1. Introduction

Fluorescence molecular imaging has become one important tool for both preclinical researches and medical practices [1]. The spatial resolution of fluorescence imaging is of fundamental importance for the success of this technique, and any advance in the resolution could result in a solid leap forward in the applications of medical diagnosis and therapy. An important method for increasing the imaging resolution is to utilize multi-photon fluorescences generated by nonlinear optical processes. Although considerable success has been achieved by using such emissions, in terms of tissue penetration, their applications are mostly limited to planar imaging, e.g., in multi-photon fluorescence microscopy [2], rather than in deep biological tissue, as the required high excitation power density for the generation of multi-photon fluorescence cannot be achieved in highly scattering media.

Upconverting nanoparticles (UCNPs) doped with rare earth ions can generate upconverted emissions with large anti-Stokes shift upon excitation of near infrared (NIR) light at very low excitation intensity, typically ≪ 1 W/cm² [3], by accumulating the energy of multiple excitation photons [4]. Due to the unique optical properties, UCNPs have been extensively employed as luminescent biomakers in various biomedical areas, including optical microscopy [5, 6], in vivo optical imaging [7, 8] and diffuse optical tomography [9, 10], as well as bioassays [11], thus becoming one important class of luminescent contrast agents [12]. The most notable improvement made by the use of UCNPs is that the developed techniques can become insensitive to the autofluorescence from biological tissues and thus achieve high sensitivity [13, 14]. Furthermore, the use of NIR excitation light can provide greater penetration depths than that of visible light and minimize the photodamage to the biological specimen involved. In addition, the multi-photon nature of upconversion emissions render high spatial imaging-resolution [15], due to their nonlinear excitation-power-density dependence [16]. In previous studies, we investigated the use of two-photon upconversion emission from NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ core-shell UCNPs in fluorescence diffuse optical imaging and tomography, and found that the spatial resolution could be significantly increased compared with using linear fluorophores [17, 18].

Similar to the two-photon emission, higher-order multi-photon upconversion emissions located within the tissue optical window can also be achieved under moderate excitation conditions, such as the three-photon upconversion emission band around 650 nm from Tm³⁺ ions [3, 19]. Due to the even steeper excitation-intensity dependence of such emissions, superior resolution can be expected than that obtained with two-photon emission. For instance, Caillat et al. demonstrated that non-linearity of three- and four-photon upconversion emissions allowed achieving higher lateral resolution in multiphoton microscopy than two-photon upconversion emission [20]. The merit of such higher-order upconversion for diffuse optical imaging has not been investigated, which constitutes the scope of the present work.

In this study, the improvement in the spatial resolution by using multi-photon upconversion emissions was systematically investigated, through both numerical simulations and imaging experiments. A resolution improvement by a factor of 1.2 was found when employing three-photon upconversion emission compared with using two-photon emission, while the improvement of using even higher-order emission is limited. The main barrier to the use of three-photon upconversion emissions is their low quantum yield. It is demonstrated that this limitation can be partly overcome by utilizing pulsed excitation approach.

2. Numerical simulations

In this study, the excitation field (Φ_x) and the emission field (Φ_m) were modeled using two coupled diffusion equations:

Photon migration was simulated for the linear emission, as well as for nonlinear multi-photon emissions, including two-photon, three-photon, and four-photon emissions. The schematic of the simulation case is illustrated in Fig. 1. The tissue was described as a brick with dimensions of x × y × z = 32 mm × 32 mm × 17 mm, while the fluorescent inclusion as a 1.2-mm-thick disk with a diameter of 3.0 mm. The laser excitation was modeled as a Gaussian beam with full width at half maximum (FWHM) of 1mm, corresponding to that used in the experiments, and was moved over the bottom tissue surface. For each source position, the exiting fluorescence from the top surface of the tissue was calculated and spatially integrated. The resulting fluorescence intensity was presented as a function of the source position, forming a three-dimensional excitation-emission profile. The FWHM was extracted from the two-dimensional cross-section of the excitation-emission profile through the peak. The absorption and reduced scattering coeffients for the excitation wavelength were assigned to μ_ax = 0.52 cm⁻¹ and μ′_sx = 10.1 cm⁻¹, respectively, while for the emission wavelength, the optical properties were set to μ_am = 0.20 cm⁻¹ and μ′_sm = 15 cm⁻¹. All simulations were performed using COMSOL Multiphysics^® connected with Matlab^®. In the simulation, much smaller grid size was used than in the experiments, in order to provide accurate theoretical prediction.

