MATERIALS AND METHODS

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1 REDISTRIBUTION OF LOAD OF INJURED LOWER CERVICAL SPINE UNDER AXIAL COMPRESSION USING FEM E. C. Teo 1 and H. W. Ng 1 1 School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore mecteo@ntu.edu.sg ABSTRACT In human spine, any ligamentous injury, degenerated disc or facetectomy leads to certain degrees of spinal instability. There are limited studies using finite element method (FEM) simulating these effects to evaluate the biomechanical response of spine under various physiological load configurations. This parametric study was conducted to evaluate the roles of ligaments, facets, and disc nucleus in the transmission of load from superior to inferior vertebral level of human lower cervical spine (C4-C6) using the FE approach. Accordingly, a 3-dimensional FE model of the C4-C6 cervical spine, consisted of 11,187 nodes and 7,730 elements modeling the bony vertebrae, articulating facets, intervertebral dics, and associated ligaments, was developed and its predicted results were validated against published data under axial compression load configurations. The FE model was further modified accordingly to investigate the role of disc, facets and ligaments in preserving cervical spine motion segment stability under same load configuration. The passive intact FE model predicted the non-linear force displacement response of the human cervical spine, with increasing stiffness at higher loads. The simulated injured models predicted the role of ligaments, facets or disc nucleus in preserving the cervical spine stability in term of redistribution of load. KEYWORDS Spinal biomechanics, disc nucleus, ligaments, facet, load transmission, cervical spine INTRODUCTION Spinal instability has been a subject of considerable debate and its cause has not been clearly established. Clinically, spinal stability is defined as unstable if the spinal motion segment exhibits abnormally large increase in rotational or translational displacements (or reduction in stiffness) under physiological load. Many in vitro biomechanical analyses showed the detrimental consequences of different ligamentous injuries and provided the certain assumptions about clinical stability of human spine [Yoganandan et al, 1989, Coffee et al., 1988, Shea et al., 1991, Wen et at., 1993]. Resection of the facet capsule alone, without disruption of the bony facet, showed that under torsion, the rotational displacement increased by 1% after a 25% capsule resection, 19% after a 50% resection, and 25% after a 75% or 100% resection [Raynor et al., 1985, Zdeblick et al., 1993]. These in vitro studies are expensive, surgically invasive, time consuming coupled with limited availability of specimens. Many investigators had turned to FE analysis to study the biomechanics of cervical spine. Yoganandan et al. (1996) developed the first FE model of normal C4-C6 spine based on a cervical specimen and 1-mm computed tomographic (CT) scanned slices, and analyzed it under compression mode. Maurel et al. (1997) developed a 3-dimensional spinal segment using simplified geometry parameters (planes, ellipses, cylinders, blocks, etc) and validated it under flexion, extension,

