## Materials and Methods
### Models
#### 4.3.2 In-Vivo Predictions
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Tissue** & \multicolumn{2}{c}{**Coefficients, (m\({}^{-1}\))**} & **Refractive Index, (1)** \\ \cline{2-4}  & **Absorption, \(\mu_{a}\)** & **Reduced Scattering, \(\mu_{s}^{\prime}\)** & \(n\) \\ \hline Fat [35] & 3 & 950 & 1.455 \\ Gland [35] & 6 & 1100 & 1.4 \\ Muscle [34] & 23 & 130 & 1.37 \\ Tumor [36] & 7 & 1400 & 1.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optical properties of the biological domains that were used in the simulations. The values were obtained from Refs. [34; 35; 36]. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Tissue** & \multicolumn{2}{c}{**Specific Capacity Heat**} & **Thermal Conductivity** & **Density** & **Metabolic Heat** & **Blood Perfusion** \\  & \(c\) **[J (kg K)\({}^{-1}\)]** & \(\lambda\) **[W (mK)\({}^{-1}\)]** & \(\rho\) [kg m\({}^{-3}\)]** & \(Q_{\text{met}}\) [W m\({}^{-3}\)]** & \(\omega_{\text{b}}\) [s\({}^{-1}\)]** \\ \hline Fat & 2348 & 0.21 & 911 & 400 & 0.0002 \\ Gland & 2960 & 0.48 & 1041 & 700 & 0.0005 \\ Muscle & 3421 & 0.48 & 1090 & 700 & 0.0008 \\ Tumor & 3770 & 0.48 & 1050 & 8720 & 0.0001 \\ Blood & 3617 & - & 1050 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermo-physical properties of the biological domains that were used in the simulation. The values were obtained from Refs. [31; 33]Thermal DamageThe Arrhenius injury model was used to estimate tissue destruction. The model, which relates temporal temperature to cell death, is defined by [53]:  
\[\Omega(\tau)=A\int_{0}^{\tau}\exp\left(\frac{-E_{a}}{RT(t)}\right)\mathrm{d}t \tag{11}\]  
where \(E_{a}\) (J mol\({}^{-1}\)) is the activation energy, \(A\) (s\({}^{-1}\)) is a scaling factor and \(R=8.3\) (J mol\({}^{-1}\)K\({}^{-1}\)) is the gas constant. The values for \(E_{a}\) and \(A\) were obtained from Ref. [33] as 302 kJ mol\({}^{-1}\) and \(1.18\times 10^{44}\) s\({}^{-1}\) respectively. \(\Omega=1\) corresponds to the 100% irreversible cell damage. Model ImplementationThis FEM model was developed with the COMSOL Multiphysics 5.2 software package (Comsol, Inc. Burlington MA, USA). All properties and dimensions were added explicitly to the FEM model as parameters and variables under the \"Global Definition\" and \"Model\" nodes, respectively. Equations (9) and (10) were added as analytic functions under the \"Global Definition\" node. The 2D axisymmetrical model was used to reduce simulation time. The light distribution was achieved by implementing Equation (5) as an analytic function. The temperature distribution was achieved using the bio-heat heat transfer application mode. Each tissue was represented with a separate \"biological tissue\" node. The boundary and initial conditions were specified as follows: a Dirichlet condition, T = 37 \({}^{\circ}\)C, at \(\Gamma_{1}\); a Neumann condition, \(\mathbf{n}\cdot(\lambda\
abla T)=h\cdot(T_{\text{ext}}-T)\) at \(\Gamma_{2}\) where the heat transfer coefficient, \(h\) was equal to 13.5 Wm\({}^{-2}\)K\({}^{-1}\) and \(T_{\text{ext}}\) = 25 \({}^{\circ}\)C and continuity, \(\mathbf{n}\cdot(\lambda_{1}\
abla\) T\({}_{1}-\lambda_{2}\
abla\) T\({}_{2})\) = 0 at all interior boundaries. A temperature of 37 \({}^{\circ}\)C (for the normal body) was used as the initial temperatures in all domains of the model. The heat source was added to the bio-heat transfer application mode as a user-defined heat source. The cell death model was implemented with the \"Coefficient Form PDE\" application mode. To achieve a time integration, the coefficients \(d_{a}\) and \(f\) were set to 1 and Equation (11), respectively. All other coefficients were set to zero. The initial conditions were: \(S=\partial S/\partial t=0\). In order to enhance the accuracy of results, we resolved the model with successively smaller element sizes and compared results, until an asymptotic behavior of the solution emerged. The comparison was done by analyzing the temperature at the interface between tumor and the tissue.