Computational analysis of two atlantoaxial fixation methods

Copyright © IFAC Modelling and Control in Biomedical Systems, Melbourne, Australia, 2003

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COMPUTATIONAL ANALYSIS OF TWO ATLANTOAXIAL FIXATION METHODS Hua Wang, Bo Hu, Jing Bai

Department ofBiomedical Engineering. Tsinghua University. Beijing. P. R. China

Abstract: The objective of this study is to analyze the biomechanical properties of two atlantoaxial surgical fixation methods: the Harms' method and the Tan's method. A nonlinear three-dimensional finite element model of atlas and screws has been established to predict the different biomechanical performance of these two methods. Four external mechanical conditions have been applied in succession, and the maximal value and distribution of the reaction forces have been obtained and discussed. This work provides a technique to perform biomechanical analysis of clinical bone fixation methods by computer simulation. Copyright ©2003 IFAC Keywords: Finite element analysis, Finite element computation, Computer simulation, Mechanical properties, models

The Harms' method: This is a novel technique to stabilize the atlantoaxial joint using bilateral insertion of minipolyaxial screws, two in both sides of the Cl lateral mass and another two through the symmetrical pars interarticularis of C2 into the pedicle, followed by bilateral rods fixation. .

I. INTRODUCTION It is well known that the human atlantoaxial complex

is vulnerable to drastic external impact. However, this part has significant physiological functions and crucial to human's life. Many kinds of orthopaedic atlas-axis (C I-C2) fixation methods have been developed to fix and brace the injured joint during the C I-C2 joint fusion therapy. Nevertheless, clinical experiments to attest those fixation methods are dangerous and expensive, and the differences are sometimes ambiguous. In this study, by computer simulation, our analysis is confined to show the biomechanical properties of two innovative fixation methods: the Harms' method (Harms J, 2001) and the Tan's method (TAN, Mingsheng, 2002). Exposed to the same external forces, these methods show different biomechanical responses, especially the different internal reaction forces around the interface between screws and bone. A finite element model of the atlas is developed based on the Visible Human Project dataset (National library of Medicine, Visible Human Project from 1986), and various mechanical conditions have been applied to analyze these two fixation methods.

The Tan's method: This is also an updated surgical method which is characterized by the bilateral insertion of screws, two in both side of the Cl posterior arch into the lateral mass and another two also through the symmetrical pars interarticularis of C2 into the pedicle, followed by bilateral rods fixation. Main Difference: The main difference of these two methods lies in the screw insertion of the atlas. Harms' screws will be inserted into the Cl lateral mass and Tan's screws will be inserted into the Cl posterior arch (Fig. I ). The latter's feasibility was approved by measuring 50 dry samples of atlas and 5 successful clinical practices (TAN, Ming-sheng, 2002). Because of the different lengths of the screws and different anatomic structures of the lateral mass and the posterior arch, these two surgical methods will hold different biomechanical properties.

2. METHODS

2.2 Finite element model design

2.1 Description ofthe two surgicalfIXation methods

A nonlinear three-dimensional finite element model of human atlas has been developed based on the image

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Table. I Finite element models in this study. Structure Atlas (Harms) Atlas (Tan) Screw (Harms) Screw (Tan)

Modelling 100192 99926 1306 1572

T4 T4 T4 T4

Young's Modulus (E/MPa)

Poission's Ratio (V) 0.30 0.30 035 0.35

5000 5000 105,000 105,000

Reference Gignac et al., Gignac et al., Amit Gefen, Amit Gefen,

2000 2000 2002 2002

XX T4 represents XX tetrahedron elements used in model.

The T;,n's SCrews

Fig.1 Screw and the represent represent

insertion of Cl by the Harms' method Tan's method. The hollow arrows the Harm' s screws and the black arrows the Tan's screws.

Fig.2 Demonstration of condition 1 Condition 2: Two forces are bilaterally exerted on the transverse processuses of Cl. The left one is directly forward, and the right one is directly backward with the same magnitude of lOON. With the external torque which will cause the atlas to turn in the horizontal plane, these forces are simulating the action of rotating head clockwise. (Fig.3)

dataset of the VHP. The model contains 101,498 tetrahedron elements (atlas plus screws) and 20,672 nodes, which ensure the precision of the simulation. Different screw models have also been established according to the different fixation methods and firmly implanted into the bone without any gaps. They can be treated as displacement fixed in three dimensions during the analysis. The material properties of the atlas and the screw models have also been defined (Table I). During the analysis confined to screws and bone interaction, the muscles can be neglected. (Wynarsky and Schultz, 1991)

2.3 External mechanical conditions

Based on a commercial software of finite element analysis (MSC. Marc/Mentat 2001, MSC. Software Cooperation), the two fixation methods have been tested under four types of external mechanical conditions, which have significant clinical meanings. All the forces exerting on the atlas should be no more than 200N, in order to prevent the Jefferson fracture (Bozkus H., et al., 2001). All the conditions are set in order to subject the bone and the screws to pure moments in flex ion, extension or lateral bending. (Puttlitz CM, et al.. 200 I).

