# Multivariate Analysis of Laser-Induced Tissue Ablation: Ex Vivo Liver Testing
## 3 Results and Discussion  
Figure 3 demonstrates cross-sectional images of the liver tissue ablated at various conditions; (a) constant P of 160 W; (b) constant TS of 5 mm/s; and (c) constant BS of 1.1 mm\({}^{2}\). The tissue section represents the central vertical cross-section. In the case of constant P, significantly more tissue ablation (20.9 \(\pm\) 3.3 mm\({}^{2}\)) occurred with slower TS and smaller BS (left image; Figure 3a) due to higher irradiance along with longer interaction time (i.e., 400 W/mm\({}^{2}\) and 10 s for left image). On the other hand, the highest TS and the largest BS resulted in relatively smaller irradiance (89 W/mm\({}^{2}\)) and shorter interaction time (1 s), leading to superficial tissue ablation (3.2 \(\pm\) 0.3 mm\({}^{2}\) for right image; \(p\)\(<\) 0.05). Thus, it was noted that both TS and BS were deterministic factors for tissue ablation. Figure 3b demonstrated that for constant TS, the degree of tissue removal (6.9 \(\pm\) 0.8, 6.5 \(\pm\) 0.6, and 5.3 \(\pm\) 0.7 J/mm\({}^{2}\) for left, middle, and right images, respectively) increased in the order of irradiance (i.e., 300, 145, and 111 W/mm\({}^{2}\) for left, middle, and right images, respectively). However, compared to Figure 3a, the increase rate of the tissue ablation was relatively less evident (6.5-fold for Figure 3a vs. 1.3-fold for Figure 3b), implicating that in spite of constant TS, the variations in other parameters (P and BS) could interactively compensate ablation efficiency. Lastly, constant BS in Figure 3c showed that the ablation efficiency increased with decreasing TS and increasing P. In spite of 40% lower irradiance (109 W/mm\({}^{2}\)), the left image showed almost two-fold enhancement in the ablated area (12.4 \(\pm\) 4.4 mm\({}^{2}\); \(p\)\(<\) 0.05), compared with the right image (6.8 \(\pm\) 0.8 mm\({}^{2}\) and 180 W/mm\({}^{2}\)). TS was thus more deterministic than P on the ablation efficiency, given the constant values of BS. Therefore, according to Figure 3, three parameters interactively affected the degree of tissue removal particularly after application of high laser power. To investigate parametric effects of P, TS, and BS on ablation efficiency, BBD was performed. Figure 4 exhibits parametric analysis on AR as a function of P, TS, and BS. Two parameters were evaluated simultaneously while another parameter was fixed (fixed parameters: (a) TS; (b) BS; and (c) P). The upper images represented a low value of the fixed parameter whereas the lower images showed a high value of the fixed one. In the case of the fixed TS (Figure 4a), both the high and  
Figure 3: Images of ablated tissue at various testing conditions: (**a**) constant power (160 W); (**b**) constant treatment speed (5 mm/s); (**c**) constant beam size (1.1 mm\({}^{2}\)). Bar = 1 mm. the low values demonstrate that AR was maximized at P ranging between 180 and 200 W and BS of 0.4 mm\({}^{2}\). Thus, AR was linearly contingent upon both P (proportional) and BS (inversely proportional) at the fixed TS, in that high P and low BS can result in high irradiance. Figure 4b with the fixed BS presents that AR was still maximized at P of 180-200 W, which was similar to Figure 4a. However, the optimal TS ranged between 6 and 7 mm/s, which was quite larger than the low value of TS (1 mm/s; longer irradiation time). The current finding implies that longer interaction time (i.e., slower TS) was hardly necessary to maximize AR. In fact, the beam divergence from the fiber could reduce the irradiance lower than ablation threshold as the ablation crater became deeper. Furthermore, clinical laser prostatectomy considers both the amount of tissue removal and the total lasing time equally significant. Lastly, Figure 4c exhibits that for both high and low values of P, AR was maximized at BS of 0.4 mm\({}^{2}\) and TS of 6-7 mm/s, which was comparable to Figure 4a,b.