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Zhang J, Zhang G, Chen Y, Li K, Zhao F, Yi H, Su L, Cao X. Regularized reconstruction based on joint smoothly clipped absolute deviation regularization and graph manifold learning for fluorescence molecular tomography. Phys Med Biol 2023; 68:195004. [PMID: 37647921 DOI: 10.1088/1361-6560/acf55a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 08/30/2023] [Indexed: 09/01/2023]
Abstract
Objective.Fluorescence molecular tomography (FMT) is an optical imaging modality that provides high sensitivity and low cost, which can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labeled probe noninvasively. In the field of preclinical cancer diagnosis and treatment, FMT has gained significant traction. Nonetheless, the current FMT reconstruction results suffer from unsatisfactory morphology and location accuracy of the fluorescence distribution, primarily due to the light scattering effect and the ill-posed nature of the inverse problem.Approach.To address these challenges, a regularized reconstruction method based on joint smoothly clipped absolute deviation regularization and graph manifold learning (SCAD-GML) for FMT is presented in this paper. The SCAD-GML approach combines the sparsity of the fluorescent sources with the latent manifold structure of fluorescent source distribution to achieve more accurate and sparse reconstruction results. To obtain the reconstruction results efficiently, the non-convex gradient descent iterative method is employed to solve the established objective function. To assess the performance of the proposed SCAD-GML method, a comprehensive evaluation is conducted through numerical simulation experiments as well asin vivoexperiments.Main results.The results demonstrate that the SCAD-GML method outperforms other methods in terms of both location and shape recovery of fluorescence biomarkers distribution.Siginificance.These findings indicate that the SCAD-GML method has the potential to advance the application of FMT inin vivobiological research.
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Affiliation(s)
- Jun Zhang
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Gege Zhang
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Yi Chen
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Kang Li
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Fengjun Zhao
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
| | - Huangjian Yi
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
| | - Linzhi Su
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
| | - Xin Cao
- School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- National and Local Joint Engineering Research Center for Cultural Heritage Digitization, Xi'an, Shaanxi 710127, People's Republic of China
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Yi H, Ma S, Yang R, Zhang L, Guo H, He X, Hou Y. Adaptive Sparsity Orthogonal Least Square with Neighbor Strategy for Fluorescence Molecular Tomography. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023; 2023:1-4. [PMID: 38083170 DOI: 10.1109/embc40787.2023.10340086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2023]
Abstract
Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive optical imaging technique which has been widely applied to disease diagnosis and drug discovery. However, FMT reconstruction is a highly ill-posed problem. In this work, L0-norm regularization is employed to construct the mathematical model of the inverse problem of FMT. And an adaptive sparsity orthogonal least square with a neighbor strategy (ASOLS-NS) is proposed to solve this model. This algorithm can provide an adaptive sparsity and can establish the candidate sets by a novel neighbor expansion strategy for the orthogonal least square (OLS) algorithm. Numerical simulation experiments have shown that the ASOLS-NS improves the reconstruction of images, especially for the double targets reconstruction.Clinical relevance- The purpose of this work is to improve the reconstruction results of FMT. Current experiments are focused on simulation experiments, and the proposed algorithm will be applied to the clinical tumor detection in the future.
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Chen Y, Du M, Zhang J, Zhang G, Su L, Li K, Zhao F, Yi H, Wang L, Cao X. Generalized conditional gradient method with adaptive regularization parameters for fluorescence molecular tomography. OPTICS EXPRESS 2023; 31:18128-18146. [PMID: 37381530 DOI: 10.1364/oe.486339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/08/2023] [Indexed: 06/30/2023]
Abstract
Fluorescence molecular tomography (FMT) is an optical imaging technology with the ability of visualizing the three-dimensional distribution of fluorescently labelled probes in vivo. However, due to the light scattering effect and ill-posed inverse problems, obtaining satisfactory FMT reconstruction is still a challenging problem. In this work, to improve the performance of FMT reconstruction, we proposed a generalized conditional gradient method with adaptive regularization parameters (GCGM-ARP). In order to make a tradeoff between the sparsity and shape preservation of the reconstruction source, and to maintain its robustness, elastic-net (EN) regularization is introduced. EN regularization combines the advantages of L1-norm and L2-norm, and overcomes the shortcomings of traditional Lp-norm regularization, such as over-sparsity, over-smoothness, and non-robustness. Thus, the equivalent optimization formulation of the original problem can be obtained. To further improve the performance of the reconstruction, the L-curve is adopted to adaptively adjust the regularization parameters. Then, the generalized conditional gradient method (GCGM) is used to split the minimization problem based on EN regularization into two simpler sub-problems, which are determining the direction of the gradient and the step size. These sub-problems are addressed efficiently to obtain more sparse solutions. To assess the performance of our proposed method, a series of numerical simulation experiments and in vivo experiments were implemented. The experimental results show that, compared with other mathematical reconstruction methods, GCGM-ARP method has the minimum location error (LE) and relative intensity error (RIE), and the maximum dice coefficient (Dice) in the case of different sources number or shape, or Gaussian noise of 5%-25%. This indicates that GCGM-ARP has superior reconstruction performance in source localization, dual-source resolution, morphology recovery, and robustness. In conclusion, the proposed GCGM-ARP is an effective and robust strategy for FMT reconstruction in biomedical application.
