Bioluminescence tomography using eigenvectors expansion and iterative solution for the optimized permissible source region

Highly robust reconstruction framework for three-dimensional optical imaging based on physical model constrained neural networks

Objective. The reconstruction of three-dimensional optical imaging that can quantitatively acquire the target distribution from surface measurements is a serious ill-posed problem. Traditional regularization-based reconstruction can solve such ill-posed problem to a certain extent, but its accuracy is highly dependent ona priorinformation, resulting in a less stable and adaptable method. Data-driven deep learning-based reconstruction avoids the errors of light propagation models and the reliance on experience and a prior by learning the mapping relationship between the surface light distribution and the target directly from the dataset. However, the acquisition of the training dataset and the training of the network itself are time consuming, and the high dependence of the network performance on the training dataset results in a low generalization ability. The objective of this work is to develop a highly robust reconstruction framework to solve the existing problems.Approach. This paper proposes a physical model constrained neural networks-based reconstruction framework. In the framework, the neural networks are to generate a target distribution from surface measurements, while the physical model is used to calculate the surface light distribution based on this target distribution. The mean square error between the calculated surface light distribution and the surface measurements is then used as a loss function to optimize the neural network. To further reduce the dependence ona prioriinformation, a movable region is randomly selected and then traverses the entire solution interval. We reconstruct the target distribution in this movable region and the results are used as the basis for its next movement.Main Results. The performance of the proposed framework is evaluated with a series of simulations andin vivoexperiment, including accuracy robustness of different target distributions, noise immunity, depth robustness, and spatial resolution. The results collectively demonstrate that the framework can reconstruct targets with a high accuracy, stability and versatility.Significance. The proposed framework has high accuracy and robustness, as well as good generalizability. Compared with traditional regularization-based reconstruction methods, it eliminates the need to manually delineate feasible regions and adjust regularization parameters. Compared with emerging deep learning assisted methods, it does not require any training dataset, thus saving a lot of time and resources and solving the problem of poor generalization and robustness of deep learning methods. Thus, the framework opens up a new perspective for the reconstruction of three-dimension optical imaging.

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Self-Training Strategy Based on Finite Element Method for Adaptive Bioluminescence Tomography Reconstruction

Bioluminescence tomography (BLT) is a promising pre-clinical imaging technique for a wide variety of biomedical applications, which can non-invasively reveal functional activities inside living animal bodies through the detection of visible or near-infrared light produced by bioluminescent reactions. Recently, reconstruction approaches based on deep learning have shown great potential in optical tomography modalities. However, these reports only generate data with stationary patterns of constant target number, shape, and size. The neural networks trained by these data sets are difficult to reconstruct the patterns outside the data sets. This will tremendously restrict the applications of deep learning in optical tomography reconstruction. To address this problem, a self-training strategy is proposed for BLT reconstruction in this paper. The proposed strategy can fast generate large-scale BLT data sets with random target numbers, shapes, and sizes through an algorithm named random seed growth algorithm and the neural network is automatically self-trained. In addition, the proposed strategy uses the neural network to build a map between photon densities on surface and inside the imaged object rather than an end-to-end neural network that directly infers the distribution of sources from the photon density on surface. The map of photon density is further converted into the distribution of sources through the multiplication with stiffness matrix. Simulation, phantom, and mouse studies are carried out. Results show the availability of the proposed self-training strategy.

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 Multilevel Probabilistic Cerenkov Luminescence Tomography Reconstruction Framework Based on Energy Distribution Density Region Scaling

Cerenkov luminescence tomography (CLT) is a promising non-invasive optical imaging method with three-dimensional semiquantitative in vivo imaging capability. However, CLT itself relies on Cerenkov radiation, a low-intensity radiation, making CLT reconstruction more challenging than other imaging modalities. In order to solve the ill-posed inverse problem of CLT imaging, some numerical optimization or regularization methods need to be applied. However, in commonly used methods for solving inverse problems, parameter selection significantly influences the results. Therefore, this paper proposed a probabilistic energy distribution density region scaling (P-EDDRS) framework. In this framework, multiple reconstruction iterations are performed, and the Cerenkov source distribution of each reconstruction is treated as random variables. According to the spatial energy distribution density, the new region of interest (ROI) is solved. The size of the region required for the next operation was determined dynamically by combining the intensity characteristics. In addition, each reconstruction source distribution is given a probability weight value, and the prior probability in the subsequent reconstruction is refreshed. Last, all the reconstruction source distributions are weighted with the corresponding probability weights to get the final Cerenkov source distribution. To evaluate the performance of the P-EDDRS framework in CLT, this article performed numerical simulation, in vivo pseudotumor model mouse experiment, and breast cancer mouse experiment. Experimental results show that this reconstruction framework has better positioning accuracy and shape recovery ability and can optimize the reconstruction effect of multiple algorithms on CLT.

