Abstract:The complex motion and geometry of the spine in the cervical region makes it difficult to determine how loads are distributed through adjacent vertebrae or between the zygapophysial (facet) joints and the intervertebral disc. Validated finite element modes can give insight on this distribution. The aim of this contribution was to produce direct validation of subject-specific finite element models of Functional Spinal Units (FSU׳s) of the cervical spine and to evaluate the importance of including fibre directio… Show more
“…Actually, the AF can be modeled as a reinforced matrix fiber. Particularly, the matrix or ground substance has been modeled using the energy functions of Mooney-Rivlin [13][14][15][16][17][18] and Yeoh [19][20][21][22][23][24][25][26]. However, we did not find any study that supported the use of these energy functions and how they affect the mechanical behavior of the AF.…”
Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.
“…Actually, the AF can be modeled as a reinforced matrix fiber. Particularly, the matrix or ground substance has been modeled using the energy functions of Mooney-Rivlin [13][14][15][16][17][18] and Yeoh [19][20][21][22][23][24][25][26]. However, we did not find any study that supported the use of these energy functions and how they affect the mechanical behavior of the AF.…”
Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.
“…As soft tissues cannot be distinguished in the micro-CT images, a systematic protocol was developed to create the annulus and nucleus regions of the disc based on the diameter ratio measured in the first part of this study and assuming relatively straight sides from one endplate to the other, which is a good approximation for bovine caudal discs [ 8 ]. Finite-element models were produced using the segmented geometry and underlying greyscale, with a homogeneous linear tetrahedral mesh with a size based on previous studies [ 5 ]. Figure 2.…”
The development of current surgical treatments for intervertebral disc damage could benefit from virtual environment accounting for population variations. For such models to be reliable, a relevant description of the mechanical properties of the different tissues and their role in the functional mechanics of the disc is of major importance. The aims of this work were first to assess the physiological hoop strain in the annulus fibrosus in fresh conditions (n = 5) in order to extract a functional behaviour of the extrafibrillar matrix; then to reverse-engineer the annulus fibrosus fibrillar behaviour (n = 6). This was achieved by performing both direct and global controlled calibration of material parameters, accounting for the whole process of experimental design and in silico model methodology. Direct-controlled models are specimen-specific models representing controlled experimental conditions that can be replicated and directly comparing measurements. Validation was performed on another six specimens and a sensitivity study was performed. Hoop strains were measured as 17 ± 3% after 10 min relaxation and 21 ± 4% after 20–25 min relaxation, with no significant difference between the two measurements. The extrafibrillar matrix functional moduli were measured as 1.5 ± 0.7 MPa. Fibre-related material parameters showed large variability, with a variance above 0.28. Direct-controlled calibration and validation provides confidence that the model development methodology can capture the measurable variation within the population of tested specimens.
“…This approach has been accomplished using motion‐capture technology dynamic measurements of cervical spine physiology, and by inducing the instability of two states of activities. More recently, finite element analysis has been adopted to analyze the mechanics of limited movement in the upper cervical‐spine‐instability model, and to reveal relationships between mechanical changes and instability of the cervical spine ligament.…”
Objectives
To establish a dynamic three‐dimensional (3D) model of upper cervical spine instability and to analyze its biomechanical characteristics.
Methods
A 3D geometrical model was established after CT scanning of the upper cervical spine specimen. The ligament of the specimen was fatigued to establish the upper cervical spine‐instability model. A 100‐N preloaded stress was applied to the upper surface of the occipital bone, and then a 1.5‐Nm moment was applied in the occipital‐sagittal direction to simulate upper cervical spine flexion and extension. Subsequently, the 3D dynamic model was established based on trajectory data that were measured using a motion‐capture system. The stress on the main ligament and the relative motion angle of the joint were analyzed.
Results
The shape of the model grid was regular and the total number of its units was 627 000. After finite‐element analysis was conducted, results of the ligament stress and relative movement angle were obtained. After the upper cervical spine instability, the pressure of the alar ligament during the upper cervical spine extension was increased from 2.85 to 8.12 MPa. The pressure of the flavum ligament was increased during the upper‐cervical spine flexion, from 0.90 to 1.21 MPa. The pressure of the odontoid ligament was reduced during the upper cervical spine flexion and extension, from 10.46 to 6.67 MPa and 25.66 to 16.35 MPa, respectively. The pressure of the anterior longitudinal ligament and cruciate ligament was increased to a certain degree during upper cervical spine flexion and extension. The pressure of the anterior longitudinal ligament was increased during flexion and extension, from 7.70 to 10.10 MPa and 10.45 to 13.75 MPa, respectively. The pressure of the cruciate ligament was increased during flexion and extension, from 2.29 to 4.34 MPa and 2.32 to 4.40 MPa, respectively. In addition, after upper cervical spine instability, the articular‐surface relative‐movement angle of the atlanto‐occipital joint and atlanto‐axial joint had also changed. During upper cervical spine flexion, the angle of the atlanto‐occipital joint was increased from 3.49° to 5.51°, and the angle of the atlanto‐axial joint was increased from 8.84° to 13.70°. During upper cervical spine extension, the angle of the atlanto‐occipital joint was increased from 11.16° to 12.96°, and the angle of the atlanto‐axial joint was increased from 14.20° to 17.20°. Therefore, the movement angle of the atlanto‐axial joint was most obvious after induction of instability.
Conclusion
The 3D dynamic finite‐element model of the upper cervical spine can be used to analyze and summarize the relationship between the change of ligament stress and the degree of instability in cervical instability. Frequent or prolonged flexion activities are more likely to lead to instability of the upper cervical spine.
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