Size dependent variation in the fractal dimensions of herpes simplex epithelial keratitis

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Abstract
Dendritic ulcers, the commonest manifestation of herpes simplex epithelial keratitis (HSEK) are fractals. It is likely that their fractal properties alter if they progress to a geographic appearance. This study investigates the relationship of maximum ulcer diameter (Feret's diameter) to area (Dm) and perimeter fractal dimensions (Ds), parameters of the complexity of their areas and outlines respectively. For dendritic ulcers in the size range of 1.6–3.2 mm, Dm = 1.41 ± 0.06 and Ds = 1.40 ± 0.04 (mean ± SD). With increasing ulcer size, a progressive divergence of the values of Dm and Ds occurred, such that values of 1.75 and 1.22 respectively were found at a maximum diameter of 8.4 mm. These results imply that as ulcers enlarge, their outlines become less irregular and they fill more of a 2-dimensional plane. Dm and Ds are useful parameters in quantifying the progression of HSEK from dendritic to amoeboid morphology and could have a role in the assessment of ulcer response to pharmacological intervention. A knowledge of the fractal properties of HSEK may increase understanding of the mechanisms of ulcer formation and viral spread.