Cellular and geometric control of tissue growth and mitotic instability

A mathematical model is presented for the control of growth by a diffusible mitotic inhibitor. The stability of growth is examined as a function of the values of the parameters describing the production, transport and decay of the mitotic inhibitor, and also as a function of the geometry of growth of the growing tissue. Comparisons are made between patterns of mitosis in the mathematical model and experimentally observed mitotic patterns in tissue culture experiments (Folkman & Hochberg, 1973). It is shown that cellular parameters which closely reproduce mitotic patterns for growth as a three-dimensional sphere, lead to self-limiting growth in three dimensions but limitless growth in two dimensions. This observation, that the stability of growth can depend on the geometry of growth is in agreement with earlier results from tissue culture experiments of Folkman & Hochberg (1973). Experimental approaches which can be used to study the relative effects of vascularization, nutrition, mitotic inhibition and growth geometry in normal and cancerous growth are suggested.