Effects of endodontic treatment on apparent Young's modulus of human teeth: in vitro study using speckle interferometry.

The introduction of new techniques for endodontic procedures requires the analysis of the biomechanical behavior of dental structures. Digital speckle shearing pattern interferometry (DSSPI) is a nondestructive optical measuring technique that allows one to directly quantify deformations in teeth that are subjected to stress. DSSPI technique was applied to measure small deformations caused by flexion in different types of teeth. The test was carried out both before and after endodontic treatment with the ProTaper method in order to evaluate the variation of dental elasticity, taking into the account the type of tooth and the endodontic treatment. The results obtained show that dental elasticity, established by means of the apparent Young's modulus, before and after the endodontic treatment, differs between incisors and premolars. The endodontic process does not affect dental elasticity (p>0.7). Specifically, 57.1% of central incisors and 56.3% of second premolars slightly increase their elasticity after the endodontic process. In turn, 42.9% of central incisors and 43.7% of second premolars slightly decrease elasticity. The endodontic treatment especially affects the "neutral fibre"; therefore, there is little influence on elasticity by flexion. However, after finishing the process, the channel was restored with material, which can slightly increase tooth elasticity in some cases.

Validity conditions for the radiative transfer equation.

We compare the radiative transfer equation for media with constant refractive index with the radiative transfer equation for media with spatially varying refractive indices [J. Opt. A Pure App. Opt. 1, L1 (1999)] and obtain approximate conditions under which the former equation is accurate for modeling light propagation in scattering media with spatially varying refractive indices. These conditions impose restrictions on the variations of the refractive index, the gradient of the refractive index, the divergence of the rays, the frequency of modulation, and the widths of light pulses, which are related to the mean refractive index, the absorption coefficient, and the reduced scattering coefficient of the medium. Each condition is geometrically interpreted. Some implications of the results are discussed.