Three-dimensional microvascular networks fractal structure: potential for tissue characterization?

It has been shown that the fractal dimension of 2D microvascular networks can discriminate between normal vs. tumor tissue (Gazit et al., 1995, 1997). We have determined the fractal characteristics of five 3D microvascular networks and conclude on the correlation between the computed fractal characteristics and the nature of the tissue of origin. The networks considered in the fractal analysis study were one rat tumor network (RT), one nude mouse tumor (NMT), one hamster skeletal muscle (HSM), one rat cremaster (RC), and one rat cerebral cortex (RCC). The networks were digitized in a 3D lattice starting from the known length, diameter and position of each segment in the network. The digitization process was performed such that the ratio between the initial occupation fraction of the vessels in the network and the occupation fraction after digitization is close to one. The resultant cubic lattices were analyzed using the concept of asymptotic fractals. The fractal dimension df, and the minimum path dimension dmin (that measures the tortuosity of the vessels) were determined for all the networks. Fractal behavior was noticed on length scales from 1-1.3 decades, dependent on the actual network size. The values obtained for the fractal dimension for the RT, NMT, RCC, RC and HSM microvascular networks are respectively, 2.6, 2.2, 2.29, 2.12 and 2.08. For the minimum dimension the values obtained are: 1.2, 1.1, 1.16, 1.1, and 1.1. By analyzing the available data, preliminary conclusions lead us to believe that a correlation between the fractal characteristics and tissue type might exist. Another important aspect is that the 3D RT microvascular network seems to have a percolation-like scaling which can be beneficial in monitoring the growing pattern using invasion percolation growth models. However, for general conclusions to be drawn, more networks have to be analyzed.

Duke Scholars

Author Shiva Kumar Das Radiation Oncology

Author Mark Wesley Dewhirst Radiation Oncology