1. Introduction

We propose a novel material, the rare-earth doped nanoparticles (NPs), which may be suitable for photo-induced local heating of cancer tumors for hyperthermia [1]. The idea of heating is centered on the process of multiphonon relaxation (MR) of the optical excitation energy in the RE doped crystals. In the field of rare-earth doped fluorescent and laser materials intra-center multiphonon relaxation usually competes with radiative relaxation [2]. In the single frequency model of lattice vibrations a decrease of the phonon number p = ∆E/ℏω_eff. bridging the energy gap ∆E between two electronic levels by one raises the rate of multiphonon transition by one or two orders of magnitude [3]. If the number of phonons is equal or less than three (p ≤ 3), the RE ions fluorescence almost completely quenches by multiphonon relaxation, because the rate of multiphonon transition is on the nanosecond or even picosecond time scale that is 10⁵ – 10⁷ times faster than the spontaneous emission decay rate of the RE ions.

However, the negative effect of MR in case of fluorescent materials can be used as a positive effect for nanoscaled heaters. We propose “non-fluorescent” nanocrystals instead of fluorescent ones. For this we reduce a fluorescent quantum yield from almost unity typical for metastable levels of the RE ions to 10⁻⁵ – 10⁻⁷ raising the rate of MR comparing to radiative rate. In so doing we choose the RE ion, which enables immediately after laser irradiation to start multistage (cascade) multiphonon relaxation process down to the ground level with efficiency of photon energy transformation to heat close to unity. A Dy³⁺ ion embedded into the YPO₄ crystal matrix having simultaneously a wide phonon spectrum (ћω_max. = 1100 cm⁻¹ [4]) and permiting up to 100% substitution of the Dy³⁺ ion for Y³⁺ [5] meets this requirement. Also, the phosphate water-dispersible crystalline nanoparticles can be produced rather easily as opposed to the oxide NPs, which are usually produced using solvent-free techniques or in oily solvents. These NPs are harder to disperse in water, which is essential for biomedical applications. Besides yttrium ortophosphate is biocompatible with human tissues. The energy level diagram of the Dy³⁺ ion allows for choosing laser excitation wavelength between 760 (⁶F_3/2), 811 (⁶F_5/2), or 914 nm (⁶F_7/2) (Fig. 1and Fig. 2) in the near IR spectral range fitting the transparency window of biological tissues (750 – 950 nm [6]). It has real advantage over the fluoride crystal matrixes, where even in the LiYF₄ host crystal with the most extended phonon spectrum among fluoride crystals the maximal phonon energy does not exceed ћω_max. = 560 cm⁻¹ [7]. The use of the fluoride hosts would increase the number of phonons bridging the energy gaps for the ⁶H_11/2 → ⁶H_13/2 and ⁶H_13/2 → ⁶H_15/2 transitions of Dy³⁺ to four and five for LiYF₄ and to six and seven for the LaF₃ crystal host, respectively. The latter has the lowest maximal phonon frequency ћω_max. = 400 cm⁻¹ [8] among fluoride crystals. As a result the MR rates of the ⁶H_11/2 and ⁶H_13/2 levels in the Dy³⁺ doped fluoride matrixes would have been comparable with their spontaneous emission decay rates, and significant amount of the optical excitation energy would have emitted by photons rather than phonons. However, for highly concentrated Dy³⁺ doped fluoride samples like DyF₃ the concentration quenching may compensate the low phonon spectrum of the matrix.

 

Fig. 1 Energy level diagram with indication of multiphonon transitions (solid arrows downward) in the Dy³⁺: YPO₄ crystalline nanoparticles under direct laser excitation into the ⁶F_3/2, ⁶F_5/2, and ⁶F_7/2 levels of the Dy³⁺ ion.

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Fig. 2 Reflectance spectrum of the DyPO₄ sample at room temperature measured by Laser Electronic LESA-01-Biospec spectra analyzer with tunable femtosecond Chameleon laser excitation. The spectrum is recorded by diffuse reflection of white light from a thin layer of powder. Y axis is the relative units.

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The heating kinetics for a nanoparticle suspended in a medium can be derived in the assumption that the thermal equilibrium in the phonon subsystem is set during the time τ much shorter than the flow time of radiative and non-radiative transitions, i.e. the lifetime of nonequilibrium phonons is much shorter than the flow times of radiative and non-radiative transitions

The first term describes the temperature rise due to the absorption of laser radiation and transforming it into heat. The second term describes the loss of heat by transferring heat energy to the environment. We used Newton's law of cooling to obtain this term. Here θ is a temperature of environment medium. The first term is

The main result is that the temperature of NP increases linearly with increasing the spectral density of absorbed laser radiation and concentration of RE dopant, and decreases with increasing the S/V ratio that is with the decreasing the size of nanoparticle. At the same time transformation of light to heat does not depend on the size of the NP (Eq. (2)). Therefore, the surrounding medium may be heated more for smaller nanoparticle.

