Development of a Nonlinearly Cervicothoracic Column
This study used the piublished finite-elemet model by the current authors [16]. It was established an osseo-ligamentous cervicothoracic model from C2 to T1 segments using computed tomography (CT) of a 55-year-old male volunteer without any cervical disease. The CT images of his cervicothoracic column with 1-mm transverse slice separation were reconstructed in three dimensions with triangular surface meshes using PhysiGuide software, version 2.3.1 (Pou Yuen Technol8ogy Co., Changhua, Taiwan). The surface meshes were further transformed into a solid model with smooth and seamless surfaces by using SolidWorks software, version 2018 (SolidWorks Corporation, Concord, MA, USA).
The cervicothoracic model consisted of vertebral bodies, posterior bony elements, endplates, intervertebral discs, and surrounding ligaments (Fig. 1). Vertebral body were composed of a cortical shell and a cancellous core. The articulating surfaces of the paired facet joints were cautiously prepared to ensure interfacial contact during excessive motion. The curved gaps of the healthy facet joint were consistently 0.5 mm in an unloaded neutral position [17]. The endplate was modeled as a 1-mm plate, sandwiched between the vertebral body and intervertebral disc. An intervertebral disc consisted of an annular fibrosus and a nucleus pulpous. The annulus fibrosus was modeled as a hyperelastic composite [18], while the nucleus pulpous was simulated as a cavity filled with noncompressive fluids.
The ligaments included the anterior longitudinal ligament, posterior longitudinal ligament, supraspinous ligament, interspinous ligament, intertransverse ligament, ligamentum flavum, and facet capsular ligament. The ligaments were modeled as the tension-only springs to join their attachment points on adjacent vertebrae (Table 1). The insertions and origins of the ligaments on the right and left sides were assumed symmetrical with respect to the sagittal plane. Except for the cancellous core, the constitutive laws of all bony tissues were assumed to be linearly elastic and isotropic. The material properties of bones, endplates, discs, and ligaments were obtained from the literature (Table 1) [17-19].
The C4-C7 segments were simulated as moderate degeneration with the height reduced by 33%, the annulus area expanded by 40%, the nucleus modulus increased by 66%, and the facet gap decreased by 0.3 mm because of dehydration (Fig. 2A) [20]. For the PAP construct, the artificial disc was instrumented into the C5-C6 segment and the peek cages were inserted to the C4-C5 and C6-C7 segments. For the APP construct, the C4-C5 segment was instrumented with an artificial disc and two peek cages were removed to the C5-C7 segments (Fig 2C).
The artificial disc and intervertebral cage used in this study were the Prestige LP Cervical Disc System (Medtronic Sofamor Danek, Memphis, TN, USA) and Cervios system (Synthes, Paoli, PA, USA). The spikes of the cages were neglected for computational efficiency (Fig. 1B). Placement of the artificial disc and peek cages were monitored by an orthopedic surgeon. This study used the terms “cranial” and “caudal” to denote the different cages and adjacent (C3-C4 and C7-T1) segments, respectively (Figs. 2B and 2C).
Finite-element Analyses
The bottom surface of the T1 vertebral body was fully constrained and the cervicothoracic column was flexed by the follower and concentrated loads (Fig. 1). The follower loads (73.6 N) were used to stabilize the cervicothoracic column and simulated by the tube–slider–cable mechanism in which the slider could slide along the tube hole and the springs were connected piece-by-piece by the sliders [19]. The tubes were placed at optimal sites posterior to the center of each vertebral body [21]. The pulling load was exerted at the cable end in the tangential direction of the cable curve. The concentrated loads (1.0-Nm moment) were driven from the head weight and muscular contractions, and applied at the cervicothoracic end [19]. Using the displacement-controlled method [22], the criterion for controlling the same motion was adopted as a reasonable approach for evaluating the implant-induced effects on the adjacent segments and implants.
The interfaces of facet joints and artificial disc were modeled as the surface-to-surface contact elements, which allow separation and slippage thereby reducing friction.16,17 The other interfaces between implants and tissues were assumed to be bonded. All implant materials were assumed to have linearly elastic, homogeneous, and isotropic material properties throughout (Table 1). The calculated von Mises stresses of all implants were compared with the yielding strength of the corresponding material to validate the assumption of linear elasticity.
An automatic algorithm was used to generate the ten-node tetrahedral solid elements to mesh the cervicothoracic constructs. The mesh refinement was locally controlled at the high stress-concentrated sites and articulating surfaces. Using an aspect ratio and a Jacobian check, the quality of all elements was monitored to avoid sharp discontinuities and unrealistically high stress concentrations. Mesh refinement was conducted for modeling accuracy until excellent monotonic convergence behavior with <5% difference in the total strain energy was achieved. A nonlinear algorithm with a large-deformation formula and direct-sparse solver was used via SolidWorks simulation software.
Validation of the Finite-element Model
Experimental and numerical comparisons were used to validate the simplifications and assumptions of the current model. Using the experimental and numerical data of Kallemeyn et al. [18], the assumed loads (1.0 Nm) were exerted onto the cervicothoracic top of the C2-C7 model to calculate the cervical range-of-motion (i.e. disc angle) of the current model. The calculated results were validated by the total disc angles for flexion, extension, bending, and rotation. For the facet forces, the current C3-C6 model was validated by the extension data of Jung et al. [19] During the validation, the initially chosen elastic moduli of the disc and some ligaments were slightly modified within the physiological range to improve the consistency with the cadaveric results.
Five indices were chosen to evaluate the effects of the hybrid strategy on the adjacent tissues and implants, including disc angles, disc stresses, facet forces, cage stresses, and stress and articulation of artificial disc. The von Mises stress was used as the index of the equivalent stress in this study. The disc and cage stresses were defined as the average value of the stresses within the overall disc and cage, respectively. The facet force was the sum of normal contact at the right and left facet joints. After flexion, the articulation of the artificial disc was defined as the relative slippage of the articulating surfaces.