High-dynamic-range fluorescence molecular tomography for imaging of fluorescent targets with large concentration differences

Lichao Lian; Yong Deng; Wenhao Xie; Guoqiang Xu; Xiaoquan Yang; Zhihong Zhang; Qingming Luo

doi:10.1364/OE.24.019920

1. Introduction

Hybrid fluorescence molecular tomography and X-ray computed tomography (FMT-XCT) plays an important role in the in vivo study of physiological and pathological processes of small animals [1]. FMT is used to noninvasively resolve the three-dimensional (3D) spatial distribution of fluorescent markers associated with molecular and cellular functions [2]. XCT is used to provide anatomical information that can be used for FMT reconstruction [3]. In the past, FMT-XCT has been widely used in the research of mouse models of diseases, including lung cancer [4,5], brain tumors [6], atherosclerosis [7], and Alzheimer’s disease [8].

A charge-coupled device (CCD)-based free-space FMT-XCT system performs better than a traditional fiber and photomultiplier tube (PMT)-based system because it allows the acquisition of a rich data set of excitation and emission light and is easy to combine with other imaging modalities to form a multimodality imaging system [9]. However, the limited dynamic range of a CCD severely diminishes the quality of the projection images when the signals have a wide range of intensity. This limitation further decreases the localization and quantitative accuracy of the FMT. For example, when the FMT reconstruction region contains both early- and advanced-stage tumors, the fluorescence signals from the latter can be much stronger than those from the former. For samples with highly heterogeneous absorption or irregular shapes, light attenuation is dramatically different before detection. A more common situation is fluorescent targets with large differences in concentration embedded in the samples, leading to a large difference in intensity between the weak signal region and the strong signal region. Furthermore, the near-infrared transmittance for different biological tissues have a large difference [10]. In these cases, when the CCD used in FMT has insufficient dynamic range, the quality of the projection images captured by the CCD is greatly diminished. A longer exposure time may lead to oversaturation of high-intensity areas, whereas a relatively short exposure time will produce low signal-to-noise (SNR) images with compromised image quality. These small errors in acquired projection images can result in large errors in the reconstruction, including increased artifacts and degraded performance in localization, for weak fluorescence signals. Because biological tissues cause a high amount scattering, the inverse problem of FMT is ill posed [11]. Therefore, the limited dynamic range of a CCD greatly restricts the utility of FMT in preclinical and clinical stages of a disease.

Enhancement of the dynamic range of the FMT projection images is especially important when the signals have a wide range of intensity. Many hardware- and software-based methods have been investigated to this end. The dynamic range of images can be enhanced by improving the properties of the CCD chip; e.g., cooling the chip reduces the dark current noise coefficient, thus enhancing the dynamic range. Hardware improvements will always receive many limitations and can be costly; however, changing the software is easier. The high-dynamic-range (HDR) imaging method, which is widely used in digital cameras [12] and smartphones, is the most popular method used to enhance the dynamic range of images. Most HDR imaging methods are based on a multiple-exposure scheme in which the images can be processed using different methods. For example, Madden [13] weighted the pixels in each image by their associated sensitivity, and then combined the pixels in such a way that preserved the local luminance relationship. Debevec and Malik [14] recovered the CCD response curve and combined the low-dynamic-range images with the weighting function according to the response curve. Goshtasby [15] partitioned the image domain into uniform blocks and selected the image containing the most information for each block. The selected images were then blended together using monotonically decreasing blending functions. Fei et al. [16] combined an HDR imaging method with optical projection tomography to obtain fine details of zebrafish embryos. They removed the overexposed parts of the images and then subtracted the minor-exposure images from each image. Finally, the results were divided by the difference in exposure times to generate images with proportional intensity. Vinegoni et al. [17] combined laser-scanning microscopy with an HDR imaging method that was based on the simultaneous or sequential acquisition of progressively saturated images. The images then were combined using different sensitivities to construct an HDR image. In all these works, the HDR method is effective in enhancing the dynamic range of the images. HDR combined with biological technology greatly promotes the development and application of that technology. However, the HDR imaging method can be time-consuming because of its multiple-exposure scheme.

In this paper, we present a novel HDR-FMT method, which, to our knowledge, has not been reported previously. To assess the potential of HDR-FMT method, we used a free-space FMT-XCT system and focused on the condition in which fluorescent targets, with large differences in concentration, are embedded in the samples. This condition is common with biomedical researches and will produce fluorescence signals that have a wide range of intensity. We demonstrated our method using phantom and in vivo mouse experiments. First, a series of increasingly saturated fluorescence projection images were acquired to recover the CCD response function. Then, an HDR fluorescence projection image corresponding to every source position was constructed and used for FMT reconstruction. To compensate for the time consumed with the use of a multiple-exposure scheme, images were reconstructed with the use of iterative reweighted L1 regularization, which can effectively reduce any artifacts, even if there are fewer HDR fluorescence projection images. The results of the experiments indicated that multiple-exposure scheme can effectively enhance the dynamic range of fluorescence projection images and that HDR-FMT has a better localization performance than conventional FMT reconstruction that uses low-dynamic-range fluorescence projection images. This paper is organized as follows: section 2 covers the construction of HDR fluorescence projection images, data analysis, and experimental setup; section 3 presents and discusses the results, and section 4 is a summary of the work and a discussion of the future works.

