## 2 Materials and Methods
### Mathematical Models
The deposition of light in the tissue produces a photothermal effect, and the Pennes heat transfer equation is used to study the heat transfer in the tissue, as shown in Equation (7) [20]:  
Figure 1:0  
where \(\rho\), \(c\), \(T\), and \(k\) are the density (kg/m\({}^{3}\)), specific heat capacity [J/(kg\(\cdot\)K)], temperature (K), and thermal conductivity [W/(m\(\cdot\)K)] of the tissue, respectively; \(\rho_{b}\), \(c_{b}\), \(T_{b}\), and \(\omega_{b}\) are the density (kg/m\({}^{3}\)), specific heat capacity [J/(kg\(\cdot\)K)], temperature (K), and blood perfusion rate (s\({}^{-1}\)) of the blood, respectively; the term [\(\rho_{b}\)c\({}_{b}\)\(\omega_{b}\)(T \(-\) T\({}_{b}\))] simulates the heat sink effect caused by small capillaries; \(Q_{m}\) represents the heat generated by metabolism (W/m\({}^{3}\)), which is less influential compared to other applied heat source terms and is often neglected; \(Q_{p}\) is the heat source term during thermal ablation (W/m\({}^{3}\)), i.e., the heat generated by laser light energy deposition. To characterize the heat transfer properties between vessels and tissues, internal forced convective heat transfer conditions were set in COMSOL to simulate the effect of vessels on temperature distribution and coagulation zones [21], and the temperature and heat fluxes were assumed to be continuous at all interfaces. The heat transfer between vessels and tissues can be described by [PERSON]'s equation [22], as shown in Equation (8):  
Figure 1:1  
where \(h_{\text{b}}\) represents the heat transfer coefficient [W/(m\({}^{2}\cdot\)K)]. Blood is assumed to be a non-compressible Newtonian fluid with a steady laminar flow, neglecting the effect of shear effects [23]. According to [PERSON]'s law, the relationship between the tube diameter and the flow in the lumen [24] is obtained by assuming that the vascular flow depends on the vascular radius \(r\), as shown in (9):  
Figure 1:2  
where \(d_{i}\) is the vessel diameter (mm), \(\mu\) is the dynamic viscosity of the fluid (Pa\(\cdot\)s), \(\xi\) is the power-to-mass ratio of the pumping system, \(c\) is the constant material property of the pipe, and the constants \(\rho_{tube}\) and \(\rho_{fluid}\) are the pipe material density and fluid density, respectively. \(\xi[\rho_{tube}(c^{2}+2c)+\rho_{fluid}]\) is a constant 93.44 kgs\({}^{-3}\) m\({}^{-1}\)[13]. Thus, the intravascular flow velocity is  
Figure 1:3  
The Arrhenius model is often the gold standard for thermal damage scenarios because it considers the time factor to represent the relationship between protein thermal degradation and tissue damage at the threshold temperature and time reached. The specific equation is shown in Equation (11) [25]:  
Figure 1:4  
where \(\Omega(t)\) is the degree of tissue death (or damage integral), \(t\) is the ablation time (s), \(A\) is the frequency factor (s\({}^{-1}\)), \(E_{a}\) is the activation energy (J/mol), \(R\) is the universal gas constant (8.314 J/mol\(\cdot\)K), and \(T\) is the tissue temperature (K) in the computational domain at the specified time. The photothermal effect of tissue during ablation is a complex process in which the tissue's optical and thermal physical parameters undergo reversible and irreversible dynamic changes with increasing temperature and decreasing water content in the tissue, which ultimately affects the ablation [26].