Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method

Dual and Multi-Target Cone-Beam X-ray Luminescence Computed Tomography Based on the DeepCB-XLCT Network

BACKGROUND AND OBJECTIVE

Emerging as a hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been developed using X-ray-excitable nanoparticles. In contrast to conventional bio-optical imaging techniques like bioluminescence tomography (BLT) and fluorescence molecular tomography (FMT), CB-XLCT offers the advantage of greater imaging depth while significantly reducing interference from autofluorescence and background fluorescence, owing to its utilization of X-ray-excited nanoparticles. However, due to the intricate excitation process and extensive light scattering within biological tissues, the inverse problem of CB-XLCT is fundamentally ill-conditioned.

METHODS

An end-to-end three-dimensional deep encoder-decoder network, termed DeepCB-XLCT, is introduced to improve the quality of CB-XLCT reconstructions. This network directly establishes a nonlinear mapping between the distribution of internal X-ray-excitable nanoparticles and the corresponding boundary fluorescent signals. To improve the fidelity of target shape restoration, the structural similarity loss (SSIM) was incorporated into the objective function of the DeepCB-XLCT network. Additionally, a loss term specifically for target regions was introduced to improve the network's emphasis on the areas of interest. As a result, the inaccuracies in reconstruction caused by the simplified linear model used in conventional methods can be effectively minimized by the proposed DeepCB-XLCT method.

RESULTS AND CONCLUSIONS

Numerical simulations, phantom experiments, and in vivo experiments with two targets were performed, revealing that the DeepCB-XLCT network enhances reconstruction accuracy regarding contrast-to-noise ratio and shape similarity when compared to traditional methods. In addition, the findings from the XLCT tomographic images involving three targets demonstrate its potential for multi-target CB-XLCT imaging.

Automated Restarting Fast Proximal Gradient Descent Method for Single-View Cone-Beam X-ray Luminescence Computed Tomography Based on Depth Compensation

Single-view cone-beam X-ray luminescence computed tomography (CB-XLCT) has recently gained attention as a highly promising imaging technique that allows for the efficient and rapid three-dimensional visualization of nanophosphor (NP) distributions in small animals. However, the reconstruction performance is hindered by the ill-posed nature of the inverse problem and the effects of depth variation as only a single view is acquired. To tackle this issue, we present a methodology that integrates an automated restarting strategy with depth compensation to achieve reconstruction. The present study employs a fast proximal gradient descent (FPGD) method, incorporating L0 norm regularization, to achieve efficient reconstruction with accelerated convergence. The proposed approach offers the benefit of retrieving neighboring multitarget distributions without the need for CT priors. Additionally, the automated restarting strategy ensures reliable reconstructions without the need for manual intervention. Numerical simulations and physical phantom experiments were conducted using a custom CB-XLCT system to demonstrate the accuracy of the proposed method in resolving adjacent NPs. The results showed that this method had the lowest relative error compared to other few-view techniques. This study signifies a significant progression in the development of practical single-view CB-XLCT for high-resolution 3-D biomedical imaging.

Superfast Scan of Focused X-Ray Luminescence Computed Tomography Imaging

X-ray luminescence computed tomography (XLCT) is a hybrid molecular imaging modality having the high spatial resolution of x-ray imaging and high measurement sensitivity of optical imaging. Narrow x-ray beam based XLCT imaging has shown promise for high spatial resolution imaging of luminescent targets in deep tissues, but the slow acquisition speed limits its applications. In this work, we have introduced a superfast XLCT scan scheme based on the photon counter detector and a fly-scanning method. The new scan scheme is compared with three other scan methods. We have also designed and built a single-pixel x-ray detector to detect object boundaries automatically. With the detector, we can perform the parallel beam CT imaging with the XLCT imaging simultaneously. We have built the prototype XLCT imaging system to verify the proposed scan scheme. A phantom embedded with a set of four side-by-side cylindrical targets was scanned. With the proposed superfast scan scheme, we have achieved 43 seconds per transverse scan, which is 28.6 times faster than before with slightly better XLCT image quality. The superfast scan allows us to perform 3D pencil beam XLCT imaging in the future.

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.