2. Methods

2.1 Construction of HDR fluorescence projection images

Construction of an HDR fluorescence projection image consists of the following steps: (1) acquisition of a series of low-dynamic-range fluorescence projection images with different exposure times; (2) recovery of the CCD response function by using the low-dynamic-range fluorescence projection images; and (3) construction of the HDR fluorescence projection image using the CCD response function and low-dynamic-range fluorescence projection images.

The number $p$ and the duration $t$ of the different exposure times used in the acquisition of the low-dynamic-range fluorescence projection images were selected to ensure that the ranges of the output pixel values overlapped considerably and the images were increasingly saturated. The criteria for selecting the duration t of the exposure times are that at least one image is normally exposed and one is overexposed. In addition, the values of each pixel with different exposure times are different and at least one of them must fall in the middle section of the response curve. The minimum number p_min of different exposure times required is $⌈ R/D ⌉$ , where R is the dynamic range of the radiance that we are interested in and D is the dynamic range of the middle section of the CCD response function. Theoretically, the CCD response function can be recovered with a minimum of two images with different exposure times, but its accuracy is poor. In general, three or more images with different exposure times are required for recovering the CCD response function with higher accuracy. We denoted the low-dynamic-range fluorescence projection image as $U^{f i}$ and $U^{f i} = U_{r a w}^{f i} - U_{b g}^{f i}$ , where $U_{r a w}^{f i}$ is the directly acquired fluorescence projection image with exposure time $t_{i}$ , $U_{b g}^{f i}$ is the corresponding background noise image, and $i$ is indexed over exposure time $t_{i}$ . The conditions were assumed static, so the irradiance $E$ was constant and each pixel had the same response to the same exposure $I$ , where $I = E t$ .

Next, the low-dynamic-range fluorescence projection images $U^{f i}$ were used to recover the CCD response function. The film reciprocity equation can be written as:

U^{f i} = f (E t_{i}) .

Because f is monotonic and invertible, we inverted both sides of Eq. (1) and obtained

f^{-1} (U^{f i}) = E t_{i}

. Then we took their natural logarithm and defined the CCD response function

g = \ln f^{- 1}

to obtain

g (U^{f i}) = l n E + l n t_{i} .

The unknown parameters, irradiance

E

and response function

g

, are recovered by solving the least-squares problem that best satisfies the set of Eq. (2). A Gaussian-like weighting function

w

and a smoothness term

σ

were introduced. Thus, we obtained the following optimization form:

[g, E] = argmin ({‖ w (z) h (g, E) ‖}^{2} + σ),

where

h (g, E) = g (U^{f i}) - l n E - l n t_{i}

. The Gaussian-like weighting function

w

was introduced to give a higher weight to the middle pixel value. Because distortion fields exist in the CCD response function, the middle part of the response function is more accurate. The Gaussian-like weighting function can be written as:

w (z) = \exp [- 4 {(z - Z_{m i d})}^{2} / Z_{mid}^{2}],

where

Z_{m i d} = (Z_{\max} + Z_{\min}) / 2

,

Z_{\max}

is the maximum pixel value and

Z_{\min}

is the minimum pixel value. The Gaussian-like weighting function gives a nonlinear weight in both side of the middle pixel value which is more consistent with the CCD response curve than the Hat function used in [14]. The smoothness term

σ

was introduced to ensure that

g

was smooth. It can be written as:

σ = λ \sum_{Z_{\min} + 1}^{Z_{\max} - 1} [w (z) g'' (z)]^{2},

where

g'' (z) = g (z - 1) - 2 g (z) + g (z + 1)

and

λ

is an experimental parameter that weights the smoothness term and should be chosen appropriately for the amount of noise expected in the measurement data.

To save time and reduce computational complexity, some of the pixels were introduced into the calculation at a sampling rate of 1/4. The best estimate of the CCD response function was obtained as soon as the optimal solutions for Eq. (3) were obtained.

When the response function $g$ was recovered, it was used to construct the HDR fluorescence projection image. Similarly, the weighting function $w$ was introduced to give a higher weight to the valid data values. The HDR fluorescence projection image was then constructed as

L^{f H D R} = \frac{\sum_{i = 1}^{p} w (U^{f i}) [g (U^{f i}) - l n t_{i}]}{\sum_{i = 1}^{p} w (U^{f i})},

where

p

is the number of exposures and

i

is indexed over the exposure time

t_{i}

.

The constructed HDR fluorescence projection image $L^{f H D R}$ in Eq. (4) was expressed in the logarithmic form of radiance. According to the CCD response function which described the relationship between pixel values and log exposures, $L^{f H D R}$ was finally mapped to pixel values $U^{f H D R}$ [12] and compared with the low-dynamic-range fluorescence projection images.

Then, using the same CCD response function g, the HDR fluorescence projection image $U^{f H D R} (r_{s})$ , which corresponded to every source position $r_{s}$ , was constructed and used for FMT reconstruction. Note that if the setups of the experiments are changed, e.g., the wavelength of the detected light, the intensity of the excitation source or the EM gain of the CCD, the response function $g$ should be recalculated.

