742 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 6, JUNE 2003 Nonlinear Finite-Element Analysis and Biomechanical Evaluation of the Lumbar Spine Christian Wong*, P. Martin Gehrchen, Tron Darvann, and Thomas Kiær Abstract—A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompress- ible nucleus surrounded by nonlinear annulus fibers embedded in a solid ground substance. The purpose was to create a FEA model suitable for clinical purposes as fracture assessment, instrumenta- tion with pedicle screws, and bone remodeling. Testing of the FEA model was performed nonlinear for a number of loading conditions, and the results were compared with experimental data from the literature. The results showed good agreement. The formulation of the FEA model can be justified for the tested loading conditions. Index Terms—Computed tomography (CT) scan and lumbar spine, finite-element analysis (FEA), geometric generation. I. INTRODUCTION T HE BIOMECHANICAL relationships of the vertebral column have been examined using finite-element analysis (FEA). The purposes of FEA in the spine have been to address biomechanical issues of spine physiology [16], spinal diseases [13], surgery of the spine [7], and bone remodeling [9]. In this paper, the purpose was to create a FEA model suitable for clinical, surgical patient-specific problems as fracture stability [24], spinal instrumentation [23], and bone remodeling effects of surgery [23]. The requirements for such FEA models would be patient-specificity in geometry and should be generated within a reasonable computed analysis time if used preopera- tively. Considering these aspects automated mesh generation of the complex geometry of the region would be appropriate. The proposed FEA model consists of two adjacent vertebral bodies with an incompressible intervertebral disc and a nonlinear ligamentous apparatus. In order to evaluate this approach, the computed FEA results have been compared with experimental data derived from other studies [7]. II. METHODS AND MATERIAL In this paper, the finite element-analyses were performed with the nonlinear static module of the general purpose FEA Manuscript received June 26, 2002; revised January 10, 2003. Asterisk indi- cates corresponding author. *C. Wong is with the Department of Orthopaedics, National University Hospital of Copenhagen, Rigshospitalet, Blegdamsvej 9, 2100 Copenhagen Ø, Denmark (e-mail: cw@dadlnet.dk). P. M. Gehrchen and T. Kiær are with the Department of Orthopaedics, National University Hospital of Copenhagen, 2100 Copenhagen Ø, Denmark. T. Darvann is with the 3Dlab, School of Dentistry, University of Copenhagen, 2200, Copenhagen N, Denmark. Digital Object Identifier 10.1109/TMI.2003.814783 Fig. 1. Stress-strain curves for spinal ligaments. program, COSMOSM ® on a Silicon Graphics ® R10000 High Impact UNIX workstation. A. Material Properties and Element Types Used In general, the material types and properties were chosen as a compromise of accuracy and time-efficient analysis. 1) Vertebral Body: All trabecular bone and posterior parts were modeled by four-node three-dimensional tetrahedral solid elements (TETRA4). The cortical bone and the cortical endplates consisted of a shell layer 1- and 0.5-mm-thick surrounding the trabecular core, respectively. The cortical shell was modeled by three-node triangular thin shell elements (SHELL3). Both ele- ment types were chosen, since automated mesh generation was available in the FEA program, thus minimizing the time-con- suming manual meshing. By keeping a uniform mesh density for mesh generation of both solid elements and shell elements a total bonding situation was obtained, thus increasing accuracy. The material properties for cortical bone, trabecular bone and bony posterior parts were considered isotropic and linear, thus mini- mizing the analysis time [7]. 2) Ligaments: The ligaments were applied to the model manually. The bony insertion points were connected by two- node 3-D uniaxial elements (TRUSS3D). The directions of the el- ements were orientated along the fiber direction of the ligaments. These directions were obtained from the literature [17]. Material properties were defined as nonlinear stress-strain curves in ac- cordance to Smit et al. [20] and are illustrated in Fig. 1. Since the 0278-0062/03$17.00 © 2003 IEEE