Biomechanical study of lumbar spine with artificial disc replacement using three-dimensional finite element method

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1 Biomechanical study of lumbar spine with artificial disc replacement using three-dimensional finite element method Sangyoon Han and Kunwoo Lee Abstract Biomechanical analyses on lumbar spine under compressive load and flexion torque were performed using a nonlinear three-dimensional finite element method to evaluate the stability of artificial disc replacement. We prepared a validated intact lumbar L4-L5 motion segment and artificial disc inserted motion segment by replacing intact disc with the artificial disc which is being developed. Effects of fiber winding pattern in the artificial disc were also examined. Elasticity of the artificial disc inserted motion segment model was higher than that of the intact motion segment model. Stress concentration caused by artificial disc replacement was found in contact region between artificial disc and vertebral body. Average stress of cortical bone increased in artificial disc inserted model. The winding pattern in which fiber is wound skipping 3 slots proved more flexible in axial compression than the pattern skipping 2 slots. Key Words : Biomechanics, finite element method, artificial disc, L4, L5, motion segment 1. Introduction Individuals with degenerative discs in the lower lumbar spine are increasing these days. Most patients with symptomatic degenerative conditions in the spine are treated non-surgically with anti-inflammatory medications, physical therapy and injections. Most of these individuals will favorably respond to non-surgical methods of treatment, but a subset of individuals will continue to experience pain (10). There are some treatment options available to manage symptomatic degenerative disc disease. However, if surgery is indicated the surgical treatment of choice has traditionally consisted of a lumbar spinal fusion. However, there are a number of drawbacks to undergoing a spinal fusion. First, the ability of the bone to heal or fuse varies. The average success rate of a lumbar spinal fusion is approximately 75%-80%. Failure of the fusion to heal may be associated with continued symptoms. Second, a spinal fusion at one or more levels will cause stiffness and decreased motion of the spine. Third, having a spinal fusion at one or more levels will cause more stress to be transferred to adjacent levels. The stress may have the problem that causes new problems to develop at the other levels, which may also lead to additional back surgery (10),(14). To solve these problems of lumbar spinal fusion, artificial intervertebral disc has been developed since 1990 s in earnest. The purpose and advantage of artificial disc replacement is to replace the worn out disc, while preserving the motion at the operated spinal level. Artificial discs have a capability to absorb some loads and impacts as well. So it can solve the problem that causes another problem of other discs, which the fusion had (15). But because there has left room for research on if it is stable to fully replace an intact disc in human body with an artificial disc, lots of experimental and theoretical studies have conducted to this day. The modeling and analysis of finite element model of human lumbar spine have been developed by many researchers since Brekelmans reported the first application of finite element analysis in biomechanics in 1972, which contain whole spine model, vertebral body model, intervertebral disc and motion segment model, lumbar spine model, cervical spine model, and model of spinal conditions and instrumentation (3). The first simplified FE model was a 2D axisymmetric elastic model of a body-disc unit (16). Due to the progress in numerical schemes for modeling viscoelastic and poroelastic materials, the better mesh generation and more extensive experiments to determine the material properties, more realistic simulations can now be performed. A.Shirazi-Adle developed and validated a nonlinear viscoelastic FE model that can quantify the mechanical responses of the L2/L3 motion segment to time varying external loads (9). The motion segment model reported by Goel et al., which included muscle forces, was also developed into a model of the thoracolumbar spine by Kong et al., where forces in the muscles of the lumbar region were considered (17). They used the model to predict the behavior of the spine and load transfer paths through it during static lifting in the sagittal plane with normal and dysfunctional muscle activity. They concluded that muscle dysfunction 1