 

Fig. 1 Schematic description of the geometry used in the photon-migration simulations and optical imaging experiments.

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3. Experimental

Core–shell NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ nanoparticles, synthesized through a stoichiometric method [21], were used as the fluorescent samples. The UCNPs used in this study are not biocompatible, but they can be made biocompatible on request through surface modification and functionalization [10]. In the diffuse optical imaging experiments, a liquid tissue phantom consisting of water, intralipid and ink was used and characterized by photon time-of-flight spectroscopy (pTOFS). The amounts of different components used to make the tissue phantom were 250 mL water, 14.9 mL intralipid (Fresenius Kabi, Uppsala, Sweden; 200 mg/mL) and 0.5 mL Indian ink (Pelican Fount, Hannover, Germany; 1:100 stock solution prepared in our lab). An epoxy disk with a diameter of 3.0 mm and a thickness of 1.2 mm, mixed with UCNPs, was submerged into the tissue phantom and acted as the fluorescent inclusion. The imaging setup was arranged in a trans-illumination mode, as illustrated in Fig. 1. A continuous-wave (CW) laser diode (Thorlabs, L975P1WJ) emitting at 975 nm was employed to provide excitation. The excitation beam was scanned below the phantom in a grid pattern. An iXon EMCCD camera (Andor) was used to capture images for the scanned positions. A combination of a short-pass filter with the cut-off wavelength at 900 nm and an interference filter either at 800 nm or 650 nm was used to block the excitation light and select the desired emission bands. A more detailed description of the setup is found in our previous report [18].

4. Results and discussion

4.1. Light propagation simulations

During the simulations, the depth of the fluorescent inclusion was varied, and the corresponding FWHMs of the excitation-emission profiles were taken for the linear emission and all multi-photon emissions. Figure 2(a) presents the FWHMs as a function of the fluorescent target depth. Clearly, compared with lower-order multi-photon emissions, higher-order multi-photon emissions possess significantly smaller FWHMs in general, which will turn into spatial-resolution improvement eventually [17]. The FWHM ratios of adjacent multi-photon emissions, indicating the degree of the spatial-resolution improvement in diffuse optical imaging, are shown in Fig. 2(b). As can be seen, an improvement factor larger than 1.40 can be found at almost all imaging depths when employing two-photon emission relative to the use of the linear emission, which is in good agreement with our previous reports [17, 18]. The resolution can be further distinctly increased, nearly imaging-depth independently, by a factor of 1.23 through using three-photon emission, while the resolution improvement induced by use of even higher-order multi-photon emission is less significant. It should be noted that the fluence rates involved in the simulations are in the diffuse regime and typically below 1 W/cm², thus the conclusion here is only valid for step-wise upconversion processes where relatively low excitation power densities are required, while not applicable to conventional multiphoton processes such as multi-photon fluorescence where excitation power densities as high as 10⁶–10⁹ W/cm² are generally needed.

 

Fig. 2 COMSOL simulation of light propagation modeling the resolution using the scanning imaging method for multi-photon upconversion emissions. (a) FWHMs of the excitation-emission profiles at various fluorescent-inclusion depths. (b) Ratio of the FWHMs between multi-photon upconversion emissions of different orders.

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Although the imaging resolution can be improved using high-order multiphoton upconversion emission, the price is the typically much lower efficiency of the luminescence, resulting in poor detection limit. In addition, for multi-photon upconversion emissions with order higher than three-photon, the emission wavelength is generally located in a spectral range where biological tissues have very large absorption, thus they are less suitable for deep tissue optical imaging. In other biomedical applications that do not require high intensities as strictly, e.g., as in photoactivation of biomolecules [22], such luminescence may have broad prospects. As to three-photon upconversion emissions, despite their present much lower efficiency than two-photon upconversion emissions, with the rapid development of material engineering [23–26], one can expect the emergence of emissions with considerable efficiency and excitation/emission wavelengths suitable for diffuse optical imaging. Thus, to investigate the potential of three-photon upconversion for diffuse optical imaging is still of great interest. In the following, the advantage of three-photon upconversion emission band, represented by the red emission band of Tm³⁺ ions, in diffuse optical imaging, is studied experimently, and compared with the mostly employed two-photon upconversion emission around 800 nm from the same ions.

