Is periodontal breakdown a fractal process? Simulations using the Weierstrass-Mandelbrot function.
This paper introduces a theoretical model of periodontal disease that is multifactorial, cumulative and produces periodontal breakdown in "bursts and remissions". The simulation is based on the generalization of the Weierstrass-Mandelbrot function as an integration of a series of sinusoid fluctuations that facilitate or prevent periodontal breakdown with different frequencies, amplitudes and phases. The breakdown is produced when the integration of the factors reaches a certain threshold and is stopped when it is below it. The zeroset of the function (the set of points of the function in intersection with the time axis) is a self-similar set that corresponds to the instances when the process switches between destructive and non-destructive phases, and its fractal nature indicates that in theory, bursts of destruction do not have a characteristic duration size. If the mechanism of periodontal disease has in principle similarities to the model presented, then accurate site-specific predictions about periodontal destruction may prove an unrealizable task.
Landini
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Oral Pathology Unit, School of Dentistry, University of Birmingham, UK. G.Landini@bham.ac.uk
D016301:Alveolar Bone Loss / Q000473:pathology*; D003198:Computer Simulation; D018450:Disease Progression; D017709:Fractals; D006801:Humans; D008954:Models, Biological