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Fluorescence molecular tomography (FMT), an in vivo noninvasive imaging technology, can provide localization and quantification information for deep fluorophores. Light at wavelengths in the near-infrared (NIR-I) window from 650 nm to 950 nm has conventionally been chosen for FMT. In this study, we introduced longer NIR wavelengths within the 1100 nm to 1400 nm range, known as the “second NIR spectral window” (NIR-II). A singular-value analysis method was used to demonstrate the utility and advantages of using the NIR-II for FMT, and experiments showed an improvement in the spatial resolution in phantom studies.
© 2015 Optical Society of America
1. Introduction
Fluorescence molecular tomography (FMT) is a reliable optical imaging modality to penetrate tissues to a depth of several millimeters, or even centimeters [1]. In combination with sophisticated labeling strategies, FMT can non-invasively capture images of the distribution of fluorophores, and enable the extended-period monitoring of small animals in vivo [2]. It is a powerful tool for drug development [3], cancer research [4] and many other biomedical applications. However, the high scattering coefficient of most biological tissues hampers the performance of FMT. The diffusion of the light in biological tissues makes image reconstruction in FMT ill-posed [5], that is, (1) there may be no solution for the inverse problem; (2) the inverse problem has no unique solution; (3) the solution may not be a continuous function of the data [6]. Furthermore, this ill-posed nature results in the solving process being highly sensitive to system noise and numerical errors, which can limit the spatial resolution [7].
Many methods have been proposed to solve this problem. Combining anatomical information previously acquired by CT [8], MRI [9], or photoacoustic [10] scans into an image reconstructed by FMT will improve the spatial resolution. The regularization technique is another universal method for overcoming, to some extent, the ill-posed reconstruction problem for FMT, such as total variation-based regularization [11] and sparse-promoting regularization. Sparse-promoting regularization has been proven to offer good performance in improving the spatial resolution of FMT [12]. Early-photon technology can also be applied to high-fidelity fluorescence tomography. By detecting only ballistic photons and early-diffusive photons, the multiple scattering photons are removed. The ill-posed nature of the reconstruction mathematics resulting from the light diffusion is alleviated, and the resolution of FMT is significantly improved [13]. Upconverting nanoparticles appear as a new kind of fluorescent marker in FMT [5]. They emit an anti-Stokes shifted photon after absorbing two or more near-IR photons. By adopting quadratic upconverting nanoparticles, a more narrow sensitivity profile is achieved, and the spatial resolution can be improved [5, 14]. In addition, researchers have demonstrated that raising the number [15] and optimizing the arrangement [16] of the sources and detectors is an effective means of improving the spatial resolution of FMT. The property of the forward operator is influenced and the ill-posed nature of reconstruction is changed. With the numbers of the sources and detectors raised and the arrangement of them optimized, the ill-posed nature of the inverse problem is alleviated.
The NIR-I fluorophores have been extensively researched for both in-vitro and in-vivo imaging, given that the absorption coefficient in NIR-I is low for biological tissues. Many contrast agents, such as indocyanine green (ICG) and Cy5.5, have been developed. NIR-II is defined as that wavelength range between 1100 nm and 1400 nm [17]. The NIR-II fluorophores have been demonstrated as being promising fluorescence markers for biomedical applications [17–21]. Dai et al. reported a means of synthesizing biocompatible fluorescence single-walled carbon nanotubes (SWNT) with an emission band of between 1100 nm and 1400 nm [19]. Biocompatible Ag2S quantum dots (QDs) with an emission band in NIR-II were also reported by Wang et al. [21]. Compared to that in NIR-I, tissues exhibit a similar absorption coefficient but lower scattering coefficient in NIR-II. This unique property also makes it suitable for in vivo high-resolution biological imaging. Moreover, NIR-II provides a background-free environment for biomedical imaging [19], since the autofluorescence of biological tissues in this band is very low. Although the use of these new fluorophores has enabled unprecedented high levels of resolution in the 2D imaging of blood vessels and organs, mainly in a ballistic regime, it is still not clear if the fluorophores in NIR-II can also provide a better spatial resolution in a diffusive regime.
