Key Parameters in Phototherapy with Gold Nanorods Using Continuous Near Infrared Radiation

As nanoparticle formulations move toward human clinical trials in photothermal cancer therapy (PTT), the influence of individual key parameters on the heating efficacy must be thoroughly assessed. This work reports a systematic study on the heating performance of gold nanorods during exposure to near‐infrared radiation, evaluating the influence of nanorods concentration, total volume, laser output power, and spot area. Interestingly, the lowest concentration tested (24 µg mL−1) shows the most promising results with a SAR (Specific Absorption Rate) value of 24.6 kW gAu−1 for the highest laser power (0.8 W), spot area (0.4 cm2), volume (1 mL). The laser output power and concentration proved to be the key parameters in global heating of the sample. The cuvette's optical path length also proves to be an important parameter given that there is a threshold concentration value beyond which no significant improvement will be observed, and the higher gold mass will play a detrimental role suppressing SAR values. It is experimentally demonstrated that the multi‐parameter exploration can lead to a finer control of the performance in PTT, opening a pathway for efficient heating of low nanoparticle concentrations.


Introduction
In recent years, hyperthermia emerged as a promising treatment approach in oncology, consisting in raising the temperature of cancer cells to 40-45 °C to reach apoptosis, i.e., programmed cell death. [1,2] One way to reach local and controlled hyperthermia is via functionalizable nanostructures that are activated by external stimuli, such as electromagnetic radiation or magnetic fields. In this context, photothermal therapy (PTT) is a minimally invasive local treatment modality whose goal is to convert electromagnetic radiation into heat by stimulation of photoabsorbing agents that are administrated to the body intravenously or intratumorally. [1,2] Laser light in near-infrared (NIR) region is the energy source typically used in PTT due to its enhanced tissue penetration capability with lower absorption in biological tissues, that limits the heating of healthy surrounding tissues. [2] Among several nanomaterials, gold nanorods (AuNRs) have been extensively explored as photothermal agents due to their biocompatibility and ability to generate heat due to the absorption of electromagnetic radiation. The AuNRs heat generation phenomenon, induced by the laser irradiation, can be explained by a particular feature of metallic nanoparticlessurface plasmon resonance (SPR). [1][2][3] SPR is caused by the presence of conduction electrons that oscillate on the metallic nanoparticle surface. If the incident light wavelength is in resonance with the oscillating electrons, a high-energy state is reached, leading to a sequential relaxation in the form of heat. In this case, the light absorption results in optimal heat generation that ultimately dissipates from the particle to the surrounding media. [1,2] Phototherapy mediated by gold nanoparticles has already shown promising results in vitro and in vivo (with animal models) for different types of cancer. Manivasagan et al. demonstrated that gold nanorods ([AuNR] = 25 µg mL −1 ), duly modified for biocompatibility purposes and combined with laser irradiation (2 W cm −2 , 5 min) induced significant apoptosis (63.3%) when compared with three control groups (0.38%, 1.74%, and 12.01%) on breast cancer cells (MDA-MB-231). [4] The same study also showed that 808 nm NIR laser irradiation on tumor-bearing mice filled with these AuNRs As nanoparticle formulations move toward human clinical trials in photothermal cancer therapy (PTT), the influence of individual key parameters on the heating efficacy must be thoroughly assessed. This work reports a systematic study on the heating performance of gold nanorods during exposure to near-infrared radiation, evaluating the influence of nanorods concentration, total volume, laser output power, and spot area. Interestingly, the lowest concentration tested (24 µg mL −1 ) shows the most promising results with a SAR (Specific Absorption Rate) value of 24.6 kW g Au −1 for the highest laser power (0.8 W), spot area (0.4 cm 2 ), volume (1 mL). The laser output power and concentration proved to be the key parameters in global heating of the sample. The cuvette's optical path length also proves to be an important parameter given that there is a threshold concentration value beyond which no significant improvement will be observed, and the higher gold mass will play a detrimental role suppressing SAR values. It is experimentally demonstrated that the multi-parameter exploration can lead to a finer control of the performance in PTT, opening a pathway for efficient heating of low nanoparticle concentrations.
