Mariella Kast presents her Bachelor's thesis on "Application of biomechanical numerical analysis on experimental data"
The slides of the presentation can be found here
Abstract:
This thesis follows a model-based approach to elastography such that the inverse problem statement is solved as an optimization task. In this context, computational simulations are conducted on a medical phantom data set to validate an algorithm that has been proposed and tested on artificial examples. A main challenge consists in properly transferring experimental information to a Finite Element model with appropriate constraints. We furthermore investigate the validity of key assumptions employed by most methods to recover elasticity from ultrasound images. For in- stance, the hypothesis of plane strain is corroborated with a 3D model and minimal errors are ascertained. Results are reported for a linear and non-linear material law and the importance of choosing an appropriate regularization to handle issues of overfitting and the ill-posedness of the problem is demonstrated. We can show superior contrast of Young Modulus recovery independent of material type compared to a simple direct approach even when knowledge of boundary conditions is limited. Finally, an attempt to generate probabilistic estimates of elasticity parameters is examined in order to take apparent limitations of a deterministic approach into ac- count. Information for the last part is procured by sampling with the Metropolis algorithm and a constricted set of parameters. Resistance against local minima and more precise localization of the target is established for this method even though the model reduction to fewer parameters impeded the analysis.