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An Y, Wang H, Li J, Li G, Ma X, Du Y, Tian J. Reconstruction based on adaptive group least angle regression for fluorescence molecular tomography. BIOMEDICAL OPTICS EXPRESS 2023; 14:2225-2239. [PMID: 37206151 PMCID: PMC10191665 DOI: 10.1364/boe.486451] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Revised: 03/17/2023] [Accepted: 03/27/2023] [Indexed: 05/21/2023]
Abstract
Fluorescence molecular tomography can combine two-dimensional fluorescence imaging with anatomical information to reconstruct three-dimensional images of tumors. Reconstruction based on traditional regularization with tumor sparsity priors does not take into account that tumor cells form clusters, so it performs poorly when multiple light sources are used. Here we describe reconstruction based on an "adaptive group least angle regression elastic net" (AGLEN) method, in which local spatial structure correlation and group sparsity are integrated with elastic net regularization, followed by least angle regression. The AGLEN method works iteratively using the residual vector and a median smoothing strategy in order to adaptively obtain a robust local optimum. The method was verified using numerical simulations as well as imaging of mice bearing liver or melanoma tumors. AGLEN reconstruction performed better than state-of-the-art methods with different sizes of light sources at different distances from the sample and in the presence of Gaussian noise at 5-25%. In addition, AGLEN-based reconstruction accurately imaged tumor expression of cell death ligand-1, which can guide immunotherapy.
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Affiliation(s)
- Yu An
- the Key Laboratory of Big Data-Based Precision Medicine (Beihang University), Ministry of Industry and Information Technology of the People's Republic of China, School of Engineering Medicine, Beihang University, Beijing, 100191, China
| | - Hanfan Wang
- the CAS Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jiaqian Li
- the Key Laboratory of Big Data-Based Precision Medicine (Beihang University), Ministry of Industry and Information Technology of the People's Republic of China, School of Engineering Medicine, Beihang University, Beijing, 100191, China
| | - Guanghui Li
- the Key Laboratory of Big Data-Based Precision Medicine (Beihang University), Ministry of Industry and Information Technology of the People's Republic of China, School of Engineering Medicine, Beihang University, Beijing, 100191, China
| | - Xiaopeng Ma
- School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
| | - Yang Du
- the CAS Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jie Tian
- the Key Laboratory of Big Data-Based Precision Medicine (Beihang University), Ministry of Industry and Information Technology of the People's Republic of China, School of Engineering Medicine, Beihang University, Beijing, 100191, China
- the CAS Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
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Li J, Zhang L, Liu J, Zhang D, Kang D, Wang B, He X, Zhang H, Zhao Y, Guo H, Hou Y. An adaptive parameter selection strategy based on maximizing the probability of data for robust fluorescence molecular tomography reconstruction. JOURNAL OF BIOPHOTONICS 2023:e202300031. [PMID: 37074336 DOI: 10.1002/jbio.202300031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 03/20/2023] [Accepted: 04/14/2023] [Indexed: 05/03/2023]
Abstract
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.
