Quite recently Cerenkov luminescence imaging (CLI) has been introduced as a novel pre-clinical imaging for the in vivo imaging of small animals such as mice. The CLI method is based on the detection of Cerenkov radiation (CR) generated by beta particles as they travel into the animal tissues with an energy such that Cerenkov emission condition is satisfied. This paper describes an image reconstruction method called multi spectral diffuse Cerenkov luminescence tomography (msCLT) in order to obtain 3D images from the detection of CR. The multispectral approach is based on a set of 2D planar images acquired using a number of narrow bandpass filters, and the distinctive information content at each wavelength is used in the 3D image reconstruction process. The proposed msCLT method was tested both in vitro and in vivo using 32P-ATP and all the images were acquired by using the IVIS 200 small animal optical imager (Caliper Life Sciences, Alameda USA). Source depth estimation and spatial resolution measurements were performed using a small capillary source placed between several slices of chicken breast. The theoretical Cerenkov emission spectrum and optical properties of chicken breast were used in the modelling of photon propagation. In vivo imaging was performed by injecting control nude mice with 10 MBq of 32P-ATP and the 3D tracer bio-distribution was reconstructed. Whole body MRI was acquired to provide an anatomical localization of the Cerenkov emission. The spatial resolution obtained from the msCLT reconstructed images of the capillary source showed that the FWHM is about 1.5 mm for a 6 mm depth. Co-registered MRI images showed that the Cerenkov emission regions matches fairly well with anatomical regions, such as the brain, heart and abdomen. Ex vivo imaging of the different organs such as intestine, brain, heart and ribs further confirms these findings. We conclude that in vivo 3D bio-distribution of a pure beta-minus emitting radiopharmaceutical such as 32P-ATP can be obtained using the msCLT reconstruction approach.
© 2011 OSA
Small animal optical imaging is a well-established non-invasive method for pre-clinical research studies. For example many applications has been developed, for oncology , metabolic disease , inflammation , infectious disease .
Photons in the optical range are heavily scattered in the tissues of the animal and, thus, the light propagation can be treated as a diffusive effect. As the photons travel through tissue, a large amount are absorbed, however a fraction reach the surface of the animal and can be detected.
Quite recently Robertson  and our group [6–8] have developed a novel pre-clinical imaging approach called Cerenkov luminescence imaging (CLI) for the in vivo imaging of small animals such as mice. The developments of CLI has been also described in a commentary paper published recently .
The CLI method is based on the detection of Cerenkov radiation (CR) generated by beta particles (both electrons or positrons) as they travel into the animal tissues with an energy such that Cerenkov emission condition is satisfied . One of the most interesting and promising aspect of CLI is that it can be performed by using a conventional small animal optical imaging system based on highly cooled CCD detector.
A preliminary attempt to obtain Cerenkov light source depth estimation was described in [6,7] more precisely we showed that it is possible to obtain reasonable results by using two different region of interest (ROI) based approaches. The main goal of this work was to extend our previous results to obtain a 3D image of the Cerenkov light distribution. The multi spectral 3D image reconstruction approach used in this paper, called diffuse luminescence imaging tomography was introduced by Kuo et al  where 3D images were derived from conventional bioluminescence sources. In this work the method was extended in order to include Cerenkov light sources and, thus, to underline this particular light emission source we will refer to it as multi spectral Cerenkov luminescence tomography (msCLT).
3D CLI images were obtained by Li et al  by using two mirrors and an image reconstruction approach based on a finite element method for forward modelling. Their approach acquires images over one bandpass between 695 and 770 nm and the inverse problem is treated using a pre-conditioned conjugate gradient method. A similar 3D approach was recently proposed by Hu et al , where multiple views of the animal using a rotation stage were acquired through a single bandpass 675-775 nm filter. The complexity of such methods is that dedicated optical imaging systems need to be developed in order to include the mirrors or the rotation step, requirements for 3D imaging when only one bandpass of images is acquired.
One of the main advantages of the multispectral 3D approach described in this paper is that it offers depth resolution and localization without requiring multiple views of the animal, and such small animal optical imaging (OI) system is commercially available. The multispectral approach is based on a set of 2D planar images acquired using a series of narrow bandpass filters centered on wavelengths 20 nm apart, and the distinctive information content at each wavelength is used in the 3D image reconstruction process .