An adaptive parameter selection strategy based on maximizing the probability of data for robust fluorescence molecular tomography reconstruction

To alleviate the ill-posed of the inverse problem in fluorescent molecular tomography (FMT), many regularization methods based on L₂ or L₁ norm have been proposed. Whereas, the quality of regularization parameters affects the performance of the reconstruction algorithm. Some classical parameter selection strategies usually need initialization of parameter range and high computing costs, which is not universal in the practical application of FMT. In this paper, an universally applicable adaptive parameter selection method based on maximizing the probability of data (MPD) strategy was proposed. This strategy used maximum a posteriori (MAP) estimation and maximum likelihood (ML) estimation to establish a regularization parameters model. The stable optimal regularization parameters can be determined by multiple iterative estimates. Numerical simulations and in vivo experiments show that MPD strategy can obtain stable regularization parameters for both regularization algorithms based on L₂ or L₁ norm and achieve good reconstruction performance.

Cone-beam X-ray luminescence computed tomography based on MLEM with adaptive FISTA initial image

BACKGROUND AND OBJECTIVE

As an emerging dual-mode optical molecular imaging, cone-beam X-ray luminescence computed tomography (CB-XLCT) has shown potential in early tumor diagnosis and other applications with increased depth and little autofluorescence. However, due to the low transfer efficiency of PNPs to convert X-ray energy to visible or near-infrared (NIR) light and X-ray dose limitation, the signal to noise ratio of projections is quite low, making the quality of CB-XLCT relatively poor.

METHODS

To improve the reconstruction quality of low-counts CB-XLCT imaging, an adaptive reconstruction algorithm (named ADFISTA-MLEM) based on the maximum likelihood expectation estimation (MLEM) framework is proposed for CB-XLCT reconstruction from Poisson distributed projections. In the proposed framework, the image reconstructed by fast iterative shrinkage-thresholding algorithm (FISTA) is used as the initial image for MLEM iterations to improve reconstruction accuracy, in which both the projection noise model and the sparsity constraint of the image could be considered. For relative quantitative imaging, a specific normalization is applied to the projection data and system matrix. To determine the hyperparameter of FISTA, which may be different for different projections, an adaptive strategy (ADFISTA) is then designed for adaptive update of the hyperparameter with reconstructed image in each iteration.

RESULTS AND CONCLUSIONS

Results from numerical simulations and phantom experiments indicate that the proposed framework can obtain superior reconstruction accuracy in terms of contrast to noise ratio and shape similarity. In addition, high intensity-concentration linearity between different probe targets indicates its potential for quantitative CB-XLCT imaging.

A Joint-Parameter Estimation and Bayesian Reconstruction Approach to Low-Dose CT

Most penalized maximum likelihood methods for tomographic image reconstruction based on Bayes' law include a freely adjustable hyperparameter to balance the data fidelity term and the prior/penalty term for a specific noise-resolution tradeoff. The hyperparameter is determined empirically via a trial-and-error fashion in many applications, which then selects the optimal result from multiple iterative reconstructions. These penalized methods are not only time-consuming by their iterative nature, but also require manual adjustment. This study aims to investigate a theory-based strategy for Bayesian image reconstruction without a freely adjustable hyperparameter, to substantially save time and computational resources. The Bayesian image reconstruction problem is formulated by two probability density functions (PDFs), one for the data fidelity term and the other for the prior term. When formulating these PDFs, we introduce two parameters. While these two parameters ensure the PDFs completely describe the data and prior terms, they cannot be determined by the acquired data; thus, they are called complete but unobservable parameters. Estimating these two parameters becomes possible under the conditional expectation and maximization for the image reconstruction, given the acquired data and the PDFs. This leads to an iterative algorithm, which jointly estimates the two parameters and computes the to-be reconstructed image by maximizing a posteriori probability, denoted as joint-parameter-Bayes. In addition to the theoretical formulation, comprehensive simulation experiments are performed to analyze the stopping criterion of the iterative joint-parameter-Bayes method. Finally, given the data, an optimal reconstruction is obtained without any freely adjustable hyperparameter by satisfying the PDF condition for both the data likelihood and the prior probability, and by satisfying the stopping criterion. Moreover, the stability of joint-parameter-Bayes is investigated through factors such as initialization, the PDF specification, and renormalization in an iterative manner. Both phantom simulation and clinical patient data results show that joint-parameter-Bayes can provide comparable reconstructed image quality compared to the conventional methods, but with much less reconstruction time. To see the response of the algorithm to different types of noise, three common noise models are introduced to the simulation data, including white Gaussian noise to post-log sinogram data, Poisson-like signal-dependent noise to post-log sinogram data and Poisson noise to the pre-log transmission data. The experimental outcomes of the white Gaussian noise reveal that the two parameters estimated by the joint-parameter-Bayes method agree well with simulations. It is observed that the parameter introduced to satisfy the prior's PDF is more sensitive to stopping the iteration process for all three noise models. A stability investigation showed that the initial image by filtered back projection is very robust. Clinical patient data demonstrated the effectiveness of the proposed joint-parameter-Bayes and stopping criterion.

