Flow, Growth, and Remodelling in Fibre-Reinforced Deformable Biological Tissues and Tumour Masses

In the present thesis, we propose the study of the evolution of biological tissues, with particular attention to soft connective tissues, as articular cartilage, and on the growth and reorganisation of tumor masses during the avascular evolution. The growth, remodelling, and deformation of biological tissues are the consequences of stimuli involving different scales of observation, and yield a variation of the internal structure of tissues. This variation may be visible also at the coarse scale (i.e., the scale at which the properties of the homogenised tissue are defined) and may be coupled with the environmental interactions acting on the tissue at that scale. Within the context of Continuum Mechanics and Mixture Theory, the structural evolution of a tissue is treated as an intrinsically inelastic phenomenon. For this reason, many theories are inspired by Elastoplasticity. Articular cartilage have been considered as an example of extremely heterogeneous tissue, which is here considered as a mixture of an anisotropic, fibre-reinforced solid filled with a fluid phase. The numerical representation of the confined and the unconfined compression tests on articular cartilage are presented, and the reliability of dedicated numerical tecniques, required to account for the presence of fibres in the tissue, is discussed. The study of the evoluton of spheroidal tumour masses both in vitro and in a living environment, during the avascular stage, is discussed in the present thesis. The tumor has been described as a solid mixture, comprising both proliferating and necrotic cells, and whose growth is determined by chemomechanical stimuli. In particular, the presence of a fluid phase carring nutrients to the tumor allows for a volumetric growth, whereas the stresses that the sorrounding medium produces on the free surface of the spheroid inhibits its evolution. In the presented study, the growth and growth inhibition factors have been optimised by comparison with experimental data at hand, and then a model accounting for both growth, remodelling and anelastic distortion of the tumor has been presented. We model such phenomenon within the framework of the Continuum Mechanics, by means of the hypoteses of the Evolving Natural Configurations, and the multiplicative decomposition of the deformation gradient.