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Affiliation(s)
- Jintao Li
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Lizhi Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Jia Liu
- Xi'an Company of Shaanxi Tobacco Company, The Information Center, Xi'an, China
| | - Diya Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Dizhen Kang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Beilei Wang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Xiaowei He
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Heng Zhang
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Yizhe Zhao
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Hongbo Guo
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Yuqing Hou
- The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China
- School of Information Sciences and Technology, Northwest University, Xi'an, China
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Cao C, Xiao A, Cai M, Shen B, Guo L, Shi X, Tian J, Hu Z. Excitation-based fully connected network for precise NIR-II fluorescence molecular tomography. BIOMEDICAL OPTICS EXPRESS 2022; 13:6284-6299. [PMID: 36589575 PMCID: PMC9774866 DOI: 10.1364/boe.474982] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Revised: 10/26/2022] [Accepted: 10/30/2022] [Indexed: 06/17/2023]
Abstract
Fluorescence molecular tomography (FMT) is a novel imaging modality to obtain fluorescence biomarkers' three-dimensional (3D) distribution. However, the simplified mathematical model and complicated inverse problem limit it to achieving precise results. In this study, the second near-infrared (NIR-II) fluorescence imaging was adopted to mitigate tissue scattering and reduce noise interference. An excitation-based fully connected network was proposed to model the inverse process of NIR-II photon propagation and directly obtain the 3D distribution of the light source. An excitation block was embedded in the network allowing it to autonomously pay more attention to neurons related to the light source. The barycenter error was added to the loss function to improve the localization accuracy of the light source. Both numerical simulation and in vivo experiments showed the superiority of the novel NIR-II FMT reconstruction strategy over the baseline methods. This strategy was expected to facilitate the application of machine learning in biomedical research.
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Affiliation(s)
- Caiguang Cao
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
- These authors contributed equally
| | - Anqi Xiao
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
- These authors contributed equally
| | - Meishan Cai
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
| | - Biluo Shen
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
| | - Lishuang Guo
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, School of Engineering Medicine, Beihang University, Beijing, China
| | - Xiaojing Shi
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
| | - Jie Tian
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
- Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, School of Engineering Medicine, Beihang University, Beijing, China
- Engineering Research Center of Molecular and Neuro Imaging of Ministry of Education, School of Life Science and Technology, Xidian University, Xi'an, China
| | - Zhenhua Hu
- CAS Key Laboratory of Molecular Imaging, Beijing Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
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An Y, Bian C, Yan D, Wang H, Wang Y, Du Y, Tian J. A Fast and Automated FMT/XCT Reconstruction Strategy Based on Standardized Imaging Space. IEEE TRANSACTIONS ON MEDICAL IMAGING 2022; 41:657-666. [PMID: 34648436 DOI: 10.1109/tmi.2021.3120011] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The traditional finite element method-based fluorescence molecular tomography (FMT)/ X-ray computed tomography (XCT) imaging reconstruction suffers from complicated mesh generation and dual-modality image data fusion, which limits the application of in vivo imaging. To solve this problem, a novel standardized imaging space reconstruction (SISR) method for the quantitative determination of fluorescent probe distributions inside small animals was developed. In conjunction with a standardized dual-modality image data fusion technology, and novel reconstruction strategy based on Laplace regularization and L1-fused Lasso method, the in vivo distribution can be calculated rapidly and accurately, which enables standardized and algorithm-driven data process. We demonstrated the method's feasibility through numerical simulations and quantitatively monitored in vivo programmed death ligand 1 (PD-L1) expression in mouse tumor xenografts, and the results demonstrate that our proposed SISR can increase data throughput and reproducibility, which helps to realize the dynamically and accurately in vivo imaging.
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Liu Y, Hu X, Chu M, Guo H, Yu J, He X. A Finite Element Mesh Regrouping Strategy-Based Hybrid Light Transport Model for Enhancing the Efficiency and Accuracy of XLCT. Front Oncol 2022; 11:751139. [PMID: 35111664 PMCID: PMC8801618 DOI: 10.3389/fonc.2021.751139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 12/10/2021] [Indexed: 11/19/2022] Open
Abstract
X-ray luminescence computed tomography (XLCT) is an emerging hybrid imaging modality in optical molecular imaging, which has attracted more attention and has been widely studied. In XLCT, the accuracy and operational efficiency of an optical transmission model play a decisive role in the rapid and accurate reconstruction of light sources. For simulation of optical transmission characteristics in XLCT, considering the limitations of the diffusion equation (DE) and the time and memory costs of simplified spherical harmonic approximation equation (SPN), a hybrid light transport model needs to be built. DE and SPN models are first-order and higher-order approximations of RTE, respectively. Due to the discontinuity of the regions using the DE and SPN models and the inconsistencies of the system matrix dimensions constructed by the two models in the solving process, the system matrix construction of a hybrid light transmission model is a problem to be solved. We provided a new finite element mesh regrouping strategy-based hybrid light transport model for XLCT. Firstly, based on the finite element mesh regrouping strategy, two separate meshes can be obtained. Thus, for DE and SPN models, the system matrixes and source weight matrixes can be calculated separately in two respective mesh systems. Meanwhile, some parallel computation strategy can be combined with finite element mesh regrouping strategy to further save the system matrix calculation time. Then, the two system matrixes with different dimensions were coupled though repeated nodes were processed according to the hybrid boundary conditions, the two meshes were combined into a regrouping mesh, and the hybrid optical transmission model was established. In addition, the proposed method can reduce the computational memory consumption than the previously proposed hybrid light transport model achieving good balance between computational accuracy and efficiency. The forward numerical simulation results showed that the proposed method had better transmission accuracy and achieved a balance between efficiency and accuracy. The reverse simulation results showed that the proposed method had superior location accuracy, morphological recovery capability, and image contrast capability in source reconstruction. In-vivo experiments verified the practicability and effectiveness of the proposed method.