A deep unsupervised clustering-based post-processing framework for high-fidelity Cerenkov luminescence tomography

Cerenkov Luminescence Tomography (CLT) is a promising optical molecular imaging technology. It involves the three-dimensional reconstruction of the distribution of radionuclide probes inside a single object to indicate a tumor's localization and distribution. However, reconstruction using CLT suffers from severe ill-posedness, resulting in numerous artifacts within the reconstructed images. These artifacts influence the visual effect and may misguide the medical professional (diagnostician), resulting in a wrong diagnosis. Here, we proposed a deep unsupervised clustering-based post-processing framework to eliminate artifacts and facilitate high-fidelity CLT. First, an initial reconstructed image was obtained by a specific reconstruction method. Second, voxel data were generated based on the initial reconstructed result. Third, these voxels were divided into three groups, and only the group with the highest mean intensity was chosen as the final reconstructed result. A group of numerical simulation and in vivo mouse-based experiments were conducted to assess the presented framework's feasibility and potential. The results indicated that the proposed framework could reduce the number of artifacts effectively. The reconstructed image's shape and distribution were more similar to the actual light source than those obtained without the proposed framework.

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.

In Vivo Bioluminescence Tomography Center of Mass-Guided Conformal Irradiation

PURPOSE

The cone-beam computed tomography (CBCT)-guided small animal radiation research platform (SARRP) has provided unique opportunities to test radiobiologic hypotheses. However, CBCT is less adept to localize soft tissue targets growing in a low imaging contrast environment. Three-dimensional bioluminescence tomography (BLT) provides strong image contrast and thus offers an attractive solution. We introduced a novel and efficient BLT-guided conformal radiation therapy and demonstrated it in an orthotopic glioblastoma (GBM) model.

METHODS AND MATERIALS

A multispectral BLT system was integrated with SARRP for radiation therapy (RT) guidance. GBM growth curve was first established by contrast CBCT/magnetic resonance imaging (MRI) to derive equivalent sphere as approximated gross target volume (aGTV). For BLT, mice were subject to multispectral bioluminescence imaging, followed by SARRP CBCT imaging and optical reconstruction. The CBCT image was acquired to generate anatomic mesh for the reconstruction and RT planning. To ensure high accuracy of the BLT-reconstructed center of mass (CoM) for target localization, we optimized the optical absorption coefficients μ_a by minimizing the distance between the CoMs of BLT reconstruction and contrast CBCT/MRI-delineated GBM volume. The aGTV combined with the uncertainties of BLT CoM localization and target volume determination was used to generate estimated target volume (ETV). For conformal irradiation procedure, the GBM was first localized by the predetermined ETV centered at BLT-reconstructed CoM, followed by SARRP radiation. The irradiation accuracy was qualitatively confirmed by pathologic staining.

RESULTS

Deviation between CoMs of BLT reconstruction and contrast CBCT/MRI-imaged GBM is approximately 1 mm. Our derived ETV centered at BLT-reconstructed CoM covers >95% of the tumor volume. Using the second-week GBM as an example, the ETV-based BLT-guided irradiation can cover 95.4% ± 4.7% tumor volume at prescribed dose. The pathologic staining demonstrated the BLT-guided irradiated area overlapped well with the GBM location.

CONCLUSIONS

The BLT-guided RT enables 3-dimensional conformal radiation for important orthotopic tumor models, which provides investigators a new preclinical research capability.

