Cell growth, division and death in cohesive tissues: a thermodynamic approach

Cell growth, division and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a non-zero rate of variation of cell density. We show how linear nonequilibrium thermodynamics allows to express this rate as a combination of relevant thermodynamic forces: chemical potential, velocity divergence, and activity. We illustrate the resulting effects of the non-conservation of cell density on simple examples inspired by recent experiments on cell monolayers, considering first the velocity of a spreading front, and second an instability leading to mechanical waves.