Sprout branching of tumour capillary network growth: Fractal dimension and multifractal structure

A tumour vascular network, characterized as an irregularly stochastic growth, is different from the normal vascular network. We systematically analyse the dependence of the branching. It is found that anastomosis of tumour on time is according to a number of tumour images, and both the fractal dimensions and multifractal spectra of the tumours are obtained. In the cases studied, the fractal dimensions of the tumour vascular network increase with time and the multifractal spectrum not only rises entirely but also shifts right. In addition, the best drug delivery stage is discussed according to the difference of the singularity exponent delta alpha(delta alpha = alpha(max) - alpha(min)), which shows some change in the growth process of the tumour vascular network. A common underlying principle is obtained from our analysis along with previous results.