Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.

This paper discusses the possibilities of application of fractal geometry for cancer research. Fractal geometry is a new tool that can be extremely useful for many problems in almost every scientific field. The studies recently done in medicine show fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Cancer diagnosis can be done via determination of fractal dimension. A likelihood ratio test for the Hausdorff dimension is employed in [7] We empirically checked the obtained tests on Sierpinski Carpet and on cancer data. However, several issues arisen, especially those related to simulation of fractals which may mimic tissues. These are discussed in the present paper.