2 Fig. 1 CAD model of the artificial disc which is being developed in this study. a assembly of inner endplates, a core and an encapsulation b fiber wound on inner endplates c outer endplates destabilized the spine, reducing the role of the facet joints in transmitting loads, and shifted loads to the discs and ligaments. On the other hand, a lot of models that are added various kinds of prostheses to complement the weak point due to degenerative disc were researched and developed. C.K.Cheng developed the interbody fusion FE model to analyze the stress distribution of the adjacent disc (6). Pitzen et al. developed a FE model and validated it by performing in vitro study to predict the biomechanical behavior of the human lumbar spine in compression (8). They made a FE segment model with titanium surgical mesh and posterior screw-rod instrumentation, a model with interbody threaded fusion cages modifying intact segment model and compared them. Totoribe et al. developed a denucleation model, posterolateral fusion models classified by presence or absence of denucleation and facet fusion, and an interbody fusion model using an initially prepared L4-5 motion segment model (1). They analyzed the models under compressive load, flexion, and extension torque and concluded that when combined with facet fusion, posterolateral fusion yielded increase of load transfer across the lamina and decrease of rotation angle of about 10% under flexion-extension torque. A FE model of motion segment which an artificial disc was implanted was also developed by Goel and Dooris (7),(12). The artificial disc used in the model was ball-and-socket type model composed of polycrystalline aluminum surrounded by titanium. They imposed an axial compression load and flexion-extension torque on the model, and then compared the stress and strain results with ones of intact model. They also tried to find the model whose results was the nearest with experimental ones changing the removal quantity of annulus and position of artificial disc. They concluded that motion from a segment with an anteriorly placed disc in flexion and motion from a segment with minimal annulus removal in extension fell with one standard deviation of the in vitro motion data. The artificial disc being developed in this study is different from existing artificial discs including the one used in Dooris s study from the angle that it can bear the axial compression load with some flexibility and can do the axial rotation more stably. Because there is a core composed of synthetic resins (Hydrothane) between two endplates in our artificial disc like human one, it has some elasticity capable of axial compression whereas existing ball-socket type ones does not. Because the core and endplates are bonded together by being wound with fibers, core can not slip out of endplate and support the rotation of the motion segment stably (Fig 1). Experiments about the artificial disc in various kinds of loads have been performed. However, no threedimensional finite element analysis of artificial disc replacement using this artificial disc has been reported, nor it is possible to perform these kinds of experiments without verification of the artificial disc. In the present study, we developed validated lumbar models using the three-dimensional finite element method. And then the artificial disc in this study was inserted to intact motion segment. We examined and compared the dynamics and changes in stress distribution in artificial disc replacement with intact one and also examined the effects of fiber winding pattern. 2. Finite Element Model 2.1 Lumbar Motion Segment For preparation of a three-dimensional finite element model of the intact motion segment, L4-L5 motion segment data were obtained clinically from computed tomography (CT) scans, taken at 1.25-mm intervals, of the lumbar spine of a 101-year-old man who had no abnormal findings on roentgenograms, using a LightSpeed Plus apparatus (GE Medical Systems). To simplify the bond of intact disc and vertebrae, inferior surface of L4 vertebral body and superior surface of L5 vertebral body were flattened. The intact disc model was prepared referring to literature (1) and the intact disc and L4, L5 vertebrae were assembled using CAD Software (Solidworks, Solidworks Corp.). In the development of mesh models, we used the finite element pre/postprocessing software HyperMesh(Altair Engineering, Troy, Michigan, USA). ANSYS (ANSYS Inc. Canonsburg, PA, USA) was used for the finite element analysis solving. Intel Pentium 4 Computer (CPU: 2.02 GHz, 768MB RAM) was used for analyses. For the accurate reflection of the surface information which is obtained in CT scans, 4-node solid element was used for the construction of cortical bone, cancellous bone of vertebrae. For the construction of the end-plate, the matrix used in the annulus of the intact disc, nucleus pulposus, the core of the artificial disc, the encapsulation of the artificial disc and the endplate of artificial disc, 6- node solid element was used. The coinciding nodes were 2