2.2 Image reconstruction

Photon propagation in biological tissues was modeled using two coupled diffusion equations with Robin boundary conditions [18]. The sample surfaces were obtained by XCT. For convenience, we let $U^{f} (r_{d}, r_{s})$ represent the HDR fluorescence data $U^{f H D R} (r_{d}, r_{s})$ and also the low-dynamic-range fluorescence data $U^{f i} (r_{d}, r_{s})$ acquired with exposure time $t_{i}$ . Using the normalized Born ratio method [19], $U^{f} (r_{d}, r_{s})$ was divided by the excitation data $U^{e} (r_{d}, r_{s})$ measured at each corresponding detector position $r_{d}$ induced by a source at $r_{s}$ to yield the normalized measurements as follows:

U_{mea}^{nB} (r_{d}, r_{s}) = U^{f} (r_{d}, r_{s}) / U^{e} (r_{d}, r_{s}) .

The linear inverse problem of FMT can be expressed as [20]

U_{m e a}^{n B} = W x,

where

x

is the vectorized unknown fluorescence distribution, and

W

is the weight matrix. Iterative reweighted L1 regularization (IRL1) solved the linear, ill-posed inverse problem and the solution

x_{I R L 1}

is updated as follows:

x_{I R L 1}^{k + 1} = \underset{x \geq 0}{\arg} min \frac{1}{2} {‖ W x - U_{m e a}^{n B} ‖}_{2}^{2} + λ {‖ M^{k} x ‖}_{1},

where

λ

is the regularization parameter and

M

is a diagonal weight matrix. The diagonal elements of

M

are updated as

m_{i i}^{k + 1} = \frac{1}{| x_{i}^{k} | + α},

where i ranges over the solution

x_{I R L 1}

,

α

is a stable parameter, and k is the iteration count. The Eq. (7) was solved under the split Bregman framework and transformed into the following Bregman iteration:

(x_{I R L 1}^{k + 1}, d^{k + 1}) = min_{x, d} λ {‖ d ‖}_{1} + \frac{1}{2} {‖ W x - U_{m e a}^{n B} ‖}_{2}^{2} + \frac{μ}{2} {‖ d - M^{k} x - b^{k} ‖}_{2}^{2},

b^{k + 1} = b^{k} + (M x^{k +1} - d^{k + 1}),

where

μ

is a constant regularization parameter and

d

and

b

are intermediate parameters introduced in the calculation process.

Others had verified that the iterative reweighted L1 regularization effectively reduces the artifacts in the reconstruction results, even when using fewer fluorescence projection images [20]. This helped compensate for the time it took to construct HDR fluorescence projection images with the multiple-exposure scheme.

Because our XCT system could not clearly distinguish the organs in the lower abdominal cavity of the mouse, no prior structural information except the surface of the mouse, was used in FMT. Thus, we assumed that the FMT reconstruction region of the mouse was homogeneous and had the same absorption and reduced scattering coefficients.

2.3 Experimental apparatus

We performed the experiments using a hybrid FMT-XCT system previously reported on by our laboratory [21]. The schematic of the system is shown in Fig. 1. The XCT system consisted of an X-ray source (UltraBright, Oxford Instruments, Oxfordshire, UK) and a flat-panel X-ray detector (PaxScan2520V, Varian Medical Systems, Palo Alto, CA, USA). The XCT data were acquired using a tube voltage of 50 kVp and a tube current of 0.8 mA. The FMT components in the trans-illumination setup were orthogonal to the axis of the X-ray source. The FMT system comprised a 748-nm continuous-wave (CW) diode laser (B&W Tek, Newark, DE, USA) and an electron-multiplying CCD (EMCCD) camera (DU-897, Andor Technology Ltd, Belfast, UK). A dual-axis galvanometer scanner was used to scan the laser spot at multiple positions on the sample surface, and then the EMCCD acquired the fluorescence projection images or the excitation projection images. FMT and XCT raw data were obtained separately over 360° by rotating the rotation stage.

Fig. 1 Schematic of the experimental system.

Download Full Size | PDF

2.4 Experimental setup

(1) Acquisition of low-dynamic-range fluorescence projection images to recover the CCD response curve

In this work, we used a 30-mm-diameter homogeneous cylinder phantom made of 1% Intralipid (absorption coefficient $μ_{a}$ = 0.02 ${cm}^{- 1}$ and reduced scattering coefficient $μ_{s}'$ = 10.0 ${cm}^{- 1}$ at both excitation and emission wavelengths [22–24]). The bottom of the phantom was set as Z = 0 cm. The fluorescent targets were three transparent 2-mm-diameter glass tubes T1, T2, and T3 filled with 0.08, 0.40, and 2.00 μM DiR-BOA solution (excitation wavelength = 748 nm and emission wavelength = 780 nm), respectively. The glass tubes were spaced evenly in the phantom. The center of T1 was at (– 7.6 cm, 0.3 cm), T2 was at (6.7 cm, – 6.9 cm), and T3 was at (5.3 cm, 9.7 cm).

The phantom was fixed to the center of the rotation stage and the incident light was focused on the center of the sample surface to ensure that the effective fluorescence signals were projected onto the center of the CCD chip. The rotation stage remained stationary during the image acquisition process to maintain a static field of view. The fluorescence projection images and corresponding background noise images were acquired using different exposure times of $t_{1}$ = 1.0 s, $t_{2}$ = 2.0 s, and $t_{3}$ = 3.0 s.

(2) Phantom study

The phantom and the positions and concentrations of the fluorescent targets used in this phantom study were the same as those used above. This study was used to validate the potential and feasibility of the HDR-FMT method before studying the more heterogeneous in vivo mouse model.

