Bursts of periodontal destruction and remission, percolation phase shifts, and chaos

Bursts of periodontal destruction are modelled as percolation-driven phase shift events. Percolation theory, though widely used to study the flow of liquids through porous nonliving materials (e.g., soils and rocks), can be applied to bacterial or toxicological penetration of living tissue in only an approximate sense. However, it seems necessary that some mechanism, fundamentally similar to the percolation phase shift, is required to adequately account for bursts. Percolation theory is therefore offered as a framework for considering such events. A principal finding of percolation theory is the existence of percolation thresholds, such that when P, the independent probability that a subregion is susceptible to an invading substance, is above the threshold, the region will percolate or allow flow through, and when P is below the threshold the region will not percolate. This instantaneous transition, from a structure that will permit percolation to one that will not, is described as a phase shift. In addition, the value of P is postulated to depend on multiple factors which might constitute a chaotic system. The nonproportionality of a percolation phase shift and the nonpredictability of any specific chaotic event suggest that reliable burst predictors may, in theory, not be possible at the level of the individual site.