Characterization of Tumor Angiogenesis Using Fractal Measures

Abstract

Tumors vascular networks are different from normal vascular networks, but the mechanisms underlying these differences are not known. Underlying these mechanisms may be key to improving the efficacy of the treatment of tumor. We studied possibility to apply two types of fractal measure: fractal dimension and succolarity for characterizing medical images. We find that fractal dimension value to the normal vasculature is smaller than the results for the tumor vasculature. Moreover, for applying succolarity the results do not vary considerable with the direction in normal vasculature, while for tumor vasculature the curves differs significantly. In conclusion, the results obtained show that the fractal measure is an important tool for analyzing medical images.

Characterization and Analysis of Porosity and Pore Structures

“…Despite de Melo's quantifi cation of the concept, to date succolarity as a measure of fractal texture has received much less attention than fractality and laccunarity, although there are studies of drainage systems (Shahzad et al 2010, Mahmood et al 2011, biomedical analysis (Ichim and Dobrescu 2013;Cattani and Pierro 2013;N'Diaye et al 2013N'Diaye et al , 2015Sangeetha et al 2013) and image recognition (Abiyev and Kilic 2010). While there have, as yet, been no studies we know of quantifying the succolarity of inorganic porous materials and rocks, the potential utility of this approach is clear, and bears further testing in geological systems.…”

Vascular Fractality and Alimentation of Cancer

“…The last one (optimal distribution of the suboptimally available energy) is near the "conventional" 2/3. Another microscopic evaluation of angio-structures [76] shows lower values of α , like the fractal dimension of the normal and malignant tissues are , respectively [77]; resulting in low α values. In other evaluations, the vascular structure's dimensionality grows to 1.9, which provides the maximal energy usage of the suboptimal alimentation, and the exponent became as low as 0.525 α = .…”

Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution

“…Additional results in [13] corroborate these results, additionally showing that anti-angiogenic treatments applied to tumour vasculature lead to decreased estimates of fractal dimension. A number of further studies have been performed on both experimental images of healthy and tumour vasculature [18][19][20] as well as simulations of tumour vasculature [21,22]. These studies all tend to agree on the fractality of both healthy and tumour vasculature, and, when compared, tumour vasculature is consistently found to have a greater dimension than healthy arteriovenous networks.…”