Biomechanical modelling of soft tissues using finite element method

An accurate biomechanical model, coupled with an accurate solution of the governing differential equat ions, would be useful for the registration of images [rom different modalities during breast cancer diagnosis. Because of the large deformations and the behaviour of the breast tissue, incompressible nonlinear elasticity is required. But there is no agreed best method for solving these equations. In this thesis we investigate which finite element method (FEM) is most suitable [or breast models. We investigate both the cont inuous Galerkin FEM (CGFEM) and the discontinuous Galerkin FEM (DGFEM). We compare the linear compressible and incompressible theory using CGFEM. Alter showing the limitations of linear compressible elasticity in the case of near ly incompressible materials we use the nonlinear incompressible theory with both CGFEM and DGFEM for the forwards problem (where we assume that we know the undeformed configuration of the unloaded body, and wish to predict the deformation under a prescribed set of forces) and the backwards problem (where the deformed, loaded state of the body is known and we wish to predict the undefonned configuration) on 2D simple model problems. Between CGFErv! and DGFEM the results show similar behaviour with respect to the element size, with algebraic convergence of the error with rate which is determined by the polynomial order of the basis function used. The results of using OGFE~1 show that the scheme is not very sensitive to the choice of the method used to enforce incompressibility (between the two suggested ones) or the penalty parameter that penalizes discontinuities in the solut ion, as long as it is suffiCiently large. 'When it comes to the choice of element , different elements (triangular in different layouts and quadrilateral) give different accuracy but converge with the same rate for the same polynomial degree of the approximation. FUrther comparison of the twO schemes with respect to accuracy, st ability and speed is provided for the 20 case and this thorough investigat ion of the method's performance in 2D guides the choices made for 3D simulations. t:'sing both schemes and 3D hexahedral elements we solve the forwards and the backwards problem for simple 3D model problems and then construct models of the breast that allow us to simulate MRI and X- ray mammography. The resulls show that we can follow the clinically relevant approach of using the known deformed configuration of the breast from MRI or X- ray and perform intra~modali ty registration,EThOS - Electronic Theses Online ServiceGBUnited Kingdo