1. 3Texas Back Institute Research Foundation, Plano, TX, USA
Mesh Sensitivity Analysis for a Healthy Lumbar Spine Finite Element Model
1Ming  Xu, MS,, 1James Yang, PhD, 2Isador H. Lieberman, MD, 3Ram Haddas, PhD
1Texas Tech University, Lubbock, TX, USA; 2Texas Back Institute, Plano, TX, USA;
3Texas Back Institute Research Foundation, Plano, TX, USA
Introduction
Finite element (FE) method has been widely used in the study of human lumbar spine due to its lower cost and higher efficiency compared to the traditional experimental approach [2]. The human lumbar spine has complex geometry, material properties, and loading conditions and the geometry and material properties of lumbar spine vary greatly among different individuals [7]. To eliminate the effect of individual variability in lumbar spines, new FE models are still required for specific subjects. To build reliable new FE spine models, verification and validation are necessary [8]. The meshing sensitivity analysis is an important step in the verification of FE analysis [6]. The mesh resolution can greatly affect the accuracy in lumbar spine FE simulation and efficiency [1]. Some literature introduced a lumbar spine FE model with a coarse mesh resolution of 44,422 elements  and 54,178 nodes [1]. The purpose of this study was to analyze the mesh sensitivity in a newly built healthy lumbar spine FE model.
Discussion
In this study, mesh sensitivity for a newly developed healthy human lumbar spine FE model was performed through stress convergence. One appropriate mesh resolution consisting of 99,610 elements and 113,874 nodes was found by comparing three different mesh resolutions, which could achieve the lowest computational cost while guarantee the stress convergence in the FE analysis. Mesh 2 was considered to be stress-converged consistent with other literature reports.
Methods
A three dimensional (3D) FE model of 23-year old healthy male lumbar spine was built based on a series of CT scans [5]. The model was symmetric by the sagittal plane. The spinal segments and the intervertebral discs of levels L1-5 were included in this model. Seven major ligaments and the muscle forces were considered with necessary simplification [4]. The 3D geometry of this FE model was constructed in 3D Slicer® followed by a smoothing process in Geomagic Studio®. The smoothed outer surfaces of the spinal bones were imported into TrueGrid® for meshing purpose. Three mesh resolutions were generated separately for the FE model for each mesh (Figure 1). The meshed FE models were input into LS-DYNA® for FE analysis. The bottom of the L5 spinal bone segment was fixed. For each mesh resolution, a static load which combined a compressive force of 1,000 N with flexion moment of 7.5 Nm was applied on level L1 [4]. The compressive force was applied as follower force [3]. The percentage differences of von Mises stresses in different lumber spine locations of the FE model were calculated and compared for each mesh resolutions. .
References
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Results
The von Mises stress differences in percentage between Mesh 1 and Mesh 3, Mesh 2 and Mesh 3 were calculated and compared. The von Mises stress difference between Mesh 1 and Mesh 3 was larger than 5% in 3 out of 6 locations ranging from 2.71% to 13.67%. The von Mises stress differences between Mesh 2 and Mesh 3 in 5 out of 6 locations were less than 5% ranging from 1.14% to 5.21% (Figures 2 and 3).
Significance
The meshing method introduced in this study could be employed in the development of other subject FE lumbar spine models. The stress-converged mesh resolution found in this study could guide future meshing tasks of lumbar spine FE model as well.