2 lateral bending and torsion. Heitplatz et al., (1998) developed a simplified FE model of human spine and validated it under compressive loading with the intervertebral disc modeled using a combination of solid elements and nonlinear springs. Goel and Clausen (1998) developed a more detailed 3- dimensional spinal segment of C5-C6 from serial CT scans and validated it under flexion, extension, lateral bending and torsion. In the area of FE analysis of the injured human spine, Sharma et al., (1995) developed a 3-dimensional FE model of a lumbar motion segment to study the effect of ligament and facet and their geometry on segment responses. However, till now, a validated C4-C6 FE model to analyze the biomechanical response, in term of load re-transmission, of cervical spine to determine the role of ligaments, facets and disc nucleus under compression has not been demonstrated. Accordingly, the goal of the present study was to develop a C4-C6 FE model and validate it against published data under compressive displacement load configuration. The ability of FE model to predict the roles of ligaments, facets, and disc nucleus in the redistribution of loads of lower cervical spine under the same load configurations was evaluated. MATERIALS AND METHODS A 3-dimensional C4-C6 FE model was developed based on a 68 year-old male cadaveric cervical spine. Adopting the digitizing technique used in the simplified models of isolated cervical vertebra by Teo et al. (1994) and Maurel et al. (1997), this study utilized the digitized geometrical coordinates of a dried cadaveric cervical specimen obtained using a flexible three-dimensional movement digitizer. The C4-C6 was assumed to be symmetrical about the mid-sagittal plane, only half of the vertebrae were modeled. With the vertebral model development techniques similar for all the vertebrae, the digitizing and FE mesh generation discussed in our previous study of C1 (Teo and Ng, 2001) were adopted. Briefly, the geometrical coordinates were obtained by continuous digitizing over the outer surface profile of the vertebra and the automatic registered data of 0.1 mm intervals were then post processed to form the sections, surfaces and then watertight solid volumes for the final finite element mesh generation. Each vertebra (C4 to C6) was defined using 1,632 8-noded isoparametric solid elements for the cortical bone, the cancellous bone and the posterior arch. The modeling of the biological tissues between the adjacent vertebrae were based on mean values from literature. The intervertebral disc was defined by 1,032 8-noded solid elements and the ligaments were defined using 183 three-dimensional tension cable elements to represents the true physiological functions of ligaments. Facet joints, in previous FE studies of spine, are often represented by solid element (Yoganandan et al., 1996) or gap element (Maurel et al., 1997, Goel and Clausen, 1998) of constant spring stiffness with gap. In this study, the facet articulation was treated as a moving contact problem, defined by 202 contact elements to appropriately model the changing areas of contact of the facet articulating surfaces with increments in loading. Generally, owning to the geometrical complexity of the cervical spine, the C4-C6 FE mesh was fairly fine. The generated 3-dimensional C4-C6 FE model consisting of 11,187 nodes and 7,730 elements was developed (Figure 1). To analyze the FE model, appropriate material properties for each spinal component based from published data (Yoganandan et al., 1996, Maurel et al., 1997, Goel and Clausen, 1998) were adopted. FE ANALYSIS Validation As validation studies form the vital link between the development of the FE model and its final intended use, the FE model was analyzed and compared its predicted results against published results

3 (Shea et al., 1991, Yoganandan et al., 1996, Heitplatz et al., 1998) under 1-mm axial compressive displacement loading configuration as depicted in Figure 2. 1-mm axial displacements in 5 steps Loading Posterior C4 V/B Disc C5 V/B Anterior Disc C6 V/B Constraint B Figure 1: C4-C6 FE Model Figure 2: Loading Configuration traint dy Significance of ligaments, facets and disc nucleus studies To evaluate the relative importance of ligaments, facets, and disc nucleus analyzed under 1-mm compressive displacement, the validated C4-C6 FE model was modified accordingly to form corresponding three new models (intact segment without ligaments, intact segment without ligaments and facets, and intact segment without disc nucleus). The corresponding responses of these models were compared against the predicted responses of the validated C4-C6 segment model. RESULTS Validation The predicted mechanical response of C4-C6 FE model under axial compressive loading agreed reasonably well with published results (Shea et al., 1991, Yoganandan et al., 1996, Heitplatz et al., 1998) (Figure 3). The model predicted both non-linear and stiffening effects of the relationship between the axial compressive force and axial displacement. A difference of less than 10% was shown between the present model predicted results and the mean experimental values. The FE models by Yoganadan et al. and Heitplatz et al. showed a difference of 15% and 25% of force magnitude, respectively, from the mean experimental values at 1-mm compressive displacement. Generally, the three FE models agreed reasonably well with the experimental data. However, our intact C4-C6 FE model shown closer agreement with the experimental measurements. Significance of ligaments, facets and disc nucleus Figure 4 showed the variations in redistribution of forces transmitted to the inferior body of C6 under axial compressive displacement loading configuration of the different arbitrarily simulated injured models. The magnitude of force transmitted down to the inferior portion of the model was reduced under the compressive displacement load for models simulating facetectomy and degraded nucleus. The total sectioning of ligaments was not significant, obviously, in this load configuration. The differences in the redistribution of force transmission between the segment model without ligaments and facet and segment without disc nucleus against the validated intact C4-C6 showed a shift in the load carrying capacity of the disc to facets as compressive displacement increased. At lower compressive prescribed displacement, the disc transmitted 100% of the force but reduced to about 55% at higher load.