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Affiliation(s)
- Yanqiu Liu
- Key Laboratory for Radiomics and Intelligent Sense of Xi'an, Northwest University, Xi'an, China.,School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Xiangong Hu
- Key Laboratory for Radiomics and Intelligent Sense of Xi'an, Northwest University, Xi'an, China.,Network and Data Center, Northwest University, Xi'an, China
| | - Mengxiang Chu
- Key Laboratory for Radiomics and Intelligent Sense of Xi'an, Northwest University, Xi'an, China.,Network and Data Center, Northwest University, Xi'an, China
| | - Hongbo Guo
- Key Laboratory for Radiomics and Intelligent Sense of Xi'an, Northwest University, Xi'an, China.,School of Information Sciences and Technology, Northwest University, Xi'an, China
| | - Jingjing Yu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, China
| | - Xiaowei He
- Key Laboratory for Radiomics and Intelligent Sense of Xi'an, Northwest University, Xi'an, China.,School of Information Sciences and Technology, Northwest University, Xi'an, China.,Network and Data Center, Northwest University, Xi'an, China
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Zhang P, Fan G, Xing T, Song F, Zhang G. UHR-DeepFMT: Ultra-High Spatial Resolution Reconstruction of Fluorescence Molecular Tomography Based on 3-D Fusion Dual-Sampling Deep Neural Network. IEEE TRANSACTIONS ON MEDICAL IMAGING 2021; 40:3217-3228. [PMID: 33826514 DOI: 10.1109/tmi.2021.3071556] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Fluorescence molecular tomography (FMT) is a promising and high sensitivity imaging modality that can reconstruct the three-dimensional (3D) distribution of interior fluorescent sources. However, the spatial resolution of FMT has encountered an insurmountable bottleneck and cannot be substantially improved, due to the simplified forward model and the severely ill-posed inverse problem. In this work, a 3D fusion dual-sampling convolutional neural network, namely UHR-DeepFMT, was proposed to achieve ultra-high spatial resolution reconstruction of FMT. Under this framework, the UHR-DeepFMT does not need to explicitly solve the FMT forward and inverse problems. Instead, it directly establishes an end-to-end mapping model to reconstruct the fluorescent sources, which can enormously eliminate the modeling errors. Besides, a novel fusion mechanism that integrates the dual-sampling strategy and the squeeze-and-excitation (SE) module is introduced into the skip connection of UHR-DeepFMT, which can significantly improve the spatial resolution by greatly alleviating the ill-posedness of the inverse problem. To evaluate the performance of UHR-DeepFMT network model, numerical simulations, physical phantom and in vivo experiments were conducted. The results demonstrated that the proposed UHR-DeepFMT can outperform the cutting-edge methods and achieve ultra-high spatial resolution reconstruction of FMT with the powerful ability to distinguish adjacent targets with a minimal edge-to-edge distance (EED) of 0.5 mm. It is assumed that this research is a significant improvement for FMT in terms of spatial resolution and overall imaging quality, which could promote the precise diagnosis and preclinical application of small animals in the future.