Fig.3 Demonstration of condition 2 Condition 3: Three forces are exerted directly forward on the bilateral transverses processuses and the posterior arch of C I. The forces on the two symmetric transverses processuses are both 50 N, and the middle force on the posterior arch is lOON. By simulating the external disturbance which will cause the atlas moving in the transverse plane, this condition is to verify the tightness of the screws insertion. (Fig.4)

Condition I: A force with the magnitude of 150N is perpendicularly upward exerted on the middle of the Cl posterior arch, and another force of SON on the middle of the Cl anterior arch. With the external torque which will cause the atlantoaxial joint to rotate in the sagittal plane, this condition is to simulate the action of tilting head forward. (Fig.2)

Condition 4: Two forces with the same magnitude of lOON are exerted bilaterally on the processus transverses of Cl. The left force is perpendicularly upward, and the right force is perpendicularly downward. With the external torque which will cause

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The reaction forces of the Harms' screws have the maximal magnitude from 11.18N to 12.42N. While the reaction forces on the Tan's screws are a little stronger. within the range between 12.13N and l3.48N. In both cases. the maximal forces are distributed along their screws and tend to concentrate on the middle part. Under this condition of rotating the head clockwise and anti-clockwise (the similar results because of the symmetry) in the transverse plane, special attention should be paid to strengthening the screw-bores inside the atlas.

the atlas to turn in the coronal plane, these two forces are simulating the action of tilting head laterally. (Fig.5)

4.3 Condition 3

Both reaction forces are distributed comparatively uniformly along the screws. This is because the directions of the screws insertion are the same as those of the external forces, directly forward in the horizontal plan, which will only cause an effect of pulling the screws oul. Also, the reaction forces are mainly shear forces to maintain the screws inside the atlas. The Tan's maximal force is smaller than that of the Harms', because when only shear forces are concerned, the main difference of these two methods is the length of the screws. Tan's screws are longer (24mm) (TAN, Ming-sheng, 2002), while the Harm's are shorter (about 16 mm). When same shear forces are exerted, Tan's screws may share a smaller force magnitude because of a larger interface.

Fig.4 Demonstration of condition 3

Fig.5 Demonstration of condition 4 3. RESULTS

4.4 Condition 4

The different finite element models of the Harms' fixation method and the Tan's fixation method are examined under all of the four external mechanical conditions. Because the forces applied are no more than 200N to prevent fracture, the reaction forces in the region of the interface between the bone and the screws can be used to demonstrate some biomechanical properties. The results of the simulation are presented in Table.2

This condition is to make the atlas rotate in the coronal plane. The maximal reaction force of the Harms' method is about 14.98N to 16.64N, distributing uniformly, and the counterpart of the Tan's method is around 24.57N to 27.30N. This is due to the different positions of the Harm's screws and the Tan's screws. The former are inserted into the lateral mass of C I, which will have longer levers with the axis of the C2 dens, while the latter are through the posterior arch, closer to the axis. So in order to hold the same torque, the latter may need stronger forces. Both reaction forces are distributed comparatively concentrating on the middle part of the atlas. This may be caused by the external forces. which are exerted on the two transverse processuses, closer to the middle parts of the screws.

4. DISCUSSION 4.1 Condition 1

The simulation results show that the reaction forces of the Harms' method are distributed along the interface with the maximal value between 26.92N and 29.9IN. Tan's maximal reaction forces range from about 54.34N to 60.38N. Detailed results show that the reaction forces distribution of both fixation method tend to concentrate at the entrance of the screws. This could be explained by mechanical analysis. Both screws are inserted in the transverse plan directly forward, and the main external force (150N) is exerted on the posterior arch perpendicularly, which will press the tails of the screws.

