Abstract
OBJECTIVE: To establish a three-dimensional finite element model of the cervical spine with detailed anatomical structure and to verify its validity.
METHODS: A healthy adult male was subjected to a thin-layer CT scan of the cervical spine, and the CT data was imported into Mimics 10.0 to obtain the 3D image data of the cervical spine, then imported into Geomagic, studio 9.0 to obtain the geometric model of the cervical spine, and finally the finite element model of the cervical spine was established in ANSYS 11.0. Using the same conditions as in the literature, the range of motion of each segment of the model was calculated and compared with the data in the literature to verify the validity.
RESULTS: A finite element model of the cervical spine with detailed anatomical structure was established and validated by validity.
CONCLUSION: The model has good biofidelity and can be used for further studies.
Keywords: cervical spine; finite element model; Mimics; Geomagic, studio; ANSYS
With the widespread use of MRI and continuous advances in surgical equipment and minimally invasive surgical techniques, intravertebral lesions can often be diagnosed and treated at an early stage, and long-term postoperative survival and functional improvement rates are significantly higher, so the function of the spine is increasingly of concern to physicians and patients alike. The disruption of posterior structures caused by laminectomy may result in postoperative spinal instability or deformity, which is particularly evident in the cervical spine, where mobility is greatest. Therefore, it is of obvious social and economic importance to investigate the mechanism of the occurrence of cervical instability or deformity after laminectomy, so as to improve surgical strategies and prevent the occurrence of postoperative cervical instability or deformity.
Current biomechanical models of the spine include physical models, in vivo models, ex vivo models, and computer models. The finite element model is a type of computer model that not only measures the mobility of the model in three planes, but also allows access to internal experimental data that are difficult to obtain with other models. The same finite element model can be used for multiple tests and used repeatedly, which greatly reduces the experimental cost. Among the current finite element modeling methods, image modeling extracts the boundary contour data through geometric tomographic image data obtained from CT and MRI and then completes the geometric modeling, which has a large amount of data, high modeling accuracy and relatively low cost, and is the commonly used method for modeling at present. However, the establishment and application of cervical spine model is relatively late. In order to make the cervical spine finite element model more widely used in the study of various laminectomies, this paper intends to establish a cervical spine finite element model with accurate geometry, comprehensive anatomical description and high biofidelity through CT images, and provide tools to explain the biomechanical changes after cervical laminectomy.
1.Materials and methods
1.1.Modeling environment
CPU: AMD, Athlon, 7750, dual-core, 2.70G central processing unit; memory: 4G; graphics card: ATI, Radeom, HD, 4670, 512m video memory; operating system: Windows, XP/Professional; monitor: 22 home trenches allow wine sole to swing only 500G.
1.2 Sample data collection
In order to make the established model universal, the data selected in this paper came from healthy adult male volunteers (age 22, height 1.75m, weight 65kg) who were close to the 50th percentile body size of the national population. A GE, LightSpeed, VCT computed tomography system was used to scan the cervical spine of the volunteers to obtain cervical vertebral coordinates data. During the imaging process, the cervical vertebrae of the volunteer were required to be located in the center of the scanning field, keeping the longitudinal direction unchanged, and the scanning range was from occipital to thoracic 1. The scanning conditions were 120 Kv, 280 mA, 1 mm layer thickness, and 1 mm layer spacing. 3D reconstruction of the cervical vertebrae was performed after scanning, and tomographic images in the sagittal and coronal planes were obtained. Each tomographic image was burned in DICOM format and saved on a CD-ROM.