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Wang H, Bian C, Kong L, An Y, Du Y, Tian J. A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2021; 40:1484-1498. [PMID: 33556004 DOI: 10.1109/tmi.2021.3057704] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a new type of medical imaging technology that can quantitatively reconstruct the three-dimensional distribution of fluorescent probes in vivo. Traditional Lp norm regularization techniques used in FMT reconstruction often face problems such as over-sparseness, over-smoothness, spatial discontinuity, and poor robustness. To address these problems, this paper proposes an adaptive parameter search elastic net (APSEN) method that is based on elastic net regularization, using weight parameters to combine the L1 and L2 norms. For the selection of elastic net weight parameters, this approach introduces the L0 norm of valid reconstruction results and the L2 norm of the residual vector, which are used to adjust the weight parameters adaptively. To verify the proposed method, a series of numerical simulation experiments were performed using digital mice with tumors as experimental subjects, and in vivo experiments of liver tumors were also conducted. The results showed that, compared with the state-of-the-art methods with different light source sizes or distances, Gaussian noise of 5%-25%, and the brute-force parameter search method, the APSEN method has better location accuracy, spatial resolution, fluorescence yield recovery ability, morphological characteristics, and robustness. Furthermore, the in vivo experiments demonstrated the applicability of APSEN for FMT.
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Zou W, Wang J, Hu D, Pan X. Bayesian reconstruction of fluorescent molecular tomography via iteration of measurements. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2021; 38:174-180. [PMID: 33690527 DOI: 10.1364/josaa.398996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 12/03/2020] [Indexed: 06/12/2023]
Abstract
Fluorescent molecular tomography (FMT) is an important molecular imaging technique for medical diagnosis and treatment. In FMT, a typical forward model is the diffusion approximation. However, this approximation is not valid in biological tissues with low-scattering regions. To overcome this problem, a Bayesian method in combination with the model error is proposed. Further, an iteration method of boundary measurements is incorporated into the reconstruction process to improve the efficiency of reconstruction for FMT. Simulation results obtained demonstrate that the proposed approach can effectively improve the quality of the reconstructed results and speed up the reconstruction process.
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12
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Nonconvex Laplacian Manifold Joint Method for Morphological Reconstruction of Fluorescence Molecular Tomography. Mol Imaging Biol 2021; 23:394-406. [PMID: 33415678 DOI: 10.1007/s11307-020-01568-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Revised: 11/02/2020] [Accepted: 11/19/2020] [Indexed: 10/22/2022]
Abstract
PURPOSE Fluorescence molecular tomography (FMT) is a promising technique for three-dimensional (3D) visualization of biomarkers in small animals. Morphological reconstruction is valuable and necessary for further applications of FMT owing to its innate requirement for knowledge of the molecular probe distributions. PROCEDURES In this study, a Laplacian manifold regularization joint ℓ1/2-norm model is proposed for morphological reconstruction and solved by a nonconvex algorithm commonly referred to as the half-threshold algorithm. The model is combined with the structural and sparsity priors to achieve the location and structure of the target. In addition, two improvement forms (truncated and hybrid truncated forms) are proposed for better morphological reconstruction. The truncated form is proposed for balancing the sharpness and smoothness of the boundary of reconstruction. A hybrid truncated form is proposed for more structural priors. To evaluate the proposed methods, three simulation studies (morphological, robust, and double target analyses) and an in vivo experiment were performed. RESULTS The proposed methods demonstrated morphological accuracy, location accuracy, and reconstruction robustness in glioma simulation studies. An in vivo experiment with an orthotopic glioma mouse model confirmed the advantages of the proposed methods. The proposed methods always yielded the best intersection of union (IoU) in simulations and in vivo experiments (mean of 0.80 IoU). CONCLUSIONS Simulation studies and in vivo experiments demonstrate that the proposed half-threshold hybrid truncated Laplacian algorithm had an improved performance compared with the comparative algorithm in terms of morphology.
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Meng H, Gao Y, Yang X, Wang K, Tian J. K-Nearest Neighbor Based Locally Connected Network for Fast Morphological Reconstruction in Fluorescence Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:3019-3028. [PMID: 32286961 DOI: 10.1109/tmi.2020.2984557] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive imaging modality for three-dimensional visualization of fluorescence probe distribution in small animals. However, the simplified photon propagation model and ill-posed inverse problem limit the improvement of FMT reconstruction. In this work, we proposed a novel K-nearest neighbor based locally connected (KNN-LC) network to improve the performance of morphological reconstruction in FMT. It directly builds the inverse process of photon transmission by learning the mapping relation between the surface photon intensity and the distribution of fluorescent source. KNN-LC network cascades a fully connected (FC) sub-network with a locally connected (LC) sub-network, where the FC part provides a coarse reconstruction result and LC part fine-tunes the morphological quality of reconstructed result. To assess the performance of our proposed network, we implemented both numerical simulation and in vivo studies. Furthermore, split Bregman-resolved total variation (SBRTV) regularization method and inverse problem simulation (IPS) method were utilized as baselines in all comparisons. The results demonstrated that KNN-LC network achieved accurate reconstruction in both source localization and morphology recovery in a short time. This promoted the in vivo application of FMT for visualizing the distribution of biomarkers inside biological tissue.
