TY - JOUR
T1 - Is periodontal breakdown a fractal process?
T2 - Simulations using the Weierstrass-Mandelbrot function
AU - Landini, G.
PY - 1997/4/1
Y1 - 1997/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0031111515&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0031111515
SN - 0022-3484
VL - 32
SP - 300
EP - 307
JO - Journal of Periodontal Research
JF - Journal of Periodontal Research
IS - 3
ER -