Fractal Geometry in Tumour Immunoediting

Abstract As being composed of cancer cells and myofibroblasts, different areas including cancer nest and stroma develop in tumour. The latter plays an important role in penetration of immune system. On the other hand, immune cells do not spread evenly in these areas, and don’t have the same effect on different cells. It is well established that tumour tissue has fractal properties, including unique fractional dimension along with lacunarity. In this study, partial differential equations were applied to simulate the infiltration and diffusion of immune cells in the two areas of modelled tumour tissue. Here we show that not only is fractal dimension an important factor in immunoediting, but also the fractal architecture of tumour plays a vital role in maintaining tumour in equilibrium. The significance of lacunarity is shown in the results. It is shown that tumours with smaller fractal dimension and greater lacunarity are defined as malignant, in contrast, tumours with greater fractal dimension and smaller lacunarity are defined as benign, both of which is due to immunoediting procedure occurring different relating to not just the fractal dimension but also to the pre-fractal architecture of tumour.