In this study, the laser source scanned 11 positions along the z axis at each of the 24 rotation angles (every 15°). The excitation and fluorescence projection images were acquired separately with the corresponding filters at different exposure times. The exposure times for the fluorescence projection images were $t_{1}$ = 1.0 s, $t_{2}$ = 2.0 s, and $t_{3}$ = 3.0 s. The full fluorescence projection images captured by the CCD with an exposure time of 1.0 s had a low SNR but were not oversaturated. We studied this condition to see how the low-dynamic-range fluorescence projection images affected FMT reconstruction. When the exposure time was 2.0 s, the SNR increased; however, the SNR in the weak-signal region was still low because of the low dynamic range of the CCD camera. We studied this condition to see how the low SNR in the weak-signal region resulting from the limited dynamic range affected FMT reconstruction. When the exposure time was 3.0 s, the SNR in the weak-signal region improved, but some regions appeared to be overexposed. We studied this condition to see the effect of fluorescence projection images with overexposed areas on FMT reconstruction.

The HDR fluorescence projection images were constructed using the method described above and used for FMT reconstruction. The reconstruction results were compared with each other and the quantitative performance of the HDR-FMT was evaluated.

(3) Animal study

All animal procedures are complied with the protocols approved by the Hubei Provincial Animal Care and Use Committee and with the experimental guidelines of the Animal Experimentation Ethics Committee of Huazhong University of Science and Technology.

7-week-old female C57BL/6 mice were anesthetized by intraperitoneal injection of ketamine (0.2 mg/kg) and xylazine (0.02 mg/kg) and then had their hair shaved off. Breast cancer cells (EO771, kindly provided by Dr. Rong Xiang of Nankai University, Tianjin, China) were subcutaneously injected in the upper right flank (0.5 $\times$ $10^{6}$ cells) and lower right flank (1.0 $\times$ $10^{6}$ cells).

Seven days later, the injected cells had grown into a small tumor and a large tumor in the upper and lower right flanks, respectively, and the tumor volumes were suitable for our experiment. The mice were anesthetized and shaved again. HPPS (DiR-BOA) [25] fluorescent nanoparticles were intratumorally injected into the upper tumor (25 $μL$ of 2 $μM$ ) and the lower tumor (50 $μL$ of 40 $μM$ ). Intratumoral injection is widely used to inject anti-cancer agents and drug-carrying nanoparticles into tumors so that drugs could produce a direct effect on tumor cells [26,27]. In addition, the concentrations of nanoparticles remained constant within a certain period of time, because the nanoparticles spread outside of the tumor slowly [28].

The fluorescence reflectance image was acquired using the planner imaging system [29] 30 min after the nanoparticles were injected to check the accumulation of the fluorescent probes in the tumors, after which the mice were imaged by free-space FMT-XCT. We scanned a 5 $\times$ 11 rectangular grid of source positions on the dorsal surface of the mice and the CCD camera in the opposite of the laser detected the signals coming from the ventral surface. The exposure times for the fluorescence projection images were $t_{1}$ = 0.5 s, $t_{2}$ = 1.5 s, and $t_{3}$ = 2.5 s. The lower abdominal cavity of the mouse is mostly filled with air and intestines and thus it has smaller absorption and reduced scattering coefficients than the fat or muscle [4]. Here, the absorption and reduced scattering coefficients are $μ_{a}$ = 0.2 ${cm}^{- 1}$ and $μ_{s}'$ = 12 ${cm}^{- 1}$ for both the excitation wavelength of 748 nm and the emission wavelength of 780 nm.

Using the method described above, HDR fluorescence projection images were constructed and used for FMT reconstruction. In addition, low-dynamic-range fluorescence projection images with different exposure times were used for FMT reconstruction for comparison. The reconstruction results were demonstrated and the quantitative performance of the HDR-FMT was evaluated.

3. Results and discussion

3.1 CCD response curve and HDR fluorescence projection image

The fluorescence projection images acquired by the CCD camera with exposure times of 1.0, 2.0, and 3.0 s, Figs. 2(a)–2(c), respectively, show that when the exposure time was short, the weak-signal regions had low pixel values and a low SNR. The SNR improved in the images with increased exposure time, but some regions appeared to be overexposed. The Fig. 2(d) shows the recovered response curve used to construct the HDR fluorescence projection image in Fig. 2(e) by combining the low-dynamic-range fluorescence projection images in Figs. 2(a)–2(c). In the HDR fluorescence projection image, the overexposed area is gone and the dynamic range of the fluorescence projection image is effectively improved.

Fig. 2 (a)–(c) Fluorescence projection images captured by the CCD camera with exposure times of 1.0 s, 2.0 s, and 3.0 s respectively. (d) Recovered CCD response curve, where the underlying data $(E t_{i}, U^{fi})$ are the light green dots and the solid black line is the fitted curve (x axis is $\log_{e}$ ). (e) Constructed HDR fluorescence projection image.

Download Full Size | PDF

Our results show that the multiple-exposure scheme effectively enhances the dynamic range and improves the quality of the fluorescence projection images.

3.2 Phantom experiment results

The model of the homogeneous phantom used in our experiment is shown in Fig. 3(a). The FMT reconstruction region is indicated by yellow. The concentration of DiR-BOA solution in tubes T1 (blue), T2 (green), and T3 (red) was 0.08, 0.40, and 2.00 $μM$ , respectively.

