Mesh optimization for fluorescence molecular tomography

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 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.

A fast surface reconstruction method for fluorescence molecular tomography based on cross-beam edge back projection

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 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.

Accurate small animal surface reconstruction is important for full angle non-contact fluorescence molecular tomography (FMT) systems. In this letter, an optimal surface reconstruction method for FMT is proposed. The proposed method uses a line search method to minimize the mismatch between the reconstructed three-dimensional (3D) surface and the projected object silhouette at different angles. The results show that the mean mismatches of the 3D surfaces generated on three live anesthetized mice are all less than two charge coupled device (CCD) pixels (0.154 mm). With the accurately reconstructed 3D surface, in-vivo FMT is also performed.

BackgroundThe inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regularization scheme is developed to improve the ill-posedness of the inverse problem.MethodsThe global system is decomposed level by level with the Schur complement system along two paths in the tree structure. The resultant subsystems are solved in combination with the biconjugate gradient method. The mesh for the inverse problem is generated incorporating the prior information. During the reconstruction, the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function to tackle the ill-posed nature of the inverse problem.ResultsSimulation results demonstrate that the strategy of the tree structured Schur complement decomposition obviously outperforms the previous methods, such as the conventional Conjugate-Gradient (CG) and the Schur CG methods, in both reconstruction accuracy and speed. As compared with the Tikhonov regularization method, the adaptive regularization scheme can significantly improve ill-posedness of the inverse problem.ConclusionsThe methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.

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.

Dynamic contrast enhanced magnetic resonance is used to image high-risk patients for breast cancer because of its higher sensitivity to tumors than mammography. We focus on Near Infrared Spectroscopy (NIRS) imaging and Fluorescence Molecular Tomography (FMT), emerging imaging techniques that non-invasively quantify optical properties of total hemoglobin, oxygen saturation, water content, scattering, lipid concentration and endogenous Protoporphyrin IX (PpIX) emission. We present methods on combining the synergistic attributes of DCE-MR, NIRS, and FMT for in-vivo imaging of breast cancer in three dimensions using a custom optical MR breast coil and diffusion based light modeling software, NIRFAST. We present example results from a breast cancer patient. Preliminary results show elevated hemoglobin values and water fraction. Fluorescence values in the tumor region, however, were not always elevated above the surrounding tissue as we had expected. The additional information gained from NIRS and FMT may improve the ability to distinguish between malignant and benign lesions during MR imaging. These dual modality instruments will provide complex anatomical and molecular prognostic information, and may decrease the number of biopsies, thereby improving patient care.

X-ray luminescence optical tomography (XLOT) is a promising in vivo noninvasive imaging technique. By using x-rays to irradiate nanophosphors (NPs) in imaged region, XLOT can achieve better imaging depth and higher imaging sensitivity than the widely used optical molecular tomographic imaging techniques, e.g., bioluminescence tomography (BLT) or fluorescence molecular tomography (FMT). However, compared with the anatomical imaging techniques, e.g., x-ray computed tomography (XCT), XLOT has the disadvantage of low spatial resolution limited to millimeters. To overcome the limitation, recently, many efforts have been dedicated to optimize the data acquisition schemes and improve reconstruction methods. Nevertheless, challenges remain in XLOT due to the light scattering in biological tissues and the severely ill-condition and ill-posed of the inverse problem of XLOT. To improve the spatial resolution of XLOT, inspired by super-resolution localization optical microscopy, in this work, we propose a novel imaging method, termed as SR-XLOT, which is achieved by locating the position of NPs in each frame by using the single emitter localization methods (e.g., Gaussian fitting method). After reconstructing the positions of NPs in each frame, a super-resolution XLOT image can be generated by superimposing the identified positions of NPs from all frames into one image. To evaluate the performance of the proposed SR-XLOT method, a series of numerical simulation experiments were performed. The experimental results indicate that when using SR-XLOT method, the spatial resolution of XLOT can be significantly improved, compared with the conventional reconstruction methods. As a result, the method makes it possible to implement a super-resolution XLOT imaging, which is attractive for medical diagnostic and drug research.

