A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography

Multi-target reconstruction based on subspace decision optimization for bioluminescence tomography

BACKGROUND AND OBJECTIVE

Bioluminescence tomography (BLT) is a noninvasive optical imaging technique that provides qualitative and quantitative information on the spatial distribution of tumors in living animals. Researchers have proposed a list of algorithms and strategies for BLT reconstruction to improve its reconstruction quality. However, multi-target BLT reconstruction remains challenging in practical clinical applications due to the mutual interference of optical signals and difficulty in source separation.

METHODS

To solve this problem, this study proposes the subspace decision optimization (SDO) approach based on the traditional iterative permissible region strategy. The SDO approach transforms a single permissible region into multiple subspaces by clustering analysis. These subspaces are shrunk based on subspace shrinking optimization to achieve spatial continuity of the permissible regions. In addition, these subspaces are merged to construct a new permissible region and then the next iteration of reconstruction is carried out to ensure the stability of the results. Finally, all the iterative results are optimized based on the normal distribution model and the distribution properties of the targets to ensure the sparsity of each target and the non-biasing of the overall results.

RESULTS

Experimental results show that the SDO approach can automatically identify and separate different targets, ensuring the accuracy and quality of multi-target BLT reconstruction results. Meanwhile, SDO can combine various types of reconstruction algorithms and provide stable and high-quality reconstruction results independent of the algorithm parameters.

CONCLUSIONS

The SDO approach provides an integrated solution to the multi-target BLT reconstruction problem, realizing the whole process including target recognition, separation, reconstruction, and result enhancement, which can extend the application domain of BLT.

Sparse reconstruction based on dictionary learning and group structure strategy for cone-beam X-ray luminescence computed tomography

As a dual-modal imaging technology that has emerged in recent years, cone-beam X-ray luminescence computed tomography (CB-XLCT) has exhibited promise as a tool for the early three-dimensional detection of tumors in small animals. However, due to the challenges imposed by the low absorption and high scattering of light in tissues, the CB-XLCT reconstruction problem is a severely ill-conditioned inverse problem, rendering it difficult to obtain satisfactory reconstruction results. In this study, a strategy that utilizes dictionary learning and group structure (DLGS) is proposed to achieve satisfactory CB-XLCT reconstruction performance. The group structure is employed to account for the clustering of nanophosphors in specific regions within the organism, which can enhance the interrelation of elements in the same group. Furthermore, the dictionary learning strategy is implemented to effectively capture sparse features. The performance of the proposed method was evaluated through numerical simulations and in vivo experiments. The experimental results demonstrate that the proposed method achieves superior reconstruction performance in terms of location accuracy, target shape, robustness, dual-source resolution, and in vivo practicability.

Adaptive Grouping Block Sparse Bayesian Learning Method for Accurate and Robust Reconstruction in Bioluminescence Tomography

OBJECTIVE

Bioluminescence tomography (BLT) is a promising modality that is designed to provide non-invasive quantitative three-dimensional information regarding the tumor distribution in living animals. However, BLT suffers from inferior reconstructions due to its ill-posedness. This study aims to improve the reconstruction performance of BLT.

METHODS

We propose an adaptive grouping block sparse Bayesian learning (AGBSBL) method, which incorporates the sparsity prior, correlation of neighboring mesh nodes, and anatomical structure prior to balance the sparsity and morphology in BLT. Specifically, an adaptive grouping prior model is proposed to adjust the grouping according to the intensity of the mesh nodes during the optimization process.

RESULTS

Numerical simulations and in vivo experiments demonstrate that AGBSBL yields a high position and morphology recovery accuracy, stability, and practicality.

CONCLUSION

The proposed method is a robust and effective reconstruction algorithm for BLT. Moreover, the proposed adaptive grouping strategy can further increase the practicality of BLT in biomedical applications.

Development of tomographic reconstruction for three-dimensional optical imaging: From the inversion of light propagation to artificial intelligence

Optical molecular tomography (OMT) is an imaging modality which uses an optical signal, especially near-infrared light, to reconstruct the three-dimensional information of the light source in biological tissue. With the advantages of being low-cost, noninvasive and having high sensitivity, OMT has been applied in preclinical and clinical research. However, due to its serious ill-posedness and ill-condition, the solution of OMT requires heavy data analysis and the reconstruction quality is limited. Recently, the artificial intelligence (commonly known as AI)-based methods have been proposed to provide a different tool to solve the OMT problem. In this paper, we review the progress on OMT algorithms, from conventional methods to AI-based methods, and we also give a prospective towards future developments in this domain.

