# Multivariate Analysis of Laser-Induced Tissue Ablation: Ex Vivo Liver Testing
## 3 Results and Discussion
In an attempt to assess collective effects of laser parameters, laser-induced ablation volume was quantified as a function of volumetric energy density (VED = P/[TS \(\times\) BS]; J/mm\({}^{3}\)) as shown in Figure 5. Since VED represents the amount of laser energy that was used to remove 1 mm\({}^{3}\) of tissue, the correlation between the ablation volume and VED could evaluate the overall ablation efficiency. According to Figure 5, the BBD model was validated by using the experimental data, in that a comparable tendency was found in the variations in ablation volume (\(p\) = 0.36). Regardless of the data sets, the ablation volume initially increased with VED but became saturated at higher VEDs. As the maximum ablation volume of 209 mm\({}^{3}\) occurred at VED of 400 J/mm\({}^{3}\), the highest VED should be selected to merely maximize the total tissue removal by increasing P and/or decreasing both TS and BS. Although VED effectively described the overall variations in the ablation volume, the increase rate (i.e., slope) of the ablation volume suddenly decreased at around 100 J/mm\({}^{3}\). Furthermore, to shorten laser prostatectomy times, particularly for treating large prostate glands, AR could be a more crucial factor for optimization of the ablation conditions. According to the current BBD results, the optimal VED ranged from 71 (P = 200 W, TS = 7 mm/s, and BS = 0.4 mm\({}^{2}\)) to 75 J/mm\({}^{3}\) (P = 180 W, TS = 6 mm/s, and BS = 0.4 mm\({}^{2}\)). Thus, the corresponding ablation volume was approximately 80 mm\({}^{3}\) (Figure 5). It can be conceived that the optimal parameters for laser prostatectomy could be identified prior to the onset of volumetric saturation in tissue (i.e., maximizing P and TS and minimizing BS). Both P and BS yielded a linear correlation with AR, in that the two parameters can determine the spatial distribution of power on the tissue surface  
Figure 4: Parametric analysis on ablation rate (mm\({}^{3}\)/s) with fixed parameters: (**a**) treatment speed (TS); (**b**) beam size (BS); (**c**) power (P). (i.e., irradiance). On the other hand, TS showed a non-linear (i.e., parabolic) correlation with AR, implicating that due to beam divergence and the resultant irradiance, the interaction time between laser and tissue should be optimized to achieve high ablation efficiency. In addition, unlike P and BS that are typically determined by laser system and optical fiber (device-dependent), TS is controlled by urologists during laser prostatectomy (surgeon-dependent) [16; 17]. Thus, the training on fiber movement during laser treatment would be instrumental in attaining better clinical outcomes [3]. However, the current study merely focused on ablation efficiency rather than safety. In order to enhance clinical results, the degree of tissue coagulation should additionally be considered during BBD analysis as thermal injury in tissue considerably determines wound healing after laser prostatectomy. Moreover, liver tissue was tested for the current study, which hardly reflects fibrous prostatic tissue. Thus, further BBD investigations on canine prostate models will be pursued to identify the optimal surgical parameters by considering blood perfusion, tissue denaturation, and chronic healing response. In-depth parametric optimization may further ensure efficacy and safety of laser prostatectomy for BPH patients. The purpose of the current study was to identify the maximal ablation rate to facilitate laser prostatectomy on large prostate glands (>80 cc) for clinical translation. According to Figure 5, a higher VED yielded a larger removal of tissue. For instance, at the VED of 500 J/mm\({}^{3}\), the corresponding AR is 20.5 mm\({}^{3}\)/s (=ablation volume of 205 mm\({}^{3}\)/irradiation time of 10 s). On the other hand, the optimal VED found in this study was estimated to be 75 J/mm\({}^{3}\) (Figure 4), which resulted in almost 50 mm\({}^{3}\)/s (=80 mm\({}^{3}\)/1.7 s).