Development, Verification, and Validation of a Parametric Cervical Spine Injury Prediction Model

The objective of this investigation is to develop a high fidelity, parametric finite element model of the cervical spine motion segment using a hierarchical model verification and validation approach. A technique has been developed to accurately describe the geometry of the cervical spine using a set of unique geometry parameters that are easily measured from clinical imaging systems such as Computed Tomography (CT) scans and to efficiently convert this geometry into a well-defined finite element model. Cervical spine parameters were measured from CT scans collected from a total of 73 volunteers, 50 male and 23 female. The parametric finite element model development includes a hierarchical model verification and validation (VV a model is only meant to represent the conditions in which it is validated (Ng et al., 2001). Measured geometries of the cervical spine have been used to create numerous finite element models. In the model created by Ng et al. (2001), and also used by Teo et al. (2001), the geometry was created by digitally scanning a dried cervical spine specimen from a 68-year old man. Yang et al. (1998) created a model using cervical spine geometry obtained from magnetic resonance imaging (MRI) of a 50th percentile male. The widely used KTH model was constructed using vertebral geometries based on the CT images of a 27 year old male, that were then scaled to those of a 50th percentile male (Brolin et al., 2004). Although scaling techniques have been used to develop injury criteria for dummies of various sizes (Hilker et al., 2002), this may not be a viable approach. The cervical spine geometry of females is not simply a scaled down male geometry (Mordaka et al., 2003). Therefore, a parametric cervical spine model is needed to better represent the entire population that the model is going to represent. By employing a parametric finite element model approach, finite element models can be generated by simply inputting the new geometry parameter values saving time when numerous models are going to be created, and also allowing for probabilistic analyses. Verification and validation studies form the crucial link between the development of the finiteelement model and its ultimate intended use. They are the primary processes used in quantifying and building confidence in finite element models. Verification is the process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model. Validation is the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model (American Institute of Aeronautics and Astronautics, 1998; Thacker, 2003). In short, verification deals with the mathematics associated with the model, whereas validation deals with the physics associated with the model (Roache, 1998). Hierarchical verification and validation starts from the smallest components of a finite element model increasing in complexity to the complete system model (Figure 1). The response of the model is validated at each level before continuing on to the next without modifying model parameters at the complete model level to fit the experimental data. In cr ea si ng I m po rt an ce Component Level Meso-Component Level Segment Level Complete Finite Element Model In cr ea si ng I m po rt an ce Figure 1: Verification and validation hierarchy. The objective of this investigation is to develop a high fidelity, parametric finite element model of the cervical spine motion segment using a hierarchical model verification and validation approach. A technique will first be developed to accurately describe the geometry of the cervical spine using a set of unique geometry parameters that can be measured from Computed Tomography (CT) scans. The geometry will then be used to create a well-defined finite element model. Finally, the model will be verified and validated using a hierarchical approach. Development, Verification, and Validation of a Parametric Cervical Spine Injury Prediction Model 143 METHODS Parametric Model Development A parametrically defined cervical vertebra was defined using a parametric solid modeling software package (Pro/ENGINEER) (Figure 2a). The finite element mesh was then created using TrueGrid from a surface representation of the solid model exported from Pro/Engineer (Figure 2b ). The mesh was constructed in several partitions to ensure uniform fidelity and to more easily accommodate changes in the nominal motion segment geometry resulting from perturbations in geometry parameters. After the mesh was constructed, boundary conditions were assigned to the model, and a mesh refinement study was performed to determine the mesh that would be used for the probabilistic analysis. a b Figure 2: Parametrically defined (a) solid model of the cervical vertebra and (b) mesh. Geometry Parameter Measurement CT scans of the cervical spine of 73 volunteers (23 female and 50 male) were obtained in digitized format. The CT image stacks were re-sliced to allow measurements on four different planes (Figure 3). A total of 35 parameters were measured for each vertebra, C3 through C7 (Figure 4). Four of the 35 parameters are angles, and were measured in degrees, whereas the remaining 31 parameters were measured in millimeters. A parameter index was included for each measurement: ap – articular process, pd – pedicle, sp – spinous process, tp – transverse process, and vb – vertebral body. All of the measurements were performed using a freely available image processing software package (ImageJ 1.34, National Institutes of Health, USA). A single researcher made all of the parameter measurements to maintain consistency and minimize error.