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During development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at the level of individual cells that reflect a realistic stochasticity and nonuniformity expected in cellular systems. Averaging the discrete results predicts population-level properties of the system, which match those of the continuous model. This dual approach provides an understanding of the interaction between the individual-level and population-level aspects of a developmental growth process. Both models are applied to a case study involving the developing intestinal tract of a quail embryo. A nonuniform growth model accurately predicts the positions of measurable biological landmarks within the growing tissue. Furthermore, the discrete model provides a framework for modeling the interactions between growing tissues and other biological mechanisms, such as cell motility and proliferation on an expanding tissue.

Modeling proliferative tissue growth: A general approach and an avian case study