Connection in Human Lumbar Spine: Finite Element Preliminary Study
COPS CYPS
Fig 3.4 Fatigue life cycles of COPS and CYPS under cyclic bending force of 150 N
4 Discussion
In this study, an innovative-developed feasible computational approach was introduced to study the fatigue life of the interactions between the PS and vertebral bony tissues (or synthetic bony tissues). Compared with the traditional experimental approaches, the computational approach introduced in this study had advantages of lower cost and higher efficiency. It is challenging to validate the fatigue prediction method introduced in this study because great inter-subject variations exist in the material properties and anatomies of spinal bony tissues (DREISCHARF et al., 2014). Thus, the modeling method in this study was validated against experimental results obtained from polyurethane foam with known and stable material properties instead of the cadaveric vertebra sample. Since the fatigue calculation was based on the stress/strain history of FE elements obtained from the FE analysis, the accuracy of the FE model is critical. Validated FE models of the vertebra and the PSs from our
1,00E+00
previous study were employed in this study. Besides, SWT fatigue equation indicated that the fatigue life of the material is related with the mean stress in the material during the entire loading process instead of the maximum stress at any particular time point. The magnitude of the loading condition alone is not sufficient to accurately predict the fatigue life of one type of material. The frequency of the loading and the loading history during the entire loading process are required for fatigue analysis as well.
In the quasi-static cantilever bending test between the PS and the polyurethane foam, the von Mises stress and deflection of the PSs predicted in this study were consistent with the results reported by CHAO et al. (2008). Under identical loading conditions, COPS had significantly smaller von Mises stress and deflection. In order to test the fatigue life predicting capability of the proposed method, fatigue life cycles of the validated PS-foam FE models were calculated under identical loading condition with mechanical tests performed by CHAO et al. (2008). The immediate failure of the PS is related to the von Mises stress at failing time point whereas the fatigue failure of the PS is related to the mean stress the PS withhold (CHAO et al., 2008). Thus, it is possible that the immediate failure and the fatigue failure will occur at different sites on the PS under certain type of loading. To illustrate this point, von Mises stress contour plot of CYPS under bending force of 400 N and fatigue damage contour plot of CYPS under cyclic bending force of 400 N are shown in Fig 4.1. The sites with maximum von Mises stress and the sites with least fatigue life cycles were close yet not identical. This suggested that fatigue behavior of the PS should be studied separately from the immediate holding capability, which should be thoroughly considered in the design process of PS. In light of the fact that fatigue damage of PS could not be fully eliminated in the post-surgical subjects, fatigue failure of the PS should also be considered during clinical practice (CHAO et al., 2008). In clinical observations, fatigue damage of the PS commonly occurred at the body-head junction of the PS (CHAO et al., 2008; BRASILIENSE et al., 2013). The fatigue life cycles of PS predicted in this study were within one standard deviation range of the mean value of those obtained from mechanical tests (CHAO et al., 2008). However, it is worth noticing that the fatigue life cycles predicted in this study (fatigue life cycle of CYPS under cyclic bending force of 400 N is 265) was close to the lower boundary of the range (290±35) reported by CHAO et al. (2008). The reason might be due to the difference between the fatigue failure criteria applied in this study and in the mechanical test (CHAO et al., 2008). CHAO et al. (2008) considered fatigue failure of PS when the displacement of the actuator was beyond 10 mm or when the number of testing cycles was more than one million whereas the fatigue life cycles of PS predicted in this study was the fatigue life cycle of the first failing element. If the fatigue failure process could not finish within short period of time, considerable difference would exist between the simulation result in this study and the experimental observation. However, based on experimental data reported by CHAO et al. (2008), no plastic deformation of the PS was observed and after certain amount of loading cycle, sudden fatigue damage was able to finish within short period of time, which explained why the fatigue life predicted in this study was still reasonably close to the experimental result.