lead to a complete tumor removal with no regrowth observed over the therapeutic period of 20 days. [4] In parallel, Sangnier et al. studied the photothermal effect of four gold nanoparticles morphologies and the resulting induced cancer cell death within extra or intracellular localizations (internalized before PTT) on human prostate cancer (PC3) cells. For cancer cells exposed to 808 nm NIR irradiation (0.3 W cm −2 , 10 min) with gold nanorods ([AuNR] = 98.5 µg mL −1 ) the number of cancerous viable cells decreases to 38% in the extracellular situation and to 11% in the intracellular situation, this way highlighting the effectiveness of PTT treatment. [5] Taking advantage of the surface modification capability of gold nanorods with specific antibodies that promote cancer-cell targeting, Zhang 3 ). [6] Maltzahn et al.
showed that polyethylene glycol (PEG) coated AuNRs intravenous injected into tumor-bearing mice (20 mg Au kg −1 ) could accumulate in tumor (≈7% ID g −1 at 72 h post injection) and be rapidly heated to over 70 °C by NIR laser irradiation (2 W cm −2 , 5 min). In their work, within 10 days all the irradiated PEG-AuNR-targeted tumors were completely eradicated with no evidence of tumor regrowth. [3,7] All these mentioned reports evaluated the effectiveness of PTT through cell viability studies, but the figure of merit SAR (Specific Absorption Rate) is also often employed to compare the nanoparticle heating efficiency in a given environment. [1,5,8,9] In this context, Espinosa et al.
reported an intensive study that evaluated the influence of different shaped gold nanostructures with regard to peak absorption position and heat generation efficiency. [1] Among all the studied nanostructures AuNRs showed the larger temperature raise (ΔT ≈ 20 °C). For a [AuNR] = 150 µg mL −1 in an aqueous dispersion, SAR values reached 3 and 10 kW g Au −1 , at laser power densities of 0.3 or 1 W cm −2 , respectively. [1] In 2020, Sangnier et al. reported a similar study and in apparently similar conditions (aqueous solution, 808 nm NIR radiation, [AuNRs] = 150 µg Au mL −1 and 0.3 W cm −2 ) the estimated SAR values were ≈6 kW g Au −1 , which is twice the value previously mentioned. [5] Given the discrepancies, what are the parameters that truly influence the SAR? How each individual experimental parameter affects the global heating of a sample? This work aims to fill some of these knowledge gaps, reporting a systematic study on the heating performance of such nanostructures during exposure to NIR radiation. Throughout the experiments several parameters were considered, including the laser output power (W) or power density (W cm −2 ), spot area, AuNRs concentration and the volume of the aqueous solution in which the latter were suspended. Knowing how each one of these parameters influences the global heating of a sample, one can optimize the AuNRs heating performance which will be translated into more efficient photothermal therapy protocols. Figure 1a,b presents, respectively, a scanning electron microscopy (SEM, FEI Quanta 400FEG high resolution (HR)) image of the gold nanorods before and after laser irradiation. These data demonstrates that laser irradiation does not affect the morphology of the AuNRs, and that their shape is maintained intact after successive irradiations. Before irradiation the AuNRs present an average length and diameter of 51.7 ± 9.3 nm and 12.2 ± 3.4 nm, respectively. After irradiation the dimensions are similar, 55.4 ± 10.5 nm and 13.7 ± 3.2 nm (Figure 1c,d). These nanostructures exhibit plasmon resonance peaks, as observed on the absorbance spectra of Figure 1e, with maximum around 497 and 801 nm. These peaks are related, respectively, to the transversal and longitudinally localized surface plasmon resonances (LSPR) of AuNRs with aspect ratio close to 4, this way covering the NIR window. [2,3,10]

Role of Laser Output Power and the Effect of Concentration
The results presented in this sub-section are related to the influence of the laser output power and the gold nanorods concentration. Here, the heating curves were obtained in a fixed solution volume (1 mL) and laser spot area (0.4 cm 2 ) for the concentrations 24, 75, and 200 µg mL −1 in a 1 cm optical path (OP) cuvette. The laser output power was varied in the 0.2-0.8 W (or power density 0.5-2 W cm −2 ) range for each concentration. For all cases, the heating curves were also obtained in an only-water solution of the same volume to infer about the effective contribution of the gold nanorods in the sample heating. This contribution of the temperature variation on water-only solution was not subtracted on the subsequent heating curves obtained with the AuNRs diluted, but its results are plotted for comparison. All the values related to maximum temperature variation (fitted parameters) and SAR (W g Au −1 ) calculated from the data presented in Figure 2 are summarized in Table S1 (Supporting Information). The photo-induced heating curves are presented in Figure 2a where it is noticeable that after a few minutes under radiation exposure a plateau temperature is reached. At this stage the heating and the losses to surroundings are already counterbalanced, keeping the temperature of the solution stable. Independently of the nanorods concentration and the laser power, the temperature plateau is reached few minutes (around 400 s) after laser irradiation starts.