Bayesian sparse-based reconstruction in bioluminescence tomography improves localization accuracy and reduces computational time

Bioluminescence tomography (BLT) provides fundamental insight into biological processes in vivo. To fully realize its potential, it is important to develop image reconstruction algorithms that accurately visualize and quantify the bioluminescence signals taking advantage of limited boundary measurements. In this study, a new 2-step reconstruction method for BLT is developed by taking advantage of the sparse a priori information of the light emission using multispectral measurements. The first step infers a wavelength-dependent prior by using all multi-wavelength measurements. The second step reconstructs the source distribution based on this developed prior. Simulation, phantom and in vivo results were performed to assess and compare the accuracy and the computational efficiency of this algorithm with conventional sparsity-promoting BLT reconstruction algorithms, and results indicate that the position errors are reduced from a few millimeters down to submillimeter, and reconstruction time is reduced by 3 orders of magnitude in most cases, to just under a few seconds. The recovery of single objects and multiple (2 and 3) small objects is simulated, and the recovery of images of a mouse phantom and an experimental animal with an existing luminescent source in the abdomen is demonstrated. Matlab code is available at https://github.com/jinchaofeng/code/tree/master.

A hybrid clustering algorithm for multiple-source resolving in bioluminescence tomography

Bioluminescence tomography is a preclinical imaging modality to locate and quantify internal bioluminescent sources from surface measurements, which experienced rapid growth in the last 10 years. However, multiple-source resolving remains a challenging issue in BLT. In this study, it is treated as an unsupervised pattern recognition problem based on the reconstruction result, and a novel hybrid clustering algorithm combining the advantages of affinity propagation (AP) and K-means is developed to identify multiple sources automatically. Moreover, we incorporate the clustering analysis into a general multiple-source reconstruction framework, which can provide stable reconstruction and accurate resolving result without providing the number of targets. Numerical simulations and in vivo experiments on 4T1-luc2 mouse model were conducted to assess the performance of the proposed method in multiple-source resolving. The encouraging results demonstrate significant effectiveness and potential of our method in preclinical BLT applications.

Evaluation of On- and Off-Line Bioluminescence Tomography System for Focal Irradiation Guidance

In response to the limitations of computed tomography (CT) and cone-beam CT (CBCT) in irradiation guidance, especially for soft-tissue targets without the use of contrast agents, our group developed a solution that implemented bioluminescence tomography (BLT) as the image-guidance modality for preclinical radiation research. However, adding such a system to existing small animal irradiators is no small task. A potential solution is to utilize an off-line BLT system in close proximity to the irradiator, with stable and effective animal transport between the two systems. In this study, we investigated the localization accuracy of an off-line BLT system when used for the small animal radiation research platform (SARRP) and compared the results with those of an on-line system. The CBCT was equipped on both the off-line BLT system and the SARRP, with a distance of 5 m between them. To evaluate the setup error during animal transport between the two systems, the mice underwent CBCT imaging on the SARRP and were then transported to the off-line system for a second CBCT imaging session. The normalized intensity difference of the two images and the corresponding histogram and correlation were computed to evaluate if the transport process perturbed animal positioning. Strong correlation (correlation coefficients >0.95) between the SARRP and the off-line mouse CBCT was observed. The offset of the implanted light source center can be maintained within 0.2 mm during transport. To compare the target localization accuracy using the on-line SARRP BLT and the off-line system, a self-illuminated bioluminescent source was implanted in the abdomen of anesthetized mice. In addition to the application for dose calculation, CBCT imaging was also employed to generate the mesh grid of the imaged mouse for BLT reconstruction. Two scenarios were devised and compared, which involved localization of the luminescence source based on either: 1. on-line SARRP bioluminescence image and CBCT; or 2. off-line bioluminescence image and SARRP CBCT. The first scenario is assumed to have the least setup error, because no animal transport was involved. The second scenario examines if an off-line BLT system, with the mesh generated from the SARRP CBCT, can be used to guide SARRP irradiation when there is minimal target contrast in CBCT. Stability during animal transport between the two systems was maintained. The center of mass (CoM) of the light source reconstructed by the off-line BLT had an offset of 1.0 ± 0.4 mm from the true CoM derived from the SARRP CBCT. These results are comparable to the offset of 1.0 ± 0.2 mm using on-line BLT. With CBCT information provided by the SARRP and effective animal immobilization during transport, these findings support the utilization of an off-line BLT-guided system, in close proximity to the SARRP, for accurate soft-tissue target localization. In addition, a dedicated standalone BLT system for our partner site at the University of Pennsylvania was introduced in this study.

Bioluminescence Tomography-Guided Radiation Therapy for Preclinical Research

PURPOSE

In preclinical radiation research, it is challenging to localize soft tissue targets based on cone beam computed tomography (CBCT) guidance. As a more effective method to localize soft tissue targets, we developed an online bioluminescence tomography (BLT) system for small-animal radiation research platform (SARRP). We demonstrated BLT-guided radiation therapy and validated targeting accuracy based on a newly developed reconstruction algorithm.

