Third-order Simplified Spherical Harmonics Research Articles

Diagnostic Evaluation of Rheumatoid Arthritis (RA) in Finger Joints Based on the Third-Order Simplified Spherical Harmonics (SP3) Light Propagation Model

This work focuses on the evaluation of third-order simplified spherical harmonics (SP3) model-based image reconstruction with respect to its clinical utility to diagnose rheumatoid arthritis (RA). The existing clinical data of 219 fingers was reconstructed for both absorption and scattering maps in fingers by using the reduced-Hessian sequential quadratic programming (rSQP) algorithm that employs the SP3 model of light propagation. The k-fold cross validation method was used for feature extraction and classification of SP3-based tomographic images. The performance of the SP3 model was compared to the DE and ERT models with respect to diagnostic accuracy and computational efficiency. The results presented here show that the SP3 model achieves clinically relevant sensitivity (88%) and specificity (93%) that compare favorably to the ERT while maintaining significant computational advantage over the ERT (i.e., the SP3 model is 100 times faster than the ERT). Furthermore, it is also shown that the SP3 is similar in speed but superior in diagnostic accuracy to the DE. Therefore, it is expected that the method presented here can greatly aid in the early diagnosis of RA with clinically relevant accuracy in near real-time at a clinical setting.

Investigation of total diffuse-photon-density-wave field in semi-infinite turbid media based on the extrapolated Beer–Lambert law

The accurate description of the total diffuse-photon-density-wave field inside turbid media, especially in the near-field region, is extremely critical but challenging for many decades. Here, the total diffuse-photon-density-wave field of semi-infinite turbid media was calculated by the third-order simplified spherical harmonics approximation (SP3) and compared with Monte Carlo simulations. To improve the SP3 approximation, the extrapolated Beer–Lambert law model considering the contribution of the coherent-photon-density-wave in the near-field region was proposed and implemented by Levenberg–Marquardt and universal global optimization methods. Last, we demonstrated the superiority of the proposed model over the existing model in fitting the accuracy and applicable source–detector distance range. The high accuracy and simplicity of the proposed model would be extremely helpful for biomedical applications involving photothermal radiometry, and rapidly determining optical properties of media, along with photoacoustic imaging and photodynamic therapy.

The Differences Between the Two Forms of Semi-Analytical Nodal Methods on Solving the Third-Order Simplified Spherical Harmonics Method Equations1

Solving the third-order simplified spherical harmonics method (SP3) equations is one of the key points in the development of advanced reactor calculation methods and has been widely concerned. The semi-analytical nodal method (SANM), based on transverse-integrated diffusion equation, has the advantages of high accuracy and convenience for multigroup calculation. Due to its advantages, the method is expected to be used in solving the SP3 equations. However, the traditional SANM is not rigorous since the expansion process does not take the special modality of the SP3 equations and their analytical solutions into consideration. There are two modalities of the SP3 equations, so there are two traditional SANM forms on solving the SP3 equations, and the differences between the two forms will be very important in further research on the SANM. A code is developed to solve the SP3 equations under the two different forms. After the calculation of the same benchmark, the difference between the two forms on solving the SP3 equations is found. According to the results, and in view of the special modality of the SP3 equations, points on a more rigorous SANM for solving the SP3 equations are discussed.

Hybrid radiosity-SP3 equation based bioluminescence tomography reconstruction for turbid medium with low- and non-scattering regions

To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP3) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.

A compact frequency-domain photon migration system for integration into commercial hybrid small animal imaging scanners for fluorescence tomography

The work presented herein describes the system design and performance evaluation of a miniaturized near-infrared fluorescence (NIRF) frequency-domain photon migration (FDPM) system with non-contact excitation and homodyne detection capability for small animal fluorescence tomography. The FDPM system was developed specifically for incorporation into a Siemens micro positron emission tomography/computed tomography (microPET/CT) commercial scanner for hybrid small animal imaging, but could be adapted to other systems. Operating at 100 MHz, the system noise was minimized and the associated amplitude and phase errors were characterized to be ±0.7% and ±0.3°, respectively. To demonstrate the tomographic ability, a commercial mouse-shaped phantom with 50 µM IRDye800CW and 68Ga containing inclusion was used to associate PET and NIRF tomography. Three-dimensional mesh generation and anatomical referencing was accomplished through CT. A third-order simplified spherical harmonics approximation (SP3) algorithm, for efficient prediction of light propagation in small animals, was tailored to incorporate the FDPM approach. Finally, the PET-NIRF target co-localization accuracy was analyzed in vivo with a dual-labeled imaging agent targeting orthotopic growth of human prostate cancer. The obtained results validate the integration of time-dependent fluorescence tomography system within a commercial microPET/CT scanner for multimodality small animal imaging.