3 Fig. 2 Detailed finite element model of an L4-L5 ligamentous motion segment. a Dorsal view; b side view; c top view; d intact intervertebral disc Table 1. Element types and material properties used in models of the intact lumbar spine Material Element type Young s modulus Poisson ratio References (E:MPa) (v) Cortical bone 4-Node solid (1) Cancellous bone 4-Node solid (1) End plate 6-Node solid (1) Nucleus pulposus 6-Node solid (1) Annulus ground 6-Node solid (1) Annulus fiber 2-Node cable (5) Facet Contact Surface merged for all the nodes especially in contact area between vertebral body and disc. The material properties of each element were determined by examining the literature (Table 1, Table 2) Intact Motion Segment Model(I model) In modeling the intact disc, the annulus was regarded as composite material consisting of fiber embedded in the matrix. Annular fibers were modeled with a threedimensional cable element responding to tension only. Elements of fibers were aligned in eight layers to form a crisscross pattern placed at an angle of 30 to the horizontal plane of the disc (Fig.2). We assumed the fiber has linear properties as Goel did in his study (5). Matrix was modeled with pentahedra which were made dividing a hexahedron to 2 pieces. Endplates which are in between vertebral body and intact disc were made using pentahedron elements to coincide the nodes between the vertebral body which is made of tetrahedron and the intact disc made of pentahedron. Ligaments were modeled using the cable element with resistance tension only, and each element was arranged in the anatomical direction. The cross-sectional area of each ligament was obtained from the literature (1), (27),(28), (29). The material properties of ligaments were regarded as linear properties for simplification of analysis (Table 2) (8). The facet joint was treated as a nonlinear frictionless three-dimensional contact problem. Contact is assumed 3

4 Table 2. Young s modulus and cross-sectional areas of lumbar ligaments and number of two-node cable elements used in models of the lumbar spine Ligaments Young s modulus No. of elements Cross-section References (E:MPa) (mm 2 ) ALL(anterior longitudinal ligament) (1),(6) PLL(posteror longitudinal ligament) (1),(6) LF(ligamentum flavum) (1),(6) ITL(intertransverse ligament) (1),(6) ISL(interspinous ligament) (1),(6) SSL(supraspinous ligament) (1),(6) Table 3. Material properties used in models of the artificial disc Material Usage Element type Young s modulus Poisson ratio References (E: MPa) (v) Titanium Endplate 6-Node solid 110, (7) Hydrothane Core 6-Node solid (18) HPPE Fiber 2-Node cable 100,000 - Silicon Rubber Encapsulation 6-Node solid (23) to have smaller stiffness and the surface contact element can be used for three-dimensional surface to surface contact problems in ANSYS. A total of 89 target surfaces were used for L5 superior surface and 82 contact surfaces were used for the L4-inferior facet surface (Fig. 3c) Artificial disc inserted motion segment model Artificial disc model The artificial disc consists of 5 parts outer endplate, inner endplate, core, fiber, encapsulation (Fig 1). The artificial disc which is being developed has similar structure to human intact disc while existing ball-socket type artificial discs do not. It has the core made from Hydrothane in the center and the inner endplates which have 17slots are bonded together without friction (Fig. 1a). Fibers made from High Pressure Polyethylene(HPPE), are wound at 30 to the inner endplates skipping 2 or 3 slots in 5 layers (Fig. 1b). In this study, comparison analyses of properties of artificial disc whose fibers are wound skipping 2 slots (2-slot model) with ones of artificial disc whose fibers are wound skipping 3 slots (3-slot model) were performed (Fig. 3b). Outer endplates have roles to fix the position of the artificial disc and to bond inner endplates to them easily (Fig. 1c). In this study, to simplify the finite element model, an outer endplate and an inner endplate are merged into one endplate (Fig. 3a). Fibers were realized through using and connecting 2- node cable elements from the nodes of upper part of endplate to the nodes of lower part. The material properties of the artificial disc were described in table Artificial disc inserted motion segment model(a model) The artificial disc which is being developed was inserted where the intact disc had existed as the information of L4-L5 vertebrae, ligaments of the intact model was maintained. The nodes neighboring on contact area of superior and inferior surface of vertebra were all coincided. The anterior longitudinal ligament was removed because it s removed in real surgery (Fig. 3d) Loading and boundary condition The inferior surface of the L5 vertebral body and its inferior facet were fixed in all directions. Loads used in this study were axial compressive forces and flexion moment. The maximum loads for compression used in our analyses were referred to those reported in the literature (20), (21), (22). The maximum loads for flexion used in our analyses were the physiological maximum loads used in experiments described in the literature (2). Regarding the site of the compressive loading, to avoid the effects of local concentration of load, total load was divided into some concentrative loads whose number is the number of the appropriate nodes and was applied to the nodes. For compression loading, an axial compressive force of up to 1000N was loaded on the center of the surface of the L4 vertebral body in ten steps by an incremental loading method. For flexion loading, a pure flexion moment of up to 15 N-m was applied to a pair of axial compression forces at the anterior and posterior ends on the surface of the L4 vertebral body in 15 steps by an incremental loading method. The center of the upper surface of the L4 vertebral body was used to measure the axial displacement and the center of the lower surface of the L4, in addition, was used to measure the rotation angle. For nonlinear analyses, force control was used as the numerical procedure and the Newton-Raphson 4