Fig. 3 Comparison of phantom study results. (a) 3D view of the cylindrical phantom with three embedded fluorescent targets. (b)–(d) Reconstruction using the fluorescence projection images acquired with exposure times of 1.0, 2.0, and 3.0 s, respectively. (e) HDR-FMT reconstruction using the constructed HDR fluorescence projection images. (f) Average reconstructed FMT intensity as a function of true DiR-BOA concentration. The reconstructed values were normalized to the maximum value. The red triangle, the cyan circle, and the black circle indicate the results of the fluorescent targets in (b)–(d), respectively. The blue triangles indicate the result of HDR-FMT in (e) and the blue line represents its linear fit result. [Fluorescence signals in (b)–(e) are on a logarithmic scale and the 3D rendering was implemented using AMIRA software, FEI Company, Hillsboro, OR, USA].

Download Full Size | PDF

Figures 3(b)–3(d) show the results of FMT reconstruction obtained using low-dynamic-range fluorescence projection images with exposure times of 1.0, 2.0, and 3.0 s, respectively. For clarity, the reconstructed values are given on a natural logarithm scale. Figures 3(b) and 3(c) show that the fluorescent target T1, with the lowest DiR-BOA concentration, could not be reconstructed and there are many unwanted artifacts because the fluorescence projection images obtained with exposure times of 1.0 and 2.0 s had low pixel values and a low SNR; these factors negatively affected the FMT results. In Fig. 3(d), a few signals were reconstructed beside the true position of the fluorescent target T1, but the values were far less than the actual values, so much so that they almost could not be recognized. In addition, the reconstructed result had unwanted artifacts because although the SNRs of the fluorescence projection images captured with an exposure time of 3.0 s were improved, there were overexposed areas that adversely affected FMT reconstruction. The HDR-FMT result presented in Fig. 3(e) shows that the three fluorescent targets, with their different concentrations, were correctly localized with few artifacts.

We then chose three regions and each of them shared the same center with the corresponding fluorescent target. The area size of the cross-section of each region was about five times bigger than that of the true fluorescent target. The height of the volume was equal to that of the true fluorescent target. Figure 3(f) presents the average reconstructed FMT intensities of the fluorescent targets shown in Figs. 3(b)–3(e) as a function of true DiR-BOA concentration. As the fluorescent target T1 cannot be reconstructed by using the fluorescence projection images acquired with exposure times of 1.0, 2.0, and 3.0 s, we only performed the linear fitting for the HDR-FMT data and it shows an excellent linear response ( $R^{2}$ = 0.9975).

From the above results, we conclude that the low SNR and overexposed areas in the originally captured fluorescence projection images lead to degraded reconstruction results, i.e., the limited dynamic range of a CCD definitely affects the FMT results. The HDR-FMT reconstruction obtained from the constructed HDR fluorescence projection images significantly improves the localization performance and reduces the artifacts in the reconstruction results with good quantification. In addition, these results show that the multiple-exposure scheme is effective in enhancing the dynamic range of fluorescence projection images. However, the shape of target T3 in Fig. 3(e) reconstructed with HDR method seems worse when compared with the reconstructed targets T3 in Figs. 3(b)–3(d). The deteriorated image quality mainly arise from the error of the recovered CCD response function. The magnitude of error depends on the numbers of exposures and pixels for the calculation. With the increased numbers of exposures and pixels, the accuracy of the CCD response function will increase and thus the image quality can be further improved.

3.3 In vivo experiment results of tumor-bearing mice

The fluorescence reflectance image of the mouse was acquired 30 min after the injection of fluorescent nanoparticles. Figure 4(a) is the fluorescence reflectance image and Fig. 4(b) is the fluorescence reflectance image superimposed on the corresponding white light image. T1 and T2 indicate the upper tumor and the lower tumor, respectively. The fluorescent nanoparticles accumulated in the tumors are clearly seen so that the tumor positions can be marked correctly. The ratio of the intensities of T2 to T1 in the fluorescence reflectance image of Fig. 4(a) was approximately 12.

Fig. 4 Comparison of the results of the tumor-bearing mouse study. (a) Fluorescence reflectance image. (b) Fluorescence reflectance image superimposed on a white light image. Tumors are labeled T1 and T2. (c) 3D rendering of the mouse and highlighted tumor areas (in the white dashed circles). Region between the two dashed lines was used for FMT reconstruction. (d)–(f) 3D rendering of mouse skin based on XCT and fluorescence signals based on FMT reconstruction using low-dynamic-range fluorescence projection images obtained with exposure times of 0.5, 1.5, and 2.5 s, respectively. (g) 3D rendering of mouse skin and fluorescence signals based on HDR-FMT. (h) Overlay of oblique sections obtained from XCT and HDR-FMT. White arrows point to the reconstructed FMT signals. (i) Intensity profiles of the HDR-FMT and low-dynamic-range reconstructed results. The red, cyan, yellow, and gray lines represent the reconstructed results of HDR-FMT, exposure time of 0.5 s, 1.5 s, and 2.5 s, respectively. [Coordinate system was defined by D (dorsal), V (ventral), Cr (cranial), Cd (caudal), L (left), and R (right). 3D renderings in (c)–(g) were implemented using AMIRA software.]

