Computational Multiscale Methods for Inverse Estimation of Effective Properties of Poroelastic Tissues

• Applicants: Privatdozent Dr. Alfonso Caiazzo; Professor Dr. Daniel Peterseim
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 455719484

Magnetic resonance elastography (MRE) is a medical imaging technique that allows to detect quantitative mechanical changes in tissue structure by measuring the propagation of shear and compression waves inside living tissues. This technique can therefore be used to diagnose and monitor, non invasively and in vivo, tissue diseases such as cancer and fibrosis. Due to practical limitations of the clinical examination process, MRE data are available on a relatively coarse spatial scale (order of millimeters). The current models employed for parameter estimation are therefore limited to considering effective tissues with mostly uniform macroscopic parameters. However, in several relevant applications it is important to gain insight beyond the observable effective scale, i.e., gathering information related to microstructures, or tissue interstitial pressure.In the case of pressure, current invasive techniques (catheterization and perforation) can only be used in extreme cases. Non-invasive examination are therefore necessary to enable early stage diagnostic also in patients with moderate symptoms. This project aims to develop novel mathematical models and computational methods for addressing the characterization of multiscale properties of vascularized tissues (such as porosity or interstitial pressure), in the context of MRE. The gap between the available low resolution data and the spatial scale of the quantities of interests (e.g., pressure in the microvasculature) shall be bridged by numerical homogenization.The main objectives include (i) a new multiscale descriptions of soft tissue mechanics based on a non-matching immersed method to efficiently model the crucial interaction between (one-dimensional) blood vessels and (three-dimensional) tissue; (ii) the derivation of surrogate models of the effective tissue based on numerical homogenization; and (iii) the application of these methods for the inverse estimation of tissue mechanical properties using internal tissue displacement fields, i.e., a typical setting of MRE examinations.From the clinical point of view, the results of this project will open new perspectives for targeting the non-invasive diagnosis of hypertension from MRE data - fostering the existing interdisciplinary collaborations with clinical partners.The successful implementation of these scientific goals at the intersection of mathematical modeling, computational methods, numerical analysis and scientific computing will build upon the core competencies of the PIs on computational and multiscale modeling of flow and tissue, and on intense research collaborations in the fields of multiscale computational mechanics and reduced-order modeling. The close collaboration with radiology departments of Charité-Universitätsmedizin Berlin and Universitätsklinikum Augsburg will allow the validation of the developed mathematical models and computational tools, to ensure the envisioned clinical relevance of the project.

• DFG Programme: Research Grants