1.3. Modeling process
The CT images in DICOM format were imported directly into Mimics (version number: 10.0, Materialise, Belgium) software to pre-process the data. After clarifying the orientation of the images in 3D space, the software automatically forms the bone tissue contour curves at each level. The contour line data of the cervical spine bones were extracted by grayscale values in the Mimics software. Using the software’s default CT bone threshold range of 226-3071, after selecting the bone in the desired area for modeling, the Mimics software automatically extends the connected areas within the gray value range according to the gray value of the selected area, while automatically removing the unconnected areas within this gray value range. Then delete the unwanted images, make some editorial corrections to the remaining images, and save them as stl files. This stl format file was imported into Geomagic, studio software (, version number: 9.0, Geomagic, USA), and considering the complexity of the cervical spine structure and the requirements for cervical spine geometric accuracy in the study, the point side method was used for inverse modeling, and the vertebral body was divided into multiple regions according to the curvature change of each part, and the point cloud data of each region was fitted to generate The cervical spine geometry model was generated by fitting the point cloud data of each region. The generated solid model was then converted into a 3D solid model using the smoothing algorithm and format conversion function, and the generated solid model was saved as an iges format file, which was read by ANSYS software (version number: 11.0, ANSYS, Inc., USA) to obtain the solid of the cervical vertebrae. The divided lines on the solid surface were used to form a segmentation surface to divide the cervical vertebra into vertebral body, small joints, lamina, spinous process, pedicle and transverse process. Using the extrude function, the solids of the endplates are generated using the upper and lower surfaces of the two adjacent cervical vertebrae that have been divided. Then the surface is generated using the two endplates of the same vertebral space, and a closed surface is finally formed by first connecting the lines between the two surfaces and then generating the surfaces, and the nucleus pulposus and fibrous ring are generated proportionally using the closed surface. The same method is used to generate the solid anterior and posterior longitudinal ligaments on the anterior and posterior surfaces of the vertebral body. The final solid model of the cervical spine is obtained.
Different structures need to be simulated using different unit types, and their material parameters are mainly referred to published references [1-4]. The average thickness of the cortical bone shell is set to 0.3 mm, the thickness of the anterior longitudinal ligament is set to 1.5 mm, and the thickness of the posterior longitudinal ligament is set to 2.3 mm. while the small joints are defined as frictionless face-to-face contact. In order to save computational analysis time, the cervical bones are approximated by isotropic materials. Then the tetrahedral meshing method is used to dissect the model and generate a full cervical spine finite element model.
The validation of the model is a key part of the continuous improvement of the finite element model to its final applicability [5]. The same loading method and boundary conditions as for Ng [3] were used, as shown in Fig. 4. 1. and 5 Nm of pure torque was loaded on the upper surface of the C2 vertebral body according to the right-handed spiral rule along the 1,2,3 coordinate directions to generate the torque in the corresponding sagittal, coronal, and axial planes to simulate the loading of anterior-posterior flexion and extension, left and right lateral bending, and left and right axial rotation. The response of the model was compared with the experimental results of literature [3,,6-11] to verify the validity of the model under the same loading boundary conditions.
2. Results
The proposed cervical spine model contains six cervical vertebrae, five intervertebral discs and the corresponding ligaments and joint capsules, and the vertebral body, transverse process, pedicle, small joint, pedicle and spinous process of the cervical vertebrae, and the end plate, nucleus pulposus and annulus fibrosus of the intervertebral disc are simulated separately. The model was built with accurate geometry, comprehensive anatomical description and high biofidelity. The entire cervical spine model consists of 344,932 solid units, 9,190 shell/wire units, and a total of 434590 nodes.
The validation of the model utilizes the intersegmental mobility of the cervical spine (segmental rotation angle, °) as an indicator, and the validity of this model under flexion-extension, lateral bending, and rotational loading is verified using the results of in vivo, ex vivo, and finite element studies by other scholars (see Tables 2~4). From the comparison results, it can be seen that the intersegmental range of motion of the present model under each load mode is in general agreement with the trend of published literature data.
3. Discussion
The human cervical spine is a complex structure with three basic biomechanical functions: motor function, load-bearing function, and protective function. The cervical spine stabilization system consists of three parts: the passive system (vertebrae, intervertebral discs and ligaments), the active system (muscles and tendons surrounding the cervical spine) and the nervous system [12]. The cervical spine is an integrated force system consisting of vertebrae, intervertebral discs and surrounding muscles and ligaments, which is very difficult to analyze mechanically.