The paper is organized as follows: in section 2 the mathematical formalism of the msCLT image reconstruction algorithm is briefly described. The main results obtained using msCLT for ex vivo and in vivo images are presented in the results section 3. In particular an example of 3D 32P-ATP bio-distribution fused with an MRI in a control nude mouse is shown. Discussion and conclusions then follow.
2. Materials and methods
2.1 msCLT reconstruction formalism
As already mentioned in the introduction the mathematical formalism of the msCLT 3D multispectral image reconstruction approach was introduced in ref  and, thus, only the main results will be described here for the sake of clarity. Diffusion theory can be successfully applied to describe the light photons transport in weakly absorbing turbid media, more precisely when the absorption coefficient μa is much smaller than the reduced scattering coefficient μs. In this case the photon density (photons/mm3) ρ(x) can be modelled using the steady-state diffusion equation:Eq. (1) for a point source can be derived by considering locally the object as a infinite plane boundary oriented tangentially to the object surface.
In order to compute the source intensity solution s(x) on a voxel basis the problem must be discretized as follows:
Including data from images at several wavelengths helps to constrain the solution, it is thus useful to rewrite Eq. (2) as:
As Eq. (3) tends to be ill-conditioned, a regularized non negative (s ≥0) least square (NNLS) optimisation algorithm is used to solve for s as follows:Eq. (4). Surface data can be obtained for example by using anatomical data from Computed Tomography (CT), from Magnetic Resonance Imaging (MRI) or as in this study, by mapping the animal surface using the method of structured light.
The 1/λ2 wavelength dependence of the Cerenkov spectrum  was included in the G* kernel matrix and the spectrum was normalised at 500 nm. The wavelength-dependent scattering and attenuation coefficients were chosen depending on the imaged tissues.
The reconstruction process follows  where the solution voxel parameterization is adaptively refined from a starting size of 5 mm to 1.25 mm in two steps of refinement by a factor of 2. The Lagrange multiplier was set to the largest singular value of G*, reduced by a factor of 100 for the phantom reconstructions, and by a factor of 30 for the in vivo experiment.
2.2 Source depth estimation using msCLT
CLI images were acquired in the IVIS 200 optical imager (Caliper Life Sciences, Alameda, USA). The IVIS 200 is equipped with a back-thinned, back-illuminated CCD camera cooled at −90 °C. The CCD has an active array of 1920 x 1920 pixels with a dimension of 13 microns.
The CR spectral data were measured by acquiring six images with the narrow band (FWHM ~20 nm) emission filters (centered on 560 nm, 580 nm, 600 nm, 620 nm, 640 nm and 660 nm) with the following parameters: exposure time ranging from 5 to 300 seconds, f=1, binning B=8 and with a Field of View=12.8 cm. Images were acquired and analyzed with Living Image 4.0 (Caliper Life Sciences) and were corrected for dark measurements. The msCLT image reconstruction algorithm uses the a module of the Living Image software, and this algorithm can be run on a desktop PC. For this study, a theoretical Cerenkov emission spectrum is implemented into the algorithm module.
Source depth measurements were performed by filling a small capillary (1.0 mm diameter) with 0.5 MBq of 32P-ATP. The capillary was placed between slices of chicken breast in order to simulate photon scattering and attenuation in the tissues. The capillary was placed at different source depths (6, 9, 11 mm) and the msCLT reconstruction was performed by considering the absorption and scattering coefficients found in . The six wavelengths were used in the capillary reconstruction. However, in the in vivo case, the shorter wavelength images (560, 580 nm) for the in vivo data were dominated by emission from unspecific probe circulation in the shallowest regions of the tissue and contributes to many shallow intensities in the reconstruction . Therefore, these wavelengths were omitted from the reconstruction of the mouse. In simulation, when wavelengths 600-660 nm data were used in the reconstruction for the mouse muscle optical properties, reconstruction parameters such as depth and solution width were not considerably different (data not shown) as compared to reconstructions with data sets comprising of the 560-660 nm wavelength data. The simulation studies gives us confidence that the in vivo reconstructions using mouse muscle optical properties are not significantly degraded for data which includes only the 600-660 nm wavelengths. The optical properties of chicken breast, however, is less attenuating than mouse muscle, by approximately 7-fold for wavelengths >600 nm. Spatial resolution is degraded with low attenuation wavelength data, therefore adding the 560 nm and 580 nm data brings an advantage for the chicken breast reconstructions.
