Yujie Lu

Source Reconstruction for Spectrally-resolved Bioluminescence Tomography with Sparse A priori Information

Through restoration of the light source information in small animals in vivo, optical molecular imaging, such as fluorescence molecular tomography (FMT) and bioluminescence tomography (BLT), can depict biological and physiological changes observed using molecular probes. A priori information plays an indispensable role in tomographic reconstruction. As a type of a priori information, the sparsity characteristic of the light source has not been sufficiently considered to date. In this paper, we introduce a compressed sensing method to develop a new tomographic algorithm for spectrally-resolved bioluminescence tomography. This method uses the nature of the source sparsity to improve the reconstruction quality with a regularization implementation. Based on verification of the inverse crime, the proposed algorithm is validated with Monte Carlo-based synthetic data and the popular Tikhonov regularization method. Testing with different noise levels and single/multiple source settings at different depths demonstrates the improved performance of this algorithm. Experimental reconstruction with a mouse-shaped phantom further shows the potential of the proposed algorithm.

Evaluation of the simplified spherical harmonics approximation in bioluminescence tomography through heterogeneous mouse models

In vivo bioluminescence imaging (BLI) has played a more and more important role in biomedical research of small animals. Bioluminescence tomography (BLT) further translates the BLI optical information into three-dimensional bioluminescent source distribution, which could greatly facilitate applications in related studies. Although the diffusion approximation (DA) is one of the most widely-used forward models, higher-order approximations are still needed for in vivo small animal imaging. In this work, as a relatively accurate and higher-order approximation theory, the performance of the simplified spherical harmonics approximation (SPN) in BLT is evaluated detailedly in heterogeneous small animals. In the numerical validations, the SPN based results demonstrate better imaging quality compared with diffusion approximation heterogeneously under various source locations over wide optical domain. Although the evaluation for the effects of the optical property mismatch indicates the sensitivity of SPN is similar with DA model in the source localization, it may offer improved performance with much less artifacts. In what follows, heterogeneous experimental BLT reconstructions using in vivo mouse further evaluate the capability of the higher-order method for practical biomedical applications.

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 SP(3)-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 SP(3)-based reconstruction algorithm.

A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations

Bioluminescence imaging (BLI) makes it possible to elucidate molecular and cellular signatures to better understand the effects of human disease in small animal models in vivo. The unambiguous three-dimensional bioluminescent source information obtained by bioluminescence tomography (BLT) could further facilitate its applications in biomedicine. However, to the best of our knowledge, the existing gradient-type reconstruction methods in BLT are inefficient, and often require a relatively small volume of interest (VOI) for feasible results. In this paper, a fast generalized graph cuts based reconstruction method for BLT is presented, which is to localize the bioluminescent source in heterogeneous mouse tissues via max-flow/min-cut algorithm. Since the original graph cuts theory can only handle graph-representable problem, the quadratic pseudo-boolean optimization is incorporated to make the graph representable and tractable, which is called generalized graph cuts (GGC). The internal light source can be reconstructed from the whole domain, so a priori knowledge of VOI can be avoided in this method. In the simulation validations, the proposed method was validated in a heterogeneous mouse atlas, and the source can be localized reliably and efficiently by GGC; and compared with gradient-type method, the proposed method is about 25-50 times faster. