**6.1 Haptic rendering**

180 Haptics Rendering and Applications

shear, flexion/extension, lateral bending and torsion is created (Figure 16). After that, the translational and torsional stiffnesses of the spring structure are determined. Finally, since adding this spring structure into the spine model is quite troublesome, a bushing element

that can specify all stiffness properties of the structure is used instead (Figure 17).

Fig. 16. The spring structure used in the spine model

**5.7 Validation of the detailed spine model** 

presented as follows:

2001).

Fig. 17. An equivalent bushing element replacing the spring structure

model (2007) and experimental data (McGill & Norman, 1987).

To validate the detailed spine model presented above, two approaches are used and

 With the same extension moment generated in upright position, axial and shear forces in the L5-S1 disc calculated in the model are compared to those obtained from Zee's

 While a subject holds a crate of beer weighing 19.8 kg, the axial force of the L4-L5 disc is computed and compared with in-vivo intradiscal pressure measurements (Wilke et al.,

In the first approach, a gradually increasing horizontal force was applied onto the vertebra T7 of the spine model from posterior to anterior in the sagittal plane. From this force, axial Haptic rendering is the process of applying forces to give the operators a sense of touch and interaction with physical objects. Typically, a haptic rendering algorithm consists of two parts: collision detection and collision response. Figure 18 illustrates in detail the procedure of haptic rendering. Note the update rate of haptic rendering has to be maintained at around 1000 Hz for stable and smooth haptic interaction. Otherwise, virtual surfces feel softer. Even worse, the haptic device vibrates.

To observe the locomotion and study dynamic properties of the spine model quickly, conveniently and more realisticly, haptic technique can be integrated into a spine simulation system. In this study, for two types of spine models developed using finite element method as well as multi-body method in LifeMOD software, the haptic rendering process has two main stages: the rigid stage and the compliant stage. Without pressing the stylus button of the PHANToM device, the users can touch and explore the whole spine model since it is considered to be rigid throughout. After the users locate a specific vertebra where he/she wishes to apply force, they can then press the PHANToM stylus button and push or drag the vertebra in any direction to make the whole spine model deform. Once the stylus button is pressed, the system switches from rigid stage to compliant stage. The haptic rendering algorithms in these two stages will be clearly presented in the following sections. Figure 19 shows the complete haptic simulation process in the system.