2.3 Spatial resolution simulations and measurements
The spatial resolution measurements were performed by using the same msCLT images of the capillary described in the previous section. The full with half maximum (FWHM) of a capillary profile was calculated to estimate the spatial resolution of the 3D images.
In order to investigate the spatial resolution variation with respect to the Cerenkov source position the FWHM was calculated at the three different capillary depths.
The spatial resolution value is highly dependent on the tissue optical proprieties, and, thus, it is useful to compare the experimental FWHM measured using ex vivo slices of chicken breast with respect to the resolution achievable in vivo in a mouse. In order to perform such comparison a slab of tissue with in vivo mouse muscle optical properties was modeled as a 3D isosceles trapezoid, with parallel sides 40 mm and 75 mm in length, 20 mm in height, and 40 mm width. A 1 mm diameter cylindrical tubes 15 mm in length was modeled with Cerenkov spectral emission, placed at depths 4, 6, 8, and 10 mm horizontally in the slab and at a number of separation distances.
Another set of simulations were performed in order to investigate the ability of the msCLT algorithm to distinguish two small sources close to each other as suggested in . The smallest spacing between the sources at which they are still separately distinguishable in the reconstruction is considered at 33% Michelson contrast, and can be noted as a function of depth. The cylinders were modeled on a 0.2 mm cubic grid. The noiseless photon density data at the top surface (narrower of the parallel sides) was forward modeled using the Green's function Equations described in . Photon density data were modeled for 580, 600, 620, 640 and 660 nm.
2.4 In-vivo 32P-ATP bio-distribution measurements
In order to validate in vivo the proposed msCLT image reconstruction scheme a control two nude mice were injected with 10 MBq of 32P-ATP. During injection and images acquisition the mouse was kept under gaseous anaesthesia (2% of isoflurane and 1 l/min of oxygen). All the animal handling was approved by the Institutional Ethical Committee according to the regulations of the Italian Ministry of Health and to the European Communities Council (86/609/EEC) directives.
A dynamic planar CLI scan were performed for 60 minutes after tracer injection, more precisely 10 images were acquired without any filter every 6 minutes using exposure time=300 seconds, f=1, binning B=8 and with a Field of View=12.8 cm.
CLI spectra of the animals were acquired for 30 min after 2 and 4 days from the tracer injection and were measured with the following parameters: exposure time=300 seconds, f=1, binning B=8 and with a Field of View=12.8 cm. A whole body MRI of the mouse was acquired immediately after OI in order to provide an anatomical localization of the Cerenkov source. The MR image were acquired using a T2W sequence with the following parameters: TR = 8388.2 ms, TE = 76.0 ms. The resulting image has a trans-axial pixel size of 0.156 mm and a slice thickness of 2.00 mm. In order to reduce OI-MRI co-registration errors the mouse was fixed to a rigid custom made multimodality bed that can be easily insert into the MR bore. The OI and MR image registration was performed by manual registration whereby the animal surface determined by structured light and MR were matched in the 3D viewing perspectives.
After day 4 one mouse was euthanized and all the organs were removed and imaged using the same imaging parameters as for in vivo imaging.
3.1 Capillary image reconstruction at different source depths
Results of the msCLT reconstructed depth versus the experimental capillary depth are reported in Fig. 1 . The data show the correlation between experimental and reconstructed measures obtained with the use of the Cerenkov theoretical spectrum optical properties of the chicken breast from .
Depth error measurements are presented in Table 1 as one can see the error range is between 1.7% and 6.7%, The R2 calculated considering a fit with the identity line is also shown.
