Influence of the mechanical properties of the necrotic core on the growth and remodelling of tumour spheroids

Multicellular tumour spheroids (MCTSs) are complex biological materials, undergoing both growth, due to cell proliferation, and remodelling, thanks to the ability of cells to reorganize the bonds among them. In this paper, we study the mechanical behaviour of MCTSs, treated as porous materials, composed of cells and filled with water, and we use the notion of evolving natural configurations to incorporate cells’ capability to reorganize and proliferate. We model the MCTS as possibly made up of three concentric layers: the necrotic core, either calcified of filled by liquid, the quiescent region, composed by cells that are alive but not dividing and the outermost proliferative ring. The resulting system of equations is used to simulate the response of a quiescent tumour spheroid when an external load is applied and the proliferation of a MCTS in response to nutrients, either when the aggregate is let free to expand or when it is compressed by the external environment. The results show the importance of remodelling on the capability of cells to redistribute inside the living structure and the influence of the mechanical properties of the inner necrotic structure, when its size is relevant.