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Int J Dent. 2019 Oct 3;2019:7528154. doi: 10.1155/2019/7528154. eCollection 2019.

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

Author information

Dental Sciences, Durban University of Technology (DUT), Durban, South Africa.
Chemistry, Durban University of Technology (DUT), Durban, South Africa.
Discipline of Dentistry, University of KwaZulu-Natal (UKZN), Durban, South Africa.
Institute of Systems Science, Durban University of Technology, Durban 4000, South Africa.



A mathematical model making using of the Verhulst logistic equation was developed to predict the remineralization behaviors of desensitizing paste.


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@TiO2, 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.


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@TiO2 and Colgate Pro-relief. It was, however, found that the trajectory for the Sensodyne repair was a bit complex, thus making the prediction difficult.


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.

Conflict of interest statement

The authors declare that they have no conflicts of interest.

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