An example of 3D msCLT reconstruction of the 32P-ATP filled glass rod at 9 mm depth is shown in the bottom part of Fig. 2 . The shape and the position of the rod inside the phantom are well visible in the trans-axial image.
3.2 Spatial resolution simulations and measurements
In order to further investigate the performances of the msCLT algorithm to distinguish two small sources placed close to each other, a set of simulations were performed as described in the material and methods section. From the simulation studies involving two rods, the separation can be perceived at 33% contrast at twice the widths given in Fig. 3 . The figure hows the variation of the FWHM (measured from a capillary profile) with respect to the source depth. The best value of the FWHM measured using ex vivo chicken breast slices is found at 6 mm, in this case the FWHM is equal to 1.5 and increases with depth.
It is interesting to notice that the FWHM obtained from ex vivo spatial resolution measurements and the simulation performed considering in vivo muscle optical properties showed that the FWHM values are comparable.
3.3 In vivo bio-distribution of 32P-ATP
Figure 4 shows the tissue time activity curves of different organs, by looking at the plot it is possible to notice an increase of signal from the bladder because of tracer elimination and also a moderate uptake in the bones due to the fraction of unlabeled 32P in the solution.
Figure 5 presents an example of CLI images acquired respectively within one hour after 32P-ATP injection, as one can see the images show a tracer uptake particularly in the abdominal region and in the bladder.
Figure 6 shows a comparison between the measured and the estimated photon density from the brain region when the convergence condition of the msCLT reconstruction algorithm (Eq. (4) is achieved. As one can see there is a good agreement between the data and the forward model results from the final converged reconstruction source distribution. The images also show a tracer uptake in the mandible region.
Figure 7 shows a msCLT trans-axial slice co-registered with MRI in the cranial region. The image shows a very good agreement between the location of the Cerenkov source and the corresponding anatomical region.
Figures 8 , 9 and 10 present the measured with respect to the estimated photon density coming from the thorax region and the 3D images obtained using the msCLT reconstruction algorithm for the same anatomical region. It is very interesting to notice in the slice corresponding to the thorax a 32P-ATP uptake in the heart and in the ribs region, showing a good in vivo spatial resolution.
In particular Fig. 10 shows a 3D whole body msCLT of the animal. As one can see by looking at the panel on the right it is possible to distinguish the internal organs such as the heart and the intestine of the animal.
In order to validate the 3D images obtained using msCLT reconstruction, we acquired a series of ex vivo CLI images of the intestine, brain, heart and ribs. In this case the animal were euthanized after four days from tracer injection.
As one can see by looking at Fig. 11 CLI images of the different organs showed a 32P-ATP uptake in these anatomical regions of the mouse, in agreement with the msCLT reconstructed images.
In section 3 results obtained by using a chicken breast phantom and both in vivo and ex vivo mouse imaging were presented. The chicken breast phantom with a capillary source placed at different depths allowed us to investigate the performances of the msCLT algorithm in recovering the true source position. We found that the source depth errors ranges between 0.9 and 6.7%. In a previous paper  we calculated the source depth using two ROI based methods, different optical parameters and we found that the msCLT approach allows a slight improvement in the recovery of the source depth. However it is important to underline here that the choice of the optical parameters is a crucial aspect and need to be further investigated.
The spatial resolution obtained from the msCLT reconstructed images of the capillary source placed at different depths showed that the FWHM is about 1.5 mm for a 6 mm depth. This is a preliminary but still very encouraging result since the FWHM value can be compared to the spatial resolution that can be obtained for example by using state of the art small animal SPECT/PET tomographs .
The spatial resolution begin to degrade for a depth greater than 10 mm, however given the size of a mouse, this problem can be partially solved by acquiring OI in supine or prone position depending on the location of the lesion. The spatial resolution performances of the msCLT reconstruction algorithm was also investigated by performing a set of simulation considering two small sources placed close to each other. The plot in Fig. 3 shows the smallest spacing between rods at which they are separately distinguishable.
Comparison between ex vivo spatial resolution measurements using published chicken breast optical properties and the simulation performed considering in vivo muscle optical properties showed that the FWHM values are comparable. This is quite important results since it show that we can correctly extrapolate ex vivo (chicken breast) spatial resolution measurements to in vivo imaging. This is also confirmed qualitatively by looking at 3D in vivo 32P-ATP images as will be discussed below.