OPK_SNCA: Optimized prior knowledge via sparse non-convex approach for cone-beam X-ray luminescence computed tomography imaging

BACKGROUND

The development of Cone-beam X-ray luminescence computed tomography (CB-XLCT) has allowed the quantitative in-depth biological imaging, but with a greatly ill-posed and ill-conditioned inverse problem. Although the predefined permissible source region (PSR) is a widely used way to alleviate the problem for CB-XLCT imaging, how to obtain the accurate PSR is still a challenge for the process of inverse reconstruction.

METHODS

We proposed an optimized prior knowledge via a sparse non-convex approach (OPK_SNCA) for CB-XLCT imaging. Firstly, non-convex L_p-norm optimization model was employed for copying with the inverse problem, and an iteratively reweighted split augmented lagrangian shrinkage algorithm was developed to obtain a group of sparse solutions based on different non-convex p values. Secondly, a series of permissible regions (PRs) with different discretized mesh was further achieved, and the intersection operation was implemented on the group of PRs to get a reasonable PSR. After that, the final PSR was adopted as an optimized prior knowledge to enhance the reconstruction quality of inverse reconstruction.

RESULTS

Both simulation experiments and in vivo experiment were performed to evaluate the efficiency and robustness of the proposed method.

CONCLUSIONS

The experimental results demonstrated that our proposed method could significantly improve the imaging quality of the distribution of X-ray-excitable nanophosphors for CB-XLCT.

A robust elastic net-ℓ1ℓ2reconstruction method for x-ray luminescence computed tomography

Objective. X-ray luminescence computed tomography (XLCT) has played a crucial role in pre-clinical research and effective diagnosis of disease. However, due to the ill-posed of the XLCT inverse problem, the generalization of reconstruction methods and the selection of appropriate regularization parameters are still challenging in practical applications. In this research, an robust Elastic net-ℓ₁ℓ₂reconstruction method is proposed aiming to the challenge.Approach. Firstly, our approach consists of ℓ₁and ℓ₂regularization to enhance the sparsity and suppress the smoothness. Secondly, through optimal approximation of the optimization problem, double modification of Landweber algorithm is adopted to solve the Elastic net-ℓ₁ℓ₂regulazation. Thirdly, drawing on the ideal of supervised learning, multi-parameter K-fold cross validation strategy is proposed to determin the optimal parameters adaptively.Main results. To evaluate the performance of the Elastic net-ℓ₁ℓ₂method, numerical simulations, phantom and in vivo experiments were conducted. In these experiments, the Elastic net-ℓ₁ℓ₂method achieved the minimum reconstruction error (with smallest location error, fluorescent yield relative error, normalized root-mean-square error) and the best image reconstruction quality (with largest contrast-to-noise ratio and Dice similarity) among all methods. The results demonstrated that Elastic net-ℓ₁ℓ₂can obtain superior reconstruction performance in terms of location accuracy, dual source resolution, robustness and in vivo practicability.Significance. It is believed that this study will further benefit preclinical applications with a view to provide a more reliable reference for the later researches on XLCT.

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.

High-speed X-ray-induced luminescence computed tomography

X-ray-induced luminescence computed tomography (XLCT) is an emerging molecular imaging. Challenges in improving spatial resolution and reducing the scan time in a whole-body field of view (FOV) still remain for practical in vivo applications. In this study, we present a novel XLCT technique capable of obtaining three-dimensional (3D) images from a single snapshot. Specifically, a customed two-planar-mirror component is integrated into a cone beam XLCT imaging system to obtain multiple optical views of an object simultaneously. Furthermore, a compressive sensing based algorithm is adopted to improve the efficiency of 3D XLCT image reconstruction. Numerical simulations and experiments were conducted to validate the single snapshot X-ray-induced luminescence computed tomography (SS-XLCT). The results show that the 3D distribution of the nanophosphor targets can be visualized much faster than conventional cone beam XLCT imaging method that was used in our comparisons while maintaining comparable spatial resolution as in conventional XLCT imaging. SS-XLCT has the potential to harness the power of XLCT for rapid whole-body in vivo molecular imaging of small animals.

