摘要
A tumour vascular network, characterized as an irregularly stochastic growth, is different from the normal vascular network. We systematieally 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 eases 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 δα（δα = αmax - αmin）, 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.
A tumour vascular network, characterized as an irregularly stochastic growth, is different from the normal vascular network. We systematieally 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 eases 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 δα（δα = αmax - αmin）, 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.
基金
Supported by the National Basic Research Programme of China under Grant No 2006CB708612, the Natural Science Foundation for Young Scientists of Zhejiang Province Grant No RC02096, the National Natural Science Foundation of China under Grant No 10572130, and the Natural Science Foundation of Zhejiang Province under Grant No Y607425.
