*2.4. Convergence Test*

Convergence tests were performed on the intact model. First, the displacement of a reference point at the center of the T10 superior endplate was measured under a 150 N axial preload. Four different amounts of elements, 190,432, 208,776, 309,217, and 555,384, were compared for the displacements. By setting the displacement of the T10 superior endplate in a model consisting of 1,199,183 elements as the reference value, the errors of the simulations with the total number of elements reduced were all within 4.9 percent. Next, the maximum von Mises stress in posterior elements under a 150 N axial preload was compared. Compared to the reference model, the error of the four models with the total number of elements reduced were all within 7.9 percent. For material stress, it is generally expected that the error may be greater than displacement in FE models [30]. In the present

model, we selected the model consisting of 309,217 elements for the intact model based on the small relative displacement error of 2.84% and a von Mises stress error of 4.18%, with the element size ranging from 1.0 to 2.0 mm. The convergence tests were performed on the implant models, including the pedicle screws and titanium cage. For the titanium cage, a final model consisting of 134,203 elements with mesh sizes ranging from 0.4 to 0.6 mm was selected. The error was 3.96% compared to the reference model with 220,141 elements. For the pedicle screw, a final model with 13,927 elements and element size ranging from 0.1 to 1.0 mm was selected. The error was 0.92% compared to the 23,550 element reference.
