Fractal Geometry in Tumour Immunoediting

Abstract As being composed of cancer cells and myofibroblasts, different areas including cancer nest and stroma develop in tumor. 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. Tumor tissue has fractal properties, including a unique fractional dimension along with lacunarity. In this study, by utilizing partial differential equations, we simulate the infiltration and diffusion of immune cells in two areas of modelled tumor tissues. Here, we show that not only is fractal dimension an important factor in immunoediting, but also the fractal architecture of tumor plays a vital role in maintaining tumor in equilibrium. The results show the significance of lacunarity. We define tumor malignancy in models with smaller fractal dimensions and greater lacunarities, in contrast, benign tumors have greater fractal dimensions and smaller lacunarities. Sierpinski Carpet random pre-fractal produces a better model for tumor immunoediting in comparison with non-deterministic Brownian fractal as it reflects immunoediting stages in a more beneficial way for tumor.