Control of tissue growth by locally produced activator: Liver regeneration

• The model proposed is focused on the kinetics of tissue growth.
• To motivate the model, liver regeneration is briefly discussed.
• The Hill equation is used to describe control of cell proliferation.
• Typical kinetics are shown for rapid and slow activator diffusion.
• Fits of measured kinetics of liver regeneration are shown as well.

In general, the tissue development is controlled by growth factors and depends on the biomechanics of cells. The corresponding kinetic models are focused primarily on the early stages of the development. The attempts to construct such models for the later stages are still rare. One of the notable examples here is liver regeneration. Referring to this process, the author proposes and analyzes a generic kinetic model describing the regulation of tissue growth by locally produced activator. The model includes activator diffusion and control of the rate of cell proliferation which is described by using the Hill expression. Although this control may be moderately or strongly non-linear, the qualitative changes in the regeneration kinetics are predicted to be modest. For moderately non-linear control, the evolution of the tissue volume to the steady-state value exhibits an initial relatively short linear stage and then becomes slightly slower so that the whole kinetics is close to exponential. For strongly non-linear control, the linear stage dominates and/or the kinetics may exhibit a S-like shape feature which is, however, rather weak. The identification of such qualitative features in experimentally measured kinetics is shown to be difficult, because the error bars in the experiments are typically too large.