Investigation of a simple coded-aperture based multi-narrow beam x-ray luminescence computed tomography system

The purpose of this paper is to introduce and study a multi-narrow beam X-ray Luminescence Computed Tomography (XLCT) system based on a simple coded aperture. The proposed XLCT system is studied through simulations of x rays and diffuse light propagation and the implementation of the multi-narrow beam XLCT reconstruction algorithm. The relationship between the reconstructed quality of the XLCT image and the pass-element distribution of the coded aperture mask is investigated. The coded aperture that produces the best image quality metrics for the numerical phantom is selected for the XLCT system. The effects of detection positions and the number of projection angles are also investigated for considering the scanning efficiency and system structural complexity. The results demonstrate that the proposed multi-narrow beam XLCT system is competent in resolving targets with high complexity when comparing with the coded aperture compressed sensing XLCT system based on a complicated mask. It can also offer an enhancement in scanning efficiency in comparison with the conventional multi-narrow beam XLCT system.

Restarted primal-dual Newton conjugate gradient method for enhanced spatial resolution of reconstructed cone-beam x-ray luminescence computed tomography images

Cone-beam x-ray luminescence computed tomography (CB-XLCT) has been proposed as a promising imaging tool, which enables three-dimensional imaging of the distribution of nanophosphors (NPs) in small animals. However, the reconstruction performance is usually unsatisfactory in terms of spatial resolution due to the ill-posedness of the CB-XLCT inverse problem. To alleviate this problem and to achieve high spatial resolution, a reconstruction method consisting of inner and outer iterations based on a restarted strategy is proposed. In this method, the primal-dual Newton conjugate gradient method (pdNCG) is adopted in the inner iterations to get fast reconstruction, which is used for resetting the permission region and increasing the convergence speed of the outer iteration. To assess the performance of the method, both numerical simulation and physical phantom experiments were conducted with a CB-XLCT system. The results demonstrate that compared with conventional reconstruction methods, the proposed re-pdNCG method can accurately and efficiently resolve the adjacent NPs with the least relative error.

Adaptive shrinking reconstruction framework for cone-beam X-ray luminescence computed tomography

Cone-beam X-ray luminescence computed tomography (CB-XLCT) emerged as a novel hybrid technique for early detection of small tumors in vivo. However, severe ill-posedness is still a challenge for CB-XLCT imaging. In this study, an adaptive shrinking reconstruction framework without a prior information is proposed for CB-XLCT. In reconstruction processing, the mesh nodes are automatically selected with higher probability to contribute to the distribution of target for imaging. Specially, an adaptive shrinking function is designed to automatically control the permissible source region at a multi-scale rate. Both 3D digital mouse and in vivo experiments were carried out to test the performance of our method. The results indicate that the proposed framework can dramatically improve the imaging quality of CB-XLCT.

Principal Component Analysis Based Dynamic Cone Beam X-Ray Luminescence Computed Tomography: A Feasibility Study

Cone beam X-ray luminescence computed tomography (CB-XLCT) is a promising imaging technique in studying the physiological and pathological processes in small animals. However, the dynamic bio-distributions of probes in small animal, especially in adjacent targets are still hard to be captured directly from dynamic CB-XLCT. In this paper, a 4D temporal-spatial reconstruction method based on principal component analysis (PCA) in the projection space is proposed for dynamic CB-XLCT. First, projections of angles in each 3D frame are compressed to reduce the noises initially. Then a temporal PCA is performed on the projection data to decorrelate the 4D problem into separate 3D problems in the PCA domain. In the PCA domain, the difference between dynamic behaviors of multiple targets can be reflected by the first several principal components which can be further used for fast and improved reconstruction by a restarted Tikhonov regularization method. At last, by discarding the principal components mainly reflecting noise, the concentration series of targets are recovered from the first few reconstruction results with a mask as the constraint. The numerical simulation and phantom experiment demonstrate that the proposed method can resolve multiple targets and recover the dynamic distributions with high computation efficiency. The proposed method provides new feasibility for imaging dynamic bio-distributions of probes in vivo.

Improved Block Sparse Bayesian Learning Method Using K-Nearest Neighbor Strategy for Accurate Tumor Morphology Reconstruction in Bioluminescence Tomography

OBJECTIVE

Bioluminescence tomography (BLT) is a non-invasive technique designed to enable three-dimensional (3D) visualization and quantification of viable tumor cells in living organisms. However, despite the excellent sensitivity and specificity of bioluminescence imaging (BLI), BLT is limited by the photon scattering effect and ill-posed inverse problem. If the complete structural information of a light source is considered when solving the inverse problem, reconstruction accuracy will be improved.

METHODS

This article proposed a block sparse Bayesian learning method based on K-nearest neighbor strategy (KNN-BSBL), which incorporated several types of a priori information including sparsity, spatial correlations among neighboring points, and anatomical information to balance over-sparsity and morphology preservation in BLT. Furthermore, we considered the Gaussian weighted distance prior in a light source and proposed a KNN-GBSBL method to further improve the performance of KNN-BSBL.

