Ekaterina Sherina

Simon Hubmer, Stefan Kindermann, Ekaterina Sherina

We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability.

Ekaterina Sherina, Lisa Krainz, Wolfgang Drexler et al.

We present a novel multi-modal optical coherence photoacoustic elastography (OCPE) framework, which combines two imaging modalities, optical coherence tomography (OCT) and photoacoustic tomography (PAT), to enable complementary absorption-scattering measurements for the extraction of quantitative tissue features via quasi-static elastography. For this, we develop a sophisticated hybrid inversion algorithm for merging the complementary information layers contained in both OCT and PAT-based elastography measurements, and perform systematic evaluations to assess the impact of hybrid elastography data on strain and stiffness reconstructions. Studies on a silicone elastomer phantom demonstrate that the combined OCT-PAT approach outperforms single-modality OCT elastography and PAT elastography, yielding higher strain signal-to-noise ratio and improved stiffness estimates. These results establish the advantage of multi-modal complementary imaging and data merging for accurate, high-resolution elastographic strain and stiffness mapping in both scattering and absorbing materials.