## 1 Introduction  
In endodontics, anatomical complexities and root canal system irregularities can reduce the capacity of a three-dimensional sealing in eradicating bacteria. Therefore, ultrasonic and sonic activations have been suggested during obturation procedures to improve the quality of the seal. They enhance the injection of filling materials into isthmuses [1], lateral canals [2, 3], and dentinal tubules [1, 4] and reduce gaps with denser root filling [5, 6], although they do not affect calcium silicate-based cement tubular penetration [7]. Sealer penetration is crucial in increasing the interaction between filling material and dentin, enhancing the ability of the sealing and promoting entombment of residual bacteria within the tubules [8, 9, 10, 11, 12, 13, 14, 15]. Obturation techniques have changed over the years, improving root canal filling to reduce the risk of coronal, lateral, and apical leakage and bacterial recolonization, factors that have a significant impact on the long-term outcomes of endodontic treatments [16]. Although several studies have been conducted to improve the quality of sealing and to perfect the different techniques, lateral canals and anatomical complexities such as isthmus or delta continue to be factors of uncertainty in endodontic treatments [17]. Among the different techniques, continuous wave compaction and Thermafil ([PERSON]/[PERSON], Ballagues, Switzerland) are the best known. The former, a variant of [PERSON]'s warm vertical obturation compaction, consists of the Elements Obturation Unit, which contains a System B (EIE Analytic Technology, Orange, CA, USA) device and a gutta-percha extruder in a motorized handpiece; disposable cartridges of gutta-percha are heated rapidly, and the unit shuts off automatically to prevent overheating of the material. The latter consists of a plastic core coated with alpha-phase gutta-percha and a heating device that controls the temperature. After heating the carrier in a special oven for a certain time, the dentist inserts it into the canal without twisting or turning it. Although continuous wave compaction is considered a time-consuming technique with a long learning curve and the impossibility of applying it correctly in curved and narrow canals, especially in correspondence with very conservative conicity and preparation diameters (20.05; 25.04), which is related to instrumentation performed in the apical third, Thermafil has been proposed as an efficient obturation system for vertical condensation of warm thermo-plasticized gutta-percha, characterized by rapid execution, predictable results, and a short learning curve [18], and is particularly effective in narrow and anatomically complex root canals [19; 20]. Nevertheless, it has some shortcomings, such as difficulties in post space preparation and the risk of making ledges or lateral root perforations [21]. Another limitation results from the rapid temperature drop due to the heating process, which takes place outside the tooth and leads to a reduction in the thermoplastic effect; this may have a negative impact on the filling of the lateral canals and the quality of the seal [22]. To overcome these limitations, sonication applied during carrier-based obturation could create a thermohydrodynamic phenomenon that keeps Thermafil warm during insertion and pushes gutta-percha and sealer deeper into root canal irregularities, increasing the packability and compressive strength of the sealer [23]. This study aimed to determine the effects of sonication of the carrier-based obturation on the sealer penetration into dental tubules. In the current literature, there are several studies describing the crucial role of sonication in improving the sealer penetration [24; 25], but the possibility of combining the filling system with the sealer has not been investigated.