Multifractal and Lacunarity Analysis of Microvascular Morphology and Remodeling

Abstract

Purpose-Classical measures of vessel morphology including diameter and density are employed to study microvasculature in endothelial membrane labeled mice. These measurements prove sufficient for some studies; however they are less well suited for quantifying changes in microcirculatory networks lacking hierarchical structure. We demonstrate automated multifractal analysis and lacunarity may be used with classical methods to quantify microvascular morphology.Methods-We present an automated extraction tool with a processing pipeline to characterize 2D representations of 3D microvasculature, using multifractal analysis and lacunarity. We apply our analysis on four tissues and the hyaloid vasculature during remodeling.Results-We found that the vessel networks analyzed have multifractal geometries and that kidney microvasculature has the largest fractal dimension and the lowest lacunarity compared to microvasculature networks in the cortex, skin, and thigh muscle. Also, we found that during hyaloid remodeling, there were differences in multifractal spectra reflecting the functional transition from a space filling vasculature which nurtures the lens to a less dense vasculature as it regresses, permitting unobstructed vision.Conclusion-Multifractal analysis and lacunarity are valuable additions to classical measures of vascular morphology and will have utility in future studies of normal, developing and pathological tissues.

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

“…An object is considered multifractal when its different regions have different fractal properties [18]. Researchers have demonstrated the network of vessels of the retina as a multifractal object, a fact which has been proved through generalized dimensions and singularity spectrum [15,19]. Furthermore, the singularity spectrum has the capacity to evidence the disorders in the retinal vascular architecture with diseases [19].…”

“…Since the fractal dimension describes how much space is filled, but does not indicate how the space is filled by the fractal structure, the lacunarity can solve this problem by making a distinction between different objects with the same fractal dimension [14,15]. The lacunarity is a parameter that indicates the distribution of gap sizes throughout the object embedded in an image, it is able to identify different fractal structures that have the same fractal dimension [14].…”

Fibrous Dysplasia Characterization Using Lacunarity Analysis

“…Lacunarity could also be used to quantify the severity of disease or to differentiate benign from malignant tumors. Literature presents various examples of the use of lacunarity in other scenarios, such as to assess osteoporosis [12], microvascular morphology [26], to analyze the behavior of prostate cancer [27] and breast tumor lesions [28], and to measure cell cancer behavior [29].…”

Tissue Engineering

“…Demonstrates the technique principles and through practice, skilled technicians can complete the surgery in five minutes allowing for a high throughput approach. Furthermore, with automated image analysis tools and good sample sizes, this technique can allow for detailed analysis of the microvasculature [15].…”