Multiscale Mathematical Modelling and Numerics of Growth and Structural Adaptation of Soft Biological Tissues and Tumour Masses - ASynergetic Approach Encompassing Electro-Chemo-Mechanical Phenomena, (2015-2017) - Responsabile Scientifico
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Biological tissues are constituted by cells and intercellular components. Hydrated tissues host an interstitial fluid that conveys nutrients to the cells and removes the products of the cellular metabolism, thereby establishing the mass transfer necessary for the cellular activities. The fluid comprises also ionic species that interact chemically, electrically and mechanically with the cells and the other intercellular constituents. Moreover, a tissue responds to environmental stimuli by varying its mass and shape, and reorganising its internal structure. Such reorganisation, known as remodelling or structural adaptation, manifests itself in different ways (e.g., reorientation of collagen fibres in cartilage, healing of wounds, and change of the adhesion properties of cellular aggregates), influences the processes occurring among the cells and intercellular constituents, and triggers the evolution of the macroscopic properties (e.g., permeability and elasticity) by which tissues are often characterised. The history of a tissue, thus, comprehends interactions occurring at different levels of resolution, each level being characterised by its time and length scales. This is also true for tumours, in which the macroscopic behaviour of cells is dictated by subcellular processes. The scope of this proposal is to develop mathematical models and computational strategies capable of: quantifying, for a given set of applied stimuli, to which extent the cellular and intercellular processes, that are necessary for growth and remodelling, are modulated by growth and remodelling themselves, and vice versa; solving the inverse problem, i.e., managing the stimuli necessary for determining such loop of interactions. To reach these goals, it is necessary to elaborate discrete models of cellular dynamics, continuum models of growth and remodelling, and reactive flow models in heterogeneous and anisotropic structures, and couple those reciprocally through level-transfer algorithms.