(a)
(b)
Fig 4.1 CYPS Contour plots: (a) von Mises stress (MPa) under static bending force of 400 N; and (b) fatigue life cycles under cyclic bending force of 400 N
In the PS-vertebra bending test, since the fatigue life cycles of the bony tissues were significantly smaller than those of the PS, fatigue failure of the PS-bone interaction was considered to be the bony tissues. As the magnitude of cyclic bending load linearly increased, the fatigue life of the bony tissues exponentially reduced. This suggested that long-term high loads on post-surgical spine would greatly reduce the fatigue life of the PS-bone bond, which increased the risks of PS loosening and even fatigue breakage. As shown in Fig 4.2, the fatigue failure occurred first at the elements around the outer edge of the screw hole in the vertebra for both COPS and CYPS. Fatigue life cycles of the elements in vertebra tend to be more uniformly distributed along the outer edge when inserted with COPS than those when inserted with CYPS, which might be the potential reason for the better fatigue performance of COPS.
(a)
(b)
Fig 4.2 Contour plots of fatigue life cycles under cyclic bending forces of 75 N, 100 N, 125 N, and 150 N: (a) COPS; and (b) CYPS
One limitation of this pilot study was that deterministic FE model of vertebra was utilized. To better predict the realistic fatigue behavior of the PS-bone interaction, subject-specific material properties are recommended (DREISCHARF et al., 2014), which could be partially obtained from the medical image. The computational approach introduced in this study matched well with the experimental study for the PS, where the sudden fatigue occurred after certain amount of loading cycles.
Greater error was assumed when gradual fatigue failure took place. However, in the literature, most experimental fatigue studies for the PS-vertebra interactions were designed to reach fatigue failure in a short period of time. Thus, the computational approach introduced in this study was able to act as a reasonable alternative for the experimental study. Due to errors introduced by the inter-subject variations in the material properties of the spinal tissues, the exact values of the fatigue life cycles of the vertebra might not necessarily apply to all the subjects. However, the method introduced in this study was able to provide general trend of the fatigue performance of the PS-bone interaction, which was also the main objective of this method. In this study, only one vertebra inserted with one PS was tested under simplified uniaxial loading conditions to study the fatigue life of PS-vertebra interaction, which was set to be identical with the experimental study in the literatures (CHAO et al., 2008;
BRASILIENSE et al., 2013; AKPOLAT et al., 2016). However, PS was subjected to complex multiaxial loading conditions including both force and bending moment during physiologic spinal loading environment. In this study, the only one set of deterministic input parameters were employed for the fatigue analysis. In the future study, sensitivity analysis will be performed for the fatigue analysis input parameters.
Furthermore, the fatigue analysis method introduced in this study will be utilized to study the fatigue behavior of PS-bone interaction within multi-segment spine FE models under physiological spinal movements. It is of clinical value to compare the fatigue behaviors of the PS-bone interaction with different surgical plans and under different types of spinal movements.
5 Conclusion
This study introduced one feasible computational approach to predict the fatigue behavior of the screw-bone interactions. The predicted fatigue life cycles in this study were validated against the experimental data in the literature. The fatigue life prediction method introduced in this study is a reasonable alternative for the screw-bone experimental test. By comparing the contour plots of the von Mises stress and fatigue life cycles on the PS, this study suggested that the sites with maximum von Mises stress and most likely fatigue failure are not consistent. Thus, fatigue damage of PS should be studied separately from the immediate breakage of the PS. In the PS-vertebra bending test, small amount of loading increase will exponentially reduce the fatigue life of the screw-bone bond, which suggested that post-surgical patient should avoid applying high load on the spine for a longer serving life of the spinal implant. In the future work, the modeling method validated in this study will be utilized to study the fatigue behaviors of the screw-bone interaction under physiological spinal loading environment within multi-segment spine FE models.
List of references
Akpolat, Y. T.; Inceoglu, S.; Kinne, N.; Hunt, D.; Cheng, W. K.: Fatigue performance of cortical bone trajectory screw compared with standard trajectory pedicle screw, Spine 2016, 41(6), pp.E335-E341.
Amaritsakul, Y.; Chao, C. K.; Lin, J.: Biomechanical evaluation of bending strength of spinal pedicle screws, including cylindrical, conical, dual core and double dual core designs using numerical simulations and mechanical tests, Medical Engineering &
Physics 2014, 36(9), pp.1218-1223.
