A NEW APPROACH TO MODELING THE FORMATION OF NECROTIC REGIONS IN TUMORS

We present a mathematical model of the growth of tumours. The cells in the tumour are taken to proliferate and die at rates determined by th e concentration of oxygen which diffuses into the tumour across its su rface. Tumour cells are assumed to be composed primarily of water whil e the extracellular water is taken to move through the tumour as a por ous media Bow between the cells. Exchange of water between the two is governed by cell proliferation. We model the mass of cells as an invis cid fluid with the pressure in the fluid, keeping the cells loosely pa cked together. Cells move in response to pressure in both fluids until the extracellular water pressure exceeds the cell pressure, resulting in the rupture of the tumour cells as they are ripped from one anothe r. The resulting model is one of porous media flow with distributed so urces and sinks determined by the oxygen concentration. The boundary c onditions change type depending on whether the tumour surface is retre ating or advancing. Retreating interfaces leave ruptured cells creatin g necrotic regions. An example of the model behaviour in one dimension is presented.