Indeed, this theory does not claim to be an accurate quantitative description. It does not take into account the inhomogeneity of the intensity distribution of the laser beam, laser light scattering, heat transfer peculiarities in the powder, size distribution of the NPs, and a number of other factors, which have to be considered to construct a quantitative theory. To create one it is also necessary to obtain experimental data on the kinetics of the temperature distribution in the powder in the plane perpendicular to the propagation direction of the laser beam. These studies can be carried out later. However, the simplified theory can be used for qualitative interpretation of experimental regularities of nanoparticles powder heating kinetics. Employing the Y_1-xDy_xPO₄ nanocrystals, we study the regularities of heating of the NPs under near IR laser irradiation.

2. Experimental results and discussion

Samples were prepared using microwave-hydrothermal treatment of freshly precipitated gels. The samples preparation and details on laser heating experiments are presented in the Appendix.

Laser heating by 811 and 914 nm wavelengths demonstrates almost linear dependence of the local temperature increase ∆T on the laser power of a powder surface hottest area (425 x 425 μm) taking from the central pixel of the camera image for direct excitation into the ⁶F_5/2 and ⁶F_7/2 levels of Dy³⁺ in the DyPO₄ and Y_0.525Dy_0.475PO₄ nanocrystals Fig. 3.Also, the heating increases in proportion with increasing of Dy³⁺ concentration. Qualitatively, these results are consistent with Eqs. (2) and (4).

 

Fig. 3 The local temperature increase ∆T of the Y_1-xDy_xPO₄ powder taken from the hottest pixel of the image of the powder surface on the IR camera after laser irradiation versus laser power. Excitation was done into the ⁶F_5/2 (811 nm) and ⁶F_7/2 (914 nm) levels of Dy³⁺ in the scanning microscope spot mode. Temperature measurements were done when approaching the steady-state. The laser parameters and details of the optical scheme of excitation are given in the Appendix.

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Also we found a linear increase of the local temperature increase ∆T of the powder hottest area with the increase in Dy³⁺ concentration in the range from 1 to 47.5 mol.% of Dy³⁺ and low decline from linearity for DyPO₄ for all three excitation wavelengths, 760, 811, and 914 nm Fig. 4. We may attribute the latter to surface water evaporation.

 

Fig. 4 The local temperature increase ∆T of the Y_1-xDy_xPO₄ powder taken from the hottest pixel of the image of the powder surface on the IR camera after 100 mW laser irradiation versus the concentration of Dy³⁺. Excitation was done in the scanning microscope spot mode. Temperature meausrements were done when approaching the steady-state.

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We measured the heating efficiency of the powder Φ = ΔT / (P f) as a ratio of its local temperature increase (ΔT) to the product of the oscillator strength of the absorption transition (f) [10] and the quantity of laser power (P). We obtained the highest heating efficiency, more than one degree per mW when exciting into the top ⁶F_3/2 level of Dy³⁺ in the DyPO₄ nanocrystals (Table 1), and the lowest, less than 0.3 degree per mW, while exciting into the third top the ⁶F_7/2 level, which both relax by one-phonon transition. Also, we excited the second top the ⁶F_5/2 level, which relaxes by 2-phonon transition, and obtained higher heating efficiency than exciting into the third top the ⁶F_7/2 level. We found that the heating efficiency does not correlate with the MR rate of the excited level. Otherwise it would be higher for the ⁶F_7/2 level relaxing with the emission of just one phonon than for ⁶F_5/2 relaxing with the emission of two phonons. We conclude that in the system under study the efficiency of heating is proportional to a number of multiphonon transitions with p ≤ 3 in the cascade nonradiative relaxation process, which is maximal for the upper ⁶F_3/2 level (N = 12) and minimal for the lowest ⁶F_7/2 level (N = 10), or in other words the higher is the initially excited level, the more electronic energy is transferred to heat, ceteris paribus. A decrease of the Dy³⁺ concentration reduces the heating efficiency (Table 1) in accordance with the dependence shown in Fig. 3.