Observing Figure 2a, one can see that the laser output power parameter has a clear influence on the temperature variation of the solution. A maximum value of ΔT = 25.9 °C was achieved for 200 µg mL −1 (excluding the initial 5 s [11,12] ) and decreasing the concentration to 24 µg mL −1 , a ΔT = 20.4 °C is reached. It is seen that the greatest temperature variation is associated with the largest laser output power employed. This can be explained based on the heat contribution of a large number of individual gold nanorods, where each generates a certain amount of heat (Q, W) under laser irradiation. The Q value can be obtained as the product of absorption cross-section area (C abs , m 2 ) and laser fluence (I, W m −2 ): [8] www.advmatinterfaces.de Therefore, for each concentration with a given cross section area, the amount of heat generated is directly proportional to the laser power. This is clearly reflected in the obtained results, where for each concentration a linear increase of maximum temperature variation with the laser power can be seen ( Figure 2d). However, the heating rate, dT/dt, decreases when increasing the concentration (Figure 2e), which is associated to a decrease in the C abs , that corresponds to the effective area that absorbs the light energy impinging upon the nanorods and is strongly dependent on the concentration under resonant conditions. It is also possible to verify that, regardless of the used concentration, the maximum temperature variation does not undergo major changes (Figure 2e). By increasing the concentration from 24 to 200 µg mL −1 only a small increase in the ΔT of 1.4 and 5.5 °C was achieved, respectively, for the lowest (0.2 W) and highest (0.8 W) laser powers. The same cannot be said regarding its heating efficiency (detailed later in Section 4.1), evaluated as dissipated power per unit of mass of material (W g Au ). In this regard, one can see that all SAR values increase with the laser power, but the solution of 24 µg mL −1 clearly stands out reaching 2.45 × 10 5 W g Au −1 (Figure 2f). This means that larger concentrations do not necessarily reflect greater heating efficiency. In fact, the results suggest precisely the opposite, revealing that the solution of lower concentration presents the best heating performance.

Role of the Cuvette's Optical Path
An explanation for the outcome results presented in the previous section could be related to the cuvette´s optical path and laser penetration depth. Just to recall, the results obtained in a 1 cm OP cuvette showed a significant change in ΔT (°C) between the first two concentrations (24 and 75 µg mL −1 ) that no longer holds for the third (200 µg mL −1 ). This result suggests that for the highest concentration, the laser beam energy is not crossing through the sample and consequently the AuNRs present in the solution are not being evenly illuminated. In such model, there is a threshold in AuNRs concentration value, above which the solution becomes completely opaque to NIR Figure 1. Scanning electron microscopy (SEM) images of the gold nanorods a) before laser irradiation. b) after laser irradiation. c) Gold Nanorod length distribution before (51.7 ± 9.3 nm) and after (55.4 ± 10.5 nm) irradiation. d) Gold Nanorod diameter distribution before (12.2 ± 3.4 nm) and after (13.7 ± 3.2 nm) irradiation. e) Absorbance spectra of AuNRs not irradiated (red) and irradiated (black curve) with the highest laser power (0.8 W), obtained at concentration [Au] = 75 µg mL −1 .
www.advmatinterfaces.de beam, AuNRs become unevenly illuminated and the maximum ΔT (°C) values observed saturate. This translates into a decrease in the C abs and subsequently, into a lower amount of heat generation. To verify if effectively higher concentrations (such as 200 µg mL −1 ) may be sufficient to make the solution "opaque" to NIR radiation we repeated the experiment with a narrower cuvette with 1 mm OP and 0.5 mL volume. Results are presented in Figure 3.