In order to understand the changes in the mobility, internal stresses, etc. of the cervical spine, this study decided to use the finite element method to build a biomechanical model of the cervical spine. This study followed the elements of finite element modeling of the cervical spine proposed by Yoganandan [13]: anatomical profile (geometric features), material properties, boundary conditions and loads, and model validation, so that the model constructed accurately represents the entity being modeled. From the modeling results, it can be seen that the model has accurate geometry, comprehensive anatomical description, and high biofidelity, which can be used for cervical spine curvature and mobility studies under various laminectomy conditions and provides a tool for interpreting biomechanical changes after cervical laminectomy.
3.1. Geometric characteristics of the cervical spine finite element model
The two-dimensional model of the cervical spine established by Saito et al. in 1991 was overly simplistic in its geometric model of the vertebral body and internal joints, resulting in unrealistic results of load distribution and pressure distribution [14]. the three-dimensional finite element model of C0-T1 (including the vertebral body, disc and posterior structures and ligaments) established by Kleinberger et al. due to the lack of important anatomical structures such as articular protrusions, led to certain limitations and unsatisfactory application results [15]. In contrast, late Voo et al. used, CT data and FE model software I-DEAS to reconstruct a three-dimensional model of the cervical spine [16]. This model provided an accurate surface geometry of the cervical spine, including the articular surfaces and their relative positions between the cervical vertebrae, which was far superior to the model of Kleinberger and Saito et al.
In order to make the geometric features of the constructed model accurate and credible, in this study, thin-layer CT scans were performed on the cervical spine of volunteers, and then the skeletal geometric features of this model were read directly from the thin-layer (layer thickness 1 mm) CT scan data (DICOM format) by the specialized software MIMICS, and the outer surface of the vertebrae was extracted after image processing in MIMICS, and the data were converted to reverse engineering software Geomagic can read the data in stl format. The stl file was processed with Geomagic, and the triangular mesh was divided into surfaces. When dividing the surfaces, care was taken to save them as iges format files readable by the FEA software. Direct geometric modeling based on thin-layer CT and DICOM format data can accurately reflect the anatomical contours of the skeleton. In addition, the geometric model created by MIMICS also preserves the density information inside the bone, thus providing the convenience of defining different material properties according to different densities.
The geometric information of soft tissues such as ligaments, endplates, nucleus pulposus, and fibrous rings cannot be accurately obtained on the original CT images, and generally requires a combination of anatomical studies and cadaveric frozen thin serial sections to determine the ligament starting and ending points, length, broad band, and cross-sectional area, as well as the area and thickness of endplates, nucleus pulposus, and fibrous rings [13,,17,,18]. In this study, information on cadaveric frozen sections could not be obtained, and geometric information on soft tissues was obtained from anatomical studies.
3.3, Material properties of the cervical spine finite element model
The models created in finite element modeling are ultimately used in studies to simulate the biomechanical response of an organism, so the biofidelity of the model is also important. This is mainly related to the material of the model, therefore, the definition of the material is also a key part of the finite element model building. Because of the late start of cervical spine research and the scarcity of material data related to cervical spine, the material definition of early models was relatively simple, such as the model built by Kleinberger et al. defined the vertebrae as rigid material, the intervertebral disc as elastic material, the ligaments as linear elastic material, etc. The materials used in the whole model were relatively single, which was far from the complex and diverse materials of the actual cervical spine [15 ]. At the same time, because the lumbar spine and the cervical spine are relatively similar in composition and structure, and there is a relatively rich literature, some researchers have started to use the material parameters of the lumbar spine instead of the cervical spine material parameters. However, the biomechanical roles of the cervical and lumbar spine in the human structure are different, and their material properties are naturally different, and simple material substitution can lead to inaccurate and even distorted modeling results.Kumaresan et al. concluded that the material properties of soft tissues have a greater influence on the internal and external responses of the cervical spine than those of hard tissue structures [19].Ng et al. found that that the material properties of the intervertebral fibrous ring, cancellous bone and cortical bone have a significant effect on the biomechanics of the cervical spine [20].
