  We present a theoretical framework based on an extension of dynamical density
functional theory (DDFT) for describing the structure and dynamics of cells in
living tissues and tumours. DDFT is a microscopic statistical mechanical theory
for the time evolution of the density distribution of interacting many-particle
systems. The theory accounts for cell pair-interactions, different cell types,
phenotypes and cell birth and death processes (including cell division), in
order to provide a biophysically consistent description of processes bridging
across the scales, including describing the tissue structure down to the level
of the individual cells. Analysis of the model is presented for a single
species and a two-species cases, the latter aimed at describing competition
between tumour and healthy cells. In suitable parameter regimes, model results
are consistent with biological observations. Of particular note, divergent
tumour growth behaviour, mirroring metastatic and benign growth
characteristics, are shown to be dependent on the cell pair-interaction
parameters.
