Introduction

Optical molecular imaging, especially planar bioluminescence and fluorescence imaging, has been extensively applied in preclinical research, particularly with small animal models such as genetically modified mice and murine tumor xenografts. Tomographic optical molecular imaging localizes the source position and should provide more accurate biological information compared to its planar counterpart [1]. The possibility and potential of bioluminescence tomography (BLT) [2, 3] and fluorescence molecular tomography as standalone imaging modalities have been investigated using phantoms and mouse experiments [4, 5]. To develop a practical, accurate, and robust BLT system, more factors need to be investigated, such as in vivo validation strategies and more precise reconstruction algorithms among others. To validate the optical source information, physical and in vitro methods are commonly used in phantom- and nonbiological mouse-based experiments. In vivo imaging strategies, such as computed tomography (CT), are also used to validate artificial source-based optical experiments [6]. Due to the poor soft tissue contrast in preclinical CT imaging, it is difficult to identify the optical source in vivo based on anatomical information only. New in vivo validation strategies are necessary to develop tomographic optical molecular imaging. In the transition from phantom-based feasibility investigations to in vivo biological research, several assumptions affect source reconstruction quality [7]. Although the diffusion approximation (DA) has been widely used, the method becomes inaccurate when the bioluminescence sources are near the surface, or in tissues with high and anisotropic absorption [7, 8]. This inaccuracy leads to reduced information acquired from bioluminescence sources. Reconstruction algorithms based on high-order approximations to the radiative transfer equation (RTE) should improve these results and need to be further developed [8]. In addition, a priori information, such as spectrally resolved measurements [9, 10] and permissible source region [11], is indispensable to constrain the possible solutions in BLT reconstruction.

In this paper, an in vivo validation strategy based on positron emission tomography (PET) is proposed for tomographic bioluminescence imaging. An in vivo mouse experiment was performed with a luciferase-based tumor xenograft. After acquiring multiple spectral optical data, the bioluminescence source was localized with SP3- and DA-based reconstruction algorithms and compared to PET and CT acquired data. The reconstructed results not only show the advantages of PET-based in vivo validation compared with traditional CT-based methods but also demonstrate the effectiveness and potential of the SP3-based BLT reconstruction algorithm.

Materials and Methods

In the experiment, three types of imaging modalities, that is, X-ray CT, PET, and optical imaging, were used. To maintain the animal in the same position throughout the whole procedure, a glass holder was fabricated to support the mouse. To realize multi-view detection, two mirrors were used to acquire the photon distribution from two side views. A murine tumor cell line, MC38fluc, transfected to provide constitutive expression of firefly luciferase, was used to generate a tumor xenograft in the abdomen of a nude mouse and allowed to develop for 3 weeks. To perform the imaging experiments, the animal was anesthetized and injected with the optical substrate (luciferin). Optical data was gathered 10 min after substrate administration using the Maestro 2 in vivo Imaging System (CRI, Woburn, MA, USA). The filter bandpass width was set to 20 nm, and optical data at four wavelengths (600, 620, 640, and 660 nm) was collected. The exposure time for each wavelength was 5 min. Fig. 1a shows a mouse photograph and the corresponding optical data at 660 nm. The image signal-to-noise ratio (SNR) ranged from 6.81 to 7.27 (SNR was calculated by Savg/Navg at four wavelengths, where Savg and Navg are the averages of the image signal and noise). Since the optical signals are weak and the sensitivity of this particular detection system is low, the image SNR is low. However, the nature of the optical filter [12] allowed the photon distribution on the mouse surface to be observed for arbitrary wavelength bands. Because the tumor position after 3 weeks was very close to the mouse abdomen, the photon distribution could not be acquired from the two side views. After finishing the bioluminescence optical signal acquisition, the PET tracer (18F-fluorodeoxy-glucose (18F-FDG)) was injected intravenously into the mouse. After 1 h uptake, the animal was imaged using a microCT and a high resolution preclinical PET system (Siemens Preclinical Solutions, Knoxville, TN, USA) to obtain the CT and PET images shown in Fig. 1b, c. Localization of the tumor position from the PET images is facilitated due to the high 18F-FDG uptake compared to background. However, the same is not true when analyzing the CT images due to the similar density contrast between the tumor and other tissues in the animal abdomen. These data clearly show the advantages of PET imaging for in vivo optical imaging validation. After all the collection of the imaging data, the mouse was euthanized and dissected to confirm the tumor location. A tumor mass of approximately 3 mm diameter was found attached to the small intestine, shown in Fig. 1d. To realize the spectrally resolved BLT reconstruction with the high-order approximations to the RTE, we have developed a fully parallel reconstruction framework with the simplified spherical harmonics approximation (SPN) [13]. Regarding the SP3 approximation, its mathematical model and boundary formula are [14]

