Recent Development on Mathematical Models Including Human Root Dentin and the Other Applications

The first aim of this paper is to survey some mathematical models including human root dentin and the other applications. It is well-known that formation, evolution, diseases and treatments of the tooth, jaws, mouth and surrounding tissues are directly related to mathematical models and their applications. In order to improve and investigate mathematical models with their algorithms, we need to understand the complex and challenging root canal system, which is an important factor for instrumentation, preparation and obturation of the tooth root canals. Therefore, root canal length, curvature, conicity, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, to design and realize a method for analyzing the geometric characteristics of human root canals is come forward and mathematical models appear to be a suitable way to examine the geometric properties of root canals. The second aim of this paper is to provide a good reference for manufacturers of root canal instruments and for dentists to better understand the geometry of root canals as well as the limits they might have with the root canal treatment. Moreover, we give further remarks and observations on new and old mathematical models and related mathematical subjects such as the Laplace transform, the Mittag-Leffler function and the other derivative and integral formulas. Finally, we give some open questions with observations on our models.