ABSTRACT
This chapter discusses a numerical approximation of the Oster-Murray model of chemotaxis in two-dimensions. Chemotaxis is the process by which cells aggregate under the influence of a secreted chemical substance. This cellular aggregation underlies such physiological processes as cartilage formation and the acceptance or rejection of donated organs. The model for chemotaxis that is employed herein is due to G. F. Oster and J. D. Murray and the interested reader is referred there for a full biological justification of its assumptions. The primary variables of this model are cellular concentration and chemoattractant concentration (c). The cells are presumed to be randomly motile and to “convect” in response to the gradient of c. In addition, the cells are presumed to secrete the chemoattractant in a fashion described by Michaelis-Menten saturation.
