**4.1 Geometric modeling of vertebrae**

170 Haptics Rendering and Applications

spine model, in order to enhance the human-computer interaction. Based on the results of spine deformation obtained from the haptic online FE simulator, the offline FEA spine model again is used to reproduce the same deformation and hence to provide more detailed deformation and vertebrae's stress/strain information, which the haptic beam FE model is

Effective haptic interaction requires a high updating rate of around 1kHz and only a simple FE spine model can be used without significant latency. FE solvers for haptic interfaces are often restricted to linear or simple non-linear solutions. Most research on FE simulation of the spine uses tetrahedral or brick element types in order to obtain thorough representations of spinal deformation. However, a haptic interface's requirement for high updating rate makes it difficult to use solid elements in the haptic virtual environment, because these often result in huge numbers of elements and nodes. Therefore, a beam element was chosen for this real-time haptic simulator. The beam element type provides very limited information concerning stress and strain of vertebrae or inter-vertebral discs, which is potentially important for representing realistic behaviour. In order to provide stress/strain information of spinal deformation, commercial FEA software (in this case ABAQUS) is employed using a tetrahedral element and computed offline. The complete simulation is achieved in two steps. Firstly, simulation in the online haptic simulator obtains quick, intuitive but relatively rough

not capable to provide. Figure 6 shows the architecture of the system.

Fig. 6. Architecture of the modelling system

In order to create a geometric model, a healthy spine is preferable to a specific diseased one. For our system, a resin spine prototype (Budget Vertebral Column CH-59X Life Size 29" Tall), which is cast from a Chinese-Singaporean cadaver, was digitized to create the geometric model of the spine (Figure 7(a)). A common method used to build computer models of the spine is by stacking computed tomography (CT) images sequentially to develop and discretize the 3D solid model. However, with this method, the computer model does not properly represent the surface geometry of the highly irregular vertebra, especially its posterior part. For this reason we used laser scanning of the individual surfaces of the model vertebrae to generate the initial point-cloud data set as can be seen in Figure 7(b). Spline (NURBS) surface models were then constructed based on the polygonal meshes generated from the scan data (Figure 7(c) and (d)). These NURBS models can then be used as templates for CAD model generation. Customized models can be obtained by modifying these templates according to dimensional specifications taken from individual patients (Mastmeyer et al., 2006). Once the geometric models of vertebrae have been prepared, FE models can be constructed according to these geometric models.

Fig. 7. Process of geometric modeling
