Performance investigation of SP3 and diffusion approximation for three-dimensional whole-body optical imaging of small animals

Unrolled-DOT: an interpretable deep network for diffuse optical tomography

SIGNIFICANCE

Imaging through scattering media is critical in many biomedical imaging applications, such as breast tumor detection and functional neuroimaging. Time-of-flight diffuse optical tomography (ToF-DOT) is one of the most promising methods for high-resolution imaging through scattering media. ToF-DOT and many traditional DOT methods require an image reconstruction algorithm. Unfortunately, this algorithm often requires long computational runtimes and may produce lower quality reconstructions in the presence of model mismatch or improper hyperparameter tuning.

AIM

We used a data-driven unrolled network as our ToF-DOT inverse solver. The unrolled network is faster than traditional inverse solvers and achieves higher reconstruction quality by accounting for model mismatch.

APPROACH

Our model "Unrolled-DOT" uses the learned iterative shrinkage thresholding algorithm. In addition, we incorporate a refinement U-Net and Visual Geometry Group (VGG) perceptual loss to further increase the reconstruction quality. We trained and tested our model on simulated and real-world data and benchmarked against physics-based and learning-based inverse solvers.

RESULTS

In experiments on real-world data, Unrolled-DOT outperformed learning-based algorithms and achieved over 10× reduction in runtime and mean-squared error, compared to traditional physics-based solvers.

CONCLUSION

We demonstrated a learning-based ToF-DOT inverse solver that achieves state-of-the-art performance in speed and reconstruction quality, which can aid in future applications for noninvasive biomedical imaging.

A Finite Element Mesh Regrouping Strategy-Based Hybrid Light Transport Model for Enhancing the Efficiency and Accuracy of XLCT

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 (SP_N), a hybrid light transport model needs to be built. DE and SP_N models are first-order and higher-order approximations of RTE, respectively. Due to the discontinuity of the regions using the DE and SP_N 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 SP_N 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.

Harnessing the Power of Hybrid Light Propagation Model for Three-Dimensional Optical Imaging in Cancer Detection

Optical imaging is an emerging technology capable of qualitatively and quantitatively observing life processes at the cellular or molecular level and plays a significant role in cancer detection. In particular, to overcome the disadvantages of traditional optical imaging that only two-dimensionally and qualitatively detect biomedical information, the corresponding three-dimensional (3D) imaging technology is intensively explored to provide 3D quantitative information, such as localization and distribution and tumor cell volume. To retrieve these information, light propagation models that reflect the interaction between light and biological tissues are an important prerequisite and basis for 3D optical imaging. This review concentrates on the recent advances in hybrid light propagation models, with particular emphasis on their powerful use for 3D optical imaging in cancer detection. Finally, we prospect the wider application of the hybrid light propagation model and future potential of 3D optical imaging in cancer detection.

Bioluminescence Tomography Based on One-Dimensional Convolutional Neural Networks

Bioluminescent tomography (BLT) has increasingly important applications in preclinical studies. However, the simplified photon propagation model and the inherent ill-posedness of the inverse problem limit the quality of BLT reconstruction. In order to improve the reconstruction accuracy of positioning and reconstruction efficiency, this paper presents a deep-learning optical reconstruction method based on one-dimensional convolutional neural networks (1DCNN). The nonlinear mapping relationship between the surface photon flux density and the distribution of the internal bioluminescence sources is directly established, which fundamentally avoids solving the ill-posed inverse problem iteratively. Compared with the previous reconstruction method based on multilayer perceptron, the training parameters in the 1DCNN are greatly reduced and the learning efficiency of the model is improved. Simulations verify the superiority and stability of the 1DCNN method, and the in vivo experimental results further show the potential of the proposed method in practical applications.

δ-SPN approximation for numerical modeling of directional sources and scattering

We propose the δ-SP_N approximation for the frequency domain coupled radiative transfer equations modeling fluorescence with collimated incident beams and present its numerical implementation using the finite element method. The performance of the proposed model is investigated with respect to Monte Carlo simulations and the standard SP_N approximation over sub-centimeter domains for various optical properties. We find that the δ-SP_N approximation is more accurate than the SP_N in the near-source region, and provides improved estimates of phase and partial currents, at both excitation and emission wavelengths, over a wider range of optical properties. The accuracy of the δ-SP_N model improves with increase in approximation order for normally incident beams.