Probability method for Cerenkov luminescence tomography based on conformance error minimization

Cerenkov luminescence tomography (CLT) was developed to reconstruct a three-dimensional (3D) distribution of radioactive probes inside a living animal. Reconstruction methods are generally performed within a unique framework by searching for the optimum solution. However, the ill-posed aspect of the inverse problem usually results in the reconstruction being non-robust. In addition, the reconstructed result may not match reality since the difference between the highest and lowest uptakes of the resulting radiotracers may be considerably large, therefore the biological significance is lost. In this paper, based on the minimization of a conformance error, a probability method is proposed that consists of qualitative and quantitative modules. The proposed method first pinpoints the organ that contains the light source. Next, we developed a 0-1 linear optimization subject to a space constraint to model the CLT inverse problem, which was transformed into a forward problem by employing a region growing method to solve the optimization. After running through all of the elements used to grow the sources, a source sequence was obtained. Finally, the probability of each discrete node being the light source inside the organ was reconstructed. One numerical study and two in vivo experiments were conducted to verify the performance of the proposed algorithm, and comparisons were carried out using the hp-finite element method (hp-FEM). The results suggested that our proposed probability method was more robust and reasonable than hp-FEM.

Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification

Combining two or more imaging modalities to provide complementary information has become commonplace in clinical practice and in preclinical and basic biomedical research. By incorporating the structural information provided by computed tomography (CT) or magnetic resonance imaging (MRI), the ill poseness nature of bioluminescence tomography (BLT) can be reduced significantly, thus improve the accuracies of reconstruction and in vivo quantification. In this paper, we present a small animal imaging system combining multi-view and multi-spectral BLT with MRI. The independent MRI-compatible optical device is placed at the end of the clinical MRI scanner. The small animal is transferred between the light tight chamber of the optical device and the animal coil of MRI via a guide rail during the experiment. After the optical imaging and MRI scanning procedures are finished, the optical images are mapped onto the MRI surface by interactive registration between boundary of optical images and silhouette of MRI. Then, incorporating the MRI structural information, a heterogeneous reconstruction algorithm based on finite element method (FEM) with L 1 normalization is used to reconstruct the position, power and region of the light source. In order to validate the feasibility of the system, we conducted experiments of nude mice model implanted with artificial light source and quantitative analysis of tumor inoculation model with MDA-231-GFP-luc. Preliminary results suggest the feasibility and effectiveness of the prototype system.

Hybrid multilevel sparse reconstruction for a whole domain bioluminescence tomography using adaptive finite element

Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments.

Multi-modal molecular diffuse optical tomography system for small animal imaging

A multi-modal optical imaging system for quantitative 3D bioluminescence and functional diffuse imaging is presented, which has no moving parts and uses mirrors to provide multi-view tomographic data for image reconstruction. It is demonstrated that through the use of trans-illuminated spectral near infrared measurements and spectrally constrained tomographic reconstruction, recovered concentrations of absorbing agents can be used as prior knowledge for bioluminescence imaging within the visible spectrum. Additionally, the first use of a recently developed multi-view optical surface capture technique is shown and its application to model-based image reconstruction and free-space light modelling is demonstrated. The benefits of model-based tomographic image recovery as compared to 2D planar imaging are highlighted in a number of scenarios where the internal luminescence source is not visible or is confounding in 2D images. The results presented show that the luminescence tomographic imaging method produces 3D reconstructions of individual light sources within a mouse-sized solid phantom that are accurately localised to within 1.5mm for a range of target locations and depths indicating sensitivity and accurate imaging throughout the phantom volume. Additionally the total reconstructed luminescence source intensity is consistent to within 15% which is a dramatic improvement upon standard bioluminescence imaging. Finally, results from a heterogeneous phantom with an absorbing anomaly are presented demonstrating the use and benefits of a multi-view, spectrally constrained coupled imaging system that provides accurate 3D luminescence images.

Comparative studies of l(p)-regularization-based reconstruction algorithms for bioluminescence tomography

Inverse source reconstruction is the most challenging aspect of bioluminescence tomography (BLT) because of its ill-posedness. Although many efforts have been devoted to this problem, so far, there is no generally accepted method. Due to the ill-posedness property of the BLT inverse problem, the regularization method plays an important role in the inverse reconstruction. In this paper, six reconstruction algorithms based on l(p) regularization are surveyed. The effects of the permissible source region, measurement noise, optical properties, tissue specificity and source locations on the performance of the reconstruction algorithms are investigated using a series of single source experiments. In order to further inspect the performance of the reconstruction algorithms, we present the double sources and the in vivo mouse experiments to study their resolution ability and potential for a practical heterogeneous mouse experiment. It is hoped to provide useful guidance on algorithm development and application in the related fields.

