Conical spring and localised region methodologies for modelling of soft tissue deformation - Omar, Nadzeri (2017)
Considerable research efforts have been dedicated to the development of virtual reality simulators that facilitate medical students in learning anatomy and surgery in the virtual environment and to allow surgeons to rehearse the surgical procedures. The level of realism depends upon the simulation accuracy and the computational efficiency of underlying deformable models. Ideally, the deformable models should be able to simulate accurately mechanical behaviours of soft tissues with real-time visual and force feedback. Modelling soft tissue deformation is not an easy task. Due to the complexity of soft tissue properties, many methods have been proposed to model soft tissue properties. One of the most well-known methods is the Finite Element Method (FEM). In this method, the soft tissue is represented by multiple elements that are derived based on complex mathematical formulations. It has been proven that the method is able to simulate soft tissue properties accurately, but it requires high computational cost to produce real-time interaction. In this regard} the Mass Spring Method (MSM) has been proposed as an alternative. The traditional MSM model simulates soft tissue deformation by discretising the soft tissue into several mass points that are connected to each other by linear springs. The major advantage of MSM is it has an excellent computational performance. However1 the MSM application is limited to linear deformation, which does not represent the actual behaviour of the soft tissue deformation. In this thesis1 an improved MSM model has been proposed to simulate the complex behaviour of soft tissue deformations. The improved MSM model is called conical spring model which considers the general behaviour of soft tissue deformation that is a combination of linear and nonlinear responses. Piecewise approach is used to discretise each response individually} and the conical spring methodology is used to model the deformation behaviours during all the responses. The piecewise approach gives precision in modelling while the conical spring methodology that was founded on stiffness variation1 has improved the accuracy of the simulation due to its ability to model any type of linear and nonlinear responses. Moreover, the generated conical spring model is based on the force propagation approach. The computational performance of the model relies on the number of nodes involved in the propagation of the force. Inherently, computational time can be improved by considering the nodes only in a deformation area, and ignoring the other nodes. Soft tissue deformation commonly occurs only within a local region. As the effect of the deformation outside the local region is very little, it can be ignored in real practice. In this thesis, methods to define the local region were proposed. The methods are based on the linear elastic theory. As reported in Chapter 4 of this thesis, the localised region was generated based on displacement value induced when the simulation model was subjected to an external load. The Boussinesq method, which is widely used in the soil mechanics, was used to estimate the induced displacement value. However, the Boussinesq method is limited to the isotropic material. Therefore, as described in Chapter 5, the study has extended the isotropic localised region to anisotropic localised region by introducing an anisotropic factor which was derived based on cross-anisotropic properties. By using the anisotropic factor, the anisotropic localised region is determined from the corresponding isotropic case. Alternatively, in Chapter 6, we have presented a localised region that was generated based on stress value induced during a loading process. It is shown for point load type of contact, in comparison to ABAQUS analysis, stress based localisation has a better accuracy than the displacement based localisation. However, the stress value that is also determined using the Boussinesq method, has no relation to the material properties. Hence, a combination of the Hertzian and the Boussinesq method was used to generate localised regions with respect to the material properties and loading conditions. In the final chapter, contributions of the study were discussed/ and some of the future works to expand the research were listed out.