A number of methods for processing and analysing biomedical images have been developed which are particularly important for image-aided diagnosis and image-guided therapeutical procedures. Among the methods developed, the method for accurate and robust registration of pre- and intra-operative images and the method for correcting for intesity inhomogeneities in microscopical and magnetic resonance images, are the most important. It was indicated that membrane nanostructures form a system which form the infrastructure of the biological cell. We contributed to better understanding of the physical conditions which determine the stability of anorganic nanotubes, which recently became the subject of intensive research. Our experimental and theoretical results in the field of cell biomechanics add to the better understanding of the physical mechanism of budding and vesiculation of the cell membrane. Knowing the mechanism of the budding process is essential for understanding the functions of normal and pathological cells. In the field orthopaedic biomechanics we have shown that the positive outcome of surgical interventions of the hip strongly depends on preoperative optimization of the contact stress distribution in the hip joint articular surface. We have introduced a new framework for the understanding of cardiovascular regulation. It is based on the fact that the blood flow does not consist of just a steady component, but also includes oscillatory components. The latter consist of several oscillatory modes, each acting on its own characteristic timescale and resulting from a specific physiological process. We have contributed insight into the understanding of the underlying physiological origin of these oscillatory components, especially those acting on a very low frequency scale and involved in the regulation of vessel's conductance/resistance. This new knowledge has laid the foundations for a new, non-invasive, diagnostic approach that can be used for early detection of cardiovascular diseases. Our experimental and theoretical results have contributed to a better understanding of nonlinear and stochastic characteristics of the cardiovascular system. We were among the first to show that the cardio-respiratory systems can synchronize, and were the first to show that information about the degree of interaction can serve as a measure of the depth of anaesthesia and may be used to detect changes in the system as the result of a specific cardiovascular disease. We have also contributed new methods for analysis of the direction and nature of couplings among interacting nonlinear systems.