**4.4 The reproduction of haptic simulation result in the offline FEA simulator**

Although the haptic real-time simulation of the beam FE spine model helps us to understand better the kinematics of the whole thoracolumbar spine, it provides very limited information concerning stress and strain of vertebrae. If a full picture of the deformation behavior of the spine is required, it is important to study and obtain the information of stress/strain of vertebrae. Therefore, offline simulations following the haptic simulation are necessary to carry out and provide this useful information. Our system allows the user to pick interesting moments of particular spine shape during haptic simulation and reproduce

Development of a Detailed Human Spine Model with Haptic Interface 175

In following subsections, the developing process of a detailed musculo-skeletal spine model is presented thoroughly. This process includes five main stages such as generating a default human body model, discretizing the default spine segments, implementing ligamentous soft

The usual procedure of generating a human model is to create a set of body segments followed by redefining the fidelity of the individual segments. The body segments of a complete standard skeletal model are first generated by LifeMOD depending on the user's anthropometric input. The model used in this study was a median model with a height of 1.78 m and a weight of 70 kg created from the internal GeBod anthropometric database. By default, LifeMOD generates 19 body segments represented by ellipsoids. Then, some kinematic joints and muscles are generated for the human model. Figure 10 shows the base

To achieve a more detailed spine model, the improvement of the default spine model mentioned above is required and can be done in the three following steps: refining the spine

From the base human model, the segments may be broken down into individual bones for greater model fidelity. Every bone in the human body is included in the generated skeletal model as a shell model. To discretize the spine region, the standard ellipsoidal segments representing the cervical (C1-C7), thoracic (T1-T12) and lumbar (L1-L5) vertebral groups are firstly removed. Based on input such as center of mass location and orientation of each vertebra, the individual vertebra segment is then created. Figure 11 shows all ellipsoidal segments of 24 vertebrae in the cervical, thoracic and lumbar regions after discretizing.

The muscles are attached to the respective bones based on geometric landmarks on the bone graphics. With the new vertebra segments created, the muscle attachments to the original segment must be reassigned to be more specific to the newly created vertebra segments. The physical attachment locations will remain the same. Figure 12(a) and (b) shows the anterior

segments, reassigning muscle attachments and creating the spinal joints.

tissues, implementing lumbar back muscles and adding intra-abdominal pressure.

**5.2 Generating a default human body model** 

model in this study.

Fig. 10. Default human body model

**5.3 Discretizing the default spine segments** 

the similar deformation of spine in the offline FEA simulator for greater detail. By this means, the user can obtain desired spine deformations conveniently in the haptic simulator and then observe every detail of stress/strain of vertebrae in the offline FEA simulator.

A straightforward way to reproduce the same deformation in the offline FEA simulator is to record the position and orientation of each vertebra along the spine and then apply the positional constraints to every vertebra of the offline spine model. However, this greatly increases the risk of finite element computation error because of too many constraints involved. In practice, we found this method almost always makes the FEA solver fail to converge. Another plausible way is to record the force vector and the vertebrae under the load in the haptic simulator and reproduce the same load condition in the offline FEA simulator. However, the deformation of spine is not solely determined by the load due to the high non-linearity of the spine. Plus, during surgery, the forces are often not directly applied to a vertebra; instead, surgeons often manipulate instruments, which are linked to one or multiple vertebrae. Therefore, this method is not feasible.

Our solution is firstly to record the position and orientation of vertebrae which are directly under the external forces or are constrained during the haptic simulation, then apply the position and orientation constraints only to these vertebrae in the offline FEA simulator. The position and orientation of a vertebra can be represented with the positions of point A ~ E of the vertebrae's beam elements model (shown in Figure 8). The procedure of reproducing the deformed spine in the offline FEA simulator is as follows:

