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We present a theoretical framework based on an extension of dynamical densityfunctional theory (DDFT) for describing the structure and dynamics of cells inliving tissues and tumours. DDFT is a microscopic statistical mechanical theoryfor the time evolution of the density distribution of interacting many-particlesystems. The theory accounts for cell pair-interactions, different cell types,phenotypes and cell birth and death processes (including cell division), inorder to provide a biophysically consistent description of processes bridgingacross the scales, including describing the tissue structure down to the levelof the individual cells. Analysis of the model is presented for a singlespecies and a two-species cases, the latter aimed at describing competitionbetween tumour and healthy cells. In suitable parameter regimes, model resultsare consistent with biological observations. Of particular note, divergenttumour growth behaviour, mirroring metastatic and benign growthcharacteristics, are shown to be dependent on the cell pair-interactionparameters.

Dynamical density functional theory based modelling of tissue dynamics: application to tumour growth