## 2 Materials and Methods
### Experimental Setup
#### 2.2.2 Skin Phantom  
The agar skin phantom for this study is based on the tissue-mimicking phantom used in the research of [PERSON] and [PERSON], as this composition is accurate for thermal modeling [35]. A solution of 4% of lab-grade agar powder (Himedia labs, Einhousen, Germany) and distilled water is used to match the thermal properties of human skin. To create the skin phantom, the process involves dissolving agar powder gradually in distilled water to create a solution with a concentration of 4.0%. This solution, comprising water and agar, is then heated until it reaches the melting temperature of agar, which is 85 to 95 \({}^{\circ}\)C [54]. Once melted, the agar solution is carefully poured into molds and left to cool for several hours until it solidifies and takes on a gelatinous texture. The 3D-printed moulds used for this experiment create an agar-agar specimen of cylindrical shape with a diameter of 100 mm and a thickness of 10 mm. Three different molds are used, as shown in Figure 2: a flat mold which resembles flat skin and a second mold which imitates an ulcerating skin lesion. The ulceration has a diameter of 5 mm and a height of 3 mm. The thickness of the ulceration is determined based on the classification by [PERSON] et al. They categorized ulcerated melanoma into two groups: excessive ulcerations (>5 mm or >70%) and minimal/moderate ulcerations (<5 mm or <70%) [55]. The diameter of the ulcerating melanoma, specifically the 5 mm diameter, is determined according to the study conducted by [PERSON] et al. [56]. In their research, they classified the data into three categories:  
Figure 1: Camera setup with an Optris Xi400 microscope optics thermal camera placed at 100 mm above the skin phantom surface. The field of view at the object surface is 34.2 mm \(\times\) 25.7 mm with a pixel size or Instantaneous Field of View (IFOV) of 90 μm and a Measurement Field of View (MFOV) of 3 \(\times\) 3 pixels or 0.27 mm.  
no ulceration, ulceration width ranging from 1 to 6 mm, and ulceration width greater than 6 mm. The skin phantom is placed on an aluminum heated bed and covered with paper tape to decrease the high reflectivity of the aluminum in the infrared spectrum. The temperature of the heated bed is set to 37 \({}^{\circ}\)C, which resembles the core body temperature of 37\({}^{\circ}\)[42]. To monitor the depth of cooling penetration in the skin phantom for various cooling methods, Platinum Resistance Pt100 Thin Film Detectors (RS Pro) are utilized. These detectors are inserted into the agar substrate. The Pt100 Resistance Temperature Detector (RTD) used in this case has a probe diameter of 1.2 mm and a probe length of 1.6 mm. It has a rapid response time of 0.1 s and is capable of sensing temperatures within the range of \(-50\) to 500 \({}^{\circ}\)C. The RTD is connected to a MAX31865 RTD-to-digital converter manufactured by Maxim Integrated. This converter is then connected to an Arduino microcontroller, which utilizes software capable of reading the RTD and temperature values at a frequency of once per second. In this setup, one RTD is inserted into the substrate at a depth of 5 mm, precisely at the center of the lesion. The second RTD is placed at the bottom of the skin phantom, reaching a depth of 9 mm. These detectors provide valuable temperature measurements to track the cooling process and assess the depth of penetration in the skin phantom.