Mechanical characterisation and FEM modelling of biological deformation for surgical simulation

This thesis sought to explore the use of minimally invasive surgery via biomechanical simulation of soft tissue deformation and needle path planning insertion. When surgeons are placed under mechanical stress, human brain cells exhibit the viscoelastic behaviour of solid structures. However, the behavioural mechanisms of tissues/cells are not yet fully understood, and more information is needed to reliably calculate tissue/cell deformation. The research objectives and methodologies were: First, to objectively investigate and characterise the mechanical properties of biological tissues/cells by using experimental atomic force microscopy (AFM) data (see CHAPTER 3). This method was used to analyse the cell's mechanical behaviours with a developed numerical algorithm. The difference between two human brain cells (normal HNC-2 and U87 cancer cells) was studied to determine their mechanical properties so that these could then be applied to our proposed 3D model (see CHAPTER 5). Second, using the measured experimental AFM data, a system identification of AFM characterisation was implemented in another chapter (CHAPTER 4), which for comparison, was based on a MATLAB algorithm. The results showed that the model that was identified for AFM matched the measured experimental AFM data. Third, to establish a finite element method (FEM) for real-time modelling of nonlinear soft tissue deformation behaviours using a three-dimensional (3D) dynamic nonlinear FEM; this method was developed to establish the large-range deformation of tissue/cells with second- order Piola-Kirchhoff stress (CHAPTER 5). A Newmark numerical process was implemented to solve the partial differential equations (PDEs) that resulted from the FEM. Experimental analysis of biological human brain cells was conducted to verify and validate the nonlinear FEM for simulating deformation. Fourth, to establish a method for real-time motion plan modelling of nonlinear needle deflection during needle insertion using the third objective to implement the nonlinear FEM for needle path planning. Last, to use an application of bio-heat transfer of potential needle tip path planning by applying a bioheat transfer-based method (CHAPTER 6); this method was established for optimal path planning for needle insertion in the presence of soft tissue deformation. A bio- heat transfer was used to develop a temperature distribution for path planning to reach the target and avoid obstacles in cubic, liver and brain cell models. The algorithm defines the optimal path for needle tip placement; the needle tip placement is determined by the temperature distribution, which in turn, is based on soft tissue deformation that occurs in the process of needle insertion. When force was applied during the needle penetration process, the deflection accrued was based on the geometry of nonlinear material. Based on our simulation of 3D FEM discretisation of the Pennes' Bio-heat Transfer Equation, the distribution of the temperature from single point temperature sources was performed to determine the degree of transient thermal. Furthermore, the distribution was used to model thermal stresses and strains within the cell/tissue, which result from the heat source. The main contribution to this field is building a new conceptual design methodology for characterisation of the mechanical properties of biological cells by extracts of the mechanical properties of two biological human brain cells (normal HNC-2 and cancer U87 MG cells), and the experimental use of AFM for the first time. Also, linear FEM for soft tissue/needle insertion with large deformation is developed and adapted to our three-dimensional dynamic FEM soft tissue/cell modelling using numerical integration methods. Verification of the experimental work and the proposed method is examined mathematically and systematically using a system identification schema. Moreover, bio-heat transfer for needle insertion is implemented based on the proposed FEM soft tissue deformation modelling to represent path planning. The investigation of needle insertion into soft tissue/cell deformation using bioheat transfer FEM has not been done before