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Cai M, Zhang Z, Shi X, Hu Z, Tian J. NIR-II/NIR-I Fluorescence Molecular Tomography of Heterogeneous Mice Based on Gaussian Weighted Neighborhood Fused Lasso Method. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:2213-2222. [PMID: 31976880 DOI: 10.1109/tmi.2020.2964853] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Fluorescence molecular tomography (FMT), which can visualize the distribution of fluorescence biomarkers, has become a novel three-dimensional noninvasive imaging technique for in vivo studies such as tumor detection and lymph node location. However, it remains a challenging problem to achieve satisfactory reconstruction performance of conventional FMT in the first near-infrared window (NIR-I, 700-900nm) because of the severe scattering of NIR-I light. In this study, a promising FMT method for heterogeneous mice was proposed to improve the reconstruction accuracy using the second near-infrared window (NIR-II, 1000-1700nm), where the light scattering significantly reduced compared with NIR-I. The optical properties of NIR-II were analyzed to construct the forward model for NIR-II FMT. Furthermore, to raise the accuracy of solution of the inverse problem, we proposed a novel Gaussian weighted neighborhood fused Lasso (GWNFL) method. Numerical simulation was performed to demonstrate the outperformance of GWNFL compared with other algorithms. Besides, a novel NIR-II/NIR-I dual-modality FMT system was developed to contrast the in vivo reconstruction performance between NIR-II FMT and NIR-I FMT. To compare the reconstruction performance of NIR-II FMT with traditional NIR-I FMT, numerical simulations and in vivo experiments were conducted. Both the simulation and in vivo results showed that NIR-II FMT outperformed NIR-I FMT in terms of location accuracy and spatial overlap index. It is believed that this study could promote the development and biomedical application of NIR-II FMT in the future.
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Kong L, An Y, Liang Q, Yin L, Du Y, Tian J. Reconstruction for Fluorescence Molecular Tomography via Adaptive Group Orthogonal Matching Pursuit. IEEE Trans Biomed Eng 2020; 67:2518-2529. [PMID: 31905129 DOI: 10.1109/tbme.2019.2963815] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
OBJECTIVE Fluorescence molecular tomography (FMT) is a promising medical imaging technology aimed at the non-invasive, specific, and sensitive detection of the distribution of fluorophore. Conventional sparsity prior-based methods of FMT commonly face problems such as over-sparseness, spatial discontinuity, and poor robustness, due to the neglect of the interrelation within the local subspace. To address this, we propose an adaptive group orthogonal matching pursuit (AGOMP) method. METHODS AGOMP is based on a novel local spatial-structured sparse regularization, which leverages local spatial interrelations as group sparsity without the hard prior of the tumor region. The adaptive grouped subspace matching pursuit method was adopted to enhance the interrelatedness of elements within a group, which alleviates the over-sparsity problem to some extent and improves the accuracy, robustness, and morphological similarity of FMT reconstruction. A series of numerical simulation experiments, based on digital mouse with both one and several tumors, were conducted, as well as in vivo mouse experiments. RESULTS The results demonstrated that the proposed AGOMP method achieved better location accuracy, fluorescent yield reconstruction, relative sparsity, and morphology than state-of-the-art methods under complex conditions for levels of Gaussian noise ranging from 5-25%. Furthermore, the in vivo mouse experiments demonstrated the practical application of FMT with AGOMP. CONCLUSION The proposed AGOMP can improve the accuracy and robustness for FMT reconstruction in biomedical application.