Three-dimensional noninvasive monitoring iodine-131 uptake in the thyroid using a modified Cerenkov luminescence tomography approach

Background

Cerenkov luminescence tomography (CLT) provides the three-dimensional (3D) radiopharmaceutical biodistribution in small living animals, which is vital to biomedical imaging. However, existing single-spectral and multispectral methods are not very efficient and effective at reconstructing the distribution of the radionuclide tracer. In this paper, we present a semi-quantitative Cerenkov radiation spectral characteristic-based source reconstruction method named the hybrid spectral CLT, to efficiently reconstruct the radionuclide tracer with both encouraging reconstruction results and less acquisition and image reconstruction time.

Methodology/Principal Findings

We constructed the implantation mouse model implanted with a 400 µCi Na¹³¹I radioactive source and the physiological mouse model received an intravenous tail injection of 400 µCi radiopharmaceutical Iodine-131 (I-131) to validate the performance of the hybrid spectral CLT and compared the reconstruction results, acquisition, and image reconstruction time with that of single-spectral and multispectral CLT. Furthermore, we performed 3D noninvasive monitoring of I-131 uptake in the thyroid and quantified I-131 uptake in vivo using hybrid spectral CLT. Results showed that the reconstruction based on the hybrid spectral CLT was more accurate in localization and quantification than using single-spectral CLT, and was more efficient in the in vivo experiment compared with multispectral CLT. Additionally, 3D visualization of longitudinal observations suggested that the reconstructed energy of I-131 uptake in the thyroid increased with acquisition time and there was a robust correlation between the reconstructed energy versus the gamma ray counts of I-131 (). The ex vivo biodistribution experiment further confirmed the I-131 uptake in the thyroid for hybrid spectral CLT.

Conclusions/Significance

Results indicated that hybrid spectral CLT could be potentially used for thyroid imaging to evaluate its function and monitor its treatment for thyroid cancer.

Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.

Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis

Dynamic fluorescence diffuse optical tomography (D-FDOT) is important for drug delivery research. However, the low spatial resolution of FDOT and the complex kinetics of drug limit the ability of D-FDOT in resolving metabolic processes of drug throughout whole body of small animals. In this paper, we propose an independent component analysis (ICA)-based method to perform D-FDOT studies. When applied to D-FDOT images, ICA not only generates a set of independent components (ICs) which can illustrate functional structures with different kinetic behaviors, but also provides a set of associated time courses (TCs) which can represent normalized time courses of drug in corresponding functional structures. Further, the drug concentration in specific functional structure at different time points can be recovered by an inverse ICA transformation. To evaluate the performance of the proposed algorithm in the study of drug kinetics at whole-body level, simulation study and phantom experiment are both performed on a full-angle FDOT imaging system with line-shaped excitation pattern. In simulation study, the nanoparticle delivery of indocynaine green (ICG) throughout whole body of a digital mouse is simulated and imaged. In phantom experiment, four tubes containing different ICG concentrations are imaged and used to imitate the uptake and excretion of ICG in organs. The results suggest that we can not only illustrate ICG distributions in different functional structures, but also recover ICG concentrations in specific functional structure at different time points, when ICA is applied to D-FDOT images.

A linear correction for principal component analysis of dynamic fluorescence diffuse optical tomography images

The analysis of dynamic fluorescence diffuse optical tomography (D-FDOT) is important both for drug delivery research and for medical diagnosis and treatment. The low spatial resolution and complex kinetics, however, limit the ability of FDOT in resolving drug distributions within small animals. Principal component analysis (PCA) provides the capability of detecting and visualizing functional structures with different kinetic patterns from D-FDOT images. A particular challenge in using PCA is to reduce the level of noise in D-FDOT images. This is particularly relevant in drug study, where the time-varying fluorophore concentration (drug concentration) will result in the reconstructed images containing more noise and, therefore, affect the performance of PCA. In this paper, a new linear corrected method is proposed for modeling these time-varying fluorescence measurements before performing PCA. To evaluate the performance of the new method in resolving drug biodistribution, the metabolic processes of indocyanine green within mouse is dynamically simulated and used as the input data of PCA. Simulation results suggest that the principal component (PC) images generated using the new method improve SNR and discrimination capability, compared to the PC images generated using the uncorrected D-FDOT images.

