Fractal Analysis in Human Pathology

.Living structures may be described as being in a self-organizing, fluctuating steady-state far from equilibrium. 1 Self-organization and a state far from equilibrium are characteristics of chaotic structures. Chaotic structures present fractal geometry, so is not too astonishing that the branching pattern of the airways in the lung or the arterial vascular pattern of the cardiovascular system have been described with fractal properties. 2–4 Like coastlines, a tumor examined by light microscopy has a complex, irregular border and retains a similar level of complexity over a range of magnifications. 5–7 Euclidean morphometric measurements were found to be invalid outside precisely defined conditions of resolution and magnification. 8 In our Institute we are applying fractal dimension analysis to study human tumors at light and ultrastructural levels. Here, we present data obtained studying the epithelial-connective tissue interface in basal cell carcinoma of the skin, the boundaries of invasive bladder carcinomas (urothelial neoplasia), and the lymphocytic nuclear membrane in mycosis fungoides and chronic dermatitis.