# Multivariate Analysis of Laser-Induced Tissue Ablation: Ex Vivo Liver Testing
## 2 Methods  
In order to apply BBD for tissue ablation, three laser parameters were selected: power (P), treatment speed (TS), and beam size (BS). The selected parameters were considered significant factors that could affect clinical outcomes of laser prostatectomy. Using the three laser parameters, BBD was implemented to optimize the rate of tissue removal. Since it is desirable to avoid the extreme values for the three variables (P, TS, and BS) in the ablation process, BBD was a preferred method, compared with CCD [14]. Table 1 shows the coded factor levels for BBD for three-level and three-variable system. The levels of +1, -1, and 0 mean the high, low, and middle values, respectively. Two-level full factorial was repeated three times for two factors (i.e., levels of +1 and -1) while keeping one factor at the middle value (i.e., level of 0). For example, the first set of four points in Table 1 was to keep BS at the middle value with two-level full factorials for P and TS. Then, P and TS were set at the middle value in that order. Lastly, the center points (C) were added to provide stability and to estimate curvature. Generally, three-factor BBD uses three center points. Thus, the total number of the sample points was 15. The selected samples in the BBD are displayed in Figure 1a. The samples are at the center of the edges and in the center of the design space. Figure 1b shows an experimental setup of ex vivo laser-induced tissue ablation. For the current feasibility study, bovine liver tissue was selected as a surrogate model due to easy procurement and abundance. Unlike prostatic tissue, the liver tissue could be sufficiently prepared for a wide range of repeated tests. In spite of different optical properties, the bovine liver could thus be the proper sample for the initial testing particularly to reduce the number of test conditions. The liver tissue was procured from a local slaughterhouse. All the samples were prepared in a size of 2 \(\times\) 2 cm\({}^{2}\) and stored at 4 \({}^{\circ}\)C in saline to prevent any dehydration and structural deformation prior to laser testing. Each specimen was placed in a tissue holder and covered with a metal plate containing a rectangular aperture (1 \(\times\) 1 cm\({}^{2}\)). Thus, the tissue surface exposed through the aperture was merely ablated during the irradiation. A motion controller was used to manipulate the movement of the tissue holder along the _x-y-z_ directions. The controller thereby determined both beam size (distance-dependent) and treatment speed. A customized quasi-Q-switched 532 nm laser system was employed to irradiate high power laser light on the tissue surface and to achieve photothermal ablation. A 600-\(\mu\)m multi-mode optical \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rank** & **P*** & **TS*** & **BS*** \\ \hline
1 & \(-1\) & \(-1\) & 0 \\
2 & \(1\) & \(-1\) & 0 \\
3 & \(-1\) & \(1\) & 0 \\
4 & \(1\) & \(1\) & 0 \\
5 & \(-1\) & \(0\) & \(-1\) \\
6 & \(1\) & \(0\) & \(-1\) \\
7 & \(-1\) & \(0\) & \(1\) \\
8 & \(1\) & \(0\) & \(1\) \\
9 & \(0\) & \(-1\) & \(-1\) \\
10 & \(0\) & \(1\) & \(-1\) \\
11 & \(0\) & \(-1\) & \(1\) \\
12 & \(0\) & \(1\) & \(1\) \\ C ** & \(0\) & \(0\) & \(0\) \\ C & \(0\) & \(0\) & \(0\) \\ \hline \hline \end{tabular}  
* P = power, TS = treatment speed, and BS = beam size, ** C = central point.  
\end{table} 
Table 1: Coded factor levels for Box–Behnken design for three-variable system  
Figure 1: Schematic illustration of parametric analysis: (**a**) Box–Behnken Design (BBD); (**b**) experimental setup for laser-induced tissue ablation. fiber (flat-ended; NA = 0.22) was used to deliver the laser light to the targeted tissue. The physical distance between the fiber tip and the tissue surface regulated various beam spot sizes. During the tissue ablation, saline was supplied to the irradiated spot at 5.6 mL/min for convective cooling and fiber tip cleaning to emulate clinical situations. Table 2 summarizes three-level values of each parameter for ablation experiments.