Abstract:

The inverse problem of electrocardiology might provide a powerful clinical investigation method for visualising the electrical activity of the heart. To use this method one requires accurate models of the human torso and heart. The objective of this work was to create an accurate model of the human ventricles including the valves from images recorded using Magnetic Resonance Imaging (MRI). This model is used as a "generic" model, and is adapted to a given individual with a host mesh fit to spatially registered Ultrasound (US) images.

Abstract:

A generic model of the human ventricles is created from Magnetic Resonance Images (MRI) and customised to a given patients heart using Ultrasound data with a host mesh fitting procedure. The motivation for this work is to provide individual and accurate models for the solution of the inverse problem in electro- cardiology.The first objective was the creation of a surface model of the human ven- tricles. This was constrained by several factors, due to the desired application for the inverse problem. A bi-cubic Hermite basis function with quadri-lateral elements is chosen, which is an efficient shape descriptor with first and second order continuity across element boundaries. The ventricles and the valve plane is modelled with three independent surface meshes. The whole model is closed to fulfil the boundary conditions of the inverse problem.The second objective was the adaption of this surface model to a given patients heart. MRI is the most accurate, but also most expensive imaging technology. 3D Ultrasound is cheap, but some areas are barely visible, e.g. the right ventricular free wall. Thus Ultrasound alone is insufficient to develop a complete model from. The host mesh fitting procedure combines the advantages of both imaging technologies. In areas with Ultrasound data the model gets adapted to the new positions and elsewhere the generic model is used to fill in the missing features.The generic model is first embedded as a slave mesh inside the host mesh by making the nodes relative to the ξ-coordinates of the host mesh. After a gross alignment, the Ultrasound data is projected onto the surfaces of the slave mesh yielding pairs of points for the subsequent fitting procedure of the host mesh. Finally, the slave mesh is updated to the new host mesh.An additional objective of this work was the creation of a volumetric model of the ventricular walls. This uses a tri-cubic Hermite interpolation function. The main constraint of this model in the creation is in retaining consistency in its ξ-directions, leading to a complicated mesh topology.

Abstract:

Biomechanical modeling of the lung is essential for predicting geometric uncertain‐ties during radiotherapy and minimally invasive surgery, such as Video‐Assisted Tho‐racoscopic Surgery (VATS). This thesis presents the development of an automated,open‐source computational pipeline that directly bridges medical image processingwith the finite element method (FEM). Implemented as a custom software extensionfor 3D Slicer, the system utilizes the GetFEM solver to simulate patient‐specific lungkinematics based on clinical CT data.To manage large deformations and the complex interaction between the lung andthe chest wall, a compressible Neo‐Hookean material model was coupled with anintegral large‐sliding frictionless contact formulation. The initially ill‐posed, contact‐free boundary value problem was resolved using a specific load‐stepping procedurefeaturing a non‐linear, saturating stabilization force. From a software engineeringperspective, the extension successfully encapsulates the C++ finite element routineswithin a Python‐based environment. It automates the entire workflow from volumet‐ric mesh generation to the continuous B‐Spline back‐transformation of simulatedmesh displacements into the voxel‐based image domain.Validation on a physiological respiration dataset (4D‐CT) yielded a minimum Tar‐get Registration Error (TRE) of approximately 4.0 mm. Systematic parameter gridsearches confirmed established literature: Poisson’s ratio dictates the geometric ac‐curacy of the deformation, whereas the absolute Young’s modulus exerts a secondaryinfluence on the final shape, provided pressure boundaries are proportionally scaled.To evaluate the framework under massive finite strains, the pipeline was experi‐mentally applied to a surgical lung collapse scenario utilizing a retrograde expansionstrategy. While valuable for testing mathematical model stability, this application ex‐posed the physical boundaries of homogeneous, purely contact‐driven macroscopicmechanics, resulting in non‐physical airway displacements. Furthermore, the analy‐sis of simulated density alterations via a novel experimental metric, the Median In‐tensity Volume Ratio (MIVR), demonstrated that spatial image warping merely inter‐polates existing voxel intensities and cannot adequately replicate the physical massinflux of air. Ultimately, this work proves the fundamental feasibility of integratingcomplex, contact‐based biomechanical lung simulations directly into the 3D Slicermedical computing environment, providing a transparent foundation for evaluatingmacroscopic organ deformations.