Table 1. The Heating Efficiency Φ of the Y_1-xDy_xPO₄ Nanocrystals Depending on the Number (N) of Multiphonon Transitions with p ≤ 3 in the Cascade Nonradiative Relaxation Process (ℏω_max ≈1100 cm^−1a)

View Table

At the same time, the heating time of the powder is very short. For example, the rise time of the temperature from room temperature to 340K at the hottest spot of the DyPO₄ powder under pulsed 811 nm laser irradiation in the scanning microscope spot mode with average power of 30 mW is approximately one second only Fig. 5, upper curve. The temperature drops back to room temperature within the same time. This is an indication of inertialess heating, which enables setting precise duration for hyperthermia, which may be very important for selective treatment of cancer tumors without disturbing healthy tissues. Besides, the laser power used for heating was low, tens of mW only that together with fast heating time to the required temperature may result in low doses of laser irradiation of human body during hyperthermia treatment. We found that the rates of heating and cooling are independent on excitation wavelength Fig. 5. The laser irradiation at 850 nm, which is out of energy resonance with Dy³⁺ energy levels Fig. 2, does not indicate significant heating of the powder Fig. 5, lower curve, which confirms that the heating is a result of the multiphonon relaxation from the excited Dy³⁺ electronic states.

 

Fig. 5 The local temperature kinetics of the hottest area of the DyPO₄ nanocrystals powder (0.425 x 0.425 mm) taken from the hottest pixel of the image on the IR camera of the powder surface under laser irradiation in the scanning microscope spot mode with the average power of 30 mW at different excitation wavelengths, from top to bottom 811 (red), 914 (dark red), 760 (green), and 850 nm (blue). The laser was switched, on and off, every second.

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It is seen that the temperature of the NPs can be rather high, much higher than it is necessary for cancer hyperthermia treatment. However for colloidal solutions the maximal achievable local temperatures will be lower than for the powders. This requires a separate study including the development of direct and indirect methods for the temperature measurements.

We believe that it could be possible to synthesize the core-shell NPs with photon emissive core doped by Nd³⁺ ion [11] and heat emissive shell doped by Dy³⁺ using the same YPO₄ crystal matrix for simultaneous near IR tumor imaging and cancer laser hyperthermia treatment.

3. Conclusion

We propose a novel material, the Y_1-xDy_xPO₄ nanocrystals, which may be suitable for laser-induced local heating of cancer tumors for hyperthermia. The heating mechanism based on multiphonon relaxation of optical excitation. The local temperature of the nanoparticles powder linearly increases with increasing irradiation laser power and Dy³⁺ concentration. At the same time the efficiency of the local heating Φ is proportional to the energy of the initially excited electronic level. The proposed method allows for high rates of cooling and heating, which may result in precise spacing and timing during hyperthermia treatment. The laser power used for heating is rather low, tens of milliwatts that together with short heating time to the required temperature may result in low doses of laser irradiation of human body for treatment.

Appendix

1. Sample preparation

As starting compounds for preparation of the Y_1-xDy_xPO₄ nanoparticles (x = 0.01, 0.05, 0. 475 and 1) we used DyCl₃•6H₂O (Aldrich, 99.995% purity), Y(NO₃)₃•4H₂O (Aldrich, 99.999% purity) and K₂HPO₄•3H₂O (Aldrich, 99.9% purity). For the synthesis we prepared solutions of 5 mmols of the mixture of DyCl₃•6H₂O and Y(NO₃)₃·4H₂O, taken in corresponding stoichiometric proportions, in 10 ml of deionized water, as well as solution of 5 mmols of K₂HPO₄·3H₂O in 30 ml of deionized water. After that we added the solution of rare-earth salts dropwise to the solution of phosphate under vigorous stirring and left it for 15 min keeping the stirring on. We diluted the freshly precipitated gel in mother solution with 10 ml of deionized water, transfered it into 100 ml Teflon autoclave and expose to microwave-hydrothermal (MW-HT) treatment (200°C, 2 hours) using a Berghof Speedwave-4 laboratory device (2.45 GHz, 1 kW maximum output power). After the treatment the samples were centrifuged, washed several times with deionized water and air-dried at 100°C for 5 hours.

We performed the X-ray diffraction analysis of the NPs using the «Rigaku D/MAX 2500» diffractometer (CuKα-radiation) and identified diffraction peaks using the JCPDS database. Instrumental broadening of the reflections was measured on the bases of standard material SRM-660 (LaB6). Physical broadening (β) of reflections was calculated using Voigt decomposition method. The mean size of the coherent scattering region (CSR) in the direction normal to the observed atomic planes was estimated using the Scherrer equation [12].