In this study, an FMT system based on an InGaAs charge coupled device (CCD) camera was developed. To compare the performance of NIR-I and NIR-II, an electron-multiplying CCD camera was incorporated into the system. DiR and Ag2S QDs were used as the fluorophores in NIR-I and NIR-II, respectively. Singular value analysis was also performed in the simulation study. Slab- and mouse-shaped phantoms were used for the system validation.
2. Material and methods
2.1 Experimental apparatus
The experimental setup is shown in Fig. 1. The system consists of a fiber-coupled 748-nm diode laser (B&W Tek, U.S.), a two-dimensional scanner (WN202WA100X100, Winner Optical Instruments Group Company, China), and an InGaAs CCD camera (XEVA-353, XenIC, Belgium). An EMCCD camera (DU897, Andor, U.K.) is also incorporated into the system. The laser emitted from the fiber is focused by a collimator to project a laser spot with a diameter of 0.6 mm on the imaging object, to give an optical power density of 200 mW/cm2. The collimator is fixed to the scanner to enable raster scanning. The scanner and the cameras are controlled by the data-acquisition PC. The fluorescence from the imaging object in NIR-I and NIR-II is delivered to the EMCCD camera and the InGaAs CCD camera, respectively, by using a dichroic mirror (DMLP900L, Thorlabs, U.S.). Another long-pass filter (BLP01-980R-25, Semrock, U.S.) is placed in front of the short-wavelength infrared lens (SWIR-25, Navitar, U.S.) which is fixed to the InGaAs CCD camera. The EMCCD camera is also equipped with a long-pass filter (LP02-780RU-25, Semrock, U.S.) and a camera lens (FV3526L-C, Myutron, Japan).
Fig. 1 (a) Schematic of experimental setup used for FMT detection both in NIR-I and NIR-II using silicon and InGaAs cameras, respectively. An excitation beam scanned one side of the slab. A dichroic mirror separated the fluorescence in NIR-I and NIR-II. (b) Two fluorescence tubes, containing either DiR or Ag2S QDs, were placed in the slab-shaped phantom, 7 mm from the surface.
2.2 Theoretical and numerical methods
The propagation of fluorescent light in biological tissues can be calculated by applying Born approximation, which is valid for weak fluorescent concentrations. The average measured intensity ratio is related to the fluorophore distribution [22]:
where denotes the normalized average intensity ratio. is the calculated average photon intensity at induced by a source at at the excitation wavelength. denotes the average intensity at induced by a source at at the excitation wavelength. is the fluorophore distribution. is the diffusion coefficient at the emission wavelength. denotes the Green function describing the propagation of photons from to . is a unitless calibration factor determined experimentally. In this study, , , and were calculated by Monte Carlo simulations accelerated by the application of a graphics-processing unit [23].
The inverse problem of FMT can be modeled as a linear inverse problem. The fluorophore distribution in biological tissues is to be reconstructed. The linear relationship between the normalized Born ratio and fluorophore distribution can be obtained by discretizing Eq. (1), as follows:
where is the normalized Born ratio, is referred to as the weight matrix, and is the discretized fluorophore distribution in biological tissues. There are many algorithms for solving Eq. (2). For this study, the conjugate gradient method was utilized in the reconstruction. Tikhonov regulation was used to improve the reconstruction quality.