4 Experimental Values, Shea et al, 1991 Linear model, Yoganandan et al., 1996 Simplified model, Heitplatz et al., 1997 Basic model C o m p ressive D isp lacem ent (mm) Figure 3: Validation analysis:-comparison of the C4-C6 model predicted responses against published results under axial compressive displacement Force (N) Basic Model Without Ligaments Without Ligaments and Facets Without Disc Nucleus Compressive Displacement (mm) Figure 4: Predicted redistribution of load DISCUSSION As the cervical spine is a complex biomechanical system containing both passive structural and active neuromuscular components, the FEM is well suited for parameterized analytical study, it offers the advantages in the handling of complex geometric configurations as well as material and geometric non-linearity. In this study, a 3-dimensional C4-C6 FE model of the human cervical spine was developed based on actual geometric data of the dried specimens. All the important anatomic features and linear material characteristics of the facet articulation surfaces, posterior arch, intervertebral disc were defined. The model was analyzed in axial compressive load configurations with specific purposes. Validation is the most important step in the FE analysis when modeling anatomical structures model to produce reliable predictions for a variety of complex investigations. Accordingly, the load and constraints adopted in the validation analysis under axial compressive load configurations were identical to the published literature (Shea et al., 1991). For the applied compressive displacement at C4, the predicted reaction at C6 (i.e. the force transmitted to C6) was compared with the published experimental results and analytical models predictions (Shea et al., 1991, Yoganandan et al., 1996, Heitplatz et al., 1998). Once the initial validation studies have been completed, the authors believe that the model can be used as a specimen with repeatability and reproducibility characteristics that is ideal for various biomechanical studies, such as ligamentous, facets, and disc injuries.

5 In this study, the FE models developed effectively simulate the general non-linear behavior of the human cervical spine function unit (C4-C6) under axial compressive loading. The definite roles of the ligamentous tissues, articulating facets and disc nucleus in the stability of the human cervical spine cannot be disputed and were clearly shown in the analyses. Under compressive loading (Figure 4), a significant difference in the magnitude of redistribution of force has been predicted for the model without the disc nucleus. The predicted results showed that the nearly incompressible disc nucleus is highly effective for the transmission of force in the cervical spine under axial loading and the removal of the disc nucleus reduced the this compressive load by 75%. For healthy cervical spine, the results predicted that the facets and disc shared the load quite equally at higher loads, but the role of facets in load carrying capacity reduced significantly at lower compressive load. The results predicted the facets articulations contribute considerably to the stability of the cervical spine under larger axial compressive loading. The removal of either the facets or the disc nucleus affected the stiffness of the cervical spine drastically, and the segment became more flexible in mobility under compression, resulting in instability of the cervical spine under physiological load. The removal of ligaments did not affect the stability of the human spine under compression due to the characteristics of the tensile cable element defined. Our analysis on the total removal of disc nucleus to simulate the extreme case of disc degeneration, whereby the functional compressibility of the nucleus is totally lost, predicts significant changes in force redistribution (hence segment stiffness). Cervical spinal motion segments without the disc nucleus causes the disc to be less effective in its load-bearing role. These observations for the C4-C6 were in good agreement with the conclusions reported by Shirazi-ADL et al., (1984) for the lumbar spine segment. Although the model and analysis are quite comprehensive, several factors, besides mechanical properties variations, can account for the difference between the predicted results and the experimental data. The current model is mid-sagittally symmetric and thus will not predict any coupled motions. The current results are also limited by the use of linear elastic and homogeneous material properties. However, because of the good prediction from a combination of linear material properties and nonlinear geometry in the present study, we speculate that nonlinear material properties of the disc and ligaments may not be significant in the range of loading used in current study. CONCLUSIONS In summary, a 3-dimensional geometrical and mechanical accurate FE model based on actual geometry has been successfully developed for lower cervical spine (C4-C6). The passive FE model prediction was compared against published data under axial compressive configuration. The FE model predicted the non-linear response of the lower cervical spine segment. The parametric study undertaken to investigate the roles of facets and ligaments revealed the distinct role of these spinal components in preserving cervical spine stability passively under this load configuration. The FEM of analysis adopted here could supplement experimental research in understanding the clinical biomechanics of human cervical spine under different modes of load/displacement vectors, and as design tool for implant fixation. REFERENCES Coffee M S, Edwards W T, Hays W C and White III A A. (1988) Biomechanical properties and strength of the human cervical spine. Orthop Trans 12, 476.

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