Download Full Size | PDF

The tumor-bearing mouse underwent in vivo FMT-XCT imaging [Fig. 4(c)] immediately after the fluorescence reflectance imaging. XCT was performed first. Figure 4(c) shows that T1 and T2 projected out from the surface of the mouse and that T1 was smaller than T2.

Figures 4(d)–4(f) show 3D renderings of mouse skin based on XCT and fluorescence signals based on FMT reconstruction obtained using low-dynamic-range fluorescence projection images with different exposure times. The arrows indicate the reconstructed fluorescence signals. Figure 4(d) shows T1 was not localized and there were some unwanted artifacts in the reconstructed result. Figure 4(e) shows that T1 and T2 were localized, but there were large errors in the reconstruction region. T1 and T2 were localized in Fig. 4(f), which corresponds to the longest exposure time of 2.5 s, but there were still large errors in the reconstruction result.

Figure 4(g) is a 3D rendering of mouse skin based on XCT and fluorescence signals based on HDR-FMT, with the white arrows indicating the reconstructed fluorescence signals. It shows that HDR-FMT correctly localized the fluorescent-marked tumors and the reconstruction result had few artifacts. The ratio of the average reconstructed concentration in T2 to that in T1 was 29.7, which has good quantitative accuracy of 51.5% when the ratio is compared with that of the true concentrations, i.e., 20. For a clear display of the HDR-FMT result, oblique sections through the tumors were taken from both XCT and HDR-FMT, at the same place on the mouse and overlaid [Fig. 4(h)]. The fluorescence signals based on the HDR-FMT result were consistent with the tumor positions based on the XCT result; therefore, the tumor positions were localized correctly by HDR-FMT. Figure 4(i) presents the intensity profiles of the reconstructed results. The red line represents the intensity profile along the green line on the oblique section of HDR-FMT shown in Fig. 4(h). Similarly, the intensity profiles of the low-dynamic-range reconstructed results along the corresponding line on theirs oblique sections are also obtained and shown in Fig. 4(i). Note that the oblique sections associate with low-dynamic-range reconstructed results are not displayed here. From the intensity profiles in Fig. 4(i), it can be seen that HDR-FMT method can recover the intensity profile of the fluorescent targets with the best accuracy.

From the above results, we conclude that FMT reconstructions using low-dynamic-range fluorescence projection images were inaccurate. Because of the short exposure time, the fluorescence projection images acquired by the CCD camera had a low SNR; as the exposure time increased, the overexposed area appeared in the fluorescence projection images. Both the low SNR and the overexposed areas resulting from the limited dynamic range of the CCD definitely have a negative effect on FMT reconstruction. That’s why the weak signals were not reconstructed or reconstruction results contained large errors in Figs. 4(d)–4(f). Whereas HDR-FMT correctly localized the fluorescent-marked tumors with good quantitative accuracy and hardly any artifacts. In general, HDR-FMT improved the localization performance and had a good quantitative accuracy. These results were consistent with the results of the phantom study.

4. Conclusion

The limited dynamic range of a CCD adversely affects FMT results when there is a large difference in the concentrations of fluorescent targets. It greatly restricts the use of FMT in many biomedical situations. Our study showed that the HDR-FMT method presented here enhanced the dynamic range of the fluorescence projection images and improved the localization performance of FMT with good quantitative accuracy. Based on these characteristics, HDR-FMT can be used for the preclinical and clinical stages of a disease to enhance the ability of FMT to correctly reconstruct weak fluorescence signals and improve localization. HDR-FMT has experimentally overcome the limitations of FMT caused by the CCD to some degree and will further expand the application of FMT.

However, the FMT reconstruction results were affected and restricted by conditions other than the concentration of the fluorescent markers [30], including the forward model [31], reconstruction methods [32], the complexity of the physiological environment, and the absorption and scattering properties of the samples [33], all of which contributed to localization and quantification errors. Despite rapid and promising developments, the location and especially the quantitative accuracy were still limited due to the ill-posed nature of the FMT inverse problem [3]. Improving the quantification performance was valuable and challenging work but it needed to be done if HDR-FMT was to be used for clinical and research purposes. To improve quantitative accuracy, the use of multimodality schemes was needed to introduce functional and prior structural information that was crucial to FMT reconstruction [34,35].

Our method has its own disadvantages. Because three or more images obtained with different exposure times are needed to construct an HDR fluorescence projection image, the acquisition of an HDR fluorescence projection image was more time-consuming than that of a low-dynamic-range fluorescence projection image. This extra time increases the risk of photobleaching and phototoxicity [36] and, even worse, of damaging the CCD. Fortunately, the iterative reweighted L1 regularization used in the inverse problem of HDR-FMT can be used to obtain a satisfying reconstruction result with fewer HDR fluorescence projection images. For example, in our experiments, when Tikhonov regularization method is used for FMT reconstruction, measurement data of more than 30 azimuths is required. While reconstruction based on iterative reweighted L1 regularization, measurement data of 24 azimuths is enough to obtain a satisfying result. Therefore, the time consumed using the multiple-exposure scheme can be compensated for by using fewer HDR fluorescence projection images. Another way to reduce the imaging time consumption is the application of the simultaneous multi-directional data acquisition systems using mirrors or multiple cameras [37–39]. This method helps to get the full surface measurement data of the object simultaneously in one step or in one view. It greatly reduces the acquisition time of the measurement data and at the same time the 360-degree measurement data improves the image reconstruction quality. When it is combined with HDR-FMT, it will enhance the advantage of HDR imaging and also promote the development of FMT.