RESULTS

The results of numerical simulations and in vivo glioma-bearing mouse experiments demonstrated that KNN-BSBL and KNN-GBSBL achieved superior accuracy for tumor spatial positioning and morphology reconstruction.

CONCLUSION

The proposed method KNN-BSBL incorporated several types of a priori information is an efficient and robust reconstruction method for BLT.

Feasibility study of three-dimensional multiple-beam x-ray luminescence tomography

X-ray luminescence tomography (XLT) is a promising imaging technology based on x-ray beams, with high-resolution capability. We developed a fan-beam XLT system, where the x-ray beam scans the object at predefined directions and positions. As the scanning at one position needs to cover the object, the data acquisition time is usually long. To improve spatial resolution, we propose a three-dimensional multiple-beam x-ray luminescence imaging method, in which the x rays are modulated by an x-ray fence-modulation component. The proposed method can produce multiple x-ray beams and ensure spatial resolution along the longitudinal direction as well as the transverse plane. The proposed methods of single-source experiments can achieve 0.62 mm in location error and 0.87 in the dice coefficient while 1.32 mm in location error and 0.63 in the dice coefficient in the double-source experiment. The simulation experiments show that our proposed method can achieve better results at different depths than the traditional scanning method. It is also demonstrated that the best simulation results can be achieved with the smallest x-ray width.

Method for improving the spatial resolution of narrow x-ray beam-based x-ray luminescence computed tomography imaging

X-ray luminescence computed tomography (XLCT) is an emerging hybrid imaging modality which has the potential for achieving both high sensitivity and spatial resolution simultaneously. For the narrow x-ray beam-based XLCT imaging, based on previous work, a spatial resolution of about double the x-ray beam size can be achieved using a translate/rotate scanning scheme, taking step sizes equal to the x-ray beam width. To break the current spatial resolution limit, we propose a scanning strategy achieved by reducing the scanning step size to be smaller than the x-ray beam size. We performed four sets of numerical simulations and a phantom experiment using cylindrical phantoms and have demonstrated that our proposed scanning method can greatly improve the XLCT-reconstructed image quality compared with the traditional scanning approach. In our simulations, by using a fixed x-ray beam size of 0.8 mm, we were able to successfully reconstruct six embedded targets as small as 0.5 mm in diameter and with the same edge-to-edge distances by using a scanning step as small as 0.2 mm which is a 1.6 times improvement in the spatial resolution compared with the traditional approach. Lastly, the phantom experiment further demonstrated the efficacy of our proposed method in improving the XLCT image quality, with all image quality metrics improving as the step size decreased.

Single-view cone-beam x-ray luminescence optical tomography based on Group_YALL1 method

Single-view cone beam x-ray luminescence optical tomography (CB-XLOT) has the merit of short data acquisition time, which is important for resolving fast biological processes in vivo. However, challenges remain in the reconstruction of single-view CB-XLOT. In our previous work, by using the sparsity-based reconstruction method, we have demonstrated the feasibility of single-view CB-XLOT. But, when the imaging conditions become complicated (e.g. multiple adjacent nanophosphors (NPs) contained in imaged object), it is difficult to resolve each NP by the previous method. To solve the problem, we hereby present a sparsity reconstruction method based on group information, termed Group_YALL1. The imaging performance of single-view CB-XLOT can be further improved by utilizing the group sparsity characteristic of NPs as a priori knowledge of reconstruction constraint. To assess the capability of the method, we used a customized CB-XLOT/XCT system to perform the numerical simulation and physical phantom experiments. The experimental results demonstrate that compared with the former sparse reconstruction method (e.g. YALL1), the proposed Group_YALL1 method can accurately resolve the NPs embedded in the object, even if they are close to each other. The acquired location error is less than 1 mm. Hence, this method has the potential to greatly reduce the data acquisition time while preserving a high imaging quality.

Focused x-ray luminescence computed tomography: experimental studies

X-ray luminescence computed tomography (XLCT) is an emerging hybrid molecular imaging modality and has shown great promises in overcoming the strong optical scattering in deep tissues. Though the narrow x-ray beam based XLCT imaging has been demonstrated to obtain high spatial resolution at depth, it suffers from a relatively long measurement time, hindering its practical applications. Recently, we have designed a focused x-ray beam based XLCT imaging system and have successfully performed imaging in about 7.5 seconds per section for a mouse sized object. However, its high spatial resolution capacity has not been fully implemented yet. In this paper, with a superfine focused x-ray beam we design a focused-x-ray luminescence tomography (FXLT) system for spatial resolution up to 94 μm. First, we have described our design in details. Then, we estimate the performance of the designed FXLT imaging system. Lastly, we have found that the spatial resolution of FXLT can be further improved by reducing the scan step size, which has been demonstrated by numerical simulations.