METHODS AND MATERIALS

The BLT system was designed to dock with the SARRP for image acquisition and to be detached before radiation delivery. A 3-mirror system was devised to reflect the bioluminescence emitted from the subject to a stationary charge-coupled device (CCD) camera. Multispectral BLT and the incomplete variables truncated conjugate gradient method with a permissible region shrinking strategy were used as the optimization scheme to reconstruct bioluminescent source distributions. To validate BLT targeting accuracy, a small cylindrical light source with high CBCT contrast was placed in a phantom and also in the abdomen of a mouse carcass. The center of mass (CoM) of the source was recovered from BLT and used to guide radiation delivery. The accuracy of the BLT-guided targeting was validated with films and compared with the CBCT-guided delivery. In vivo experiments were conducted to demonstrate BLT localization capability for various source geometries.

RESULTS

Online BLT was able to recover the CoM of the embedded light source with an average accuracy of 1 mm compared to that with CBCT localization. Differences between BLT- and CBCT-guided irradiation shown on the films were consistent with the source localization revealed in the BLT and CBCT images. In vivo results demonstrated that our BLT system could potentially be applied for multiple targets and tumors.

CONCLUSIONS

The online BLT/CBCT/SARRP system provides an effective solution for soft tissue targeting, particularly for small, nonpalpable, or orthotopic tumor models.

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

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

Algorithm for localized adaptive diffuse optical tomography and its application in bioluminescence tomography

A reconstruction algorithm for diffuse optical tomography based on diffusion theory and finite element method is described. The algorithm reconstructs the optical properties in a permissible domain or region-of-interest to reduce the number of unknowns. The algorithm can be used to reconstruct optical properties for a segmented object (where a CT-scan or MRI is available) or a non-segmented object. For the latter, an adaptive segmentation algorithm merges contiguous regions with similar optical properties thereby reducing the number of unknowns. In calculating the Jacobian matrix the algorithm uses an efficient direct method so the required time is comparable to that needed for a single forward calculation. The reconstructed optical properties using segmented, non-segmented, and adaptively segmented 3D mouse anatomy (MOBY) are used to perform bioluminescence tomography (BLT) for two simulated internal sources. The BLT results suggest that the accuracy of reconstruction of total source power obtained without the segmentation provided by an auxiliary imaging method such as x-ray CT is comparable to that obtained when using perfect segmentation.

A generalized hybrid algorithm for bioluminescence tomography

Bioluminescence tomography (BLT) is a promising optical molecular imaging technique on the frontier of biomedical optics. In this paper, a generalized hybrid algorithm has been proposed based on the graph cuts algorithm and gradient-based algorithms. The graph cuts algorithm is adopted to estimate a reliable source support without prior knowledge, and different gradient-based algorithms are sequentially used to acquire an accurate and fine source distribution according to the reconstruction status. Furthermore, multilevel meshes for the internal sources are used to speed up the computation and improve the accuracy of reconstruction. Numerical simulations have been performed to validate this proposed algorithm and demonstrate its high performance in the multi-source situation even if the detection noises, optical property errors and phantom structure errors are involved in the forward imaging.

Self-calibrated algorithms for diffuse optical tomography and bioluminescence tomography using relative transmission images

Reconstruction algorithms for diffuse optical tomography (DOT) and bioluminescence tomography (BLT) have been developed based on diffusion theory. The algorithms numerically solve the diffusion equation using the finite element method. The direct measurements of the uncalibrated light fluence rates by a camera are used for the reconstructions. The DOT is self-calibrated by using all possible pairs of transmission images obtained with external sources along with the relative values of the simulated data and the calculated Jacobian. The reconstruction is done in the relative domain with the cancelation of any geometrical or optical factors. The transmission measurements for the DOT are used for calibrating the bioluminescence measurements at each wavelength and then a normalized system of equations is built up which is self-calibrated for the BLT. The algorithms have been applied to a three dimensional model of the mouse (MOBY) segmented into tissue regions which are assumed to have uniform optical properties. The DOT uses the direct method for calculating the Jacobian. The BLT uses a reduced space of eigenvectors of the Green's function with iterative shrinking of the permissible source region. The reconstruction results of the DOT and BLT algorithms show good agreement with the actual values when using either absolute or relative data. Even a small calibration error causes significant degradation of the reconstructions based on absolute data.