4.5 Concerning the different anatomic strucflIres

In the discussion above, only reaction forces are considered. However, material properties of atlas are not uniform, which may cause difference in force magnitude and distribution. The section of the posterior arch where the Tan's screws are inserted is closely surrounded by the cortical bone (Victor M. Spitzer and David G. Whitlock. 1998) with a larger Young' Modulus at about IO,OOOMPa, while the inner region of the lateral mass where the Harms' screws are implanted has more cancellous bone which is much softer, with a significantly smaller

4.2 Condition 2

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Table.2 Simulation results: numerical ranges ofthe maximal reaction forces in magnitude (N) Test Condition

The Hann' s method

The Tan's method

Condition I

26.92-29.91

54.34-60.38

Condition2

11.l8-12.42

12.13-13.48

Condition3

9.571-10.63

7.086-7.874

Condition4

14.98-16.64

24.57-27.30

Range of the maximal reaction forces in magnitude indicates two numerical boundaries, which the strongest reaction force is within. Young's Modulus of 450MPa. Therefore, although the reaction forces of the two methods in condition 2 are nearly the same, they may have different effects on the atlas-screws interface.

REFERENCES Amit Gefen. (2002). 'Computational simulations of stress shielding and one resorption around existing and computer-designed orthopedic screws', In: Medical & Biological Engineering & Computing 2002, VoI. 40, pp. 311-322. Bozkus H., Karakas A. and Hanci M., et al. (JUN. 2001). 'Finite element model of the Jefferson fracture: comparison with a cadaver model', In: EUROPEAN SPINE JOURNAL, Vol. 26 (22), pp. 2467-2471. Gignac, D. Aubin, C.E., Dansereau, J., and Labelle, H. (2000). 'Optimisation method for 3D bracing correction of scoliosis using a FE model', In: Eur. Spine, Vo1.9, pp. 185-190 Guo, Shifu (200 I). Anatomy ofclinical orthopaedics pp. 73 - 77, published by Shandong Science and Technology Publishing Company, Shandong province, P. R. China Harms J, Melcher RP. (NOV. 15 2001). 'Posterior C I-C2 fusion with polyaxial screw and rod fixation', In: SPINE, Vol.26(22), pp. 2467-2471. National library of Medicine, Visible Human project from 1986. World Wide Website links to user sites for applications, sources, products, tools, and mirror sites using images from the Visible Human Project (VHP), at: http://www.nlm.nih.gov/research/visible/visible_ human.html. Puttlitz CM, Goel VK, Traynelis VC, Clark CR, (NOV 15 2001), 'A finite element investigation of upper cervical instrumentation', In: SPINE, Vol. 26 (22), pp. 2449-2455. TAN Ming-sheng, ZHANG Guang-bo, LI Zi-rong, et al. 'Anatomic study of atlas and the pass using screw fixation via posterior arch and lateral mass'. In: Chinese Journal of Spine and Spinal Cord 2002, Vol. 12(1), pp. 5-8. Victor M. Spitzer, David G. Whitlock (1998). Atlas of the visible Human Male. pp. 27-34, published by Jones and Bartlett Publishers, Inc. 40 Tall Pine Drive. Sudbury, MA 01776, USA Wynarsky, G.T. and Schultz, A. B. (1991). 'Optimization of skeletal configuration: studies of scoliosis correction biomechanics'. In: 1. Biomech., Vol. 24, pp.721-73

In addition, the main physiological function of the atlantoaxial complex is to rotate in the horizontal plane, which means turning the head left (max 37.so) or right (max 38.7°), (Guo, Shifu, 2001) and the ability of the atlantoaxial complex to rotate in the sagittal plane is very small (downward max 8.9° and upward max 5.9°)(Guo, Shifu, 2001). So examing the performance of atlantoaxial surgical fixation methods in condition 2 has its special clinical significance. 4.6 Summary In this study, reaction forces in the atlas under different mechanical conditions have been investigated by using a three-dimensional finite element analysis method. With the model established in this work, two different fixation methods have been compared in a force distribution view. This is a preliminary study of the mechanical performance of the atlantoaxial surgical fixation methods. It still needs further study before a more precise conclusion can be drawn. Our next step is to construct finite element models of atlas with a realistic material property concerning the anatomic structures of cortical bone and cancellous bone and to analyze the stress distribution both in the atlas and along the screws to predict the high-risk region of bone fracture and interface abrasion. This study provides a technique to perform biomechanical analysis of surgical bone fixation methods with computer simulation. By furthering our work, we will obtain a clearer idea and more information from the biomechanical aspect, which will potentially contribute to clinical therapy. ACKNOWLEDGEMENTS This work is supported by National Natural Science Foundation of China. The authors wish to express their sincere appreciation to Dr. Tan, Mingsheng and Dr. Wang, Huimin for their help in designing the external mechanical test conditions.

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