**4. Finite element modeling of the spine**

In context of most researchers mainly focusing on modelling partially the spinal regions, the construction of a finite element model of the human spine can be useful for clinicians to investigate clinical problems by predicting its biomechanical behaviour. A beam finite element (FE) spine model for haptic interaction is built based on a solid FE spine model, which is created in offline finite element analysis (FEA) software. The mechanical properties of the beam FE spine model are tuned so that its deformation behavior is very similar to that of the offline solid spine model. Furthermore, the online beam FE spine model is greatly simplified as compared to the offline solid FEA model and hence more appropriate for realtime simulations. Haptic feedback is provided in the real-time simulation of the beam FE

Development of a Detailed Human Spine Model with Haptic Interface 171

results. The displacement and deformation of the spine from the haptic simulator is then input to the offline FEA application for further detailed analysis. This offline computation is carried out when there is no direct haptic interaction and sufficient computational time.

Initially, two types of FE models, beam element and tetrahedral element models, were created based on 3D models of scanned vertebrae. Material properties of FE models should be validated before simulation. In the haptic simulator, a user can push or pull any vertebra in any arbitrary direction to observe the resulting deformation of the whole spine. After the user is satisfied with the deformation of spine model in haptic simulator, the displacements of some focused vertebrae are input to the offline commercial FEA application for more

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

A major concern is the high updating rate that is required for haptic rendering. Low rates can result in instability or vibration when using the haptic device. The FE model for haptic

detailed simulation and the results of stress and strain information can be obtained.

models can be constructed according to these geometric models.

**4.1 Geometric modeling of vertebrae** 

Fig. 7. Process of geometric modeling

**4.2 Finite element modeling for haptic rendering** 

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

Fig. 6. Architecture of the modelling system

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 results. The displacement and deformation of the spine from the haptic simulator is then input to the offline FEA application for further detailed analysis. This offline computation is carried out when there is no direct haptic interaction and sufficient computational time.

Initially, two types of FE models, beam element and tetrahedral element models, were created based on 3D models of scanned vertebrae. Material properties of FE models should be validated before simulation. In the haptic simulator, a user can push or pull any vertebra in any arbitrary direction to observe the resulting deformation of the whole spine. After the user is satisfied with the deformation of spine model in haptic simulator, the displacements of some focused vertebrae are input to the offline commercial FEA application for more detailed simulation and the results of stress and strain information can be obtained.
