**3. Overview of human spine structure**

The spinal column (Figure 1) extends from the skull to pelvis and is made up of 33 individual vertebrae that are stacked on top of each other. The spinal column can be divided into 5 regions: 7 cervical (C1-C7), twelve thoracic (T1–T12), and five lumbar vertebrae (L1– L5) in the lower back, five bones (joined together in adults) to form the bony sacrum, and 3- 5 bones fused together to form the coccyx or tailbone.

Intervertebral discs (Figure 2) are soft tissue structures situated between each of the 24 cervical, thoracic, and lumbar vertebrae of the spine. Their functions are to separate consecutive vertebral bodies. Once the vertebrae are separated, angular motions in the sagittal (forward, backward bending) and coronal planes (sideway bending) can occur.

Facet joints are paired joints which are found in the posterior of the spinal column (Figure 3). The surfaces of each joint are covered by cartilage which helps to smooth the movement between two vertebrae. Certain motions are facilitated by these joints, such as: bending forward, bending backward and twisting. In addition, people can feel pain if the joints are damaged because of the connected nerves. Some experts believe that these joints are the most common reasons for spinal discomfort and pain.

The neural elements (Figure 4) consist of the spinal cord and nerve roots. The spinal cord runs from the base of the brain down through the cervical and thoracic spine. The spinal cord is surrounded by spinal fluid and by several layers of protective structures, including the dura mater, the strongest, outermost layer. At each vertebral level of the spine, there is a pair of nerve roots. These nerves go to supply particular parts of the body.

Development of a Detailed Human Spine Model with Haptic Interface 169

Ligaments enable the spine to function in an upright position, and the trunk to assume a variety of positions. There are various ligaments attached to the spine, with the most important being the anterior longitudinal and the posterior longitudinal ligaments (Figure 4), which run from the skull to the base of the spine (the sacrum). In addition there are also many muscles attached to the spine, which further help to keep it stable. The majority of the

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

Fig. 4. Nerve roots and spinal cords

Fig. 5. Various ligaments of the spine

muscles are attached to the posterior elements of the spine.

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

Fig. 1. Spinal column

Fig. 2. Intervertebral discs

Fig. 3. Facet joints of the spine

Fig. 4. Nerve roots and spinal cords

168 Haptics Rendering and Applications

Fig. 1. Spinal column

Fig. 2. Intervertebral discs

Fig. 3. Facet joints of the spine

Fig. 5. Various ligaments of the spine

Ligaments enable the spine to function in an upright position, and the trunk to assume a variety of positions. There are various ligaments attached to the spine, with the most important being the anterior longitudinal and the posterior longitudinal ligaments (Figure 4), which run from the skull to the base of the spine (the sacrum). In addition there are also many muscles attached to the spine, which further help to keep it stable. The majority of the muscles are attached to the posterior elements of the spine.
