Validation of finite element model of human lumbar vertebrae under mechanical forces
Cite as: AIP Conference Proceedings 2137, 040004 (2019); https://doi.org/10.1063/1.5121002 Published Online: 07 August 2019
Mohankumar Palaniswamy, Anis Suhaila Shuib, Khai Ching Ng, Shajan Koshy, Karuthan Chinna, and Chin Seong Lim
Validation of Finite Element Model of Human Lumbar Vertebrae under Mechanical Forces
Mohankumar Palaniswamy
1, a)Anis Suhaila Shuib
1, b)Khai Ching Ng
1, c)Shajan Koshy
2, d)Karuthan Chinna
2, e)and Chin Seong Lim
3, f)1School of Engineering, Taylor’s University, Malaysia.
2School of Medicine, Taylor’s University, Malaysia.
3Faculty of Engineering, University of Nottingham, Malaysia.
a)Corresponding author: [email protected]
Abstract. Finite element analysis has been used extensively in medical field in investigating the degrees of movement in spine and other biomechanical forces acting on spine and other bones. Bone being nonhomogeneous in nature, developing a nonhomogeneous model of vertebral bones consume much time and a tedious process requiring anatomical knowledge.
Due to metal implants and artifacts, this process further becomes impossible or not possible at all. Thus, developing a homogeneous model for finite element analysis seems plausible. Hence, this study constructed a homogeneous model of lumbar vertebral bones along with the intervertebral disc using an image processing software, MIMICS Innovation Suite by Materialise. Constructed model was exported to ANSYS for FEA analysis. Results of this study was compared with the literature results and the percentage difference was found to be less than 5%. Wilcoxon Signed Ranks Test was done between homogeneous and nonhomogeneous geometry models and the p-value was found to be 0.052. Hence, this finite element model of lumbar vertebrae is validated and can be used for further analysis.
INTRODUCTION
Human spine consists of five lumbar vertebrae. Each lumbar vertebra is separated by an Intervertebral Disc (IVD), which allows movement between vertebrae. Their role in the spine is to act as a shock absorber. Strength of the vertebra depends upon its structure, mass, and density. In order to understand the mechanics of spine, researchers in early days used cadaver models. Several studies were performed on cadaver models. But the problem with cadaver models are its availability and storage. The cadavers which were available belongs mostly to an old age or geriatric person. Geriatric patients tend to have bone and disc degeneration, ligament laxity, deficiency in minerals and other possible complications. Thus, their bones remain brittle. When a bone strength analysis is done, it may lead to a biased result.
In order to overcome this age, availability and storage issues, researchers needed an alternate solution. The needs of researchers were fulfilled by Finite Element Analysis (FEA). FEA is a numerical method to predict how a model or structure would react with actual force, tension, pressure and other physical effects. In precise, FEA is a method used to predict how a part or assembly behaves under given conditions. It works by breaking down the large object or part into several number of finite elements in a small cubes or pyramids objects. With the help of computer, comportment of all the individual elements are compiled up to predict the comportment of the actual large object.
Proceedings of the International Engineering Research Conference - 12th EURECA 2019 AIP Conf. Proc. 2137, 040004-1–040004-10; https://doi.org/10.1063/1.5121002
Published by AIP Publishing. 978-0-7354-1880-6/$30.00
FEA is used in the medical field with the help of CT or MRI scan images called as Digital Imaging and Communications in Medicine (DICOM). From DICOM images, exact geometry of the bone or any organ can be acquired. This geometry can be converted into a finite element model and used to predict the result of given situation.
Since each individual has different anatomical structure, FEA is used to build a biomechanically effective patient specific orthosis and prosthesis, by acquiring their DICOM images. Using FEA, the mobility of spine or any angular motion occurring in a joint, termed as Range of Motion (ROM) and other biomechanical changes can be measured.
Obtaining the exact bone geometry seem to be very challenging when the DICOM images are filled with artifacts caused due to metal implants. During certain surgical procedures like scoliosis correction or vertebrectomy, a part or whole bone is removed and replaced by a metal implant. When CT scan is performed, X-rays interact with metal implant and get refracted. Thus, leading to a noisy DICOM images (refer Fig 1).
(a)
(b) (c)
FIGURE 1. DICOM image. (a) Normal image without implant exhibiting clear layers, (b) Image with implant, (c) Image after processing.
Generally, property of bone is considered as a nonhomogeneous. Both bone and IVD has two layers. Bone has cortical and trabecular, whilst, IVD has annular fibrosus and nucleus pulposus. Several bone FEA studies done prior assumed their model to be nonhomogeneous. At the same time, some FEA studies in the literature were also done on bone models assuming isotropic homogeneous properties, due to its convenience [1 - 3]. Creating a nonhomogeneous 3D model from the DICOM images with artifacts caused due to metal implants are highly impossible or not possible at all. Alternatively, creating a homogeneous model from DICOM images, even with artifacts is possible. But a new set of material properties need to be devised in order to validate the homogeneous model. Few literatures used isotropic material property for their homogeneous models, but not validated them. Hence, a validation study was needed to be done on homogeneous and nonhomogeneous models to validate the isotropic material property. The aim of this study is to validate the normal homogeneous isotropic finite element model of human lumbar vertebrae under mechanical forces with experimental data to predict its reliability by measuring the ROM.
METHODOLOGY
In order to find the reliability of homogeneous lumbar segment model, two set of validation procedure is done.
First, reliability of method and the second, reliability of geometry. To verify the reliability of method, an experimental validation procedure is done. Regarding the reliability of geometry, results from homogeneous models were compared with the nonhomogeneous models and literature data.
Experimental Validation
In order to validate the finite element method, an experimental study done by Ibrahim on rubber deformation was taken into consideration [4]. Figure 2 shows the deformation of rubber block due to application of force.
FIGURE 2. Deformation of rubber block.
From the Fig 2, it can be understood that, h is the height of rubber block, A is the area under shear (height times width), Ps is the force acting, τ is the shear stress, γ is the shear strain, δs is the deformation and G is the modulus of rigidity of rubber block. When a force is applied on the rubber block, lengthening or deformation occurs and lead to decrease in cross section. This is identified as Poisson’s ratio. When a material is stretched in one direction, it becomes thinner in the other two directions.
𝑣 𝑑𝜀
𝑑𝜀
𝑑𝜀 𝑑𝜀
𝑑𝜀
𝑑𝜀 (1)
where ε is the strain. Translational and axial strain are specified as εtrans and εaxial, respectively. x, y and z are the Cartesian coordinates of the system.
Shear stress, τ is defined as shearing force, Fs divided by the area under shear, As: 𝜏 𝐹
𝐴 (2)
While, shear strain, γ is defined as shear deformation, δs divided by the length, l:
𝛾 𝛿
𝑙 (3)
With the shear stress and shear strain identified, modulus of rigidity, G is:
𝐺 𝜏
𝛾 (4)
From the modulus of rigidity, G and Poisson’s value, v Young’s modulus, E can be calculated.
𝐸 2𝐺 1 𝜈 (5)
This study performed the same experiment using finite element model. A rubber block and metal plate were created (refer Fig 3) in Ansys Workbench version 17.2 (Ansys, Inc., U.S.A). Thickness of the plate, length, width, and height of the rubber block was 5 mm, 73 mm, 25 mm, and 153 mm.
FIGURE 3. Geometry and boundary conditions.
Connection between metal plate and rubber was set to bonded and formulation to Multi Point Constraint (MPC).
MPC is used to ensure that both the faces are in contact with each other. Model was meshed with 1 mm of mesh size.
2 N of force was applied vertically on the metal plate. This was repeated with 4 N, 6 N, 8 N, and 10 N of force. Shear stress, shear strain, and deformation were measured. The material properties of the metal plate and rubber block are provided in Table 1.
