## 2 Results
For \(P_{0}=0.5\) W, the temperature change, \(\Delta T\), increased approximately by 44.4% (from \(\approx\)9 to 13 \({}^{\circ}\)C) when concentration was increased from 0 to 24 mM (Figure 2c). When the power was increased to 1.0 W, \(\Delta T\) increased by approximately 83.3% (from \(\approx\)12 to 22 \({}^{\circ}\)C) for the same concentration. Photothermal conversion efficiency, \(\eta_{\text{exp}}\), decreased with concentration and laser power (Figure 2d). For instance, \(\eta_{\text{exp}}\) for the 6 mM solution decreased from approximately 66% to 51% when \(P_{0}\) was increased from 0.5 to 1.0 W. Furthermore, when the concentration was increased from 6 to 24 mM, \(\eta_{\text{exp}}\) decreased from 46% to 39% using the same power regimes. Generally, the trend of \(\Delta T\) recorded in this study was in agreement with measured absorbance properties and also consistent with previously reported studies [18; 19; 26]. For small NPs (<30 nm) and low concentrations, absorption dominates scattering leading to high \(\eta_{\text{exp}}\). On the other hand, scattering dominates the extinction efficiency as nanoparticle size or concentration is increased. As [Fe\({}_{3}\)O\({}_{4}\)] increases, clusters are formed due to the high surface area to volume ratio of nanoparticles [27]. These clusters act as large particles to enhance scattering leading to the reduction in \(\eta_{\text{exp}}\)[28]. Several approaches are available for the prevention of clusters. Figure 2: Photothermal characterization results. Temporal response curves for different concentrations after 5 min of irradiation with laser powers: (**a**) \(P_{0}=0.5\) W and (**b**) \(P_{0}=1.0\) W. Comparison of the corresponding (**c**) temperature change (\(\Delta T\)) and (**d**) experimental photothermal conversion efficiency (\(\eta_{\text{exp}}\)) as a function of laser power. Error bars: s.d. **Computational modeling of NP-mediated photothermal heating of breast tumor. ** The use of computational model as quantitative frameworks enables assessment and customization of the treatment parameters (NP concentration, treatment duration and irradiation protocols: duration and laser power) to potentially enhance efficacy. Thus, FEM simulations were applied to approximate photothermal heating of a Fe\({}_{3}\)O\({}_{4}\)-containing tumor embedded within a female breast using the optical diffusion approximation of the transport theory [29] and the Pennes bioheat transfer equation [30]. Figure 3 shows a schematic of 2D representation of the axisymmetric geometry of the computational model. It was configured as a heterogeneously dense [31] multi-layer block of tissue with proportions assigned according to the Breast Imaging Reporting and Data System (BIRADS) developed by American Cancer Research [32]. It consisted of various layers of normal tissue with unequal thickness. The dimensions of the model were chosen to represent a \"heterogeneously dense\" breast model [31], which consists of 20% muscle layer, 60% glandular layer and 20% fat layer. Also, a tumor is located at 55 mm from the base. The laser source was assumed to be a diode laser 810 nm placed close to the top surface of the breast model. The inset is a fragment of geometry showing control points P1\(-\)P4, where temperatures were recorded. The assigned optical, thermal and physical properties of different tissue layers were approximate values obtained from the literature [31; 33; 34; 35; 36]. Nanoparticles were assumed to be intravenously injected and uniformly distributed throughout the tumor. To characterize the temperature and thermal damage profiles, we simulated temperature-controlled heating at a maximum tumor temperature, \(T_{\text{max}}=85\)\({}^{\circ}\)C, for \(t=15\) min. The radius of the tumor, \(R\), and \(P_{0}\), were chosen to be 2.5 mm and 1 W respectively. The predicted temperature distribution (Figure 4a) was revealed to be non-uniform with the maximum temperature occurring within the tumor and decreasing radially outwards into the surrounding tissue.