In vivo imaging results showed that the msCLT reconstruction approach allow us to obtain accurate 3D bio-distribution of a pure beta-minus radiopharmaceutical such as 32P-ATP. This is a quite important and novel results since to our knowledge even if 32P-ATP has been extensively used in the past for biology experiments in vivo bio-distribution was not known. Moreover it could be used to trace the cellular metabolic activity in vivo and in particular to localize pathological sites.
Dynamic imaging performed for 60 minutes allowed us to investigate the 32P-ATP uptake in the different organs of the animals. The tissues time activity curves showed an increased tracer accumulation in the bladder and in particular in the bones. The accumulation in the bones can be explained considering the fraction of unlabeled 32P in the solution. The tracer accumulation in the liver and the brain is almost the same and is stable immediately after few minutes from 32P-ATP injection. Co-registration of msCLT reconstructed 3D images with MRI show that the different Cerenkov emission region matches fairly well the corresponding anatomical regions for the brain and the thorax.
With regard to the brain region it is interesting to notice from Fig. 7 that the reconstructed signal is quite intense despite the fact that the Cerenkov photons crosses a significant amount of brain tissue and the skull before reaching the detector.
The slices corresponding to the thorax (see Fig. 9 and 10) shows a clearly visible 32P-ATP uptake in the heart and small bone structures like the ribs. This results is in good agreement with the phantom spatial resolution measurements obtained using the capillary source. The whole body msCLT 3D of the animal (see Fig. 10) shows that it is possible to distinguish the internal organs in particular the animal intestine. This is a further in vivo evidence of the good spatial resolution achievable using the msCLT image reconstruction algorithm.
In order to further validate the results obtained using msCLT reconstruction ex vivo CLI of the different organs such as intestine, brain, heart and ribs were acquired. As one can see by looking at Fig. 11 The CLI images of the different organs showed a clear 32P-ATP uptake in these regions of the animal and, thus, confirming the results obtained using the msCLT reconstruction scheme.
In this work the MRI data were used to provide anatomical localization of the Cerenkov source, however the MRI could also be used to provide a better description of photons propagations by assigning the proper absorption and reduced scattering coefficient to each tissue. This can be done with diffusion optical tomography methods where the MRI information is used for structural hard priors . Application of the Rytov approximation is an appropriate model for the problem in heterogeneous media .
In vitro measurements performed using a small capillary source placed inside a scattering and attenuating medium show that the msCLT image reconstruction algorithm allow us to obtain source location and a spatial resolution can be compared to the state of the art small animal SPECT/PET tomographs.
In vivo results showed that accurate whole body 3D bio-distribution of a pure beta minus radiopharmaceutical can be obtained using msCLT reconstruction approach. In particular to our knowledge the in vivo bio-distribution of 32P-ATP was investigated for the first time using a 3D optical imaging technique.
Despite the preliminary nature of these results, they are very encouraging suggesting that optical imaging can be used to obtain whole body 3D images of beta emitting radiopharmaceuticals for both imaging and therapeutic purposes.
As shown by  the solution of the diffusion equation G has a strong wavelength dependence. More precisely the wavelength dependence of G is in the diffusion coefficient D and the effective absorption coefficient μeff as shown by the following equations:
Eq. (A.2) be slightly modified in order to take into account the wavelength dependence of G as follow:
where is η(λk) is the fraction of the emission source spectrum ξ(λ) that contributes to the measured signal and is defined as:
where λklow and λkhigh are respectively the lower and higher wavelength of a filter centered at the wavelength λk. Given the 1/λ2 dependence of the Cerenkov radiation spectrum, equation A.4 simplifies to:
where λmin is the minimum wavelength of the measured spectrum.
The authors would like to acknowledge the Cariverona Foundation and the Ospedale Sacro Cuore Don Calabria for the financial support. Dr. Elena Nicolato and Dr. Giamaica Conti for the help with the animal handling and MRI acquisition. We would also like to acknowledge Mr. Ali Behrooz for providing the simulations with the mouse muscle optical properties.
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