Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy?

Fractal, multifractal and lacunarity analysis applied in retinal regionsof diabetic patients with and without non-proliferative diabetic retinopathy

“…Avakian et al [11] performing fractal analysis in skeletonized images from 60-degree fundus fluorescein angiography, observed that the density values of vessels in normal retina macular region was higher than the vascular density of the retinal macular region with NPDR. Our study corroborates the results obtained by Kunick et al [12] that showed no difference between retinal images of patients with and without NPDR, utilizing fractal dimension analysis (box-couting and information dimension) in segmented images of the retinal vascular network. Diabetic patients, despite not having the signs that characterize a mild early diabetic retinopathy, show a vascular geometry similar to the patients with the disease, according to the results revealed by fractal methods (boxcounting dimension, information dimension, generalized dimensions, singularity spectrum and lacunarity parameter) and the number of bifurcation points.…”

“…Likewise, results obtained by Mendonça et al [31]; Kunicki et al [12] and Voinea and Popescu [32] were also found to be out of that condition. Considering that the mass-radius dimension of a structure is higher than the boxcounting dimension (capacity dimension) [31,32], Family et al [7], having obtained a higher correlation dimension than the mass-radius one for retinal blood vascularization, the principle D cap ≥ D inf ≥ D co was contradicted.…”

“…Doubal et al [9] have obrtained the fractal dimension of retinal vessels in the lacunar stroke and Cavallari et al [10] in the cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL). Avakian et al [11], Kunicki et al [12] and Ţălu et al [13] have used fractal methods to identify non-proliferative diabetic retinopathy (NPDR), however obtaining contradictory results.…”

Non-linear dynamics of chromosome condensation induced by colcemid

“…This is a field of research called as non-linear dynamics and the analyses of such non-linear processes disclose the fractal properties of these phenomena, such as scaling, self-similarity and fractal dimension (Liebovitch 1998;Stam 2005;Kunicki et al 2009). Selfsimilarity means that the parts of an object or process resemble to the whole object or process; scaling or dependence on the scale means that the measured properties depend on the scale at which they are realized and the fractal dimension provides a quantitative description of the irregularity of the fractal objects or processes (Liebovitch 1998;Kunicki et al 2009). It is well known that DNA has the property of selfreplication and it is the sequence of nitrogen bases purine (A and G) and pyrimidine (T and C), which probably generates the feature of fractals.…”

“…Previous study has demonstrated that the dynamical process of chromosome condensation is apparently random but in fact is a deterministic chaotic event. Fractal geometry refers to the description of structures with self-similarity in any scales (Liebovitch 1998;Stam 2005;Kunicki et al 2009). In a previous work, Lu et al (1998) demonstrated that during the transitional stage of chromosomes from premetaphase to early-metaphase, the length changes of chromosomes were chaotic, therefore, presented fractal properties.…”