A.V. Belikov, K.V. Shatilova, A.V. Skrypnik, R.G. Vostryakov
St. Petersburg State University of Information Technologies, Mechanics and Optics,Saint-Petersburg, Russia
As described earlier, following processes lead to the destruction of enamel by laser radiation: the local melting of hydroxyapatite and removal of material by the air-blast, which is caused by rapid heating and expansion of the hydroxyapatite or water in the enamel pores or cracks. It is believed that the destruction of the enamel occurs mainly on the inter-rod spaces or cracks. However, the enamel destruction products contain elements of size smaller than a prism that mean the destruction of the prisms. In this study, we believe that enamel ablation by YAG: Er laser radiation with a wavelength of 2.94 μm is due to heating and expansion of the free water contained in the enamel prisms. In this case, a cube of hydroxyapatite with an inner cube of water is taken as the unit volume of enamel. The volume of hydroxyapatite and water is 89% and 11% of unit volume (prism), respectively. We substitute the length of the cube edge of hydroxyapatite was 5 microns; the length of the cube edges of water was 2.4 microns. Since water has a high absorption coefficient of erbium laser radiation, water cube is heated by laser radiation; water boils; water evaporates and expands. Water begins to put pressure on the wall of the hydroxyapatite, because the coefficient of volume expansion of water is larger than the coefficient of volume expansion of the hydroxyapatite. Normal and shear stresses appear in the wall of the hydroxyapatite. Wall is destroyed when the maximum stress exceeds ultimate strength of hydroxyapatite. The air-blast appears due to the pressure gradient inside and outside of the cube. Destroyed hydroxyapatite is removed by the air-blast.
Material and method. In theoretical part of present research we first calculated the force which leads to the normal and tangential stresses which exceed the failure threshold of hydroxyapatite wall. We then determined the energy needed to water heating which leads to expansion of water and the appearance of destructive force. Than the removal efficiency was calculated as the ratio of remote volume to energy needed for removal. And similar steps were repeated for several layers of prisms removal. When two prisms layers are removed the thickness of the next removed layers is doubled. Force necessary for its destruction increases. Force increases in 4 times for the normal stresses, in 2 times for the shear stress. If the radiation is attenuated by the Lambert Beer's law in each layer then the energy portion absorbed in each subsequent layer Ei+1 acts on layer Ni+1 and if this energy is smaller than energy which is necessary to water heating to 120°C, then we can determine the number of layers Ni destroyed under the influence of energy Ei > Ei+1. We got the dependence of removal efficiency on the energy density of radiation.
In experimental part of present research we investigate enamel removal efficiency by pulsed YAG: Er laser. Laser operated in free running mode with energy density of 10-250 J/cm2 and pulse durations of 100±10 microseconds.
Results. Decreasing logarithmic dependence of the enamel removal efficiency on the energy density was obtained as a result of the calculations. The shape of this function follows the shape of the experimental curve, but the absolute values differ by no more than 2 times. This difference is explained by simple model: we used one-dimensional model for calculation the hydroxyapatite wall destruction as a beam. Also, the constants associated with the mechanical properties of hydroxyapatite have a significant impact. It should be noted that this model allows us to more accurately calculate the absolute values in compare with the previously described "blow-off" model, which shows the logarithmic dependence too.
Conclusions. The novel model of ablation of human tooth enamel has been offered in this work. It takes into account the structural peculiarities of enamel. Modeling results describe the logarithmic dependence. Experimental and calculated values differences are discussed.
Dr. Ksenia Vladimirovna Shatilova
ITMO University, Assistant Professor
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