Brasiliense, L. B. C.; Lazaro, B. C. R.; Reyes, P. M.; Newcomb, A.; Turner, J. L.;
Crandall, D. G.; Crawford, N. R. : Characteristics of immediate and fatigue strength of a dual-threaded pedicle screw in cadaveric spines, The Spine Journal 2013, 13(8), pp.947-956.
Chao, C.-K.; Hsu, C.-C.; Wang, J.-L.; Lin, J.: Increasing bending strength and pullout strength in conical pedicle screws: Biomechanical tests and finite element analyses, Journal of Spinal Disorders & Techniques 2008, 21(2), pp.130-138.
Dreischarf, M.; Zander, T.; Shirazi-Adl, A.; Puttlitz, C. M.; Adam, C. J.; Chen, C. S.;
Goel, V. K.; Kiapour, A.; Kim, Y. H.; Labus, K. M.; Little, J. P.; Park, W. M.; Wang, Y.
H.; Wilke, H. J.; Rohlmann, A.; Schmidt, H.: Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together, Journal of Biomechanics 2014, 47(8), pp.1757-1766.
Elder, B. D.; Holmes, S. L.; Goodwin, C.; Kosztowski, T. A.; Lina, I. A.; Locke, J. E.;
Witham, T. F.: The biomechanics of pedicle screw augmentation with cement, The Spine Journal 2015, 15, pp.1432-1445.
Fatihhi, S. J.; Harun, M. N.; Kadir, M. R. A.; Abdullah, J.; Kamarul, T.; Ochsner, A.;
Syahrom, A.: Uniaxial and Multiaxial Fatigue Life Prediction of the Trabecular Bone Based on Physiological Loading: A Comparative Study, Annals of Biomedical Engineering 2015, 43(10), pp.2487-2502.
Hight, T. K.; Brandeau, J. F.: Mathematical modeling of the stress-strain rate behavior of bone using the Ramberg-Osgood, Journal of Biomechanics 1983, 16(6), pp.445-450.
Kang, D. O.; Park, K.; Heo, S. J.; Ryu, Y. I.; Il Jeong, J.: Development and Application of VPG Simulation Technique based on Equivalent Virtual Road Profile, International Journal of Precision Engineering and Manufacturing 2010, 11(2), pp.265-272.
Liu, S.; Qi, W.; Zhang, Y.; Wu, Z.-X.; Yan, Y.-B.; Lei, W.: Effect of bone material properties on effective region in screw-bone model: an experimental and finite element study, Biomedical Engineering Online 2014, 13.
Martin, B. I.; Franklin, G. M.; Deyo, R. A.; Wickize, T. M.; Lurie, J. D.; Mirza, S. K.:
How do coverage policies influence practice patterns, safety, and cost of initial lumbar fusion surgery? A population-based comparison of workers’ compensation systems', The Spine Journal 2014, 14(7), pp.1237-1246.
Rohlmann, A.; Bergmann, G.; Graichen, F.: Loads on an internal spinal fixation device during walking, Journal of Biomechanics 1997, 30(1), pp.41-47.
Shih, K. S.; Hsu, C. C.; Hou, S. M.; Yu, S. C.; Liaw, C. K.: Comparison of the bending performance of solid and cannulated spinal pedicle screws using finite element analyses and biomechanical tests, Medical Engineering & Physics 2015, 37(9), pp.879-84.
Xu, M.; Yang, J.; Lieberman, I. H.; Haddas, R.: Lumbar spine finite element model for healthy subjects: development and validation, Computer Methods in Biomechanics and Biomedical Engineering 2016, pp.1-15.
Xu, M.; Yang, J.; Lieberman, I. H.; Haddas, R.: Finite Element Method-Based Study of Pedicle Screw-Bone Interaction, Computer Methods in Biomechanics and Biomedical Engineering, submitted.
Zander, T.; Rohlmann, A.; Bergmann, G.: Influence of different artificial disc kinematics on spine biomechanics. Clinical Biomechanics 2009, 24, pp.135-142.