TABLE 1. Material properties of rubber and metal.
Properties Metal plate Rubber block Young’s modulus
Poisson’s ratio Density
200000 MPa 0.33 7850 kg/m3
2.88 MPa 0.45 1.1 kg/m3
Prediction of ROM and Bio-Mechanical Properties
After obtaining proper approval, CT scan images of a normal young adult without any neuro-musculoskeletal disorder and calcium deficiency was obtained from Barnard Institute of Radiology, Chennai. Lumbar 3D models of the subject were developed using Materialise version 20.0 (Materialise Inc., Belgium). Four normal lumbar models were created - L1-L2, L2-L3, L3-L4, and L4-L5. Each model contained one IVD.
Mesh independence study was performed and found that the appropriate mesh element size was to be 0.9 mm.
Meshed model was exported to Ansys to perform simulation. Validation of lumbar FE models were based on linear homogeneous isotropic material properties. This assumption was verified by creating nonhomogeneous lumbar models as well for the same subject with material properties for cortical bone, trabecular bone, nucleus pulposus, and annular fibrosus. Both the homogeneous and nonhomogeneous models had same volume, but different number of nodes and elements. A linear structural analysis was carried out. Material properties were obtained from literatures [5 - 8] and provided in Table 2.
TABLE 2. Material properties of homogeneous and nonhomogeneous models.
Models Young’s modulus (MPa) Poisson’s ratio
Nonhomogeneous Cortical 12000 0.3
Trabecular 100 0.2
Nucleus pulposus 1 0.4999
Annular fibrosus 4.2 0.45
Homogeneous
Bone 200 0.3
Disc 4 0.4999
Once all these properties are set, boundary conditions were added. The inferior surface of vertebral body in bottom vertebra was set to be fixed. Moment was applied at the superior surface of the vertebral body in top most vertebra.
ROM analysis
Moment was applied individually in all the 6 directions mimicking the spinal mobility or ROM (refer Fig 4).
ROM is the measurement of the amount of movement around a specific joint or body part in terms of the angle. Flexion (X), extension (-X), left side flexion (Y), right side flexion (-Y), left rotation (Z), and right rotation (-Z).
(a) (b)
(c) (d)
FIGURE 4. Range of motion (ROM) in lumbar segment. (a) Flexion-Extension, (b) Left-Right side rotation, (c) Left-Right side flexion, (d) Nonhomogeneous model of vertebra and intervertebral disc.
10 Nm was selected to be applied, as it is sufficient enough to produce motions [9]. In this study, normal lumbar FE models were used to measure segmental ROM under 10, 7.5, and 4 Nm of moment. The results from this study was compared with the cadaver study done by Yamamoto et al., [9], Cook et al., [10], Guan et al., [11]. Shapiro-Wilk test was performed to test the normality of data. Based on its p-value, Wilcoxon Signed Rank Test was performed Wilcoxon Signed Ranks tests were conducted to check the difference of ROM between current FE model and the experimental method.
RESULTS AND DISCUSSIONS Experimental Validation
The shear stress, shear strain and deformation of both the experimental and finite element models are provided in Table 3.
TABLE 3. Results comparison between literature and this study.
Force , Fs
(N)
Stress,τ (Pa) Strain,γ (mm/mm) Deformation,δs (mm) Ibrahim [4] This
Study* Ibrahim [4] This
Study Ibrahim [4] This Study
2 522.88 522.88 4.24 4.16 0.05 0.05
4 1045.75 1045.75 9.58 9.13 0.11 0.11
6 1568.63 1568.63 15.2 14.69 0.16 0.17
8 2091.5 2091.5 21.23 20.35 0.22 0.23
10 2614.38 2614.38 26.98 25.87 0.27 0.29
*As per equation 2, both force and area were constant in both the studies.
