Statistical inference on fractals for cancer risk assessment

This paper discusses the application of fractal geometry in medicine. 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 tumours. 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. The intention of this paper is to demonstrate the potential of testing for the range of fractal dimension. We briefly discuss recent studies with fractals in medicine, in particular studies concerning cancer diagnosis. We employ the likelihood ratio test for the Hausdorff dimension and we empirically check the obtained tests on Sierpinski Carpet and on cancer data. Cancer data consists of 29 patients who have been diagnosed with renal cancer. In contrast to other applications on cancer data, we have not to investigate an area of cancerous cells. This kind of tumour is more typical for small children, therefore, non-invasive methods seem more important.