Functionalization of [Re6Q8(CN)6]4− clusters by methylation of cyanide ligands

Methylation of anionic cluster complexes [Re₆Q₈(CN)₆]⁴⁻ with ((CH₃)₃O)BF₄ or CF₃SO₃CH₃ afforded homoleptic isonitrile cluster complexes [Re₆Q₈(CH₃NC)₆]²⁺ (Q = S, Se, Te).

Regularized reconstruction based on joint L1 and total variation for sparse-view cone-beam X-ray luminescence computed tomography

As an emerging hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been proposed based on the development of X-ray excitable nanoparticles. Owing to the high degree of absorption and scattering of light through tissues, the CB-XLCT inverse problem is inherently ill-conditioned. Appropriate priors or regularizations are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, the goal of CB-XLCT reconstruction is to get the distributions of nanophosphors in the imaging object. Considering that the distributions of nanophosphors inside bodies preferentially accumulate in specific areas of interest, the reconstruction of XLCT images is usually sparse with some locally smoothed high-intensity regions. Therefore, a combination of the L₁ and total variation regularization is designed to improve the imaging quality of CB-XLCT in this study. The L₁ regularization is used for enforcing the sparsity of the reconstructed images and the total variation regularization is used for maintaining the local smoothness of the reconstructed image. The implementation of this method can be divided into two parts. First, the reconstruction image was reconstructed based on the fast iterative shrinkage-thresholding (FISTA) algorithm, then the reconstruction image was minimized by the gradient descent method. Numerical simulations and phantom experiments indicate that compared with the traditional ART, ADAPTIK and FISTA methods, the proposed method demonstrates its advantage in improving spatial resolution and reducing imaging time.

Recent methodology advances in fluorescence molecular tomography

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.

Sparse view cone beam X-ray luminescence tomography based on truncated singular value decomposition

Cone beam X-ray luminescence computed tomography (CB-XLCT) has been proposed as a promising hybrid imaging technique. Though it has the advantage of fast imaging, the inverse problem of CB-XLCT is seriously ill-conditioned, making the image quality quite poor, especially for imaging multi-targets. To achieve fast imaging of multi-targets, which is essential for in vivo applications, a truncated singular value decomposition (TSVD) based sparse view CB-XLCT reconstruction method is proposed in this study. With the weight matrix of the CB-XLCT system being converted to orthogonal by TSVD, the compressed sensing (CS) based L₁-norm method could be applied for fast reconstruction from fewer projection views. Numerical simulations and phantom experiments demonstrate that by using the proposed method, two targets with different edge-to-edge distances (EEDs) could be resolved effectively. It indicates that the proposed method could improve the imaging quality of multi-targets significantly in terms of localization accuracy, target shape, image contrast, and spatial resolution, when compared with conventional methods.

Gamma rays excited radioluminescence tomographic imaging

Background

Radionuclide-excited luminescence imaging is an optical radionuclide imaging strategy to reveal the distributions of radioluminescent nanophosphors (RLNPs) inside small animals, which uses radioluminescence emitted from RLNPs when excited by high energy rays such as gamma rays generated during the decay of radiotracers used in clinical nuclear medicine imaging. Currently, there is no report of tomographic imaging based on radioluminescence.

Methods

In this paper, we proposed a gamma rays excited radioluminescence tomography (GRLT) to reveal three-dimensional distributions of RLNPs inside a small animal using radioluminescence through image reconstruction from surface measurements of radioluminescent photons using an inverse algorithm. The diffusion equation was employed to model propagations of radioluminescent photons in biological tissues with highly scattering and low absorption characteristics.

Results

Phantom and artificial source-implanted mouse model experiments were employed to test the feasibility of GRLT, and the results demonstrated that the ability of GRLT to reveal the distribution of RLNPs such as Gd₂O₂S:Tb using the radioluminescent signals when excited by gamma rays produced from ^99mTc.

Conclusions

With the emerging of targeted RLNPs, GRLT can provide new possibilities for in vivo and noninvasive examination of biological processes at cellular levels. Especially, combining with Cerenkov luminescence imaging, GRLT can achieve dual molecular information of RLNPs and nuclides using single optical imaging technology.

Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage

With the advances of x-ray excitable nanophosphors, x-ray luminescence computed tomography (XLCT) has become a promising hybrid imaging modality. In particular, a cone-beam XLCT (CB-XLCT) system has demonstrated its potential in in vivo imaging with the advantage of fast imaging speed over other XLCT systems. Currently, the imaging models of most XLCT systems assume that nanophosphors emit light based on the intensity distribution of x-ray within the object, not completely reflecting the nature of the x-ray excitation process. To improve the imaging quality of CB-XLCT, an imaging model that adopts an excitation model of nanophosphors based on x-ray absorption dosage is proposed in this study. To solve the ill-posed inverse problem, a reconstruction algorithm that combines the adaptive Tikhonov regularization method with the imaging model is implemented for CB-XLCT reconstruction. Numerical simulations and phantom experiments indicate that compared with the traditional forward model based on x-ray intensity, the proposed dose-based model could improve the image quality of CB-XLCT significantly in terms of target shape, localization accuracy, and image contrast. In addition, the proposed model behaves better in distinguishing closer targets, demonstrating its advantage in improving spatial resolution.

Generalized Adaptive Gaussian Markov Random Field for X-Ray Luminescence Computed Tomography

OBJECTIVE

X-ray luminescence computed tomography (XLCT) is an emerging and promising modality, but suffers from inferior reconstructions and smoothed target shapes. This work aims to improve the image quality with new mathematical framework.

METHODS

We present a Bayesian local regularization framework to tackle the ill-conditioness of XLCT. Different from traditional overall regularization strategies, the proposed method utilizes correlations of neighboring voxels to regularize the solution locally based on generalized adaptive Gaussian Markov random field (GAGMRF), and provides an adjustable parameter to facilitate the edge-preserving property.

RESULTS

Numerical simulations and phantom experiments show that the GAGMRF method yields both high image quality and accurate target shapes.

CONCLUSION

Compared to conventional L2 and L1 regularizations, GAGMRF provides a new and efficient model for high quality imaging based on the Bayesian framework.

SIGNIFICANCE

The GAGMRF method offers a flexible regularization framework to adapt to a wide range of biomedical applications.

Sub-10 nm Water-Dispersible β-NaGdF4:X% Eu3+ Nanoparticles with Enhanced Biocompatibility for in Vivo X-ray Luminescence Computed Tomography

As a novel molecular and functional imaging modality, X-ray luminescence computed tomography (XLCT) has shown its potentials in biomedical and preclinic applications. However, there are still some limitations of X-ray-excited luminescent materials, such as low luminescence efficiency, poor biocompatibility, and cytotoxicity, making in vivo XLCT imaging quite challenging. In this study, for the very first time, we present on using sub-10 nm β-NaGdF₄:X% Eu³⁺ nanoparticles with poly(acrylic acid) (PAA) surface modification, which demonstrate outstanding luminescence efficiency, uniform size distribution, water dispersity, and biosafety, as the luminescent probes for in vivo XLCT application. The pure hexagonal phase (β-) NaGdF₄ has been successfully synthesized and characterized by X-ray powder diffraction (XRD) and transmission electron microscopy (TEM), and then the results of X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray spectrometry  (EDX), and elemental mapping further confirm Eu³⁺ ions doped into NaGdF₄ host. Under X-ray excitation, the β-NaGdF₄ nanoparticles with a doping level of 15% Eu³⁺ exhibited the most efficient luminescence intensity. Notably, the doping level of Eu³⁺ has no effect on the crystal phase and morphology of the NaGdF₄-based host. Afterward, β-NaGdF₄:15% Eu³⁺ nanoparticles were modified with PAA to enhance the water dispersity and biocompatibility. The compatibility of in vivo XLCT imaging using such nanoparticles was systematically studied via in vitro cytotoxicity, physical phantom, and in vivo imaging experiments. The ultralow cytotoxicity of PAA-modified nanoparticles, which is confirmed by over 80% cell viability of SH-SY5Y cells when treated by high nanoparticle concentration of 200 μg/mL, overcome the major obstacle for in vivo application. In addition, the high luminescence intensity of PAA-modified nanoparticles enables the location error of in vivo XLCT imaging less than 2 mm, which is comparable to that using commercially available bulk material Y₂O₃:15% Eu³⁺. The proposed nanoparticles promote XLCT research into an in vivo stage. Further modification of these nanoparticles with biofunctional molecules could enable the potential of targeting XLCT imaging.

