**7.2 Studying stress/strain of the finite element spine model in a prone position**

As presented above, all dynamic properties of the spine model recorded during the haptic simulation can be provided as input of offline FEA simulator for further detailed analysis. In

Development of a Detailed Human Spine Model with Haptic Interface 189

Figure 24(b) shows the spine model under deformation. The deformation is then recorded and the displacement of the focused vertebra, T12 in this case, is obtained and input into the offline FEA solver. Figure 25 shows the result from the ABAQUS offline FEA solution. Only T9 to the pelvis is shown because this region is the most interesting region if a pressing load is applied on T12. The offline FEM model consisted of cortical bones, cancellous bones, bony end plates and the intervertebral discs. The disc's annulus was represented as a composite of collagenous fiber embedded in a matrix of base substance. The nucleus was modelled as an incompressible inviscid fluid. Because intervertebral discs often experience large deformation and strains under compressive loading, the materials of the FEM spine model were non-linear. Figure 25(a) shows the tetrahedral FE model without deformation. Figure

(a) (b) (c)

**7.3 Investigating dynamic properties of the spine model under external haptic forces**  Since the finite element spine model for the haptic simulation is represented with beam element which is in fact highly simplified, it is difficult to describe precisely the dynamic properties of the real spine. Compared to this finite element spine model, the detailed musculo-skeletal multi-body spine model developed in LifeMOD can provide better information of biodynamic behaviour of the spine. Since LifeMOD software takes account of other components (such as head, ribcage, muscles, ligaments so on), the locomotion of the spine model will become much more realistic. Furthermore, by simulating the spine model in a haptically integrated graphic environment, the users (such as surgeons, trainers) can quickly and conveniently observe the locomotion as well as gain insight into the dynamic

Fig. 25. Offline FEA simulation

behaviour of the spine.

25 (b) and (c) show the von Mises stress distribution after deformation.

this section, an example of spine manipulation is demonstrated. A human body is prone on a horizontal table and a downward force is pushed on T12 vertebra. Therefore, the spine is also in prone position. All 6 DOFs of the pelvis are constrained and 2 DOFs of the T1 on the horizontal plane are constrained in order to simulate the situation where the prone posture torso is constrained by a horizontal plane underneath the torso. In the haptic simulator, downward pressing forces are applied to the T12 vertebra by the user through the PHANToM device. Figure 24(a) shows the beam element spine model at initial status without any deformation.

Fig. 23. The haptic real-time simulation of finite element spine model

Fig. 24. Spine manipulation in the haptic real-time simulator

this section, an example of spine manipulation is demonstrated. A human body is prone on a horizontal table and a downward force is pushed on T12 vertebra. Therefore, the spine is also in prone position. All 6 DOFs of the pelvis are constrained and 2 DOFs of the T1 on the horizontal plane are constrained in order to simulate the situation where the prone posture torso is constrained by a horizontal plane underneath the torso. In the haptic simulator, downward pressing forces are applied to the T12 vertebra by the user through the PHANToM device. Figure 24(a) shows the beam element spine model at initial status

Fig. 23. The haptic real-time simulation of finite element spine model

The direction of down ward pressing force

(a) (b) (c) (d) (e) (f) (g) (h)

(a) (b)

Fig. 24. Spine manipulation in the haptic real-time simulator

without any deformation.

Figure 24(b) shows the spine model under deformation. The deformation is then recorded and the displacement of the focused vertebra, T12 in this case, is obtained and input into the offline FEA solver. Figure 25 shows the result from the ABAQUS offline FEA solution. Only T9 to the pelvis is shown because this region is the most interesting region if a pressing load is applied on T12. The offline FEM model consisted of cortical bones, cancellous bones, bony end plates and the intervertebral discs. The disc's annulus was represented as a composite of collagenous fiber embedded in a matrix of base substance. The nucleus was modelled as an incompressible inviscid fluid. Because intervertebral discs often experience large deformation and strains under compressive loading, the materials of the FEM spine model were non-linear. Figure 25(a) shows the tetrahedral FE model without deformation. Figure 25 (b) and (c) show the von Mises stress distribution after deformation.

Fig. 25. Offline FEA simulation