5 Fig. 3 Finite element model of a motion segment with the artificial disc replacement a The CAD model of the artificial disc(upper side), FE model of the artificial disc(lower side); b FE modeling of the fiber winding(blue one); c facet contact surfaces; d anterolateral view of the motion segment model including vertebrae, the artificial disc, and ligaments method was used as an iterative method. The intact motion segment model, 2-slot artificial disc inserted model and 3-slot artificial disc inserted model were loaded and the axial displacement response to compressive load, rotation angle response to flexion moment and distribution of von Mises stress were analyzed and compared. 3. Results 3.1 Validation of motion segment model To verify the validity of the A model, we verified the validity of the I model. Regarding the load-displacement behavior of the intact L4-5 motion segment model under axial compression, we found the load-displacement curve was approximately linear within the range measured for axial displacement. And there is a tendency that the rigidity increased with increasing load due to the nonlinearity of the motion segment. The results obtained were similar to the results of analysis found in the literature, and are applicable to analysis of artificial disc replacement in axial compression (Fig). Regarding the load-displacement behavior of the I model under flexion, we found the load-displacement curve was also approximately linear whereas the results of other researchers had nonlinear tendencies. However, the load-displacement curve of the I model was within the range between the curve of Totoribe and the one of Shirazi-Adl, and the data had no big difference from Totoribe s, so the I model is applicable to analysis of artificial disc replacement. 3.2 Resultant displacement Response to axial compression Displacement in the 2-slot model was smaller than that in the I model by about 10 % on average indicating an increase in rigidity. On the other hand, displacement in the 3-slot model was larger than that in the I model by about 25% on average indicating decreased rigidity. In a comparison of the 2-slot and 3-slot models, axial displacement of the vertebral body was increased by about 42% on average, respectively, from the former to the latter models, indicating an increase in flexibility by more winding skip Response to flexion moments In flexion loading, the rotation angles in 2-slot model and 3-slot model were larger than the I model by about 5

6 Fig. 4 Mid-sagittal cross section of deformed segment under maximum loading in the intact model. a Compression at 1000N; b flexion at 15 N-m. a b Fig. 5 Mid-sagittal cross section of the deformed segment under maximum loading in the artificial disc replaced model with 2 winding skips (2-slot model) a Compression at 1000N b flexion at 15 N-m a b 5%, 3% each, showing that artificial disc replacement increased flexibility. 3.3 von Mises stress distribution Regarding von Mises stress distribution with compression loading, there is no serious stress concentration in the I model (Fig), and a little stress about 3 MPa is distributed on the cortical bone (Fig). However, in case of the A models, stress distributions were like below. Even though there is no stress concentration on vertebrae, large stress concentration over 30 MPa was found on endplates of the A model (Fig) and maximum 28.5 MPa was also found on the contact area of L4-L5 vertebral body with endplates (Fig). Taking the fact that the yield stress of human a Axial Displacement(mm) Intact, present study Goel and Kim Shirazi-Adl et al. Markolf Totoribe 400 Compression force rotation degree( ) Intact model, present study Totoribe shirazi markolf Flexion moment(n-m) Fig. 6 Comparison of responses to various loads in the present and previous studies. a Responses to compression. Intact, Intact model, present study; Toribe(1) 1999, Goel and Kim(23) 1989, Shirazi-Adl et al(25) 1984, Markolf(24) b Responses to flexion load. Markolf(24) 1972, Shirazi-Adl et al(26), Toribe(1) 1999 b 6