Fluorescence Molecular Tomography (FMT) is a powerful imaging modality for the research of cancer diagnosis, disease treatment and drug discovery. Via three-dimensional (3-D) imaging reconstruction, it can quantitatively and noninvasively obtain the distribution of fluorescent probes in biological tissues. Currently, photon propagation of FMT is conventionally described by the Finite Element Method (FEM), and it can obtain acceptable image quality. However, there are still some inherent inadequacies in FEM, such as time consuming, discretization error and inflexibility in mesh generation, which partly limit its imaging accuracy. To further improve the solving accuracy of photon propagation model (PPM), we propose a novel compactly supported radial basis functions (CSRBFs)-based meshless method (MM) to implement the PPM of FMT. We introduced a series of independent nodes and continuous CSRBFs to interpolate the PPM, which can avoid complicated mesh generation. To analyze the performance of the proposed MM, we carried out numerical heterogeneous mouse simulation to validate the simulated surface fluorescent measurement. Then we performed an in vivo experiment to observe the tomographic reconstruction. The experimental results confirmed that our proposed MM could obtain more similar surface fluorescence measurement with the golden standard (Monte-Carlo method), and more accurate reconstruction result was achieved via MM in in vivo application.

Fluorescence molecular tomography (FMT) is an imaging modality that exploits the specificity of fluorescent biomarkers to enable 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degree of absorption and scattering of light through tissue, the FMT inverse problem is inherently ill-conditioned making image reconstruction highly susceptible to the effects of noise and numerical errors. Appropriate priors or penalties are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, fluorescent probes are locally concentrated within specific areas of interest (e.g., inside tumors). The commonly used L2 norm penalty generates the minimum energy solution, which tends to be spread out in space. Instead, we present here an approach involving a combination of the L1 and total variation norm penalties, the former to suppress spurious background signals and enforce sparsity and the latter to preserve local smoothness and piecewise constancy in the reconstructed images. We have developed a surrogate-based optimization method for minimizing the joint penalties. The method was validated using both simulated and experimental data obtained from a mouse-shaped phantom mimicking tissue optical properties and containing two embedded fluorescent sources. Fluorescence data were collected using a 3D FMT setup that uses an EMCCD camera for image acquisition and a conical mirror for full-surface viewing. A range of performance metrics was utilized to evaluate our simulation results and to compare our method with the L1, L2 and total variation norm penalty-based approaches. The experimental results were assessed using the Dice similarity coefficients computed after co-registration with a CT image of the phantom.

Optical sensing of specific molecular target using near-infrared light has been recognized to be the crucial technology, have changing human's future. The imaging of Fluorescence Molecular Tomography is the most novel technology in optical sensing. It uses near-infrared light(600-900nm) as instrument and utilize fluorochrome as probe to take noncontact three-dimensional imaging for live molecular targets and to exhibit molecular process in vivo. In order to solve the problem of forward simulation in FMT, this paper mainly introduces a new simulation modeling. The modeling utilizes Monte Carlo method and is implemented in C++ programming language. Ultimately its accuracy has been testified by comparing with analytic solutions and MOSE from University of Iowa and Chinese Academy of Science. The main characters of the modeling are that it can simulate both of bioluminescent imaging and FMT and take analytic calculation and support more than one source and CCD detector simultaneously. It can generate sufficient and proper data and pre-preparation for the study of fluorescence molecular tomography.

The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower.

Spatially resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of an infinitely small light beam. The method is, however, prone to error in measurement because the actual boundary condition and light beam often deviate from that used in deriving the analytical solutions. It is therefore important to quantify the effect of different boundary conditions and light beams on spatially resolved diffuse reflectance in order to improve the measurement accuracy of the technique. This research was aimed at using finite element method (FEM) to model light propagation in turbid media, subjected to normal illumination by a continuous-wave beam of infinitely small or finite size. Three types of boundary conditions [i.e., partial current (PCBC), extrapolated (EBC), and zero (ZBC)] were evaluated and compared against Monte Carlo (MC) simulations, since MC could provide accurate fluence rate and diffuse reflectance. The effect of beam size was also investigated. Overall results showed that FEM provided results as accurate as those of the analytical method when an appropriate boundary condition was applied. ZBC did not give satisfactory results in most cases. FEM-PCBC yielded a better fluence rate at the boundary than did FEM-EBC, while they were almost identical in predicting diffuse reflectance. Results further showed that FEM coupled with EBC effectively simulated spatially resolved diffuse reflectance under the illumination of a finite size beam. A large beam introduced more error, especially within the region of illumination. Research also confirmed an earlier finding that a light beam of less than 1 mm diameter should be used for estimation of optical parameters. FEM is effective for modeling light propagation in biological tissues and can be used for improving the optical property measurement by the spatially resolved technique.