The study by Carter et al. concluded that the empirical function relationship between compressive strength and density of bone applies to both cancellous and cortical bone [21]. They concluded that cortical and cancellous bone are similar in composition, microscopic material properties, and are both solid and liquid biphasic porous material structures (two-phase, porous, material); the distinction between cancellous and cortical bone is based on bone porosity (bone, porosity), and this distinction is somewhat arbitrary; the material anisotropy of bone properties are partly attributed to the geometry and orientation of the pores in the bone. Currently, shell or solid cells are commonly used for the simulation of cortical bone, with Young’s modulus set at 12000 MPa [14,, 22]. The simulation of cancellous bone uses solid cells with Young’s modulus of 100-450 MPa [14,, 23]. In this study, shell and solid units were used for cortical and cancellous bone with Young’s modulus of 12,000 Mpa and 450 Mpa, respectively, and solid units were used for posterior structures as reported in the literature with Young’s modulus of 3500 Mpa [22]. The loading ranges in this study were all within the physiological range, so the method used is basically feasible.
For the articular eminence joint, some of the literature uses separate simulations of articular cartilage and synovial fluid [22]; there are also simulations using face-to-face contact elements, and since the joint is wrapped by the joint capsule and the presence of synovial membrane and synovial fluid makes the friction between the joint surfaces very small, the articular eminence joint is simulated as a face-to-face contact model in the model of this study, and both face-to-face contacts of the joint are defined as frictionless properties.
Because the biodynamic characteristics of the cervical spine model are more susceptible to changes in the properties of the soft tissue materials than those of the harder structural bones, it is important to define the material properties of the various soft tissues. Ligaments are composed of elastic and collagen fibers and are attached between adjacent vertebrae. Because ligaments are fibrous tissues, they can only withstand tension loading under loading conditions. Therefore, the ligaments of the cervical spine such as the ligamentum flavum, interspinous ligament, and supraspinous ligament were simulated using linear materials with only tension properties [19]. In the present study, the ligamentous structures were simulated using tension-only linear units, and the Young’s modulus of each ligament was 10 MPa for the ligamentum flavum, 5 MPa for the interspinous and supraspinous ligaments, and 20 MPa for the joint capsule, whereas the anterior and posterior longitudinal ligaments were simulated in solid units because of their close attachment to the anterior and posterior surfaces of the vertebral body, and their Young’s modulus was 15 MPa for both the anterior and posterior longitudinal ligaments. the endplates were simulated using shell units The Young’s modulus was 500-600, Mpa [14,, 19]. In this study, the Young’s modulus of the solid unit was positioned at 500 MPa for the endplate, and the solid unit was used for the simulation of the nucleus pulposus and the fibrous ring, both of which had a Young’s modulus of 3.4 MPa [19].
In this paper, the existing material parameters of the cervical spine were scaled appropriately in proportion and function to ensure that the material properties match their biomechanical response under loading conditions by referring to the available experimental data on cervical spine materials and by making up for the lack of plaques in the material parameters of the cervical spine to provide some uniformity among the material parameters according to the biomechanical effects of each structure of the cervical spine. Nevertheless, because the experimental data used to define the model material properties are not measured by a solid that corresponds one-to-one with its morphological properties, inconsistency between geometric shape and material properties can result. Therefore, the material parameters of the model established in this paper still need to be improved in future studies.
3.4. Validation of the cervical spine finite element model
Whether the established model can reflect the biomechanical response of the object to be simulated by the model needs to be verified, and this process is similar to the verification process of equations in mathematics. The model can only be applied to further research if it is proven reasonable through validation; if the validation is not reasonable, all experimental analysis results derived from the model will be inaccurate or even wrong [13,, 24]. Model validation usually applies a certain load to the model, records the response of the model to the applied load, and compares the response data with the response data from experiments under the same or similar conditions to see if they match and thus determine whether the model represents the real situation simulated. Strictly speaking, the finite element model should be calculated using boundary conditions and loads that are identical to those of the cadaveric experimental study, and then the results of both should be compared to verify whether the model is reasonable, and it should be verified with as many different loading methods as possible to ensure the validity.
