Phase 2 - Enabling efficient and certifiable solutions in diagnostic biomechanics by rephrasing model-based inverse problems.

• Applicant: Professor Phaedon-Stelios Koutsourelakis, Ph.D.
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 499746055

Elastography is a non-invasive imaging technique used to estimate tissue mechanical properties by analyzing its response to external forces. It plays a crucial role in diagnosing diseases like cancer and liver fibrosis, where changes in tissue stiffness serve as key indicators. However, traditional elastography methods face challenges such as high computational costs and sensitivity to noise, limiting their clinical adoption. Model-based inverse approaches improve accuracy by incorporating physical models, but their complexity makes them difficult to scale and use effectively. In the second phase of our project, we aim to refine and extend our framework to make it more scalable, efficient, and accessible for real-world applications, particularly in medical imaging and biomechanics. Our focus remains on improving the solution quality and computational efficiency of model-based inverse problems, with a special emphasis on indirect elastography. This technique, which estimates mechanical properties of tissue from deformation data, has immense diagnostic potential but remains underutilized due to computational complexity and technical barriers. To address these challenges, we will enhance scalability by extending our framework to high-dimensional problems, particularly 3D elastography. Leveraging Neural-Operator representations will allow us to dynamically model unknown fields, reducing the need for manual decisions such as basis function selection. Additionally, we aim to optimize computational efficiency by implementing adaptive strategies for selecting the most informative residuals, minimizing costs while maximizing relevant data extraction. Further improvements include physics-based zooming techniques that focus computational resources on critical regions, enabling real-time inference even on resource-limited devices. Another key objective is to improve usability, ensuring our framework is accessible to non-experts. By integrating multimodal imaging, we can enhance inference accuracy while reducing practitioner workload. Additionally, simplifying user interactions—such as automating boundary condition handling—will remove barriers that hinder adoption. The ultimate goal is to develop real-time elastography solutions deployable beyond clinical environments, broadening access to advanced diagnostics. These advancements build on the first project phase, where we introduced Weak Neural Variational Inference (WNVI), a method that eliminates the need to repeatedly solve PDEs by treating governing equations as virtual observables. This significantly reduced computational costs while maintaining accuracy, making model-based inverse problems more feasible. In this next phase, we will push these innovations further, refining our methodology and software to create a practical, scalable solution deployable across medical diagnostics, engineering, and environmental sciences.

• DFG Programme: Research Grants