$$ \left\{ {\begin{array}{*{20}{c}} { - \nabla \cdot \frac{1}{{3{\mu_{{\rm{a}}1}}}}\nabla {\varphi_1} + {\mu_{\rm{a}}}{\varphi_1} - \left( {\frac{2}{3}{\mu_{\rm{a}}}} \right){\varphi_2} = S} \\{ - \left( {\frac{2}{3}{\mu_{\rm{a}}}} \right){\varphi_1} - \nabla \cdot \frac{1}{{7{\mu_{{\rm{a}}3}}}}\nabla {\varphi_2} + \left( {\frac{4}{9}{\mu_{\rm{a}}} + \frac{5}{9}{\mu_{{\rm{a}}2}}} \right){\varphi_2} = \frac{2}{3}S} \\\end{array} } \right. $$
(1)
$$ \left\{ {\begin{array}{*{20}l} {{{\left( {\frac{{1 + B_{1} }}{{3\mu _{{{\text{a}}1}} }}} \right)}\upsilon \cdot \nabla \varphi _{1} - {\left( {\frac{{D_{1} }}{{\mu _{{{\text{a}}3}} }}} \right)}\upsilon \cdot \nabla \varphi _{2} = - {\left( {\frac{1}{2} + A_{1} } \right)}\varphi _{1} + {\left( {\frac{1}{8} + C_{1} } \right)}\varphi _{2} } \hfill} \\ {{ - {\left( {\frac{{D_{2} }}{{\mu _{{{\text{a}}1}} }}} \right)}\upsilon \cdot \nabla \varphi _{1} + {\left( {\frac{{1 + B_{2} }}{{7\mu _{{{\text{a}}3}} }}} \right)}\upsilon \cdot \nabla \varphi _{2} = {\left( {\frac{1}{8} + C_{2} } \right)}\varphi _{1} - {\left( {\frac{7}{{24}} + A_{2} } \right)}\varphi _{2} } \hfill} \\ \end{array} } \right. $$
(2)

where μ an  = μ s(1 − g n) + μ a(n = 1, 2, 3), φ i (i = 1, 2) are the composite moments relevant to the Legendre moments, μ s and μ a are the scattering and absorption coefficients, and S is the bioluminescence source. Note that μ an , φ i , and S depend on the wavelength when spectrally resolved measured data is acquired. The coefficients A 1,...,D 1,...,A 2,...,D 2 can be calculated using the formulas in [14]. Furthermore, the exiting partial current J + on the mouse surface is obtained:

$$ \begin{gathered} {J^{ +, b}} = \left( {\frac{1}{4} + {J_0}} \right)\left( {{\varphi_1} - \frac{2}{3}{\varphi_2}} \right) - \left( {\frac{{0.5 + {J_1}}}{{3{\mu_{{\rm{a}}1}}}}} \right)\upsilon \cdot \nabla {\varphi_1} \hfill \\+ \frac{1}{3}\left( {\frac{5}{{16}} + {J_2}} \right){\varphi_2} - \left( {\frac{{{J_3}}}{{7{\mu_{{\rm{a}}3}}}}} \right)\upsilon \cdot \nabla {\varphi_2} \hfill \\\end{gathered} $$
(3)

where the coefficients J 0,...,J 3 can also be calculated based on the relevant formulas in [14]. Note that SP 1 (DA) can be obtained correspondingly by setting φ 2 = 0. After a series of deductions, a simple relationship between the measurable boundary data and the unknown source distribution is established:

$$ {J^{ +, b}} = A{S^p} $$
(4)

where

$$ {J^{ +, b}} = \left[ {\begin{array}{*{20}{c}} {{J^{ +, b}}\left( {{\lambda_1}} \right)} \\\vdots \\{{J^{ +, b}}\left( {{\lambda_k}} \right)} \\\vdots \\{{J^{ +, b}}\left( {{\lambda_K}} \right)} \\\end{array} } \right],A = \left[ {\begin{array}{*{20}{c}} {{\gamma_1}G\left( {{\lambda_1}} \right)} \\\vdots \\{{\gamma_k}G\left( {{\lambda_k}} \right)} \\\vdots \\{{\gamma_K}G\left( {{\lambda_K}} \right)} \\\end{array} } \right] $$

where K is the number of the used wavelengths, γ k is the percentage at the wavelength λ k of the total energy, and G(λ k ) is the relationship matrix between the permissible source region S p and the measurable data J +,b at the wavelength λ k . The surface measured data J +,m corresponding to J +,b leads to a reconstruction failure when solving Eq. 4 directly due to the presence of noise. We can solve the bound-constrained least squares problem

$$ {\min_{0 < {S^p} < {S^{sup}}}}\Theta \left( {{S^p}} \right):{\left| {\left| {A{S^p} - {J^{ +, m}}} \right|} \right|^2} $$
(5)

where S sup is the upper bound of the source density. By minimizing the objective function Θ(S p), BLT reconstruction becomes possible. Here, the limited memory variable metric bound-constrained quasi-Newton method (BLMVM) is used for BLT reconstruction [15].

