**8. Heterogeneous ligament modelling**

Since the introduction of traditional computer graphics and modelling techniques, the primary focus has been to display and modelling of homogenous objects which have uniform interior and consist of one material throughout. This was acceptable for many situations, however, such surface-based approaches were aimed to represent the visual appearance of the external layer of objects, leaving the interior untouched. Recently, with the availability of increased computing power, the focus has shifted from surface-based to volume-based graphics, whereby volume-based architecture attempt to describe the material structure of internal regions by the use of voxels [17]. This can allow manipulation and experimentation on the physical properties of the materials, such as density, friction, elasticity, tensile strength and in so doing opens up new possibilities for experimentation. Heterogeneous objects are a step further, being solid physical objects, which consist of two or more material primitives but offering the advantage of materials that may be distributed continuously blending with each other.

For epidural needle insertion, the needle passes through several ligaments along its path to the epidural space, with each of the ligaments having different properties such as density, resistance to insertion and friction (see Section 3). A model is required to encompass these aspects of each ligament if the graphics are to be capable of displaying a true likeness of the materials in-vivo. Ligamentum flavum (LF) is heterogeneous in nature, containing both elastic tissue and fibrous tissue. Certain data describing the ligamentum flavum has been recorded in the literature and can be used to set up a heterogeneous model of the ligament. As LF thickness increases, fibrosis increases and elastic tissue decreases. The dorsal side of LF contains more fibrous tissue and less elastic tissue than the dural and middle sides, as indicated by a fibrosis Score of 1.58, 1.63, and 2.63 for dural, middle, and dorsal sides respectively [18]. The loss of elastic fibres caused by increased thickness is more pronounced along the dorsal side. A single patient has several ligamentum flava, one at each spinal level between the lamina and their thicknesses vary according to the spinal level. A study of 77 patients measured LF at spinal level L2/3, L3/4, L4/5, and L5/S1, the mean LF thickness is 2.41, 3.25, 4.08, and 2.68 mm [18]. It was shown that the thickest part of ligamentum flavum is consistently at L4/5, which is the level that endures the greatest mechanical stress. LF is crescent shaped in cross section on the horizontal plane with the thickest part in the middle. It wraps around the circular epidural space and dura. It connects to lamina above and below. The elastic fibres are yellow in colour, hence 'flava' being Latin for yellow. Each flava is a separate ligament which is clearly seen from the side of the lamina.

Object modelling software was used to create a model of the vertebrae. At the location of L2/L3 a ligamentum flavum was modelled with the thickness 2.41mm which was internally comprised of bundles of fibres (Figure 14).

**Figure 14.** The modelled ligamentum flavum between L2/L3 vertebrae.

400 Practical Applications in Biomedical Engineering

Initially the vertebrae are positioned in the standing position and are then adjusted by mathematical equations to match the current patient position. The curvature of the spine for four common patient positions was calculated using the equations. The shape of the spine was based on the four common patient positions used for epidural insertion. Our model's

The ability to flex and rotate the spine has provided the opportunity to simulate epidural insertions on patients in various positions. This is important because the feeling of insertion is different for each patient position. This novel aspect has not been attempted in epidural

Since the introduction of traditional computer graphics and modelling techniques, the primary focus has been to display and modelling of homogenous objects which have uniform interior and consist of one material throughout. This was acceptable for many situations, however, such surface-based approaches were aimed to represent the visual appearance of the external layer of objects, leaving the interior untouched. Recently, with the availability of increased computing power, the focus has shifted from surface-based to volume-based graphics, whereby volume-based architecture attempt to describe the material structure of internal regions by the use of voxels [17]. This can allow manipulation and experimentation on the physical properties of the materials, such as density, friction, elasticity, tensile strength and in so doing opens up new possibilities for experimentation. Heterogeneous objects are a step further, being solid physical objects, which consist of two or more material primitives but offering the advantage of materials that may be distributed

For epidural needle insertion, the needle passes through several ligaments along its path to the epidural space, with each of the ligaments having different properties such as density, resistance to insertion and friction (see Section 3). A model is required to encompass these aspects of each ligament if the graphics are to be capable of displaying a true likeness of the materials in-vivo. Ligamentum flavum (LF) is heterogeneous in nature, containing both elastic tissue and fibrous tissue. Certain data describing the ligamentum flavum has been recorded in the literature and can be used to set up a heterogeneous model of the ligament.

prediction for the spine shape for each of the positions is shown in Figure 13 [14].

**Figure 13.** The spine model with flexion for four common patient positions

simulation before and will increase versatility of the simulation.

**8. Heterogeneous ligament modelling** 

continuously blending with each other.

The interior structure of the ligamentum flavum has been modelled by numerous bundles of fibres extending vertically and parallel to one another, as do the elastic and fibrous tissues in-vivo. By creating this heterogeneous model of the internal structure of ligamentum flavum, the model will describe more accurately how the material responds to a needle being inserted through it. Similar models may be created for interspinous ligament and supraspinous ligament which are also both heterogeneous in nature, consisting of over three types of elastic fibres that can used to provide realistic haptic feedback.