Comparison between radiative transfer theory and the simplified spherical harmonics approximation for a semi-infinite geometry

In this study, the third-order simplified spherical harmonics equations (SP3), an approximation of the radiative transfer equation, are solved for a semi-infinite geometry considering the exact simplified spherical harmonics boundary conditions. The obtained Green's function is compared to radiative transfer calculations and the diffusion theory. In general, it is shown that the SP3 equations provide better results than the diffusion approximation in media with high absorption coefficient values but no improvement is found for small distances to the source.

Whole-Body Cerenkov Luminescence Tomography with the Finite Element SP3 Method

Generation of an accurate Cerenkov luminescence imaging model is a current issue of nuclear tomography with optical techniques. The article takes a pro-active approach toward whole-body Cerenkov luminescence tomography. The finite element framework employs the equation of radiative transfer via the third-order simplified spherical harmonics approximation to model Cerenkov photon propagation in a small animal. After this forward model is performed on a digital mouse with optical property heterogeneity and compared with the Monte Carlo method, we investigated the whole body reconstruction algorithm along a regularization path via coordinate descent. The endpoint of the follow-up study is the in vivo application, which provides three-dimensional biodistribution of the radiotracer uptake in the mouse from measured partial boundary currents. The combination of the forward and inverse model with elastic-net penalties is not only validated by numerical simulation, but it also effectively demonstrates in vivo imaging in small animals. Our exact reconstruction method enables optical molecular imaging to best utilize Cerenkov radiation emission from the decay of medical isotopes in tissues.

基于辐射传输方程三阶简化球谐近似模型的时域荧光扩散层析图像重建方法

基于辐射传输方程三阶简化球谐近似模型的时域荧光扩散层析图像重建方法

Sparsity-Promoting Tomographic Fluorescence Imaging With Simplified Spherical Harmonics Approximation

Fluorescence molecular tomography has become a promising technique for in vivo small animal imaging and has many potential applications. Due to the ill-posed and the ill-conditioned nature of the problem, Tikhonov regularization is generally adopted to stabilize the solution. However, the result is usually over-smoothed. In this letter, the third-order simplified spherical harmonics approximation to radiative transfer equation is utilized to model the photon propagation within biological tissues. Considering the sparsity of the fluorescent sources, we replace Tikhonov method with an iteratively reweighted scheme. By dynamically updating the weight matrix, L1-norm regularization can be approximated, which can promote the sparsity of the solution. Simulation study shows that this method can preserve the sparsity of the fluorescent sources within heterogeneous medium, even with very limited measurement data.

In Vivo Mouse Bioluminescence Tomography with Radionuclide-Based Imaging Validation

IntroductionBioluminescence imaging, especially planar bioluminescence imaging, has been extensively applied in in vivo preclinical biological research. Bioluminescence tomography (BLT) has the potential to provide more accurate imaging information due to its 3D reconstruction compared with its planar counterpart.MethodsIn this work, we introduce a positron emission tomography (PET) radionuclide imaging-based strategy to validate the BLT results. X-ray computed tomography, PET, spectrally resolved bioluminescence imaging, and surgical excision were performed on a tumor xenograft mouse model expressing a bioluminescent reporter gene.ResultsWith different spectrally resolved measured data, the BLT reconstructions were acquired based on the third-order simplified spherical harmonics (SP3) approximation and the diffusion approximation (DA). The corresponding tomographic images were obtained for validation of bioluminescence source reconstruction.ConclusionOur results show the strength of PET imaging compared with other validation methods for BLT and improved source localization accuracy based on the SP3 approximation compared with the diffusion approximation.

Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation

Bioluminescence imaging has been extensively applied to in vivo small animal imaging. Quantitative three-dimensional bioluminescent source information obtained by using bioluminescence tomography can directly and much more accurately reflect biological changes as opposed to planar bioluminescence imaging. Preliminary simulated and experimental reconstruction results demonstrate the feasibility and promise of bioluminescence tomography. However, the use of multiple approximations, particularly the diffusion approximation theory, affects the quality of in vivo small animal-based image reconstructions. In the development of new reconstruction algorithms, high-order approximation models of the radiative transfer equation and spectrally resolved data introduce new challenges to the reconstruction algorithm and speed. In this paper, an SP3-based (the third-order simplified spherical harmonics approximation) spectrally resolved reconstruction algorithm is proposed. The simple linear relationship between the unknown source distribution and the spectrally resolved data is established in this algorithm. A parallel version of this algorithm is realized, making BLT reconstruction feasible for the whole body of small animals especially for fine spatial domain discretization. In simulation validations, the proposed algorithm shows improved reconstruction quality compared with diffusion approximation-based methods when high absorption, superficial sources and detection modes are considered. In addition, comparisons between fine and coarse mesh-based BLT reconstructions show the effects of numerical errors in reconstruction image quality. Finally, BLT reconstructions using in vivo mouse experiments further demonstrate the potential and effectiveness of the SP3-based reconstruction algorithm.