Modified forward model for eliminating the time-varying impact in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a promising imaging technique to noninvasively resolve the three-dimensional spatial distributions of fluorescent targets associated with molecular and cellular functions. The reconstruction quality, including the localization and quantitative accuracy, are greatly improved by the use of normalized Born ratio method. However, the reconstruction quality is still far from reaching their potential of accurately visualizing biological information with a high localization and quantitative accuracy. It is because the inverse problem of FMT is severely ill-posed and is easily affected by the noise in the measurement data. Here we provided a scaling normalization method for FMT to restrain the influence of excitation noise on fluorescence molecular tomography reconstruction. In this method, we use the total intensity of the excitation data detected by CCD camera to normalize the fluorescence measurements. It's feasible to suppress excitation noise when compared with the normalized Born ration method. Furthermore, by applying singular-value decomposition to the forward matrices, we find that the method we proposed has more useful singular values than the normalized Born ratio method which means that it reduces the ill-posedness of FMT inverse problem. To examine its performance, we perform phantom experiments with a hybrid FMT-XCT system. To check the robustness of our method to excitation noise, we add 10% Gaussian white noise to the measured excitation data. The reconstruction results are compared with those of the normalized Born ratio method. The results indicate that our method has a better reconstruction results and a better noise robustness.

Fluorescence Molecular Tomography (FMT) is one of the most important preclinical research techniques, which can obtain three-dimensional reconstruction of tumors in mouse in vivo. However, the ill-posedness of FMT makes its reconstruction a challenging problem. Therefore, more effective, robust, and accurate reconstruction methods are needed to be developed to solve the FMT reconstruction problem. In this paper, a reconstruction method named multipath subspace pursuit (MSP) is applied to solve the FMT problem. At the end of an iteration, the MSP method creates several candidate support set. Through evaluating the normal of final residual vector, the best candidate can be selected as the final support set. Then the support set is used for reconstructing sense matrix to achieve the goal of FMT reconstruction. In order to verity the reconstruction result of the proposed MSP method, the simulated experiment of triple fluorescent sources and quantitative analyses of position error and relative intensity error for the experiment have been conducted. The MSP method obtains satisfactory results, and the source position error is below 1 mm. Moreover, the computation time of the MSP method is about one order of magnitude less than iterated shrinkage with the L1-norm (ISlL1) method. The MSP method not only can obtain the result of robustness but also can reduce the artifacts in the background. The above results revealed the MSP method for the potential FMT application.

Learning-based methods have been proved to perform well in a variety of areas in the biomedical field, such as biomedical image segmentation, and histopathological image analysis. Deep learning, as the most recently presented approach of learning-based methods, has attracted more and more attention. For instance, massive researches of deep learning methods for image reconstructions of computed tomography (CT) and magnetic resonance imaging (MRI) have been reported, indicating the great potential of deep learning for inverse problems. Optical technology-related medical imaging modalities including diffuse optical tomography (DOT), fluorescence molecular tomography (FMT), bioluminescence tomography (BLT), and photoacoustic tomography (PAT) are also dramatically innovated by introducing learning-based methods, in particular deep learning methods, to obtain better reconstruction results. This review depicts the latest researches on learning-based optical tomography of DOT, FMT, BLT, and PAT. According to the most recent studies, learning-based methods applied in the field of optical tomography are categorized as kernel-based methods and deep learning methods. In this review, the former are regarded as a sort of conventional learning-based methods and the latter are subdivided into model-based methods, post-processing methods, and end-to-end methods. Algorithm as well as data acquisition strategy are discussed in this review. The evaluations of these methods are summarized to illustrate the performance of deep learning-based reconstruction.