In conclusion, we presented our HDR-FMT method in which HDR fluorescence projection images are constructed and iterative reweighted L1 regularization is used in FMT reconstruction. The results of our study showed that HDR-FMT could effectively improve the localization performance of FMT with good quantitative accuracy and offers FMT as a new way of reconstructing fluorescent targets with large concentration differences. Future works will consider the optimization of time consumption and improvement of quantitative accuracy. If these factors can be improved, HDR-FMT will be an important tool for drug development and the study of disease growth and treatment effect.

Funding

Key Research and Development Program (2016YFA0201403); Science Fund for Creative Research Group (61421064); National Natural Science Fund (91442201, 61078072); Fundamental Research Funds for the Central Universities (0118187124).

References and Links

1. X. Guo, X. Liu, X. Wang, F. Tian, F. Liu, B. Zhang, G. Hu, and J. Bai, “A combined fluorescence and microcomputed tomography system for small animal imaging,” IEEE Trans. Biomed. Eng. 57(12), 2876–2883 (2010). [CrossRef] [PubMed]

2. X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007). [CrossRef] [PubMed]

3. Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18(8), 7835–7850 (2010). [CrossRef] [PubMed]

4. A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9(6), 615–620 (2012). [CrossRef] [PubMed]

5. V. Ermolayev, P. Mohajerani, A. Ale, A. Sarantopoulos, M. Aichler, G. Kayser, A. Walch, and V. Ntziachristos, “Early recognition of lung cancer by integrin targeted imaging in K-ras mouse model,” Int. J. Cancer 137(5), 1107–1118 (2015). [CrossRef] [PubMed]

6. K. M. Tichauer, R. W. Holt, K. S. Samkoe, F. El-Ghussein, J. R. Gunn, M. Jermyn, H. Dehghani, F. Leblond, and B. W. Pogue, “Computed tomography-guided time-domain diffuse fluorescence tomography in small animals for localization of cancer biomarkers,” J. Vis. Exp. 65, e4050 (2012). [PubMed]

7. M. Nahrendorf, P. Waterman, G. Thurber, K. Groves, M. Rajopadhye, P. Panizzi, B. Marinelli, E. Aikawa, M. J. Pittet, F. K. Swirski, and R. Weissleder, “Hybrid in vivo FMT-CT imaging of protease activity in atherosclerosis with customized nanosensors,” Arterioscler. Thromb. Vasc. Biol. 29(10), 1444–1451 (2009). [CrossRef] [PubMed]

8. D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-β plaques in a murine Alzheimer’s disease model,” Neuroimage 44(4), 1304–1311 (2009). [CrossRef] [PubMed]

9. N. Deliolanis, T. Lasser, D. Hyde, A. Soubret, J. Ripoll, and V. Ntziachristos, “Free-space fluorescence molecular tomography utilizing 360° geometry projections,” Opt. Lett. 32(4), 382–384 (2007). [CrossRef] [PubMed]

10. G. I. Petrov, A. Doronin, H. T. Whelan, I. Meglinski, and V. V. Yakovlev, “Human tissue color as viewed in high dynamic range optical spectral transmission measurements,” Biomed. Opt. Express 3(9), 2154–2161 (2012). [CrossRef] [PubMed]

11. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010). [CrossRef] [PubMed]

12. M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multiple exposures,” J. Electron. Imaging 12(2), 219–228 (2003). [CrossRef]

13. B. C. Madden, “Extended intensity range imaging,” Tech. Rep. (GRASP Laboratory, University of Pennsylvania, 1993), pp. 1–19.

14. P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, T. Whitted, ed. (ACM Press/ Addison-Wesley, 1997), pp. 369–378. [CrossRef]

15. A. A. Goshtasby, “Fusion of multi-exposure images,” Image Vis. Comput. 23(6), 611–618 (2005). [CrossRef]

16. P. Fei, Z. Yu, X. Wang, P. J. Lu, Y. Fu, Z. He, J. Xiong, and Y. Huang, “High dynamic range optical projection tomography (HDR-OPT),” Opt. Express 20(8), 8824–8836 (2012). [CrossRef] [PubMed]

17. C. Vinegoni, C. Leon Swisher, P. Fumene Feruglio, R. J. Giedt, D. L. Rousso, S. Stapleton, and R. Weissleder, “Real-time high dynamic range laser scanning microscopy,” Nat. Commun. 7, 11077 (2016). [CrossRef] [PubMed]

18. A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24(10), 1377–1386 (2005). [CrossRef] [PubMed]

19. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26(12), 893–895 (2001). [CrossRef] [PubMed]

20. W. Xie, Y. Deng, K. Wang, X. Yang, and Q. Luo, “Reweighted L1 regularization for restraining artifacts in FMT reconstruction images with limited measurements,” Opt. Lett. 39(14), 4148–4151 (2014). [CrossRef] [PubMed]

21. X. Yang, H. Gong, G. Quan, Y. Deng, and Q. Luo, “Combined system of fluorescence diffuse optical tomography and microcomputed tomography for small animal imaging,” Rev. Sci. Instrum. 81(5), 054304 (2010). [CrossRef] [PubMed]