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Meng H, Wang K, Gao Y, Jin Y, Ma X, Tian J. Adaptive Gaussian Weighted Laplace Prior Regularization Enables Accurate Morphological Reconstruction in Fluorescence Molecular Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2019; 38:2726-2734. [PMID: 31021763 DOI: 10.1109/tmi.2019.2912222] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fluorescence molecular tomography (FMT), as a powerful imaging technique in preclinical research, can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labelled probe noninvasively. However, because of the light scattering effect and the ill-pose of inverse problem, it is challenging to develop an efficient reconstruction method, which can provide accurate location and morphology of the fluorescence distribution. In this research, we proposed a novel adaptive Gaussian weighted Laplace prior (AGWLP) regularization method, which assumed the variance of fluorescence intensity between any two voxels had a non-linear correlation with their Gaussian distance. It utilized an adaptive Gaussian kernel parameter strategy to achieve accurate morphological reconstructions in FMT. To evaluate the performance of the AGWLP method, we conducted numerical simulation and in vivo experiments. The results were compared with fast iterative shrinkage (FIS) thresholding method, split Bregman-resolved TV (SBRTV) regularization method, and Gaussian weighted Laplace prior (GWLP) regularization method. We validated in vivo imaging results against planar fluorescence images of frozen sections. The results demonstrated that the AGWLP method achieved superior performance in both location and shape recovery of fluorescence distribution. This enabled FMT more suitable and practical for in vivo visualization of biomarkers.
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Bao B, Vasquez KO, Ho G, Zhang J, Delaney J, Rajopadhye M, Peterson JD. Blood Pharmacokinetics Imaging by Noninvasive Heart Fluorescence Tomography and Application to Kidney Glomerular Filtration Rate Assessment. J Pharmacol Exp Ther 2019; 370:288-298. [DOI: 10.1124/jpet.119.257071] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Accepted: 05/24/2019] [Indexed: 02/04/2023] Open
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Yi H, Jiao P, Li X, Peng J, He X. Three-way decision based reconstruction frame for fluorescence molecular tomography. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2018; 35:1814-1822. [PMID: 30461839 DOI: 10.1364/josaa.35.001814] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Accepted: 09/18/2018] [Indexed: 06/09/2023]
Abstract
Fluorescence molecular tomography (FMT) has been a promising imaging tool because it allows an accurate localizaton and quantitative analysis of the fluorophore distribution in animals. It, however, is still a challenge since its reconstruction suffers from severe ill-posedness. This paper introduces a reconstruction frame based on three-way decisions (TWD) for the inverse problem of FMT. On the first stage, a reconstruction result on the whole region is obtained by a certain reconstruction algorithm. With TWD, the recovered result has been divided into three regions: fluorescent target region, boundary region, and background region. On the second stage, the boundary region and fluorescent target region have been combined into the permissible region of the target. Then a new reconstruction on the permissible region has been carried out and a new recovered result is obtained. With TWD again, the new result has been classified into three pairwise disjoint regions. And the new fluorescent target region is the final reconstructed result. Both numerical simulation experiments and a real mouse experiment are carried out to validate the feasibility and potential of the presented reconstruction frame. The results indicate that the proposed reconstuction strategy based on TWD can provide a good performance in FMT reconstruction.
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An Y, Wang K, Tian J. Recent methodology advances in fluorescence molecular tomography. Vis Comput Ind Biomed Art 2018; 1:1. [PMID: 32240398 PMCID: PMC7098398 DOI: 10.1186/s42492-018-0001-6] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Accepted: 06/30/2018] [Indexed: 12/26/2022] Open
Abstract
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.
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Affiliation(s)
- Yu An
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
| | - Kun Wang
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China
| | - Jie Tian
- Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, China.
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Liu Y, Jiang S, Liu J, An Y, Zhang G, Gao Y, Wang K, Tian J. Reconstruction method for fluorescence molecular tomography based on L1-norm primal accelerated proximal gradient. JOURNAL OF BIOMEDICAL OPTICS 2018; 23:1-11. [PMID: 30109802 DOI: 10.1117/1.jbo.23.8.085002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Accepted: 07/30/2018] [Indexed: 06/08/2023]
Abstract
Fluorescence molecular tomography (FMT) has been widely used in preclinical tumor imaging, which enables three-dimensional imaging of the distribution of fluorescent probes in small animal bodies via image reconstruction method. However, the reconstruction results are usually unsatisfactory in the term of robustness and efficiency because of the ill-posed and ill-conditioned of FMT problem. In this study, an FMT reconstruction method based on primal accelerated proximal gradient (PAPG) descent and L1-norm regularized projection (L1RP) is proposed. The proposed method utilizes the current and previous iterations to obtain a search point at each iteration. To achieve fast convergence, the PAPG method is applied to efficiently solve the search point, and then L1RP is performed to obtain the robust and accurate reconstruction. To verify the performance of the proposed method, simulation experiments are conducted. The comparative results revealed that it held advantages of robustness, accuracy, and efficiency in FMT reconstructions. Furthermore, a phantom experiment and an in vivo mouse experiment were also performed, which proved the potential and feasibility of the proposed method for practical applications.
