Defensa de tesi doctoral - Sr. Stephan Gahima

This thesis advances finite element-based tools to improve atherosclerosis analysis by addressing current computational limitations. Atherosclerosis, the leading cause of ischaemic heart attacks, imposes a significant social and economic burden (estimated at around $1 trillion worldwide by 2030). In this disease, patients develop plaques from lipid accumulation in the arteries and these plaques can be prone to rupture or stable. Differentiating between these types is essential for effective clinical risk management.

Fast, accurate, and robust computational methods can streamline the clinical pipeline and ultimately may help to assess atherosclerotic analysis. We use Finite Element Method (FEM) to simulate stress in atherosclerotic sections, as peak stress plays a key role in assessing rupture risk. Our methods are based on unfitted FEM, which simplify mesh generation, save computational and pre-processing time.  Importantly, these methods can work directly on voxelized data such as medical images. The proposed unfitted approaches achieve accuracy within 5 % of that attained by classical fitted approaches and commercial software, for both linear and non-linear cases.

Moreover, these methods incorporate a flexible and realistic boundary conditions that account for the influence of surrounding tissues. We also developed an Adaptive Model Reduction (AMR) technique based on a linear hypothesis, serving as a preliminary step toward creating fast surrogate models for near-real-time simulations.Validation experiments demonstrate that AMR decrease computational resource usage by over 70 % while maintaining an accuracy within a 9 % error margin compared to high-fidelity models.  Finally, preliminary results indicate that using Topological Data Analysis (TDA) to build interpretable Machine Learning (ML) models can effectively assesses plaque rupture risk. Early experiments yield a classification accuracy of approximately 75 %, a performance comparable to established radiomics approaches.

Overall, this doctoral work demonstrates that combining advanced FEMs with interpretable ML may provides nuanced insights into atherosclerotic plaque assessment. Future research should address potential limitations such as data variability and scalability to enable broader implementation of these computational techniques in clinical practice.