In view of the research conditions and time constraints, this study was not conducted in conjunction with cadaveric experiments for validation, but only based on data from the literature. In this paper, the model was loaded with a load of 1.5 Nm in the sagittal, coronal, and horizontal planes according to the right-handed spiral rule on the upper surface of the cervical 2 vertebrae of the above model to generate the corresponding moments in the sagittal, coronal, and axial planes to simulate anterior-posterior flexion and extension, lateral bending, and rotation in the forward and reverse directions. The response of the model was compared with the literature experimental results data (data on the response of the finite element model and the discrete model to the applied load in the literature), and the response data of the present model matched the data in the literature, and the model was considered valid. This indicates that further studies can be performed on the cervical spine using these models.
However, it is evident from the model validation results that there are some deviations between the data obtained from the model developed in this paper and the data obtained by other researchers. The possible reasons for the deviations are: (1) different experimental instruments and methods; (2) different sources of data used in the experiments, such as age, gender, ethnicity, morphology, etc., may have an impact on the results; (3) because the structure and material properties of the cervical spine are very complex, the finite element model will inevitably make certain simplifications; (4) each finite element model researcher has a different understanding of the simplification method of the model, the selection of material properties parameters, the quality of the mesh division, and the quality of the solution. (4) The differences in the method of simplification, the selection of material properties, the quality of meshing, the choice of solution method, etc. may also lead to differences in the results.
3.5 Control of other parameters in the establishment of the cervical spine finite element model
So far, except for a small number of full cervical spine finite element models established in China for Chinese body type, most of the model data are collected according to the 50th percentile human body type in Europe and America, and the difference between Chinese and European body types is relatively large. According to GB, 10000-88, the 50th percentile body size of Chinese people is 168 cm in height and 59 kg in weight, which was established in 1988, while the second large-scale adult body size measurement in China has not been completed. In the past two decades, the physical quality of Chinese people has improved significantly, and in order to make the selected data the closest to the 50th percentile body size of Chinese people nowadays, the average value of Chinese 50th percentile and foreign 50th percentile human body data is used as the basis for this data selection in this paper. So that the full cervical spine model established in this paper can reflect the Chinese body shape more accurately.
Anderson et al. proposed that the accuracy of finite element studies depends on three key factors: corroboration, sensitivity testing, and validation [25]. Corroboration consists of assessing the accuracy of the values, which is mainly the effect of meshing when a large amount of software is currently used. Model sensitivity is a key step in building a valid model and is mainly related to the definition of input parameters such as model materials. Model validation, on the other hand, is the comparison of experimental data with model data under the same or similar conditions to confirm that the results of the model match the real situation simulated [22,, 26].
Both the definition of material properties and the validation of the model have been discussed in the previous section. The confirmatory factor, i.e., the meshing, is crucial for finite element studies. The quality of the mesh cells will affect the accuracy of the finite element calculation results, and studies by Vander, Sloten and Vander, Perre have shown that a mesh with poor cell quality can make the stress calculation results deviate by 7-100% [27]. Therefore, a reasonable meshing method for different models to control the cell mesh quality is an extremely important task in the finite element modeling process. At present, the main meshing methods are automatic tetrahedral meshing, automatic raster-based hexahedral meshing and mapped meshing. The tetrahedral meshing method is to lay out points in the selected area and then join them into tetrahedra. This method is one of the most popular solid meshing methods, and almost all finite element pre-processing software can implement this method of meshing. However, in the process of mesh triangulation, it is difficult to control the shape of the generated cells, and the accuracy of mesh calculation is relatively low. The automatic grid-based hexahedral meshing method is to first cover the target region with a set of disjoint grids of the same or different sizes, keep the grids that fall completely or partially within the target region, delete the grids that fall completely outside the target region, then adjust, cut and re-decompose the grids that intersect with the object boundary to make them more accurately approximate the target region, and finally, perform grid-level adjustment of the internal grids and boundary Finally, the internal raster and boundary raster are dissected at the raster level to obtain the finite element mesh of the whole target area. This method automates the mesh generation, and the mesh generation is very fast, but the quality of boundary cells is poor, and the generated cells are similar in size, so the mesh density is difficult to control. The mapped meshing method is both a structured and unstructured mesh generation method, which is to map the physical domain to be dissected into the parameter space to form a regular parameter region through an appropriate mapping function, then perform mesh dissection on the regular parameter region, and finally reverse map the mesh of the parameter domain back to the physical space to obtain a finite element mesh of the physical domain. This method has simple algorithm, fast calculation speed, good cell quality, controllable cell density, and can generate both structured and unstructured meshes. However, when the surface of the 3D solid is a very complex free-form surface, the approximation accuracy of this method is not high, the manual partitioning is difficult, and the meshing is time-consuming. The computational accuracy of raster-based hexahedral meshes and mapped meshes is comparable, and the computational accuracy of tetrahedral meshes is poor [28]. Because the surface of the cervical spine three-dimensional solid is a relatively complex free-form surface, and because this study mainly investigates the changes in the mobility and stress distribution of the model after laminectomy, the tetrahedral meshing method is used in this paper.
