# Multivariate Analysis of Laser-Induced Tissue Ablation: Ex Vivo Liver Testing
## 1 Introduction  
For decades, therapeutic laser systems have been developed and successfully employed for clinical applications in various fields such as dentistry, ophthalmology, and urology [1]. In order to achieve efficient tissue removal and minimal thermal injury, a number of laser parameters have been evaluated, including wavelength, pulse duration, energy/power, and beam size [1, 2]. In addition, a variety of surgical parameters have been investigated in terms of movement technique, repetition, and irradiation time for maximizing ablation outcomes [1, 3]. However, due to complex interactions among the parameters, laser-induced tissue ablation still requires rigorous testing to identify the optimal conditions and eventually to ensure efficacy and safety during laser treatment. One successful laser treatment is vaporization of benign prostate hyperplasia (BPH), also called laser prostatectomy. Symptomatic BPH is one of urological diseases that occur to men aged 40 years or older [4, 5]. Excessive growth of stromal tissue in the peripheral zone of the prostate causes obstruction of urination, eventually leading to dysuria, nocturia, and frequent urge [4, 6]. Other than medications that merely suppress the enlargement of the prostate, a number of surgical treatments have been developed to treat BPH, such as radiofrequency (transureth resection of the prostate; TURP), laser,microwave, and high intensity focused ultrasound (HIFU) [7; 8]. Among various methods, the laser prostatectomy has widely been accepted by surgical urologists due to hemostatic and rapid tissue removal and low complications [9]. During the laser prostatectomy, urologists typically insert an optical fiber through the urethra to deliver high laser power and then maneuver the fiber to remove prostatic tissue. Thus, various surgical parameters, such as laser power, fiber size, working distance, and movement speed, are simultaneously regulated to achieve favorable clinical outcomes [3; 10; 11]. In particular, the laser power has recently been increased to treat large prostate glands (>80 cc) and eventually to reduce the procedure time [12]. However, the efficacy of the laser prostatectomy is still contingent upon the surgeon's skills, which needs more systematic approaches to optimize the surgical parameters and to attain more effective laser prostatectomy. In fact, most surgical urologists are still dependent upon their clinical experience to select the treatment parameters. Thus, the multivariate optimization of the surgical parameters is still necessary to reveal favorable treatment conditions and eventually to provide quantitative training for the laser prostatectomy. In order to improve laser-induced ablation process, design of experiments (DOE) can be used to determine the optimal settings for the critical factors in the tissue ablation [13]. Through DOE, by selecting factors and levels that affect the performance of the ablation process, one can investigate the effect of each factor at more than one setting. A full factorial design is the most common experimental design when the purpose is to determine the critical factors and the range of the values in the study. It can evaluate every possible combination between all the factors. With an increase of a number of factors, the number of experiments in the full factorial design increases exponentially. Instead, a fractional factorial can be employed to acquire information of interactions with fewer experiments. The simplest assumption for the factorial design is the two-level approach, which assumes that there are only two levels for each factor in the natural linear process. In order to fit the output responses in a curved response surfaces, response surface method (RSM) uses additional points that can help estimate the higher-order interactions [14]. Central composite designs (CCD) and Box-Behnken designs (BBD) are the most widely used RSM design [14; 15].