X-ray luminescence computed tomography using a hybrid proton propagation model and Lasso-LSQR algorithm

X-ray luminescence computed tomography (XLCT) uses external X-rays for luminescence excitation, which is becoming a promising molecular imaging technique with superb penetration depth and spatial resolution. To achieve the tomographic mapping of luminescence distribution, accurate optical propagation model and suitable reconstruction method are two keys for XLCT, but not satisfied. To overcome the limitation of the single proton propagation model (e.g., DE, SP₃ ), we adopted a hybrid diffusion equation with third order simplified spherical harmonics (DE-SP₃ ) model for XLCT. To enable fast iteration and accurate sparse reconstruction, we also integrated in the inversion optimization, with a novel Least Square QR-factorization based on the Lasso (Lasso-LSQR) algorithm. We first simulated the light propagation in various kinds of organs under DE model and SP₃ model, respectively. By comparison with the Monte Carlo, these tissues can be categorized into two types, namely DE-fitted tissues that include muscle and lung, and SP₃ -fitted tissues including heart, kidney, liver, and stomach. According to the above classification results, we built a hybrid DE-SP₃ model to more accurately describing light transport. Numerical simulations and in vivo experiments illustrated that hybrid DE-SP₃ model achieves superior reconstruction performance in terms of location accuracy, and spatial resolution than DE, and less computational cost than SP₃ . The hybrid DE-SP₃ model materializes a balance between accuracy and efficiency for XLCT.

Development of tomographic reconstruction for three-dimensional optical imaging: From the inversion of light propagation to artificial intelligence

Optical molecular tomography (OMT) is an imaging modality which uses an optical signal, especially near-infrared light, to reconstruct the three-dimensional information of the light source in biological tissue. With the advantages of being low-cost, noninvasive and having high sensitivity, OMT has been applied in preclinical and clinical research. However, due to its serious ill-posedness and ill-condition, the solution of OMT requires heavy data analysis and the reconstruction quality is limited. Recently, the artificial intelligence (commonly known as AI)-based methods have been proposed to provide a different tool to solve the OMT problem. In this paper, we review the progress on OMT algorithms, from conventional methods to AI-based methods, and we also give a prospective towards future developments in this domain.

Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP_N) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment. Graphical abstract The filtered MLEM-based global reconstruction method for BLT.

Advances in Monte Carlo Simulation for Light Propagation in Tissue

Monte Carlo (MC) simulation for light propagation in tissue is the gold standard for studying the light propagation in biological tissue and has been used for years. Interaction of photons with a medium is simulated based on its optical properties. New simulation geometries, tissue-light interaction methods, and recording techniques recently have been designed. Applications, such as whole mouse body simulations for fluorescence imaging, eye modeling for blood vessel imaging, skin modeling for terahertz imaging, and human head modeling for sinus imaging, have emerged. Here, we review the technical advances and recent applications of MC simulation.

Coupled third-order simplified spherical harmonics and diffusion equation-based fluorescence tomographic imaging of liver cancer

For fluorescence tomographic imaging of small animals, the liver is usually regarded as a low-scattering tissue and is surrounded by adipose, kidneys, and heart, all of which have a high scattering property. This leads to a breakdown of the diffusion equation (DE)–based reconstruction method as well as a heavy computational burden for the simplified spherical harmonics equation (SP(N)). Coupling the SP(N) and DE provides a perfect balance between the imaging accuracy and computational burden. The coupled third-order SPN and DE (CSDE)-based reconstruction method is developed for fluorescence tomographic imaging. This is achieved by doubly using the CSDE for the excitation and emission processes of the fluorescence propagation. At the same time, the finite-element method and hybrid multilevel regularization strategy are incorporated in inverse reconstruction. The CSDE-based reconstruction method is first demonstrated with a digital mouse-based liver cancer simulation, which reveals superior performance compared with the SPN and DE-based methods. It is more accurate than the DE-based method and has lesser computational burden than the SPN-based method. The feasibility of the proposed approach in applications of in vivo studies is also illustrated with a liver cancer mouse-based in situ experiment, revealing its potential application in whole-body imaging of small animals.