2.3 Simulation study
For the simulation, the use of a homogeneous slab-shaped phantom of 1% Intralipid was assumed. The slab-shaped phantom measured 38 cm x 17 cm x 15 cm. Two fluorescence tubes, containing either the DiR or Ag2S QDs at a concentration of 1, were placed in the slab-shaped phantom, 7 mm from the surface. We assumed a common excitation wavelength of 750 nm, and emission wavelengths of 800 nm, 900 nm, 1000 nm, 1100 nm, 1200 nm, and 1300 nm. The optical parameters were set using an inverse adding doubling algorithm [24], based on data acquired by a spectrophotometer (Lambda 950, PerkinElmer, U.S.). The study used 48 sources with a spacing of 1 mm over a 30-mm2 field of view (FOV), and 288 detectors with a spacing of 1 mm over a 248-mm2 FOV, as shown in Fig. 1(b).
The singular-value analysis (SVA) method is always used to assess experimental setups for FMT [16]. In this study, we applied SVA to weight matrices representing the emission wavelengths. The information contained in the weight-matrix model is efficiently condensed into a singular-value spectrum.
Weight matrices were decomposed according to the following equation:
Here, and are orthonormal matrices containing singular vectors of . is a diagonal matrix that contains the singular values of . The columns of correspond to the detection-space modes while the columns of correspond to the image-space modes. The magnitude of the singular values of denotes how effectively a given image-space mode can be detected by an experimental setup [25]. Singular-value spectra can be plotted according to the singular values of . In the spectrum figure, the singular-value index is indicated by the horizontal axis while singular-value appears on the vertical axis. The slope of the singular-value spectrum decay reflects the ill-posed nature of the reconstructions. A smaller decay slope indicates that the reconstruction is less ill posed and thus would provide a higher resolution.
2.4 Phantoms study
In this study, a liquid homogeneous slab-shaped phantom and a solid homogeneous mouse-shaped phantom were used. DiR and Ag2S QDs were used as the fluorophores. The excitation wavelength of DiR was 750 nm, while the emission wavelength was 800 nm. For the Ag2S QDs, the two wavelengths were 750 nm and 1100 nm. The concentration of DiR used in this study was 1, and the concentration of Ag2S QDs was 5.
The slab-shaped phantom measured 42 cm x 17 cm x 50 cm. It incorporated a polymethyl methacrylate imaging chamber, filled with an aqueous solution of 1% Intralipid and India ink. Two capillary tubes with external diameters of 2.0 mm were used as the fluorescent targets. The tubes were again placed at a depth of 7 mm, but their separation was increased from 1 mm to 5 mm. The measured optical coefficient results are listed in Table 1. During the experiments with the slab-shaped phantom, the laser source scanned 16 x 3 positions with a spacing of 1 mm, while the 288 detectors, again with a spacing of 1 mm, covered a 248-mm2 FOV.
Table 1. Optical property parameters of slab-shaped phantom at multi-wavelengths
The mouse-shaped phantom was fabricated using 2% agar (A-0576, Sigma, U.S.), 1% Intralipid, and India ink. A solution of highly purified agar is regarded as having almost no absorption while exhibiting little scattering [26]. Thus, the scattering and absorption coefficient is determined by the concentration of the Intralipid and India ink. The same concentration of Intralipid and India ink as that of the slab phantom was used, so and were considered as being the same as in Table 1. The agar, Intralipid, and India ink were heated and stirred to form a uniform mixture, which was then poured into a mouse-shaped silicone mold. Once the mixture had solidified, a reliable solid phantom was produced. The solid, mouse-shaped, homogeneous phantom incorporated two holes with a diameter of 2 mm. These holes, measured from the surface facing the detector, were 6 mm deep, and their separation was 2 mm. A micro-CT system built by our group [27] was used to acquire the outline of the mouse phantom. During the experiments with the mouse-shaped phantom, there were 8 x 8 sources with a spacing of 2 mm, covering an area of 196 mm2, and 205 detectors covering a 195-mm2 FOV.
3. Results
3.1 Simulation study
Previous efforts to optimize the FMT experimental parameters paid considerable attention to the SVA [16, 28]. The singular-value spectrums are shown in Fig. 2(a). The different-colored curves represent different emission wavelengths. We can see that the singular-value zone between and is greatly enlarged.