4.2. Upconversion spectrum and power dependence of upconversion emission intensity

Figure 3(a) shows the upconversion spectrum of the NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ nanoparticles under excition of a CW 975 nm laser diode at a power density of 0.5 W/cm², exhibiting three major upconversion emission bands in the blue, red, and near-infrared (NIR) region, respectively. The blue emission band is not suitable for deep tissue imaging, due to the typically large light absorption of biological tissues in this spectral range, and thus will not be considered in this study. The upconversion pathways of the NIR and red emission bands are well determined [27], as depicted in the inset of Fig. 3(a). The NIR upconversion is generated through two successive energy transfer processes from excited Yb³⁺ ions to Tm³⁺ ions, eventually populating the state ³H₄ (Tm³⁺), followed by the transition ³H₄ (Tm³⁺)→³H₆ (Tm³⁺). The red emission is generated by a further energy transfer from excited Yb³⁺ ions to Tm³⁺ ions, leading to the population of the state ¹G₄ (Tm³⁺), followed by the transition ¹G₄ (Tm³⁺)→³F₄ (Tm³⁺).

 

Fig. 3 (a) The upconversion spectrum of core–shell NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ nanoparticles under excitation of a CW 975 nm laser diode at a power density of 0.5 W/cm². The spectrum was measured with a standard Ocean Optics QE65000 scientific-grade spectrometer and no extra calibration was performed. Inset: schematic energy level diagrams of Yb³⁺ and Tm³⁺ ions and the proposed upconversion pathways of the NIR and red emissions following the excitation at 975 nm. (b) The power dependency of the NIR and red upconversion emissions under CW excitation at 975 nm.

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The dependence of upconversion emission intensity on the excitation power was measured for these two emission bands. The fluorescent inclusion, made of epoxy and UCNPs, was immerged into a 17-mm-thick tissue phantom at a depth of 4 mm from the excitation source. The tissue phantom, characterized by the pTOFS system, had a reduced scattering coefficient μ′_s = 10.1 cm⁻¹ and an absorption coefficient μ_a = 0.52 cm⁻¹ at 975 nm. A CW 975 nm laser diode was used to excite the fluorescent inclusion by delivering the light through the surface of the tissue phantom. The excitation power was varied by adjusting the driving current, and one image was captured by the EMCCD camera for each power used. As shown in Fig. 3(b), the intensities of the NIR and red upconversion emissions exhibit nearly quadratic and cubic dependence on the excitation power, respectively, supporting the proposed upconversion pathways.

4.3. Diffuse optical imaging

In a previous study, we have investigated experimentally the advantage of the use of the two-photon NIR upconversion emission in diffuse optical imaging through comparing with the linear emission [17]. In the present work, effort is devoted to studying the improvement made by using the three-photon red emission with respect to the use of the two-photon NIR emission.

Excitation-emission profiles for the NIR and red upconversion emission bands were experimentally measured with the fluorescent inclusion placed into the liquid tissue phantom at a depth of 4 mm. The excitation beam was scanned over the phantom surface in a 40 × 40 grid with neighboring spots separated by 0.5 mm, as illustrated in Fig. 1. Figure 4(a) presents the normalized excitation-emission profiles for the NIR and red upconversion bands. Clearly, the profile for the red emission is evidently narrower than that of the NIR emission. The cross-sections of the excitation-emission profiles were extracted at y = 10 mm and are presented in Fig. 4(b). The estimated FWHMs are 4.4 mm and 3.6 mm for the NIR and red upconversion emission band, respectively, which agree well with the simulated values, i.e., 4.3 mm and 3.5 mm, respectively, as shown in Fig. 2(a). An improvement factor in the spatial resolution of approximately 1.23 for diffuse optical imaging can thus be expected by utilizing this three-photon upconversion emission band, in good consistent with the simulated results shown in Fig. 2(b). Although, the breadth of the excitation-emission profiles increases with the depth of the fluorescent inclusion, the profile for the red emission always has a narrower distribution than the NIR emission, yielding similar resolution improvements at various depths (data not shown). Such improvement may appear less significant than that of two-photon emission relative to linear emission, but it is still valuable for discerning more detailed structures e.g. in fluorescence diffuse optical tomography.

