## 2 Materials and Methods
### Sample Preparation and Temperature Measurement  
The root canals of the teeth were made accessible to the mechanical root canal instrumentation by using a size 10 K-file (Maillefer, Ecublens, Switzerland). After manual instrumentation, distilled water was injected into the root canals with a syringe fitted with an endodontic cannula (25G) to remove debris.  
The 4 mm tip of nickel-titanium Reciproc blue (VDW, Munich, Germany) size 25 (R25) files were fractured 5 mm from the most coronal end of the root. To facilitate the manual breakage and achieve a standard length of the fragment, a thin notch was made 4 mm from the tip of the file using a needle diamond bur (No.6889.314.010, Komet, Besigheim, Germany) with a high-speed handpiece. Figure 1 shows the steps of sample preparation for temperature measurements.  
Temperature measurements were recorded using a Testo 845 (Testo, Lenzkirch, Germany) infrared thermometer attached to a 0.5 mm diameter K-type (NiCr-Ni) thermocouple with a resolution of 0.1 \({}^{\circ}\)C and an accuracy of \(\pm 0.75\)\({}^{\circ}\)C in contact with the root surface. The thermocouple was bonded to the disto-external surface of the root at the level of the most coronal part of the broken fragment using Filtek Ultimate Flow (3M ESPE, St. Paul, MN, USA) shade A3 (3M ESPE, St. Paul, MN, USA) flowable resin-based composite. The roots bonded with the thermocouple were fixed in a ProTrain endodontic training kit platform size 2 holder (Simit Dental, Mantova, Italy). Conductive gel (room temperature, \(25\pm 1\)\({}^{\circ}\)C) of the ProTrain kit was used as a heat-conducting medium around the roots.  
Gates-Glidden (GG) drills (no. 2, 3, 4, corresponding to the root canal sizes of the three categories) were used to prepare the staging platform coronal to the fractured fragment. GG drills were changed after each five teeth considering the wear of the instrument. According  
Figure 1: Schematic figure of the sample preparation for temperature measurements.  
to our pilot study, 30 s preparation time at 2000 revolution per minute (rpm) with each GG was sufficient to prepare the root canal coronal to the fragment. The first GG was used to ensure that the ultrasonic instrument could properly access the broken nickel-titanium instrument. The second GG was modified by grinding the drill perpendicular to its long axis at its maximum cross-sectional diameter to create a flat tip ensuring staging platform preparation coronal to the fractured segment.  
During the preparation with GGs, the temperature changes were recorded. After preparation, the root canal was rinsed with 1 mL of 25 \({}^{\circ}\)C \(\pm\) 1 \({}^{\circ}\)C distilled water. The canal was then dried using two paper points corresponding to the size of the canal.  
Ultrasonic preparation was performed using a piezoelectric multifunction dental scaler, a Woodpecker UDS-E LED (Woodpecker, Guilin, China) ultrasonic device with a size 25 stainless steel ultrasonic U-file captured in a 120\({}^{\circ}\) E1 clamping tip (endochuck) (EMS, Herrliberg, Switzerland). The ultrasonic preparation of a root canal was followed by rinsing and drying, which was repeated four times per root canal, giving a period of the preparation (Figure 2). Based on the duration of ultrasonic preparation, test groups were created with preparation times of 30, 45, and 60 s (Table 1). The duration of rinsing and drying was set to 30 s. For the exact timing of the experiments, the Interval Timer program for mobile phones (Dreamspark, Taipei, Taiwan) was used, which allowed to set several time intervals per signal. Temperature changes were recorded continuously during each preparation and rinsing-drying period. Temperature at the baseline and at the end of each period was subtracted from the next record to calculate the temperature rise or drop between the periods. There was no goal of removing the fractured segment.