## 3 Discussion  
Generally, the efficacy and safety of NP-mediated PPTT depend on several independent factors such as the properties of nanomaterial (e.g., morphology, size distribution, optical absorption coefficient), biological identity (e.g., in-vivo circulation time, stability, tumor-homing) and irradiation protocols (e.g., laser beam power, shape, duration, cross-section, direction). Therefore, it requires an integrated strategy that combines experiments and models to optimally select and customize these parameters towards the realization of a reliable and efficient treatment outcome. Clearly, we acknowledge that the strategy we describe here is not exhaustive; however, our intention was to emphasize the need for a structured procedure that allows a quantitative assessment of the heat generation capabilities and predict critical optical properties of the nanoparticles that can be used in computational modeling. We show that Fe\({}_{3}\)O\({}_{4}\) NPs exhibit photothermal effects when irradiated with NIR (810 nm) light leading to photothermal generation, which increases with NP concentration and laser power. On the basis of the optical (Figure 1c) and structural (Figure 1b) properties, the absorption coefficient that \begin{table}
\begin{tabular}{l c c c c c c} \hline \multirow{2}{*}{\(\mathbf{T_{\rm max}}\)} & \multicolumn{2}{c}{\(\mathbf{R=1\) mm}} & \multicolumn{2}{c}{\(\mathbf{R=2.5\) mm}} & \multicolumn{2}{c}{\(\mathbf{R=5\) mm}} \\ \cline{2-7}  & \(\mathbf{N(\phi_{\rm v})}\) & \(V_{\rm L}(R_{\rm L})\) & \(\mathbf{N(\phi_{\rm v})}\) & \(V_{\rm L}(R_{\rm L})\) & \(\mathbf{N((\phi_{\rm v}))}\) & \(V_{\rm L}(R_{\rm L})\) \\  & **(\(\times\)10\({}^{\rm 14}\)/mL)** & **(mm\({}^{3}\))** & **(\(\times\)10\({}^{\rm 14}\)/mL)** & **(mm\({}^{3}\))** & **(\(\times\)10\({}^{\rm 14}\)/mL)** & **(mm\({}^{3}\))** \\ \hline
70 & 112.37 (5.68\%) & 2.95 (0.89) & 19.36 (0.06\%) & 20.94 (1.71) & 5.54 (0.002\%) & 44.00 (2.19) \\
85 & 166.11 (8.17\%) & 15.30 (1.54) & 27.60 (0.09\%) & 128.45 (3.13) & 7.18 (0.003\%) & 347.17 (4.36) \\
100 & 221.34 (10.6\%) & 24.43 (1.80) & 36.72 (0.13\%) & 256.20 (3.94) & 9.26 (0.004\%) & 998.31 (6.20) \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of volume, \(V_{\rm L}\), of predicted lesions and the number density, \(N\), of nanoparticles (or volume fraction, \(\phi_{\rm v}\)) used to achieve maximum tumor temperatures, \(T_{\rm max}\) (70, 85, 100 \({}^{\circ}\)C) in different tumor sizes, \(R\) (1, 2.5, 5 mm). \(R_{\rm L}\) is the radius of the lesion. was used in the computational model was predicted with the Mie scattering theory. It is worth noting here that we used the Mie theory because the NPs were spherical [45], however, the photothermal effect is not unique to only spherical iron-oxide NPs but also cubic [19], hexagonal and wire-like [18]. For such non-spherical geometries, discrete dipole approximation--a discrete solution method of the integral form of Maxwell's equations, should be used [46]. [PERSON] et al. [47] used a combination of the two methods to perform quantitative comparison of photothermal heat generation between gold nanospheres and nanorods. Estimation of \(\eta_{\text{exp}}\), which describes how the NPs dispose (scattering plus absorption) the incident electromagnetic energy, has implications for NP concentration and laser beam power to be used. Although, it was beyond the scope of this work because it has been extensively studied previously [20,48], the biodistribution and effective tumor-homing following intratumoral or i.v. administration is key to the efficacy of treatment. To this end, techniques such as PEGylation and ligand-conjugation of the NPs have been shown to enhance and modulate their performance for biomedical applications and, thus, must be considered as part of efforts to fully characterize the nanoparticles for in-vivo applications.