Experimental Cerenkov luminescence tomography of the mouse model with SPECT imaging validation

Optical molecular imaging resulting from Cerenkov radiation has become a motivating topic recently and will potentially open new avenues for the study of small animal imaging. Cerenkov-based optical imaging taken from living animals in vivo has been studied with two-dimensional (2D) planar geometry and three-dimensional (3D) homogeneous mouse model. In this study, we performed 3D Cerenkov-based luminescence tomography (CLT) using a heterogeneous mouse model with an implanted Na(131)I radioactive source, which provided the accurate location for the reconstructed source. Furthermore, single photon emission computed tomography (SPECT) was utilized to verify the results of 3D CLT. We reconstructed the localization and intensity of an embedded radioactive source with various concentrations, and established a quantitative relationship between the radiotracer activity and the reconstructed intensity. The results showed the ability of in vivo CLT to recover the radioactive probe distribution in the heterogeneous mouse model and the potential of a SPECT imaging validation strategy to verify the results of optical molecular tomography.

Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method

Bioluminescence tomography (BLT) is a promising tool for studying physiological and pathological processes at cellular and molecular levels. In most clinical or preclinical practices, fine discretization is needed for recovering sources with acceptable resolution when solving BLT with finite element method (FEM). Nevertheless, uniformly fine meshes would cause large dataset and overfine meshes might aggravate the ill-posedness of BLT. Additionally, accurately quantitative information of density and power has not been simultaneously obtained so far. In this paper, we present a novel multilevel sparse reconstruction method based on adaptive FEM framework. In this method, permissible source region gradually reduces with adaptive local mesh refinement. By using sparse reconstruction with l(1) regularization on multilevel adaptive meshes, simultaneous recovery of density and power as well as accurate source location can be achieved. Experimental results for heterogeneous phantom and mouse atlas model demonstrate its effectiveness and potentiality in the application of quantitative BLT.

3D reconstruction of light flux distribution on arbitrary surfaces from 2D multi-photographic images

Optical tomography can demonstrate accurate three-dimensional (3D) imaging that recovers the 3D spatial distribution and concentration of the luminescent probes in biological tissues, compared with planar imaging. However, the tomographic approach is extremely difficult to implement due to the complexity in the reconstruction of 3D surface flux distribution from multi-view two dimensional (2D) measurements on the subject surface. To handle this problem, a novel and effective method is proposed in this paper to determine the surface flux distribution from multi-view 2D photographic images acquired by a set of non-contact detectors. The method is validated with comparison experiments involving both regular and irregular surfaces. Reconstruction of the inside probes based on the reconstructed surface flux distribution further demonstrates the potential of the proposed method in its application in optical tomography.

In vivo quantitative reconstruction studies of bioluminescence tomography: effects of peak-wavelength shift and model deviation

Bioluminescence tomography is a novel optical molecular imaging technology. The corresponding system, theory, and algorithmic frames have been set up. In the present study, we concentrated on the analysis of quantitative reconstruction deviation from peak-wavelength shift of luminescent source and the deviation of heterogeneous mouse model. The findings suggest that the reconstruction results are significantly affected by the peak-wavelength shift and deviation of anatomical structure animal models. Furthermore, the model deviations exhibit much more influence than the wavelength shift on the reconstruction results.

In vivo quantitative bioluminescence tomography using heterogeneous and homogeneous mouse models

Bioluminescence tomography (BLT) is a new optical molecular imaging modality, which can monitor both physiological and pathological processes by using bioluminescent light-emitting probes in small living animal. Especially, this technology possesses great potential in drug development, early detection, and therapy monitoring in preclinical settings. In the present study, we developed a dual modality BLT prototype system with Micro-computed tomography (MicroCT) registration approach, and improved the quantitative reconstruction algorithm based on adaptive hp finite element method (hp-FEM). Detailed comparisons of source reconstruction between the heterogeneous and homogeneous mouse models were performed. The models include mice with implanted luminescence source and tumor-bearing mice with firefly luciferase report gene. Our data suggest that the reconstruction based on heterogeneous mouse model is more accurate in localization and quantification than the homogeneous mouse model with appropriate optical parameters and that BLT allows super-early tumor detection in vivo based on tomographic reconstruction of heterogeneous mouse model signal.

Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.