Abstract :
[en] Patient-specific finite element (FE) modelling is gaining more and more attention over the years because of its potential to improve clinical treatment and surgical outcomes. Thanks to patient-specific modelling, the design of individualised implants and prostheses, surgical pre-operative planning and simulation, and the computation of stresses and strains in a patient's organ for diagnostic purposes will become a reality in the future. This work investigates two of the most challenging tasks of patient-specific modelling: the creation of image-based finite element meshes and the development of a low-order locking-free tetrahedral element.
First, a general meshing strategy for tetrahedral mesh generation from segmented 3D images is proposed. The originality of the approach is the addition of surface reconstruction algorithm to the traditional image-to-mesh pipeline. The main advantages for this are: the generation of smooth boundaries, robustness to segmentation noise, a user-defined mesh resolution and a good fidelity of the mesh boundaries with respect to the underlying image. Also, the proposed meshing strategy is capable of generating meshes of heterogeneous structures, containing several interconnected types of tissues. Applications demonstrate that the interfaces between distinct material regions are topologically correct, i.e. the connections are edge-on-edge and node-on-node. Specific mesh decimation and mesh smoothing algorithms were designed for this multi-material tetrahedral mesh generator. In a last chapter, patient-specific hexahedral meshes are created by combining the proposed surface reconstruction algorithm with a classical voxel-conversion algorithm.
Second, a low-order tetrahedral element for the solution of solid mechanics problems involving nearly incompressible materials is developed. The formulation is based on F-bar methodologies and nodal-based formulations. As in nodal based formulations, nodal Jacobians are defined. These nodal quantities are then averaged over the element to define a modified elemental Jacobian, which is used to define a modified deformation gradient, F-bar, for the element.
Both 2D triangular and 3D tetrahedral are proposed and they can be used for both implicit and explicit analysis. The exact stiffness terms for the tangent stiffness matrix are derived so that a quadratic convergence rate in ensured for the Newton-Raphson equilibrium iterations. Most importantly, the new element can be used regardless the material model. Benchmarking 2D and 3D numerical tests using several constitutive models indicate a substantial removing of both the volumetric and the shear locking tendency of the standard linear triangle and tetrahedron, as well as an accurate distribution of strain, stress and pressure fields.
The potential of the resulting image - to - FE model procedure is demonstrated in the last part of this work, through patient-specific finite element analyses of actual biomechanical research topics.