Sensitivity evaluation and selective plane imaging geometry for x-ray-induced luminescence imaging

PURPOSE

X-ray-induced luminescence (XIL) is a hybrid x-ray/optical imaging modality that employs nanophosphors that luminescence in response to x-ray irradiation. X-ray-activated phosphorescent nanoparticles have potential applications in radiation therapy as theranostics, nanodosimeters, or radiosensitizers. Extracting clinically relevant information from the luminescent signal requires the development of a robust imaging model that can determine nanophosphor distributions at depth in an optically scattering environment from surface radiance measurements. The applications of XIL in radiotherapy will be limited by the dose-dependent sensitivity at depth in tissue. We propose a novel geometry called selective plane XIL (SPXIL), and apply it to experimental measurements in optical gel phantoms and sensitivity simulations.

METHODS

An imaging model is presented based on the selective plane geometry which can determine the detected diffuse optical signal for a given x-ray dose and nanophosphor distribution at depth in a semi-infinite, optically homogenous material. The surface radiance in the model is calculated using an analytical solution to the extrapolated boundary condition. Y₂ O₃ :Eu³⁺ nanoparticles are synthesized and inserted into various optical phantom in order to measure the luminescent output per unit dose for a given concentration of nanophosphors and calibrate an imaging model for XIL sensitivity simulations. SPXIL imaging with a dual-source optical gel phantom is performed, and an iterative Richardson-Lucy deconvolution using a shifted Poisson noise model is applied to the measurements in order to reconstruct the nanophosphor distribution.

RESULTS

Nanophosphor characterizations showed a peak emission at 611 nm, a linear luminescent response to tube current and nanoparticle concentration, and a quadratic luminescent response to tube voltage. The luminescent efficiency calculation accomplished with calibrated bioluminescence mouse phantoms determines 1.06 photons were emitted per keV of x-ray radiation absorbed per g/mL of nanophosphor concentration. Sensitivity simulations determined that XIL could detect a concentration of 1 mg/mL of nanophosphors with a dose of 1 cGy at a depth ranging from 2 to 4 cm, depending on the optical parameters of the homogeneous diffuse optical environment. The deconvolution applied to the SPXIL measurements could resolve two sources 1 cm apart up to a depth of 1.75 cm in the diffuse phantom.

CONCLUSIONS

We present a novel imaging geometry for XIL in a homogenous, diffuse optical environment. Basic characterization of Y₂ O₃ :Eu³⁺ nanophosphors are presented along with XIL/SPXIL measurements in optical gel phantoms. The diffuse optical imaging model is validated using these measurements and then calibrated in order to execute initial sensitivity simulations for the dose-depth limitations of XIL imaging. The SPXIL imaging model is used to perform a deconvolution on a dual-source phantom, which successfully reconstructs the nanophosphor distributions.

Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography

Cone-beam X-ray luminescence computed tomography (CB-XLCT) has been proposed as a new molecular imaging modality recently. It can obtain both anatomical and functional tomographic images of an object efficiently, with the excitation of nanophosphors in vivo or in vitro by cone-beam X-rays. However, the ill-posedness of the CB-XLCT inverse problem degrades the image quality and makes it difficult to resolve adjacent luminescent targets with different concentrations, which is essential in the monitoring of nanoparticle metabolism and drug delivery. To address this problem, a multi-voltage excitation imaging scheme combined with principal component analysis is proposed in this study. Imaging experiments performed on physical phantoms by a custom-made CB-XLCT system demonstrate that two adjacent targets, with different concentrations and an edge-to-edge distance of 0 mm, can be effectively resolved.

Sensitivity study of x-ray luminescence computed tomography

X-ray luminescence computed tomography (XLCT) is a hybrid molecular imaging modality that combines the merits of both x-ray imaging (high resolution) and optical imaging (high sensitivity). In this study, we have evaluated the sensitivity of XLCT with phantom experiments by scanning targets of different phosphor concentrations at different depths. We found that XLCT is capable of imaging targets of very low concentrations (27.6 μM or 0.01 mg/mL) at significant depths, such as 21 mm. Our results demonstrate that there is little variation in the reconstructed target size with a maximum target size error of 4.35% for different imaging depths for XLCT. We have, we believe for the first time, compared the sensitivity of XLCT with that of traditional computed tomography (CT) for phosphor targets. We found that XLCT's use of x-ray-induced photons provides much higher measurement sensitivity and contrast compared to CT, which provides image contrast solely based on x-ray attenuation.

A comparative study of optical properties and X-ray induced luminescence of octahedral molybdenum and tungsten cluster complexes

Octahedral W cluster complexes have more intensive X-ray excited optical luminescence than Mo ones.