Is periodontal breakdown a fractal process? Simulations using the Weierstrass-Mandelbrot function

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Abstract

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.

Details

Original languageEnglish
Pages (from-to)300-307
Number of pages8
JournalJournal of Periodontal Research
Volume32
Issue number3
Publication statusPublished - 1 Apr 1997