7 Intact, present study 2Slot artificial 3Slot artificial 6 5 Intact,present study 2Slot artificial 3Slot artificial Axial Displacement(mm) rotation degree( ) a Compression force Flexion moment(n-m) b Fig. 7 Curves of load displacement. a Responses to compression. Axial displacement in the center of the surface of the L4 vertebral body. b Responses to flexion load. a b Fig. 8 von Mises stress distribution under maximum compression loading in the intact model and the artificial disc replacement model a full view of the intact model b magnified view of the contact region in between a disc and vertebrae. There is no stress concentration found c full view of the artificial disc replacement model d magnified view of the contact region same as the intact case. There is high stress concentration found c d cortical bone is about 60 MPa into consideration (31),(32), we found that supposing this stress concentration does not let the bone yield or break, this large stress can affect the vertebrae by fatigue failure if these loads were imposed many times. Major reasons are thought like below. First, the size of the artificial disc is smaller than human intact one. Second, the Young s modulus of Titanium which has been used to make the endplate of the artificial disc is 4,700 times more than that of the human endplate. Regarding von Mises stress distribution with flexion moment, the I model and the A models all showed the large stress distribution on the area of the pedicle, the lamina and the spinous process. One of the causes of this 7

8 a, b c Fig. 9 Side view of von Mises stress distribution under maximum flexion moment a the intact model b the artificial disc replacement model with 2 winding skips c the artificial disc replacement model with 3 winding skips large stress distribution may be traced to the ligaments which pulled parts of vertebra as a reaction of the flexion moment. And the stress on the lamina area of the A models was calculated 3 times more than that on the lamina area of the I models. In the same manner with the axial compression case, there was a stress concentration on the contact area between the endplates and the vertebral bodies of the A models by about 2.5 times more than that of the I model 4. Discussion 4.1 The stability of the artificial disc compared with posterolateral fusion Totoribe demonstrated the posterolateral fusion has some elasticity by showing the results of the FE simulation that sagittal rotation angles under flexion and extension torque were at a maximum moment of 15 N-m. Compared with this, the A models indicated much more flexible tendencies than the fusion model by the results that the sagittal rotation angles of them under flexion were in the same loading condition with Totoribe s. It also shows that the A models have more flexible tendencies even than the I model. In the load-sharing aspects, Totoribe s posterolateral fusion turns out to bear less stress on cortical bone than the intact motion segment model does in compression and flexion loading. In case of artificial disc replacement, the stress on the cortical bone was less than that of intact one in compression loading. However, the stress was measured 1.5 times more than that of intact model in flexion moment indicating that artificial disc replacement bears more load on neighbor elements than posterolateral fusion. 4.2 Limits and future works There needs various kinds of FE analyses to solve the problems which referred in former discussion topic. 8 Dooris tested the stability of the artificial disc replacement changing the position of the artificial disc to 4 sides the upper, lower, left and right sides. We tested the artificial disc replacement changing only the number of winding skips. Therefore, it is needed in the future to analyze the biomechanical properties of the motion segment model which the artificial disc is inserted changing the winding pattern as well as the position and the size of it. And the optimization studies that find the best condition of the model for the good mobility and balanced load-bearing are needed also. It is worth analyzing the effects of the artificial disc replacement on other motion segment levels by preparing a L1-L5 motion segments FE model. And it will be also necessary studies to conduct not a static analysis but a fatigue test using the finite element analysis for longtern-follow-up of the artificial disc replacement. 5. Conclusion We conducted analyses on finite element model of the lumbar motion segment into which the artificial disc was inserted under axial compression and flexion loading. The analyses were compared with the ones of validated intact motion segment case. As a result, the artificial disc-inserted-model was found to be more flexible than the intact and fusion one in resultant displacements for loadings but more risky in the stress transfer to adjacent bones. Regarding the winding pattern, the model in which fiber is wound skipping 3 slots turned out more flexible than the model skipping 2 slots in axial compression and showed similar displacements in flexion moment. In addition, we gained an engineering basis that the artificial disc replacement surgery can be operated with more researches changing the size and position of the artificial disc and fatigue test simulation. Acknowledgment

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10 Compressive Strength, Bone, Vol. 7, pp ,