Multifractal and lacunarity analysis of microvascular morphology and remodeling

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 that automated multifractal analysis and lacunarity may be used with classical methods to quantify microvascular morphology.

Using multifractal analysis and lacunarity, we present an automated extraction tool with a processing pipeline to characterize 2D representations of 3D microvasculature. We apply our analysis on four tissues and the hyaloid vasculature during remodeling.

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.

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.