Conventional fluorescence molecular tomography (FMT) reconstruction requires photons penetrating the whole object, which limits its applications to small animals. However, by utilizing reflective photons, fluorescence distribution near the surface could be reconstructed regardless of the object size, which may extend the applications of FMT to surgical navigation and so on. Therefore, time-domain reflective fluorescence molecular tomography (TD-rFMT) is proposed in this paper. The system excites and detects the emission light from the same angle within a field of view of 5 cm. Because the detected intensities of targets depend strongly on the depth, the reconstruction of targets in deep regions would be evidently affected. Therefore, a fluorescence yield reconstruction method with depth regularization and a weighted separation reconstruction strategy for lifetime are developed to enhance the performance for deep targets. Through simulations and phantom experiments, TD-rFMT is proved capable of reconstructing fluorescence distribution within a 2.5-cm depth with accurate reconstructed yield, lifetime, and target position(s).

BackgroundImplicit shape-based reconstruction method in fluorescence molecular tomography (FMT) is capable of achieving higher image clarity than image-based reconstruction method. However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets.MethodsA shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg–Marquardt method rather than gradient-based methods. As a result, the priori information about the number of targets is not required anymore and the choice of step length is avoided.ResultsNumerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method.ConclusionsThe proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method.

In vivo fluorescence molecular tomography (FMT) has been a popular functional imaging modality in research labs in the past two decades. One of the major difficulties of FMT lies in the ill-posed and ill-conditioned nature of the inverse problem in reconstructing the distribution of fluorophores inside objects. The popular regularization methods based on L2, L1 and total variation (TV ) norms have been applied in FMT reconstructions. The non-convex Lq(0 < q < 1) semi-norm and Log function have also been studied recently. In this paper, we adopt a uniform optimization transfer framework for these regularization methods in FMT and compare their individual, as well as the combined effects on both small, localized targets, such as tumors in the early stage, and large targets, such as liver. Numerical simulation studies and phantom experiments have been carried out, and we found that Lq with q near 1/2 performs the best in reconstructing small targets, while joint L2 and Log performs the best for large targets.

Fluorescence molecular tomography in the near-infrared region is becoming a powerful modality for mapping the three-dimensional quantitative distributions of fluorochromes in live small animals. However, wider application of fluorescence molecular tomography still requires more accurate and stable reconstruction tools. We propose a shape-based reconstruction method that uses spherical harmonics parameterization, where fluorophores are assumed to be distributed as piecewise constants inside disjointed subdomains and the remaining background. The inverse problem is then formulated as a constrained nonlinear least-squares problem with respect to shape parameters, which decreases ill-posedness because of the significantly reduced number of unknowns. Since different shape parameters contribute differently to the boundary measurements, a two-step and modified block coordinate descent optimization algorithm is introduced to stabilize the reconstruction. We first evaluated our method using numerical simulations under various conditions for the noise level and fluorescent background; it showed significant superiority over conventional voxel-based methods in terms of the spatial resolution, reconstruction accuracy with regard to the morphology and intensity, and robustness against the initial estimated distribution. In our phantom experiment, our method again showed better spatial resolution and more accurate intensity reconstruction. Finally, the results of an in vivo experiment demonstrated its applicability to the imaging of mice.

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

In fluorescence molecular tomography, the quality of image reconstruction of fluorophore distribution is heavily reduced by the mismodeling of inaccurately known tissue optical properties. We propose an efficient sparsity-promoting Bayesian approximation error (spBAE) method to compensate for this mismodeling. The spBAE method incorporates sparsity prior into the BAE method by updating the parameters of the Gaussian prior according to its initial solution. In vivo experiments demonstrate that this new method greatly improves the reconstruction quality.

Fluorescence molecular tomography (FMT) plays an important role in in vivo small animal imaging. However, due to the diffusive nature of photon propagation in biological tissues, FMT suffers from a low spatial resolution, which limits its capability of resolving the distribution of fluorescent biomarkers. In this paper, we investigate the effect of functional and structural a priori information on the accuracy of FMT reconstruction by a hybrid FMT and X-ray computed tomography imaging system. The results from numerical simulation and phantom experiments suggest that the fluorescence targets embedded in heterogeneous medium can be localized when structural a priori information is utilized to constrain the reconstruction process. In addition, both the functional and structural a priori information are essential for the recovery of fluorophore concentration.

Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research. In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction. Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma. Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction. Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research.

Fluorescence molecular tomography (FMT) is an emerging tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is regularization techniques. Traditional methods such as Tikhonov regularization suffer from low resolution and poor signal to noise ratio. Therefore, sparse regularization techniques have been introduced to improve the reconstruction quality. The second factor is the illumination pattern. A better illumination pattern ensures the quantity and quality of the information content of the data set, thus leading to better reconstructions. In this work, we take advantage of the discrete formulation of the forward problem to give a rigorous definition of an illumination pattern as well as the admissible set of patterns. We add restrictions in the admissible set as different types of regularizers to a discrepancy functional, generating another inverse problem with the illumination pattern as unknown. Both inverse problems of reconstructing the fluorescence distribution and finding the optimal illumination pattern are solved by efficient iterative algorithms. Numerical experiments have shown that with a suitable choice of regularization parameters, the two-step approach converges to an optimal illumination pattern quickly and the reconstruction result is improved significantly regardless of the initial illumination setting.

The present full-angle, free-space fluorescence molecular tomography (FMT) system uses a step-by-step strategy to acquire measurements, which consumes time for both the rotation of the object and the integration of the charge-coupled device (CCD) camera. Completing the integration during the rotation is a more time-efficient strategy called synchronous data acquisition. However, the positions of sources and detectors in this strategy are not stationary, which is not taken into account in the conventional reconstruction algorithm. In this paper we propose a reconstruction algorithm based on the finite element method (FEM) to overcome this problem. Phantom experiments were carried out to validate the performance of the algorithm. The results show that, compared with the conventional reconstruction algorithm used in the step-by-step data acquisition strategy, the proposed algorithm can reconstruct images with more accurate location data and lower relative errors when used with the synchronous data acquisition strategy.

The adaptive finite element method (AFEM) is an effective way to retain enough resolution in selected regions while improving computational efficiency for reconstruction in fluorescent molecular tomography (FMT). In addition, background optical properties acquired by diffuse optical tomography (DOT) will improve the quality of reconstructed images. In this work, a DOT-guided adaptive reconstruction method (DGARM) is proposed, in which DOT is introduced into an adaptive reconstruction framework of FMT. Besides being used as functional a priori information in the forward modeling, the reconstructed local absorption coefficients in DOT are also used to form internal structural a priori information, which is further used to identify regions of interest (ROIs) in the mesh refinement of the adaptive procedure. Because optical properties are recovered before the formulation of FMT, a linear relationship is established between the fluorescent field and boundary measurements. We implemented numerical simulations and physical experiments to evaluate the performance of the algorithm. Compared with the strategies of uniform meshing with DOT and AFEM without DOT, DGAM improves localization accuracy of the reconstruction of fluorescence inclusion.

Fluorescence imaging is a cornerstone of preclinical research, yet its utility is hindered by semi‐quantitative limitations due to light scattering. Fluorescence molecular tomography (FMT) aims to overcome these constraints by generating 3D fluorophore maps through model‐based reconstruction. However, background fluorescence, resulting from non‐specific probe binding and autofluorescence, significantly compromises FMT image quality with severe artifacts. Solution decomposition FMT (SD‐FMT) is introduced, an innovative reconstruction method that employs an advanced prior model to decompose the solution into multiple stochastic components. The reformulated inverse problem is resolved using a hybrid projection method (HPM), ensuring robustness and efficiency. Validated through exhaustive phantom and in vivo proof‐of‐concept studies, SD‐FMT represents a paradigm shift in FMT reconstruction, with significant implications for expanding applications in preclinical research and advancing fluorescence‐guided surgical navigation.