The Application of the Logistic Equation Model to Predict the Remineralization Characteristics of Desensitizing Paste

OBJECTIVES: A mathematical model making using of the Verhulst logistic equation was developed to predict the remineralization behaviors of desensitizing paste. METHODS: The input parameter used for the model was obtained experimentally by brushing twenty-one simulated dentin specimens for seven days with three sample groups, namely, EB@TiO(2), Colgate Pro-relief, and Sensodyne repair (n = 7). A field emission scanning electron microscope (FESEM) and ImageJ software were used to observe and measure the % occluded ratio of the dentin surface. The model fittings for the three sample groups were carried out using the built-in MATLAB least-squares fitting routine fmincon in the optimization toolbox. RESULTS: The results suggest that the experimental parameter were in agreement with the model. It was found that the logistic equation model can make a future prediction of the remineralization pattern for EB@TiO(2) and Colgate Pro-relief. It was, however, found that the trajectory for the Sensodyne repair was a bit complex, thus making the prediction difficult. CONCLUSIONS: Overall, the salient feature of this study suggests that the logistic equation could be used to predict the remineralization behavior of desensitizing paste in the management of sensitive tooth.