Flux vector formulation for photon propagation in the biological tissue

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.

Compactly Supported Radial Basis Function-Based Meshless Method for Photon Propagation Model of Fluorescence Molecular Tomography

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

Improved reconstruction quality of bioluminescent images by combining SP(3) equations and Bregman iteration method

Bioluminescence tomography (BLT) has a great potential to provide a powerful tool for tumor detection, monitoring tumor therapy progress, and drug development; developing new reconstruction algorithms will advance the technique to practical applications. In the paper, we propose a BLT reconstruction algorithm by combining SP₃ equations and Bregman iteration method to improve the quality of reconstructed sources. The numerical results for homogeneous and heterogeneous phantoms are very encouraging and give significant improvement over the algorithms without the use of SP₃ equations and Bregman iteration method.

Influence investigation of a void region on modeling light propagation in a heterogeneous medium

A void region exists in some biological tissues, and previous studies have shown that inaccurate images would be obtained if it were not processed. A hybrid radiosity-diffusion method (HRDM) that couples the radiosity theory and the diffusion equation has been proposed to deal with the void problem and has been well demonstrated in two-dimensional and three-dimensional (3D) simple models. However, the extent of the impact of the void region on the accuracy of modeling light propagation has not been investigated. In this paper, we first implemented and verified the HRDM in 3D models, including both the regular geometries and a digital mouse model, and then investigated the influences of the void region on modeling light propagation in a heterogeneous medium. Our investigation results show that the influence of the region can be neglected when the size of the void is less than a certain range, and other cases must be taken into account.

Light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities based on hybrid simplified spherical harmonics with radiosity model

Modeling light propagation in the whole body is essential and necessary for optical imaging. However, non-scattering, low-scattering and high absorption regions commonly exist in biological tissues, which lead to inaccuracy of the existing light transport models. In this paper, a novel hybrid light transport model that couples the simplified spherical harmonics approximation (SPN) with the radiosity theory (HSRM) was presented, to accurately describe light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities. In the model, the radiosity theory was used to characterize the light transport in non-scattering regions and the SPN was employed to handle the scattering problems, including subsets of low-scattering and high absorption. A Neumann source constructed by the light transport in the non-scattering region and formed at the interface between the non-scattering and scattering regions was superposed into the original light source, to couple the SPN with the radiosity theory. The accuracy and effectiveness of the HSRM was first verified with both regular and digital mouse model based simulations and a physical phantom based experiment. The feasibility and applicability of the HSRM was then investigated by a broad range of optical properties. Lastly, the influence of depth of the light source on the model was also discussed. Primary results showed that the proposed model provided high performance for light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities.

Comparison of permissible source region and multispectral data using efficient bioluminescence tomography method

As a novel molecular imaging technology, bioluminescence tomography (BLT) has become an important tool for biomedical research in recent years, which can perform a quantitative reconstruction of an internal light source distribution with the scattered and transmitted bioluminescent signals measured on the external surface of a small animal. However, BLT is severely ill-posed because of complex photon propagation in the biological tissue and limited boundary measured data with noise. Therefore, sufficient a priori knowledge should be fused for the uniqueness and stability of BLT solution. Permissible source region strategy and spectrally resolved measurements are two kinds of a priori knowledge commonly used in BLT reconstruction. This paper compares their performance with simulation and in vivo heterogeneous mouse experiments. In order to improve the efficiency of large-scale source restoration, this paper introduces an efficient iterative shrinkage thresholding method that not only has faster convergence rate but also has better reconstruction accuracy than the modified Newton-type optimization approach. Finally, a discussion of these two kinds of a priori knowledge is given based on the comparison results.

A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging

Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP(N)) approximations. To fully evaluate the performance of the SP(N) approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP(N) can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

A tetrahedron-based inhomogeneous Monte Carlo optical simulator

Optical imaging has been widely applied in preclinical and clinical applications. Fifteen years ago, an efficient Monte Carlo program 'MCML' was developed for use with multi-layered turbid media and has gained popularity in the field of biophotonics. Currently, there is an increasingly pressing need for simulating tools more powerful than MCML in order to study light propagation phenomena in complex inhomogeneous objects, such as the mouse. Here we report a tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIM-OS) to address this issue. By modeling an object as a tetrahedron-based inhomogeneous finite-element mesh, TIM-OS can determine the photon-triangle interaction recursively and rapidly. In numerical simulation, we have demonstrated the correctness and efficiency of TIM-OS.

OPTICAL PROPERTY CHARACTERIZATION BASED ON A PHASE FUNCTION APPROXIMATION MODEL

Recently, we generalized the Delta-Eddington phase function and applied it to the radiative transfer equation for modeling the photon propagation in biological tissue. The resultant phase approximation model was shown to be highly accurate with a wide range of optical properties, including the strongly absorbing and weakly scattering media. In this paper, we propose phase-approximation-based method for estimating the optical parameters. Specifically, we design an iterative algorithm to take advantage of both the global search ability of the differential evolution algorithm and the efficiency of the conjugate gradient method. Then, we demonstrate the feasibility and merits of the proposed method in both numerical simulation and phantom experiments.

A Parallel Adaptive Finite Element Method for the Simulation of Photon Migration with the Radiative-Transfer-Based Model

Whole-body optical molecular imaging of mouse models in preclinical research is rapidly developing in recent years. In this context, it is essential and necessary to develop novel simulation methods of light propagation for optical imaging, especially when a priori knowledge, large-volume domain and a wide-range of optical properties need to be considered in the reconstruction algorithm. In this paper, we propose a three dimensional parallel adaptive finite element method with simplified spherical harmonics (SP(N)) approximation to simulate optical photon propagation in large-volumes of heterogenous tissues. The simulation speed is significantly improved by a posteriori parallel adaptive mesh refinement and dynamic mesh repartitioning. Compared with the diffusion equation and the Monte Carlo methods, the SP(N) method shows improved performance and the necessity of high-order approximation in heterogeneous domains. Optimal solver selection and time-costing analysis in real mouse geometry further improve the performance of the proposed algorithm and show the superiority of the proposed parallel adaptive framework for whole-body optical molecular imaging in murine models.