 

Fig. 4 (a) Excitation-emission profiles and (b) the cross-sections through y = 10 mm of the NIR and red upconversion emissions from core–shell NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ nanoparticles. The FWHMs for the cross-sections through y = 10 mm are 4.4 mm and 3.6 mm for the NIR and red upconversion emission, respectively.

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As the red and NIR emission generally exhibit cubic and quadratic power density dependence on the excitation light, respectively, the intensity ratio of I₆₅₀/I₈₀₀ will increase with the excitation intensity. This excitation-intensity dependent ratio can be used to provide additional depth information of the fluorescence inclusion after careful calibration, because the fluence rate of the excitation light is dependent on the position inside the domain. Such additional information will be useful for improving the imaging resolution, e.g., in fluorescence diffuse optical tomography.

4.4. Red emission enhancement by using pulsed excitation

Due to the sequential excitation nature of upconversion emissions, higher-order upconversion emissions generally have lower quantum yield than lower-order emissions at identical excitation intensity. Thus, the quantum yield of the red upconversion emission is lower than that of the NIR emission as indicated in Fig. 3(a), because it requires a further energy transfer upconversion step from Yb³⁺ ions to Tm³⁺ ions. The low quantum yield can be potentially improved through material engineering, e.g., optimizing the composition of the nanoparticles [26] and surface modification with optical antenna [24, 25]. In addition, this drawback of the three-photon red upconversion emission can be also greatly overcome through employing the pulsed excitation approach, proposed very recently [28]. Upconversion emission typically has an excitation-power-density dependent quantum yield, starting with a tiny value and increasing with excitation intensity until achieving a saturation level [16,29]. By adopting pulsed laser sources with high peak power and moderate average power (responsible for tissue heating), higher intrinsic quantum yield of multi-photon upconversion emission can be achieved while simultaneously suppressing the thermal side-effect of the excitation light [28].

The diode laser was modulated by an external function generator, yielding a pulse output with a repetition rate of 10 Hz and a pulse width of 10 ms. The resulting intensity of the three-photon upconversion emission band was compared with that obtained with the laser operating in the CW mode at the same average excitation intensity. As shown in Fig. 5, the upconversion emission intensity is remarkably enhanced by using pulsed excitation particularly at low average excitation intensity. It should be noted that the signal gain by the pulsed excitation is related with the pulse parameters. By wisely selecting these parameters based on the consideration of the upconversion dynamics, larger upconversion signal gain can be achieved, as discussed in our previous report [28]. The use of pulsed excitation will greatly increase the applicability of the three-photon upconversion emission in deep tissue imaging.

 

Fig. 5 The enhancement of the three-photon upconversion emission band by using pulsed excitation at various average excitation intensities. The pulsed laser source had a 10 Hz repetition rate and a 10 ms pulse width.

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5. Conclusion

We systematically investigated the potential benefit of multi-photon upconversion emissions to the spatial-resolution improvement of fluorescence diffuse optical imaging through numerical simulations. Compared with the use of the linear emission, the imaging resolution can be increased by a factor of 1.45 through using two-photon emissions, and a further resolution improvement factor of 1.23 can be expected if three-photon emissions are employed. Resolution improvement associated with even higher-order multi-photon emissions is less significant. With the benefit of two-photon upconversion emissions proved in our previous study, the resolution improvement by using three-photon upconversion emission was confirmed experimentally in this research by using core–shell NaYF₄:Yb³⁺,Tm³⁺@NaYF₄ nanoparticles. High-order upconversion emissions generally suffer from low quantum yield and the law of diminishing return, making it difficult to motivate their use in deep tissues. However, for three-photon upconversion emission, this obstacle can be partly overcome by using pulsed excitation approach.