22. G. Zhang, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013). [CrossRef] [PubMed]

23. X. Liu, D. Wang, F. Liu, and J. Bai, “Principal component analysis of dynamic fluorescence diffuse optical tomography images,” Opt. Express 18(6), 6300–6314 (2010). [CrossRef] [PubMed]

24. Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol. 52(18), 5569–5585 (2007). [CrossRef] [PubMed]

25. Z. Zhang, W. Cao, H. Jin, J. F. Lovell, M. Yang, L. Ding, J. Chen, I. Corbin, Q. Luo, and G. Zheng, “Biomimetic nanocarrier for direct cytosolic drug delivery,” Angew. Chem. Int. Ed. Engl. 48(48), 9171–9175 (2009). [CrossRef] [PubMed]

26. C.-Y. Wang, J. C. Cusack Jr, R. Liu, and A. S. Baldwin Jr., “Control of inducible chemoresistance: enhanced anti-tumor therapy through increased apoptosis by inhibition of NF-kappaB,” Nat. Med. 5(4), 412–417 (1999). [CrossRef] [PubMed]

27. Y. Kim, D. Y. Kwon, J. S. Kwon, J. H. Park, S. H. Park, H. J. Oh, J. H. Kim, B. H. Min, K. Park, and M. S. Kim, “Synergistic anti-tumor activity through combinational intratumoral injection of an in-situ injectable drug depot,” Biomaterials 85, 232–245 (2016). [CrossRef] [PubMed]

28. T. Lammers, P. Peschke, R. Kühnlein, V. Subr, K. Ulbrich, P. Huber, W. Hennink, and G. Storm, “Effect of intratumoral injection on the biodistribution and the therapeutic potential of HPMA copolymer-based drug delivery systems,” Neoplasia 8(10), 788–795 (2006). [CrossRef] [PubMed]

29. X. Yang, H. Gong, J. Fu, G. Quan, C. Huang, and Q. Luo, “Molecular imaging of small animals with fluorescent proteins: From projection to multimodality,” Comput. Med. Imaging Graph. 36(4), 259–263 (2012). [CrossRef] [PubMed]

30. A. Bogaards, H. J. Sterenborg, J. Trachtenberg, B. C. Wilson, and L. Lilge, “In vivo quantification of fluorescent molecular markers in real-time by ratio imaging for diagnostic screening and image-guided surgery,” Lasers Surg. Med. 39(7), 605–613 (2007). [CrossRef] [PubMed]

31. X. Jiang, Y. Deng, Z. Luo, K. Wang, L. Lian, X. Yang, I. Meglinski, and Q. Luo, “Evaluation of path-history-based fluorescence Monte Carlo method for photon migration in heterogeneous media,” Opt. Express 22(26), 31948–31965 (2014). [CrossRef] [PubMed]

32. Y. Deng, Z. Luo, X. Jiang, W. Xie, and Q. Luo, “Accurate quantification of fluorescent targets within turbid media based on a decoupled fluorescence Monte Carlo model,” Opt. Lett. 40(13), 3129–3132 (2015). [CrossRef] [PubMed]

33. J. F. P.-J. Abascal, J. Aguirre, J. Chamorro-Servent, M. Schweiger, S. Arridge, J. Ripoll, J. J. Vaquero, and M. Desco, “Influence of absorption and scattering on the quantification of fluorescence diffuse optical tomography using normalized data,” J. Biomed. Opt. 17(3), 036013 (2012). [CrossRef] [PubMed]

34. D. Vonwil, J. Christensen, S. Fischer, O. Ronneberger, and V. P. Shastri, “Validation of fluorescence molecular tomography/micro-CT multimodal imaging in vivo in rats,” Mol. Imaging Biol. 16(3), 350–361 (2014). [CrossRef] [PubMed]

35. Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010). [CrossRef] [PubMed]

36. R. A. Hoebe, C. H. Van Oven, T. W. Gadella Jr, P. B. Dhonukshe, C. J. Van Noorden, and E. M. Manders, “Controlled light-exposure microscopy reduces photobleaching and phototoxicity in fluorescence live-cell imaging,” Nat. Biotechnol. 25(2), 249–253 (2007). [CrossRef] [PubMed]

37. J. A. Guggenheim, H. R. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24(10), 105405 (2013). [CrossRef] [PubMed]

38. C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. M. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17(9), 7571–7585 (2009). [CrossRef] [PubMed]

39. J. H. Lee, H. K. Kim, C. Chandhanayingyong, F. Y.-I. Lee, and A. H. Hielscher, “Non-contact small animal fluorescence imaging system for simultaneous multi-directional angular-dependent data acquisition,” Biomed. Opt. Express 5(7), 2301–2316 (2014). [CrossRef] [PubMed]

High-dynamic-range fluorescence molecular tomography for imaging of fluorescent targets with large concentration differences

Abstract

1. Introduction

2. Methods

2.1 Construction of HDR fluorescence projection images

2.2 Image reconstruction

2.3 Experimental apparatus

2.4 Experimental setup

(1) Acquisition of low-dynamic-range fluorescence projection images to recover the CCD response curve

(2) Phantom study

(3) Animal study

3. Results and discussion

3.1 CCD response curve and HDR fluorescence projection image

3.2 Phantom experiment results

3.3 In vivo experiment results of tumor-bearing mice

4. Conclusion

Funding

References and Links

Cited By

Figures (4)

Equations (12)

Optics Express