Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process.

BACKGROUND: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). METHODS: The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. RESULTS: Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. CONCLUSIONS: This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

Aggressive periodontitis defined by recursive partitioning analysis of immunologic factors.

BACKGROUND: The present study aims to extend recent findings of a non-linear model of the progression of periodontitis supporting the notion that aggressive periodontitis (AgP) and chronic periodontitis (CP) are distinct clinical entities. This approach is based on the implementation of recursive partitioning analysis (RPA) to evaluate a series of immunologic parameters acting as predictors of AgP and CP. METHODS: RPA was applied to three population samples, that were retrieved from previous studies, using 17 immunologic parameters. The mean values of the parameters in control subjects were used as the cut-off points. Leave-one-out cross-validation (LOOCV) prediction errors were estimated in the proposed models, as well as the Kullback-Leibler divergence (DKL) of the distribution of positive results in AgP compared to CP and negative results in CP compared to AgP. RESULTS: Seven classification trees were derived showing that the relationship of interleukin (IL)-4, IL-1, IL-2 has the highest potential to rule out or rule in AgP. On the other hand, immunoglobulin (Ig)A, IgM used to rule out AgP and cluster of differentiation 4 (CD4)/CD8, CD20 used to rule in AgP showed the least LOOCV cost. Penalizing DKL with LOOCV cost promotes the IL-4, IL-1, IL-2 model for ruling out AgP, whereas the single CD4/CD8 ratio with a lowered discrimination cut-off point was used to rule in AgP. CONCLUSIONS: Although a test is unlikely to have both high sensitivity and high specificity, the use of immunologic parameters in the right model can efficiently complement a clinical examination for ruling out or ruling in AgP.

Smoking influences decision making in periodontal therapy: a retrospective clinical study.

BACKGROUND: Mechanical periodontal therapy consists of a non-surgical course, followed by surgical treatment to eliminate or reduce remaining pathological pockets. Only if diligent mechanical therapy fails are additional measures considered. It has been documented that smoking interferes with the host defense mechanisms. This study addresses the question is meticulous non-surgical periodontal therapy equally successful in smokers and non-smokers? If not, is a thorough and cumbersome non-surgical approach in smokers worth undertaking? METHODS: Thirty-five smokers and 35 non-smokers were selected retrospectively from a pool of 306 patients treated in a private practice over a 17-month period. All had at least 14 teeth present with 8 presenting with gingival pockets > or =6 mm. Non-surgical treatment was performed in 6 to 10 appointments and results were evaluated 6 to 12 weeks after therapy. Bleeding on probing sites with probing depths > or =5 mm were then considered for surgical treatment. RESULTS: Before treatment smokers had statistically significantly higher mean percent of pockets 4 to 5 mm and > or =6 mm (40.36+/-10.65 and 26.51+/-11.95, respectively, compared to 30.38+/-7.57 and 20.42+/-10.03 for non-smokers) and showed significantly lower proportional reduction of these parameters with treatment (50.80+/-33.76 and 81.36+/-19.82 for pocket 4 to 5 mm and 6 mm, compared to 68.43+/-21.23 and 91.7+/-8.92 for nonsmokers). A multivariate analysis gave smoking, plaque control, and initial percent of sites > or =6 mm to be significant predictors of the percent of teeth in need of further therapy. In non-smokers, treatment was apparently successful in all tooth types with the exception of upper first and second molars (28.5% failure) and lower second molar (20% failure). In smokers, rates of further treatment needs were particularly high in the premolar-molar area in both jaws, ranging from 31.4% to 48.5% for an individual tooth type; 42.8% of smokers and 11.5% of non-smokers needed further treatment in 16% of their teeth (pretest probability). A decision analysis showed that for smokers with at least 1 of 5 sites > or =6 mm, one should initiate surgical treatment, rather than first treat non-surgically. If the point of indifference that the decision is correctly set at 95%, the pretest probability should be >12%. There is a higher risk that non-surgical therapy will fail, for instance if we lower the point of indifference to 60%, the pretest probability should be >31%. CONCLUSIONS: It is concluded that smoking impairs healing after nonsurgical periodontal therapy. The decision analysis of this study questions the need for a thorough course of non-surgical treatment in smokers with advanced periodontal disease.