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Introduction

The art and science of endodontics have advanced substantially over the past decade. Clinical decision-making is becoming more complex today and requires evidence-based information . Taking data from in vitro studies as clinical evidence may be problematic. Despite all the energy invested in laboratory testing, laboratory simulations are generally rarely predictive of clinical behavior . One successful association concerns adhesive restorative materials, where laboratory and in vivo bonding-effectiveness data correlate .

Numerous clinical simulations have been carried out to investigate the sealing ability of endodontic procedures and materials. The majority of leakage tests are related to the linear measurement of tracer (an identifiable substance used to underline the interface, like colorants and radioisotopes). Colorants appear to be colored, because they absorb some wavelengths of light preferentially. Methylene blue and India ink are colorants widely used in dental leakage tests. However, endodontic leakage studies performed with tracers and especially colorants are hardly reproducible and comparable, leading to varying conclusions. It is difficult to determine if these variations are the results of the obturation technique, of experimental errors, or a combination of both . Wu and Wesselink noted that the many variables associated with tracer penetration methodology may contribute to such variations.

Since recurrent concerns have surfaced about the reliability and reproducibility of leakage studies, the Editorial Board of the Journal of Endodontics has suggested a moratorium on comparative endodontic leakage studies, effective July 2008. Instead they encourage investigation on the method’s validity. This moratorium led to the reaction of several scientific leaders in the field who responded to the moratorium by defending high quality laboratory leakage studies. In this context, this article attempts to provide a theoretical background for future investigations in order to improve the comprehension of in vitro tracer leakage studies and to determine among which conditions they can be reliable.

Modeling of liquid penetration, based on fundamental laws, is needed for the assessment of endodontic leakage studies, for the improvement of experimental methods and for the comprehension of their results. Endodontic tracer penetration is a complex process, which can be compared to liquid penetration in porous media and modeled as in different other fields . To our knowledge, only two studies were interested in the capillary action around dental structures and two others described a diffusion model for microleakage in dental restorations . In particular, it was found that the depth of tracer penetration by capillary forces depends upon the interface slit width and the hydrophobicity of the dentin and filling materials .

Here we develop two theoretical models for tracer penetration into the filled root-canal. Our first model describes an initially dry slit where the movement of tracer solution is mainly driven by capillary forces. In our second model the slit is wet and the colorant migrates by diffusion .