In task 1.1 we discuss mathematical algorithms for medical imaging like MPI. The focus is on Fourier methods and approximation results. One of the central ideas in task 1.2 is to consider order relations between values in time series instead of the values themselves, with the advantage of getting simple and robust data analysis methods.
The research task 2.1 deals with the development of integrated multi-scale modelling of biopolymers. Biopolymeric materials have found a wide variety of applications in the biomedical field ranging from sutures, pins and screws for orthopaedic surgery to local drug delivery, tissue engineering scaffolds, and endovascular stents. Biopolymeric properties are dictated by changes at the molecular level which propagate the effects through scales affecting the overall properties at the macroscale. In order to better predict biopolymeric properties, multi-scale material modelling is the overall goal.
The research task 2.2 concerns the development of patient-specific diagnostic tools in the field of cardiac surgery. The diseases affecting left heart valvular apparatuses, i.e. mitral valve (MV) and aortic root (AR), are among the most lethal cardiac pathologies, and affect approximately 10% of the population. The overall objective is the development of computational tools for the quantitative in vivo analysis of MV and AR apparatus, as well as their local blood flow hemodynamics, as a support to the understanding of their pathophysiology, the quantitative diagnosis of pathologies, the planning of surgical repair procedures, and the training of surgeons.
The research tasks 3.1 and 3.2 are related accordingly with the detection of the causality in complex systems and with the prediction\prevention of nocturnal hypoglycemia of diabetes patients. The first problem is of interest in Social Sciences and Biology, where, e. g., it is important to detect the opinion leaders in social networks and reconstruct gene regulatory networks. The second problem is important in view of more than 30 millions of European patients for whom the nocturnal hypoglycemia is one of the most feared complications. Towards these tasks the objectives are to develop new mathematical algorithms by employing recent advances in Regularization Theory, which can be seen as a relevant tool because both the above-mentioned problems can be classified as ill-posed ones.