Contrarily to the previously obtained results in the 1 cm OP cuvette (where the maximum temperature variation, ΔT, did not undergo major changes regardless of the used concentration), here ΔT is clearly seen to increase with AuNRs concentration (Figure 3a). For the highest laser power, a ΔT of 18.2 and 28.6 °C was reached for the concentrations of 75 and 200 µg mL −1 , respectively (in the 1 mm OP cuvette), in contrast with a much more subtle ΔT difference between 24.6 and  www.advmatinterfaces.de 25.9 °C that was reached for the concentrations of 75 and 200 µg mL −1 , respectively (in the 1 cm OP cuvette). This new observed trend supports the hypothesis that the laser unevenly illuminates all AuNRs in the solution as it must be above the threshold concentration value for a 1 cm OP cuvette.
In addition, we also performed laser power measurements in the positions immediately before and after the cuvette's to find out how much power was lost in the path of laser direction for every irradiation experiment. The results are organized in Tables 6 and 7 (Supporting Information) and presented in Figure S2 of (Supporting Information). Remarkably, with the smallest concentration (24 µg mL −1 ) there is already 61% of power loss across the 1 cm cuvette. Here, even the 75 µg mL −1 is already approaching to the saturation threshold, allowing only 2.23% of incident power to reach the back of the cuvette. With the highest concentration nearly all the laser power is "retained" inside the cuvette and less than 1% reaches its back, confirming once again that the solution is sufficiently concentrated to become opaque to NIR radiation. The same kind of behavior in observed for the 1 mm OP cuvette, however, in this case the solution is not yet saturated and there is still some power that completely crosses the entire cuvette (about 12.1% for the 200 ug mL −1 concentration). These results demonstrate, that for every optical path length there is a threshold concentration value beyond which no significant improvement will be observed in ΔT values and simultaneously the higher Au mass will play a detrimental role on suppressing SAR values, as can be seen in Figure 3b.

Role of Laser Spot Area
The following results were obtained with a focusing lens included in the set-up to shape the incident beam spot size area. Placing this lens at different distances along the beam path, allowed to study the effect of the laser spot area, while the laser power density was kept fixed. Here, the results were acquired for the highest concentration (200 µg mL −1 ) in three laser spot areas: i) 0.4, 0.091, and 0.054 cm 2 , in a 0.5 mL solution and with a 1 mm OP cuvette. The laser power was adjusted in each case so that the laser power density remains equal in all experiments, in the range of 0.5-2 W cm −2 .
Observing Figure 4 one can see that ΔT, and consequently SAR, increase with the size of the laser spot area, reaching a maximum 7.09, 9.24, and 28.6 °C for the highest power density (2 W cm −2 ) in the increasing areas of 0.054, 0.091, and 0.4 cm 2 , respectively. Here, since we kept the power density fixed, that corresponds to the number of photons per unit area, what is changing is the number of nanorods that are "active" under the laser irradiation and contributing to the heating. As the amount

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of generated heat becomes strongly increased in complexes composed of several Au NPs, if a larger number of nanorods are involved, due to a larger spot area, more heat is being generated. [13,14]

The Effect of Sample Volume
The last parameter under evaluation was the volume of the aqueous solution in which the AuNRs were suspended. Here, a given area of the laser spot was fixed (0.03 cm 2 ) and the volume of the solution was varied within. The acquired data, once more, included the heating curves for the three concentrations (24, 75, and 200 µg mL −1 ) on the 0.2-0.8 W power range, for three different solution volumes (0.3, 0.5, and 1 mL). It is worth to mention that different cuvettes were used throughout the experiments for set-up convenience. For the measurements performed on 1 mL solutions, a regular quartz cuvette (V = 3500 µL) was used but a smaller one (V = 1400 µL) was required for the remaining evaluated volumes (Figure 5a). Also, it was verified that, in both cuvettes, the entire area of the laser spot was always within the cuvette´s surface area to avoid losses of intensity in its walls. Figure 5b demonstrates the heating curves acquired for the lowest concentration (24 µg mL −1 ), power (0.2 W), and spot area (0.03 cm 2 ). Here it is noticeable that highest temperature variations were achieved for larger volumes, reaching the final temperatures of 30.3 and 33.4 °C for the increasing volumes of 0.3 and 0.5 mL, respectively. On one hand, this was an expected result since larger volumes contain a higher amount of gold nanorods (for a constant concentration) to absorb the NIR radiation and release it in the form