Fig. 2 Singular-value analysis of different emission wavelengths. (a) Singular-value spectra for weight matrices representing setups with different emission wavelengths. (b) Plots of the number of useful singular values, extracted as shown in (a).
As shown in Fig. 2(a), the cyan curve representing an emission wavelength of 1100 nm has the smallest slope of decay. By applying the experimentally determined threshold of , statistical results for the useful singular value above the noise threshold (SVAT) were obtained as shown in Fig. 2(b). SVAT is a measure of the amount of useful information contained in the data. The imaging performance is improved by adopting a longer wavelength. The curve with a typical NIR-II emission wavelength at 1100 nm has most useful singular values. As the number of useful singular values increases, the inverse problem is less ill-posed in nature. The anti-noise ability of the FMT reconstruction process will increase accordingly. Thus, it will be possible to obtain higher spatial resolution images with fewer artifacts [29].
3.2 Slab-shaped phantom
The initial fluorescence intensity curves were obtained by applying a pencil beam to the midpoint of the excitation side. Figure 3(a) shows the normalized fluorescence intensity of the fluorescence pattern when one tube is filled with fluorescence inclusions. The NIR-I fluorophore produced an FWHM of 10.6 mm, while the NIR-II fluorophore gave an FWHM of 8.5 mm. This improvement can be seen in Fig. 3(a). The result for the two inclusions, spaced 3 mm apart, is shown in Fig. 3(b). The curves present a bimodal pattern in NIR-II, but the two peaks disappear in the curve for NIR-I. This indirectly shows that NIR-II is better suited to separating the two inclusions, and thus more likely to attain a higher spatial resolution.
Fig. 3 Projection images before reconstruction for NIR-I fluorophore (DiR) and NIR-II fluorophore (Ag2S QDs): (a) cross-section of projection image with one fluorescence tube. (b) cross-section of projection image with two fluorescence tubes, spaced 3 mm apart.
Once the inverse problem has been solved, three-dimensional reconstructed results can be obtained. Figure 4 shows the reconstructed images for different center-to-center distances for the fluorescence tubes. Reconstructions for DiR are shown in Figs. 4(a) to 4(e), with increasing tube separations from 1 mm in Fig. 4(a) to 5 mm in Fig. 4(e). The corresponding reconstructions for the Ag2S QDs are shown in Figs. 4(f) to 4(j) for increasing tube separations, from 1 mm in Fig. 4(f) to 5 mm in Fig. 4(j). Figures 4(a-i) to Fig. 4(j-i) show 3D views of the reconstructed results, while Figs. 4(a-ii) to Fig. 4(j-ii) show the cross-sectional slices and the corresponding intensity profiles.
Fig. 4 Rows (a) to (e) and (f) to (j) are FMT reconstructions with an NIR-I fluorophore (DiR) and NIR-II fluorophore (Ag2S QDs) as the contrast agents. Column (i) shows 3D views of the results. Column (ii) shows cross-sectional slices (two-dimensional plots) and their corresponding intensity profiles (line plots) for Column (i) in the Z = 6 mm plane. The true depth was z = 7 mm. The separation distances between the fluorescence tubes were varied from 1 to 5 mm (in steps of 1 mm) in both cases.
As shown in Figs. 4(a-i) to Fig. 4(e-i), the two tubes spaced 4 mm apart can be fully separated with DiR, while the outlines of the two tubes can be seen when they are spaced 3 mm apart. The two tubes spaced 2 mm apart can be fully separated with Ag2S QDs. In Fig. 4(f-i), it can be deduced that there are two tubes, spaced 1 mm apart. The separation distances, which is the standard for determining two tubes or one, are judged by applying the Sparrow criterion in cross sectional images of 3D results [30].