Fig. 1
figure 1

Imaging of a xenograft tumor in a nude mouse. The photograph is used to map the optical data from the CCD camera onto the surface of the volumetric mesh; the computed tomography slice shows the same position cross-section with the positron emission tomography scan; dissection is used to further confirm the tumor position.

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Results

With respect to the photon distribution on the mouse surface, the volumetric mesh of half the mouse body shown in Fig. 2 was generated using the commercial software Amira 3.0 (Mercury Computer Systems, Inc. Chelmsford, MA, USA). Since the photon distribution can only be obtained from the ventral view and the photon propagation path is almost totally consisted of muscle tissue, we assumed that the reconstructed domain was homogeneous with muscle tissue. The mesh contained about 10,000 discretized points with the average element of 1.2 mm diameter. The assumed optical properties of mouse muscle are shown in Table 1. To constrain the BLT solution, a permissible source region with 5,965 discretized points was selected, that is S p = {(x,y,z)|33.0 < y < 55.0 mm, (x,y,z) ∈ Ω}, where Ω is the entire domain, as shown in Fig. 2. The acquired optical data was mapped onto the mesh surface after manual co-registration between the mesh and the mouse photograph in Amira. The differences of the optical properties at different wavelengths improve the BLT reconstruction quality. Since the optical properties at 600 and 660 nm have a large difference (as shown in Table 1), Fig. 3 shows the SP3- and DA-based reconstruction results when using 1,072 measured points and these two wavelengths. Through comparison between optical and PET reconstructed results, one can determine that the source location errors of SP3-based reconstruction are less than 1.5 mm at each direction. However, the DA-based BLT reconstruction is not as accurate. In the depth direction, the location errors are about 4 mm. Note that the background noise is very high due to nonspecific probe uptake in PET imaging. This reconstruction comparison shows the effectiveness of the SP3-based reconstruction algorithm for BLT. To further confirm the effect of spectrally resolved measured data, BLT reconstructions using measurements in one and four wavelengths were performed. The reconstructed results are shown in Fig. 4. Due to the absence of source depth information when using one wavelength, poor reconstruction results were obtained. However, when four wavelengths were used, the localization of the source center was not improved; instead, there were some artifacts in the reconstructed results compared with two wavelengths. Small differences in the optical properties between 620, 640, and 660 nm reduced the benefits from multispectral measured data, while the noise effects in the measured data became significant. Although the use of multispectral data can improve reconstructed image quality, in principle, the results are a trade-off between photon sensitivity (presence of statistical noise) and differences between optical properties.

Fig. 2
figure 2

The volumetric mesh used in bioluminescence tomography reconstruction and the photon distribution at 660 nm. The red lines are used to show the permissible source region.

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Table 1 Optical properties of actual mouse muscle [7]
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Fig. 3
figure 3

Imaging validation and bioluminescence tomography reconstruction comparison between SP3- and DA-based models. The dashed lines are used to align the boundaries of optical cross-sections with the corresponding computed tomography slices; the red lines show the center of tumor on positron emission tomography images.

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Fig. 4
figure 4

DA- and SP3-based bioluminescence tomography reconstruction comparisons with different spectrally resolved measurements. 1W, 2W, and 4W denotes that one (660 nm), two (600 and 660 nm), and four wavelengths are used. Cross-sections with blue and red boundaries are the center position of the actual and reconstructed sources, respectively. The volumetric mesh denotes reconstructed values larger than 10% of the reconstructed maximum.

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Discussions and Conclusion

To the best of the authors' knowledge, this contribution represents the first time that PET imaging has been used for in vivo BLT imaging validation. The results show the effectiveness of radionuclide imaging and the potential of high-order approximation models for BLT reconstruction. Further research will focus on mouse experiments with disease models. In using BLT with these models, validation with FDG-PET may not always be possible if the target tissue does not demonstrate adequate image contrast. For this purpose, we will be utilizing genetically modified mouse models in which target tissues for bioluminescent imaging are expressing both a bioluminescence-based reporter gene and a PET probe/PET reporter gene [16].

Although the simulated and experimental [17] SP N -based BLT reconstruction algorithm provides improved localization precision of the bioluminescent source, the sensitivity of the detection system of BLT plays a very important role in BLT reconstruction for experimental reconstructions. With the increase of the tumor depth, the optical signals on the surface of the mouse are significantly attenuated. More sensitive detection systems become necessary to improve image reconstruction. A new Optical-PET (OPET) imaging system [18] provides not only the simultaneous detection of optical signals and gamma rays but also higher sensitivity due to the natural multi-view detection mode and the photon collection from larger solid angle. More experiments will be performed on the OPET system, and relevant results will be reported in the future, especially on the effect of signal loss, image reconstruction, and sensitivity for the methodology.