## 1 Introduction  
Ultrasonic instruments, common and popular in many fields of dentistry, are nowadays an integral part of endodontic treatments [1]. Ultrasonic instruments have three main applications in endodontics: on the one hand, they help the operator to activate fluids in the root canal (e.g., sodium hypochlorite) to facilitate the removal of bacterial flora and debris; secondly, they can be used for tooth preparation; and thirdly, ultrasonic vibration can be used to remove intracanal posts and broken instruments [1]. Obstructions, such as broken instruments, are factors that make root canal treatment more difficult and affect the outcome of the procedure [2]. When instrument fracture occurs, several treatment strategies can be used: trying to remove the instrument, attempting to bypass the instrument, or sealing the root segment occupied by the broken instrument [3]. Studies using ultrasonic instrumentation to remove broken segments have reported favorable results [4], with success rates of 54.4% to 93.3%. Ultrasonic file removal methods are mostly based on the Ruddle technique or a variation of it [5]. A platform is created using a Gates-Glidden drill (2-4) prior to instrument use. The Gates-Glidden drill is modified by cutting through the maximum cross-sectional diameter perpendicular to its longitudinal axis. The ultrasonic instrument is activated at a lower power setting in the root canal, and then the fractured instrument is circulated counterclockwise or clockwise, depending on the direction of the instrument edges. The vibration transmitted by this action often causes the broken instrument fragment to loosen and then to \"pop out\" of the root canal [5]. Removal of the separated instrument is beneficial in terms of treatment prognosis because it can prevent full disinfection and hermetic sealing of the root canal [6]. To date, there is no standard procedure for the safe removal of broken instruments, although various techniques have been proposed [3]. These methods have met limited success, while often causing significant damage to the remaining root [7; 8]. The introduction of the nickel-titanium (NiTi) alloy in endodontics has allowed the fabrication of a more flexible and resistant instrument [9]. Compared to previously applied hand files, the use of this alloy has allowed for standardized and reliable root canal preparation [10]. Despite the advantages of nickel-titanium files [11], the risk of instrument breakage remains an unresolved problem for practitioners, mainly because fracture can occur without any significant distortion of the instrument [12]. Previous studies have shown that interventions with ultrasonic instruments, such as the removal of a fragment from the root canal, can cause a temperature rise on the external root surface [13; 14; 15; 16]. Heat within the root canal can be generated as a result of removing dentin around the fractured segment by specially designed tips activated by different energy levels of ultrasonic vibration. It was demonstrated that bone removal around the inferior alveolar nerve canal with an ultrasonic device can increase the canal temperature bywith 9 \({}^{\circ}\)C [16]. Despite the low thermal conductivity of dentin [17], it can transmit heat to the external surface of the root and tooth supporting tissues, leading to damage of the periodonotin. A 10 \({}^{\circ}\)C temperature rise for 60 s has been reported to result in reversible tissue damage [18; 19]. Studies, conducted to investigate the temperature rise on the external root surface during intracranial fractured endodontic files with ultrasonic devices, demonstrated a 4.2 \({}^{\circ}\)C-11 \({}^{\circ}\)C increase, depending on the unit, power setting, and duration used [14; 15; 20]. Additionally, the type of fractured instrument has also an effect on the heat amount generated during removal. Higher temperature rise was found with a fractured NiTi instrument, compared to a stainless steel fragment [20].