3.3 Mouse-shaped phantom
For the mouse-shaped phantom shown in Fig. 5(a), the 3D reconstruction results for DiR are shown in Fig. 5(c), while the reconstruction results for Ag2S QDs are shown in Fig. 5(d). Figure 5(b) shows the actual fluorescent objects inside the phantom. Figure 6(a) shows the slice of the fluorophore distribution at a height of 8 mm, which is denoted by the black curve in Fig. 5(b). Figures 6(b) and 6(c) show the corresponding reconstructed slices obtained from NIR-I and NIR-II. Both images are separately combined with Fig. 6(a). Profile plots through the vertical and transverse dashed lines in Figs. 6(a) to 6(c) are presented in Figs. 6(d) and 6(e), respectively. The triangles shown in Fig. 6(e) correspond to Line 1 in Figs. 6(a) to 6(c), while the circles correspond to Line 2.
Fig. 5 Comparison of reconstructed results of fluorophore distribution in mouse-shaped phantom. (a) Volume rendering image of mouse-shaped phantom obtained from micro-CT. Stereo (b) are the actual fluorescent objects inside the phantom. Stereo (c) and (d) are the reconstructed results obtained when using the NIR-I fluorophore (DiR) and NIR-II fluorophore (Ag2S QDs) as contrast agents. The outer shapes of the phantom in (b) to (d) were obtained by micro-CT.
Fig. 6 (a) CT slice of actual location of fluorophore in two glass tubes. (b) FMT slice obtained from the data extracted from NIR-I. (c) FMT slice obtained from data extracted from NIR-II. The profile plots through the vertical and transverse dashed lines in (a) to (c) were shown in (d) and (e). The triangles in (e) correspond to Line 1 in (a) to (c), while the circles correspond to Line 2 in (a) to (c). The units in (e) and (f) were arbitrary, since all of the data was normalized according to the maximum values of the reconstruction results.
In Fig. 6(d), the full width at half maximum (FWHM) of the CT profile plots (shown as dotted lines) on the x-axis are 1.89 mm and 1.85 mm. Profile plots obtained from NIR-I (shown as dashed lines) fail to separate the two objects on the x-axis with an FWHM value of 6.36 mm. The FWHMs of the FMT profile plots on the x-axis, as obtained from NIR-II (shown by solid lines) are 2.39 mm and 1.71 mm. In Fig. 6(e), the FWHMs of the CT profile plots (shown as dotted lines) on the y-axis are 1.96 mm and 1.89 mm. The FWHMs of the profile plots obtained from NIR-I (shown as dashed lines) on the y-axis are 6.18 mm and 6.15 mm. The FWHMs of the FMT profile plots obtained from NIR-II (shown as solid lines) on the y-axis are 5.07 mm and 4.96 mm. It is obvious that the spatial resolution has been improved on the x-axis as a result of adopting NIR-II.
4. Discussion
Absorption and scattering are basic physical processes related to light propagation in tissues. The categories of the tissues and light wavelengths are key factors affecting the two optical parameters [31]. FMT is closely related to the scattering and absorption of phantoms, and is affected by the excitation wavelengths and emission wavelengths. In this study, SVA was used to monitor the effect of the different emission wavelengths in NIR-I and NIR-II. The decay slope of the singular-value spectrum reflects the useful information contained in the weight matrix. The key results demonstrate that the results obtained with NIR-II are superior to those obtained with NIR-I.
Referring to Table 1, as the wavelength increases, the scattering properties of the slab- and mouse-shaped phantoms are both adversely affected. The absorption in NIR-II is larger than that in NIR-I. It is not easy to determine whether the increasing absorption or decreasing scattering play a positive role in attaining an improvement from the SVA results. We focused on two wavelengths, namely, 1200 nm and 1300 nm. Both phantoms exhibited a similar absorption at the two wavelengths. At a wavelength of 1300 nm, however, the phantom has a smaller scattering coefficient. The number of useful singular values with an emission wavelength of 1300 nm is greater than those having an emission wavelength of 1200 nm. From the simulation result between 1200 nm and 1300 nm, the drop in the scattering property did not have a positive impact on the change in the useful singular-value. Therefore, the improvement attained at a wavelength of 1100 nm can be attributed to the increased absorption relative to that at 800 nm. This reduction in scattering does not contribute to an improvement in the resolution. However, there is less light attenuation due to there being less scattering. The signal-to-noise ratio (SNR) is higher. The fluorescence signal is thus easier for the system to detect because of the reduced scattering. This feature makes it easier to apply NIR-II to FMT.