of heat. On the other hand, it is also true that the greater the volume, the greater the amount of heat that must be supplied to the solution to increase its temperature until stabilization. This can be observed on the saturation temperature plateau, that is reached sooner for smaller volumes (Figure 5b). In other words, the temperature stabilization, arising from the heat exchanges with the environment (liquid solution-air interface), happens faster when the sample has less material. In fact, by directly comparing the τ fitted values one can see that for all concentrations, the latter is inferior for smaller volumes (0.3 mL). Here, τ is a characteristic heating time that depends on sample properties (described later in Experimental Section). In Figure 5d, the τ values for the 0.5 and 1 mL volumes present very similar results, regardless of the concentration. At this point, it is worth to recall that the 1 mL volume measurements were obtained in a regular cuvette, whereas the remaining volumes were obtained with a small volume one, which has a narrower liquid support. Considering the heat exchanges with the surroundings arising from losses by conduction through the cuvette walls, the heat transfer (Q cond ) of the sample is proportional to the www.advmatinterfaces.de temperature difference across the layer and the heat transfer area, and inversely proportional to the thickness of the wall. This is described by Fourier's law of heat conduction, given by: where k is the thermal conductivity of the material (quartz, 3 W m −1 K -1 ), A is the surface area, ΔT is the temperature difference across the wall and Δx is the thickness of the layer. [15] This implies that the heating of a sample does not only depend on the amount of material (represented here in volume of solution under irradiation) but also on the surface area of the cuvette through which the heat exchanges take place. For comparison purposes and considering the four side walls of the cuvettes in contact with the solution, the estimated area available for heat exchanges is, respectively, 4, 3.64 and 2.52 cm 2 for the 1, 0.5, and 0.3 mL volumes. Here, the decrease in surface area, and in solution volume, is accompanied by a decrease in the τ values. The first two volumes present average τ values of 167.1 s and 127.4 s for the volume of 1 mL and 0.5 mL, respectively, on the 24 µg mL −1 concentration. The smaller volume (0.3 mL), with a lower sectional area, presented an average τ = 111.3 s (Figure 5d). The reproducibility of the measurements was verified with several experiment repetitions, which resulted in an invariability of the τ. This means that all experiments were carried out in the same thermal bath composed by the cuvette and the room where the measurements were carried out. Despite the changes on temperature variation and heating rate of the sample, the SAR values do not undergo so evident variations ( Figure 5c). As mentioned, the results suggest that the superior heating rate is obtained for smaller volumes (B fitted parameter, B = 1/τ), but the latter counterbalances with the superior temperature variations (A fitted parameter) of larger volumes so that, in the final calculation of the SAR (proportional to A* B) the values remain close to each other. For the lowest concentration (24 µg mL −1 ) and power (0.2 W), the calculated SAR values were 4.20 × 10 3 W, 5.87 × 10 3 W, and 4.84 × 10 3 W g Au −1 for the increasing volumes of 0.3, 0.5, and 1 mL. Based on the results, the volume of the solution did not turn out to be a key parameter for the nanoparticle heating efficiency but underlined very clearly its dependence and susceptibility on the set-up and irradiation conditions. The temperature variation with the laser power in water solution was also measured for the two studied volumes (0.5 and 1 mL) in the same 1 cm OP cuvette ( Figure 3 of the Supporting Information). It is observed that, for both volumes, ΔT (°C) linearly increases with power and that, for the same power, the larger volume presents larger ΔT (°C). For the highest power (0.8 W), the maximum registered ΔT was 8.62 and 17.4 °C for 0.5 and 1 mL, respectively. Therefore, contrary to the concentration effect, which is a parameter highly dependent on the plasmonic effect of the material, the effect of volume is purely a thermodynamic problem that depends on the environment surrounding the sample under heating and irradiation conditions.

Conclusions
The photo-induced heating tests performed in this systematic work demonstrated the influence of several experimental parameters, such as the AuNR concentration, laser power, laser spot area, and solution volume, on the gold nanorods heating efficiency. Throughout the experiments, three different AuNR concentrations (24, 75, and 200 µg mL −1 ) were irradiated with a laser power density in the 0.5-2 W cm −2 range, on three laser spot areas (0.4, 0.091, and 0.054 cm 2 ). Afterward, the influence of the volume of solution (0.3, 0.5, and 1 mL) was also studied.