The percentage of difference in strain between experimental study and this study was 4%. Whereas, the percentage difference in deformation was 4.81%. There was no significant difference in the shear stress. Figure 5 and Figure 6 exhibit the results of the experimental study and this study for stress-strain and deformation, respectively.
FIGURE 5. Comparison between experimental results [4] and this study for stress-strain curve 0
5 10 15 20 25 30
0 500 1000 1500 2000 2500 3000
Strain (mm/mm )
Stress (Pa)
Ibrahim [4] This study
FIGURE 6. Comparison of force-deformation results between experimental work [4] and current study
Geometry Validation
ROM analysis
The segmental ROM for flexion, extension, left side flexion, right side flexion, left rotation and right rotation motions of L1-L2, L2-L3, L3-L4, and L4-L5 for current FE model and experimental models are shown in Figure 7, Figure 8 and Figure 9.
FIGURE 7. ROM resulted from flexion, extension, left-right bending, and left-right rotation under 10 Nm moment.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
2 4 6 8 10
Deformation (mm)
Force (N)
Ibrahim [4] This study
0 1 2 3 4 5 6 7 8 9 10
Yamamoto
[9] This study Yamamoto
[9] This study Yamamoto
[9] This study Yamamoto
[9] This study
L1-L2 L2-L3 L3-L4 L4-L5
Angle ( °)
Flexion Extension L Bend R Bend L Rot R Rot
FIGURE 8. ROM comparison between literature [10] and this study under 7.5 Nm moment for flexion and side bending.
FIGURE 9. ROM comparison between literature [11] and this study under 4 Nm moment for flexion-extension, side bending and rotation.
In general, the difference of the ROM degrees between the FE models and experimental models under different moment were between -2.5° to +5°. This study compared the results of experimental ROM under different moments from 3 different literatures [9 - 11]. It shall be noticed that there is no definite pattern to be observed. In flexion extension, the ROM of L4 – L5 is higher than L3 – L4 under 10 Nm of moment. Whereas, the ROM of L4 – L5 is lower than L3 – L4 under 7.5 Nm of moment (refer Fig 10 (a)). In side flexion, the ROM of L2 – L3 is 4° higher than L1 – L2
under 10 Nm of moment. Whereas, the ROM of L2 – L3 is not even 0.5° higher than L1 – L2 under 7.5 Nm of moment 0
2 4 6 8 10 12
Cook et al.
[10] This study Cook et al.
[10] This study Cook et al.
[10] This study Cook et al.
[10] This study
Angle ( °)
Flexion Extension Side Bending
0 1 2 3 4 5 6 7 8 9
Guan et al.
[11] This study Guan et al.
[11] This study Guan et al.
[11] This study Guan et al.
[11] This study
Angle ( °)
Flexion Extension Side Bending Rotation
(refer Fig 10 (b)). It should be noted that each and every individual has a different measurement of ROM. It is not necessary or not possible for all the persons ROM to be equal or same.
(a)
(b)
FIGURE 10. Comparison between literatures under different moment. (a) Flexion-Extension, (b) Side bending.
Considering the facts that different person has different ROM, and ROM difference between this study and cadaver studies was merely -2.5° to +5°, current FE model was valid compared to experimental model.
0 2 4 6 8 10 12 14 16
L1-L2 L2-L3 L3-L4 L4-L5
Angle ( °)
Flexion Extension 10 Nm Flexion Extension 7.5 Nm Flexion Extension 4 Nm
0 2 4 6 8 10 12 14 16
L1-L2 L2-L3 L3-L4 L4-L5
Angle ( °)
Side Bending 10 Nm Side Bending 7.5 Nm Side Bending 4 Nm
Homogeneous and Nonhomogeneous models
Out of 48 ROM data obtained from 6 different simulations on 4 homogeneous and 4 nonhomogeneous lumbar models, 15 nonhomogeneous model’s ROM were greater than homogeneous model’s ROM and 9 homogeneous model’s ROM were greater than nonhomogeneous model’s ROM.Shapiro Wilk test was performed to test normality of data. Its p-value was 0.004. Since the data cannot be assumed as normally distributed based on its p-value, Wilcoxon Signed rank test was performed The ROM p-value of the Wilcoxon Signed Ranks Test was 0.052, which is higher than 0.05. This indicated that the difference in ROM between homogeneous and nonhomogeneous lumbar models is not significant according to Nonparametric Wilcoxon Signed Ranks test.