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Affiliation(s)
- Yuhao Liu
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Shixin Jiang
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Jie Liu
- Beijing Jiaotong University, School of Computer and Information Technology, Haidian District, Beijin, China
| | - Yu An
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Guanglei Zhang
- Beihang University, School of Biological Science and Medical Engineering, Beijing Advanced Innovatio, China
| | - Yuan Gao
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
| | - Kun Wang
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
- University of Chinese Academy of Sciences, Beijing, China
| | - Jie Tian
- Institute of Automation, CAS Key Laboratory of Molecular Imaging, Chinese Academy of Sciences, Beiji, China
- University of Chinese Academy of Sciences, Beijing, China
- Beijing Key Laboratory of Molecular Imaging, Beijing, China
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Ding S, Blue RE, Moorefield E, Yuan H, Lund PK. Ex Vivo and In Vivo Noninvasive Imaging of Epidermal Growth Factor Receptor Inhibition on Colon Tumorigenesis Using Activatable Near-Infrared Fluorescent Probes. Mol Imaging 2018; 16:1536012117729044. [PMID: 28884622 PMCID: PMC5595252 DOI: 10.1177/1536012117729044] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Background: Near-infrared fluorescence (NIRF) imaging combined with enzyme-activatable NIRF probes has yielded promising results in cancer detection. Objective: To test whether 3-dimensional (3-D) noninvasive in vivo NIRF imaging can detect effects of epidermal growth factor receptor (EGFR) inhibitor on both polypoid and flat tumor load in azoxymethane (AOM)-induced colon tumors or tumors in ApcMin/+ mice. Methods: The AOM-injected KK-HIJ mice received EGFR inhibitor diet or chow diet. These and ApcMin/+ mice were given cathepsin-activatable probes (ProSense 680) before imaging. In vivo imaging was performed using quantitative tomographic NIRF imaging. Ex vivo imaging and histologic examination were performed. Dual imaging by micro computed tomography (CT) and 3D NIRF imaging was used to verify tumor location. Results: Tumor load reduction by EGFR inhibition was detected ex vivo using cathepsin B probes. In vivo imaging revealed intense activation of probes only in large tumors. Dual imaging with microCT and 3D NIRF imaging improved tumor detection in vivo. Conclusions: The 3-D NIRF imaging with ProSense 680 can detect and quantify drug effects on colon tumors ex vivo. The NIRF imaging with ProSense 680 probe has limitations as a valid nonendoscopic method for intestinal tumor detection. Combing with other imaging modalities will improve the specificity and sensitivity of intestinal tumor detection in vivo.
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Affiliation(s)
- Shengli Ding
- 1 Department of Cell Biology and Physiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Randall E Blue
- 1 Department of Cell Biology and Physiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Emily Moorefield
- 1 Department of Cell Biology and Physiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Hong Yuan
- 2 Department of Radiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Pauline K Lund
- 1 Department of Cell Biology and Physiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
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Beheshti M, Ashapure A, Rahnemoonfar M, Faichney J. Fluorescence microscopy image segmentation based on graph and fuzzy methods: A comparison with ensemble method. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-17466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Maedeh Beheshti
- School of Information and Communication Technology, Griffith University, Australia
| | - Akash Ashapure
- College of Science and Engineering, Texas A&M University-Corpus Christi, USA
| | - Maryam Rahnemoonfar
- College of Science and Engineering, Texas A&M University-Corpus Christi, USA
| | - Jolon Faichney
- School of Information and Communication Technology, Griffith University, Australia
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Yi H, Wei H, Peng J, Hou Y, He X. Adaptive threshold method for recovered images of FMT. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2018; 35:256-261. [PMID: 29400892 DOI: 10.1364/josaa.35.000256] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2017] [Accepted: 12/12/2017] [Indexed: 06/07/2023]
Abstract
This paper proposes a post-processing strategy for recovered images of fluorescence molecular tomography. A threshold value is adaptively obtained from the recovered images without external interference, which is objective because it is extracted from the reconstructed result. The recovered images from simulation experiments and physical phantom experiments are processed by this threshold method. And by visualization, the processed images are clearer than those with no post-processing. The full width at half-maximum and contrast-to-noise ratio are then utilized to further verify the effectiveness of the post-processing method, being capable of removing spurious information from the original images, thus bringing convenience to users.
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