Among the evaluated conditions, the concentration and laser output power proved to be key parameters in phototherapy with gold nanorods using continuous radiation. In all cases, the SAR values increase with laser output power reaching a maximum value of 2.46 × 10 4 W g Au −1 for the highest power (0.8 W) and smallest concentration (1 mL, 0.4 cm 2 spot). A major consistent result verified under all evaluated conditions, was the fact that the lowest concentrations (24 µg mL −1 ) present higher SAR values, thus being more efficient for this application. In addition to this, it was also verified that for every cuvette's optical path length there is a threshold concentration value beyond which no significant improvement will be observed in ΔT values and simultaneously the higher Au mass will play a detrimental role on suppressing SAR values. Above this concentration the solution becomes opaque to NIR radiation.
The solution volume, on the other hand, highlight the dependence of the acquired results on set-up variations or data acquisition process. This means that the nanoparticle heating efficiency is highly sensitive not only to the experimental conditions but also on the systematic errors introduced during the measurements. A proper calibration of the thermocouple and its fixed position during irradiation are crucial factors for accurate data gathering. Even the SAR calculation method itself can lead to large variations in its value, depending on the initial assumptions considered by researchers. The results obtained in this work can be used as a starting point for future tests in more complex models, as in in vivo tests, as our multi-parameter exploration can lead to a finer control of the performance in PTT, opening a pathway for efficient heating of low nanoparticle concentrations.

Experimental Section
Materials and Methods: The measurements here reported were performed using an infrared continuous laser (MDL-III-808/1-2500 mW) operating at 808 nm. The laser was aligned in a way that its beam laterally crosses the walls of a glass cuvette filled with the AuNRs solution. The heating of the sample was measured with a type-K thermocouple and continuously confirmed with a FLIR i7 Infrared Thermal camera. Temperature measurements made by the thermal camera showed the same values with the solution irradiated with or without the thermocouple, confirming that this as no influence on the measurements. The laser power measurements were performed with a Thorlabs Power Meter Console (PM100A). The gold nanorods (10 × 41 nm, SPR = 808 nm) with reference 035E12-10-808-NPO-CHL-200-0.25 were purchased from Nanopartz (Nanopartz, Loveland, CO, USA). The AuNRs aspect ratio (AR), given by the proportion between their dimensions (length/width), is ≈4 having therefore the ideal shape to be excited by the 808 nm laser. [3,10,16] Throughout the experiments three different AuNR concentrations (24, 75, and 200 µg mL −1 ) were irradiated with a laser output power in the 0.2-0.8 W range. Beyond concentration and laser output power, the influence of the sample volume (0.3, 0.5, and 1 mL) and laser spot area (0.40, 0.091, and 0.054 cm 2 ) were also evaluated. Considering the www.advmatinterfaces.de original and largest laser spot area (0.40 cm 2 ), the applied fluences lies under the generally laser powers densities employed on preclinical PTT studies. [1,3,4,7] In this case, the used power densities were on the 0.5-2 W cm −2 range.
The acquired data included temperature stabilization (200 s), the heating of the sample upon irradiation until temperature saturation and the respective cooling once the laser was turned off. The samples were under laser irradiation for ≈16.7 min (≈1000 s). The obtained temperature versus time curves were used to calculate the SAR (Specific Absorption Rate) values by one of the most popular methods found in the literature: the Box-Lucas method (BLM). [11,12,17,18] This method, employed as a figure-of-merit to quantify and compare NP heating efficiency, relies on data fitting and analysis and supposes a non-adiabatic set-up where convective heat losses were taken under consideration. [12] Therefore, the BLM is an appropriate model for the sample temperature-time dependence that includes heat exchanges between the sample and the surroundings. [18] The Box-Lucas equation for the non-adiabatic temperature increase can be expressed as: where the parameters A and B are, respectively, related with the final temperature (i.e., A = T(t = ∞)) and the heating rate of a given sample (B = 1⁄τ). Here, τ is a characteristic heating time that depends on sample properties. The product of these parameters A*B represents the heat rate and can be used to calculate SAR by the following formulae: where c w is the specific heat capacity of water (4.186 J g −1 °C −1 ) and m Au is the total mass of gold in the sample. The heating rate of the sample was obtained by fitting the curve during sample cool down and the final temperature was obtained fitting the heating curve during laser irradiation. [11,12,16,18] For accurate SAR calculations, the timeframe selected for the fit should exclude the initial 5 s. In Box-Lucas' fitting, including this initial non-linear heating response results in a decrease in the exponential factor that fits the curvature of the temperature change as a function of time and could lead to inaccurate SAR values. [11,12]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.