(5)$$CSR=\lambda /(\beta \times \cos (\theta )),$$

where λ is the wavelength of X-ray irradiation and θ is the Bragg angle for the particular reflection studied. The transmission electron microscopy (TEM) images of the samples were taken with Leo912 AB Omega microscope under accelerating voltage 100 kV.

2. Phase composition and morphology

XRD analysis of obtained samples (NPs powder) showed Fig. 6 that they consist of pure tetragonal phase with I4₁/amd space group, isostructural to xenotime YPO₄. It is worthy to note that isostructural YPO₄ and DyPO₄ phases have almost equal lattice parameters, and due to lanthanide contraction [13] the radius of the Dy³⁺ ion is very close to the one of Y³⁺ ion. Therefore, regardless of the Y: Dy ratio in solid solution, the positions of maxima on XRD patterns remain almost the same. The synthesized samples of Y_1-xDy_xPO₄ possess high degree of crystallinity. The mean size of the coherent scattering region (CSR) depends on the value of x and changes from 40±3 nm for x = 0.01 to around 150 nm for x = 1 (the precision of CSR size determination for large sizes is rather low due to small physical broadening).

 

Fig. 6 XRD patterns of the Y_1-xDy_xPO₄ nanoparticles with x = 0.01 (red) and 1 (black).

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Morphology of the synthesized nanoparticles was studied by means of TEM Figs. 7, Fig. 8, and Fig. 9. Nanoparticles are isotropic and rather uniform. Mean size of the particles determined using the TEM data is 40±15 nm for x = 0.01, 65±22 nm for x = 0.475, and 125±45 nm for x = 1, which is in good correlation with XRD results and confirms the high degree of crystallinity of all the samples. The width of the size distribution does not vary substantially for synthesized samples. It is close to normal with slight admixture of lognormal component, which decreases with the decrease in the dysprosium content. For nanoparticles of pure DyPO₄ one can see Fig. 9 that apart from the main fraction of cuboid shape large particles, some amount of significantly smaller rod-like nanoparticles is present. Closer look to the inner structure of the larger particles and the remaining aggregates of the smaller nanoparticles allows one to suggest that formation of larger nanoparticles is due to oriented attachment and growth of rod-like nanoparticles, rather than due to Ostwald ripening. The same most likely applies to the Y_0.525Dy_0.475PO₄ nanoparticles. As for the Y_0.99Dy_0.01PO₄ nanoparticles it is hard to deduce from TEM micrographs whether they formed mainly by aggregation or growth.

 

Fig. 7 TEM image and particles size distribution of the Y_0.99Dy_0.01PO₄ nanoparticles.

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Fig. 8 TEM image and particles size distribution of the Y_0.525Dy_0.475PO₄ nanoparticles.

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Fig. 9 TEM image and particles size distribution of the DyPO₄ nanoparticles.

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3. Experimental details

We excited the Dy³⁺ ion directly into the ⁶F_3/2, ⁶F_5/2, or ⁶F_7/2 levels by pulsed tunable femtosecond laser Coherent Chameleon Ultra II with 140 fs pulse duration, repetition frequency 80 MHz, and maximal average power up to 140 mW. We used 760, 811 and 914 nm wavelengths that is into the maxima of the spectral peaks of the ⁶H_15/2 → ⁶F_3/2, ⁶F_5/2, and ⁶F_7/2 optical transitions of Dy³⁺, respectively lying in the transparency window of biological tissues (750 – 950 nm). Approximately 65 mg of the nanoparticles powder was poured between two cover glasses with a width of 1.0 mm and a thickness of 0.2 mm, laid on a glass slide. The distance between the cover glasses amounts at 0.7 mm. So, the volume of the sample was 0.14 10⁻³ cm³ Fig. 10. The excess of the powder (powder protruding above the surface of the cover glass) has been removed from the surface. The laser beam was focused on the bottom surface of the powder layer through the slide. Temperature readout was taken from the upper layer of powder. The laser irradiation was done through scanning microscope ZEISS LSM 710 in a spot mode. The laser spot had the diameter of 10 μm. The ellipticity of the laser beam is 0.9 – 1.1. We measured the temperature of nanoparticles by Remote High Sensitive IR camera JADE MWIR SC7300M, Cedip sensitive in the mid IR (3 – 5 μm) spectral range with maximal time resolution 6.7 ms. The size of a single camera pixel was 530 x 530 μm, which is a limit for spatial resolution of the temperature measurements. The imageof the area in the spot mode was projected onto the four pixels of the IR camera.

 

Fig. 10 Scheme of the experiment for temperature measurement.

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Acknowledgments

This work is supported by European Social Fund Mobilitas grant No. MTT 50.

References and links

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