During the experiment with the slab-shaped phantom, a comparison of the reconstructions shown in Figs. 4(b) and 4(g) shows that the spatial resolution that can be obtained using the NIR-II QDs is greatly superior to that which we could obtain with the NIR-I fluorophore. And the spatial resolution increases from 3 mm to 1 mm with the application of the Sparrow criterion. As the emission wavelengths change from 800 nm to 1100 nm, the absorption coefficient increases from 0.0881 mm−1 to 0.115 mm−1, and the reduced scattering coefficient decreases from 1.10 mm−1 to 0.667 mm−1. The anisotropy factor g was assumed to be a constant of 0.7 [32], and the attenuation coefficient at 1100 nm is 38% less than that obtained at 800 nm. In other words, the number of detectable photons increases with NIR-II, despite the performance of the fluorophore for NIR-I being the same as that for NIR-II, thus implying the enhancement of the sensitivity. In reality, however, the results obtained with NIR-II are much worse. First, the quantum yield for the QDs with NIR-II is only about 2% which is much lower than that obtained for the fluorophores of NIR-I, such as ICG [33]. This will severely limit the number of photons emitted. Second, even the performance of the cutting-edge detectors used with NIR-II is much worse than that of the CCD camera used with NIR-I, including the dark current, quantum efficiency, and read-out noise [34, 35]. This will severely reduce the efficiency of the detection of the emitted photons. We can say, therefore, that in our experiments, the advantages of FMT with NIR-II have not been fully explored. Even in this case, FMT with NIR-II still outperforms FMT with NIR-I in terms of spatial resolution. We can expect that, with the development of fluorophore and detector technology, it will be possible to take advantage of the versatility and power of FMT with NIR-II in broader biological applications and thus obtain superior spatial resolution and sensitivity at the same time.
The solid mouse-shaped phantom was used to further verify the applicability of this method. When NIR-II QDs are employed, the x-axis resolution exhibits a higher spatial resolution relative to that possible with NIR-I. Considering that the boundary of the phantom is irregular, thus inducing additional errors in the detecting signal, and that only a single angle is adopted, the unsatisfactory profile results for the y-axis are actually acceptable.
In the 1990s, Contini et al. mentioned that absorption is helpful for increasing the spatial resolution of two-dimensional transmission imaging in a diffused medium. However, they also pointed out that it is necessary to increase the attenuation by more than 5 orders of magnitude to obtain a factor of 4 improvement in the spatial resolution [36]. This presents a great challenge to the development of detection systems. By adopting the NIR-II fluorophore, a spatial resolution improvement and the realization of a feasible detection system can be achieved at the same time.
In conclusion, we performed experiments to verify the applicability of the NIR-II fluorophore in FMT. The contribution of different emission wavelengths to the ill-posed nature of the reconstruction problem was studied. We found that the NIR-II fluorophore can be used to improve the spatial resolution of FMT, and that an improvement from 3 mm to 1 mm can be observed in the slab-shaped phantom experiment. The SVA simulation results showed that absorption in the NIR-II region is the most important factor.
Acknowledgments
This work was supported by the National Major Scientific Research Program of China (Grant No. 2011CB910401), the Science Fund for Creative Research Group of China (Grant No. 61421064), the National Natural Science Foundation of China (Grants No. 81201067), and the Fundamental Research Funds for the Central Universities (HUST: 2013TS039). The authors would like to thank Prof. Yuandi Zhao for providing the QDs.
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