CONCLUSION
Comparing the results between experimental study and this study, the percentage difference was merely 4.81%.
The ROM for normal lumbar predicted by FE model in current study were within the range of ROM determined from the earlier experimental data. The statistical analysis showed that there is no difference in ROM between the homogeneous and nonhomogeneous models. Hence, considering a nonhomogeneous bone and disc as homogeneous does not produce any significant difference. Thus, the FE model in current study is validated and can be used for further analysis.
ACKNOWLEDGEMENTS
The authors of this study would like to thank Dr. Nalli R Yuvaraj, orthopaedic spine surgeon from Rajiv Gandhi Government General Hospital, Chennai, for his help and support during data collection.
REFERENCES
1. S. K. Eswaran, A. Gupta and T. M. Keaveny, "Locations of bone tissue at high risk of initial failure during compressive loading of the human vertebral body," Bone, vol. 41, no. 4, pp. 733-739, 19 June 2007.
2. Z. Ahmad, A. K. Ariffin and M. M. Rahman, "Probabilistic finite element analysis of vertebrae of the lumbar spine under hyperextension loading," International Journal of Automotive and Mechanical Engineering, vol. 3, no. 1, pp. 256-264, June 2011.
3. M. Shamnadh, C. Aravind and P. Dileep, "CT Based Finite Element Analysis Of Human Lumbar Vertebra With Accurate Geometric and Material Property Assumptions," International Journal of Scientific & Engineering Research, vol. 8, no. 7, pp. 121-125, July 2017.
4. N. Z. M. Ibrahim, "Analysis on a Deformation of a Rubber Block," 4 May 2015. [Online]. Available:
https://nurzaitemahaya.wordpress.com/assignments/analysis-on-a-deformation-of-a-rubber-block/. [Accessed 12 April 2018].
5. H. Li and Z. Wang, "Intervertebral disc biomechanical analysis using the finite element modeling based on medical images," Computerized Medical Imaging and Graphics, vol. 30, pp. 363-370, September 2006.
6. J. Zheng, Y. Yang, S. Lou, D. Zhang and S. Liao, "Construction and validation of a three-dimensional finite element model of degenerative scoliosis," Journal of Orthopaedic Surgery and Research, vol. 10, no. 1, pp. 189- 195, December 2015.
7. H. Li, "An Approach to Lumbar Vertebra Biomechanical Analysis Using the Finite Element Modeling Based on CT Images," in Theory and Applications of CT Imaging and Analysis, InTech, 2011, pp. 165-180.
8. L. Wang, B. Zhang, S. Chen, X. Lu, Z.-Y. Li and Q. Guo, "A Validated Finite Element Analysis of Facet Joint Stress in Degenerative Lumbar Scoliosis," World Neurosurgery, vol. 95, pp. 126-133, August 2016.
9. I. Yamamoto, M. M. Panjabi, T. Crisco and T. Oxland, "Three-Dimensional Movements of the Whole Lumbar Spoie and Lumbosacral Joint," Spine, vol. 14, no. 11, pp. 1256-1260, November 1989.
10. D. J. Cook, M. S. Yeager and B. C. Cheng, "Range of Motion of the Intact Lumbar Segment: A Multivariate Study of 42 Lumbar Spines," International Journal of Spine Surgery, vol. 9, no. 5, p. 8, 5 March 2015.
11. Y. Guan, N. Yoganandan, J. Moore, F. A. Pintar, J. Zhang, D. Maiman and P. Laud, "Moment-rotation responses
