Fractal dimension and lacunarity analysis of retinal microvascular morphology in hypertension and diabetes

Abstract

Hypertension and diabetes mellitus represent modifiable risk factors for vascular disease. They cause microvascular remodeling, and ultimately result in end-organ damage. Therefore, development of methods for noninvasive quantification of the effects of hypertension and diabetes mellitus on microvasculature is of paramount importance. The two goals of the study were: 1) to characterize the geometric complexity and inhomogeneity of retinal vasculature in hypertensive retinopathy (HR) and in proliferative diabetic retinopathy (PDR) by using box counting fractal dimension and lacunarity analysis, and 2) to determine if the combination of these two parameters can be used to describe differences in the vascular tree geometry between HR and PDR. The extended set of retinal images from the publicly available STARE database was manually segmented by our expert, validated, and made available for other researchers to use. The healthy retinal vascular network has a higher complexity (fractal dimension) compared to that in HR and in PDR. However, there is no difference in microvascular complexity between HR and PDR. The inhomogeneity of the retinal microvascular tree (lacunarity) was higher in PDR compared to HR. Lacunarity and fractal dimension together quantitatively characterize microvascular geometry in the retina with higher specificity than fractal analysis alone.