3.6. Shortcomings of the finite element model constructed in this study
Although the finite element method is theoretically applicable to any complex structure, there are still many problems to be solved in the study of cervical spine biomechanics. Although the cervical spine model developed in this paper has been validated by comparison, it does not mean that it can be used to study all problems related to cervical spine biomechanics. The model has the following deficiencies in modeling: first, the model bony structure and intervertebral disc are simulated with isotropic linear material. In fact, both bone and intervertebral disc are anisotropic viscoelastic materials. Second, the model only includes bony structures, intervertebral discs and ligaments, and lacks the simulation of muscles. However, in the cervical spine stabilization system, muscles are important active systems and play a very important role in maintaining the stability of the cervical spine. Third, the synovial joint in the model of this study is only simulated with contact elements, but not the articular cartilage, and synovial fluid respectively. The model simplifies the ligaments into several separated wire units, so that the contact between ligaments during motion is ignored. Fourth, the model validation is based on static or quasi-static experiments, while the model response to dynamic experiments such as head collision and cervical spine whipping motion is not addressed. Therefore, in the next research work there is a need to improve the simulation of synovial joints and ligaments, increase the simulation of muscles, and use more experimental data to validate the model in order to improve the reliability of the model.
The finite element model can reflect the mechanical properties of the organism at a moment and a point. However, the organism itself is tissue active and has a process of growth, maturation and decline; some damaged tissues have the ability of self-repair and shaping. The finite element model established in this study is still powerless in terms of biological adaptability. The mechanical properties of the vertebral body, ligaments, intervertebral discs and other tissues are extremely complex, and it is difficult to obtain sufficient and reliable measurement data, while the data obtained from ex vivo experiments may differ from the physiological situation, so the definition of material properties of the cervical spine finite element model in this study should be further improved. The anisotropy, inhomogeneity and nonlinearity of the cervical spine tissue materials make it difficult to determine their own structural relationships; while the division of cells, the selection of nodes, and the specification of loads and boundary conditions are to some extent artificial, and the model constructed in this study cannot fully reflect the real biomechanical properties of the human cervical spine. Therefore, the finite element model of the cervical spine has some limitations and needs to be further improved and compared with more experimental results for further verification.
4. Conclusion
The establishment of a cervical spine model is a prerequisite for cervical spine biomechanical research. In this paper, a finite element model of the cervical spine containing all major ligaments of the cervical spine (cervical 2-7,) was established based on CT image data of 50th percentile healthy adult male volunteers in Chinese. The model was simulated using 8-node shell unit, 10-node tetrahedral solid unit and 2-node line unit unit with tension only for cortical bone, cancellous bone and ligaments of cervical spine, respectively. The validity of the proposed cervical spine model was verified by using data from previous finite element models and ex vivo experiments, and the verification results showed that the model has good biofidelity and can be used for further studies. The simulation of soft tissues such as muscles, the simulation of material properties and wide applicability need to be further improved in the study of cervical spine finite element modeling.