.000 11 224.000 A8 3.600 1.391 1.002 90.003 11 240.383 A9 3.600 1.400 1.002 90.000 11 224.000 O1 3.600 1.400 1.000 104.000 11 446.500 O2 3.600 1.400 1.000 104.000 11 325.875 O3 3.600 1.400 1.000 104.000 11 224.000
could be spent on FEA development. Also, when designing a spinal cage, both the load-induced subsidence as well as pullout strength should be considered. Previously, others showed that pullout was maximized for a spiked vertebral body replacement device (varying spikes conically and pyramidically) [31] using similar parameters as in this study. The only difference was a slight variation in interface width, thus inferring that this implant was adequately designed to prevent extrusion into the spinal canal also. The trend for ridge design corresponded to the study by Hsu et al. (2010) of spikes in a cylindrical vertebral body replacement device, where minimizing the width of the interface, increasing the height, in combina-tion with increasing the obliquity, helped to minimize the subsidence [32]. In this situation, the anatomic relation-ships were simplified having used a bone body in lieu of scanned vertebral segments.
Small geometric changes play large effects in bone stress, especially with increasing structural complexity of the device. Adding clinical objectives to geometric design also makes using an ANN more attractive. For instance, a multiobjective ANN could be utilized to design a spinal fusion cage for resistance of migration and subsidence, as the design parameters do not strongly conflict. For bone screws, bending and pullout may be assessed simulta-neously. Engineers may also employ other optimization
methods, such as multiple linear regression for improving device biomechanics. ANN may have more applicability for complex devices than multiple linear regression. The latter method showed decreased reliability in the more complicated pedical screw over the tibial locking screw, while the ANN showed capacity for developing both objective functions [30]. Cages have very diverse bone-implant interface conditions; therefore further study may reveal ANN as applicable to a variety of cage designs.
ANNs, which are known tofind trends between complex input variables, have successfully been utilized in design-ing an ALIF cage for subsidence resistance, while maintaining rigidity. The geometric design of a spinal fusion cage is related to the clinical implications. The ANN revealed that the optimum parameters given this design space should reach the ends of these bounds, where CM, RW, and GA should be minimized, and RH, RO, and RR should be maximized. This design corresponded to O3, which yielded the least bone body surface stress. The FEA models correlated strongly with the ANN and could be used to predict the resistance to subsidence.
Acknowledgements The authors would like to thank Dr. Hao Li, Associate Professor of Mechanical and Aerospace Engineering, the Departments of Biological and Mechanical and Aerospace Engineering for financial support, and members of the Nanostructured and Biomedical Materials Laboratory.
Fig. 5 Comparison of FEA and ANN of the ALIF cages for the Taguchi array learning process, T1–T18, the additional runs which replaced the ANN and served as more training, A1–A9, and the optimum parameters while varying GA, O1–O3
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