## 2 Materials and Methods
### Statistical Analysis  
The primary objective of this analysis was to assess the influence of both laser power and ureteral access sheath (UAS) size on the variations in temperature. This study was designed to evaluate the effects of these factors under the conditions of gravity irrigation without on-demand manual pumping. The hypotheses aimed to discern the individual contributions of laser power and UAS size to temperature regulation during procedures, thereby providing valuable insights for optimizing operational parameters.  
Figure 1: Temperature readings from an FLIR C5 thermal imaging camera during the laser lithotripsy procedure (**left photo**) and the image of the 3D model used in the study (**right photo**). The area within the red circle indicates the highest temperature.  
The threshold for statistical significance in this analysis was set at \(\alpha\) = 0.05. An application of the Shapiro-Wilk test served to assess the normality of the distribution of variables [9]. The inquiry into the variance of temperature, as influenced by power and UAS factors (hereafter referred to as factors), was undertaken via a factorial design structure of 5 \(\times\) 2. The aligned rank transform (ART) was utilized for this analysis; this non-parametric technique enables variance analysis without the necessity of assuming equal variances among groups or the normality of residuals [10].  
The significant disparities between pairwise factor categories were assessed using post hoc pairwise comparisons, as delineated within the ART framework proposed by [PERSON] et al. [11]. Initially, a meticulous examination of the main effects within each individual factor was conducted, affording a broad understanding of the impact of each factor devoid of potential interaction effects. Subsequently, the scope of the analysis was broadened to include pairwise comparisons amongst combinations of levels across interacting factors, yielding insights into the specific disparities between these combinations. Moreover, supplementary tests were performed to pinpoint differences within the interaction effects, thereby infusing a deeper level of detail into the analysis.  
Analyses were conducted using the R statistical language (version 4.1.1; R Core Team, 2021) on Windows 10 pro 64 bit (build 19045), using the packages _rio_ (version 0.5.29), _ARTool_ (version 0.11.1), _sjPlot_ (version 2.8.14), _report_ (version 0.5.7), _psych_ (version 2.1.6; Revelle W, 2021), _ggplot2_ (version 3.4.0), _readxl_ (version 1.3.1), _dplyr_ (version 1.1.2), and _tidyr_ (version 1.2.0).  
The data under investigation comprised temperature levels, scrutinized as a function of UAS size (10/12 Fr, 12/14 Fr) and laser power (12 W--0.8 J/15 Hz, 15 W--1 J/15 Hz, 18 W--1.2 J/15 Hz, 20 W--2 J/10 Hz, 25 W--2.5 J/10 Hz) over a designated time frame. Measurements were systematically procured at 30 s intervals. At each juncture, an in-depth examination of temperature levels was conducted for every possible combination of UAS size and laser power.  
The intricacies of the technical design led to variations in the overall measurement time for the different factor combinations under investigation. Consequently, the total measurement time for each combination fluctuated, spanning a range from 12.5 to 30.5 min (this divergence in measurement time, whilst unavoidable due to the technical constraints, was meticulously accounted for in the analysis to ensure the robustness and validity of the findings). All procedures for each laser setting were repeated three times in this study.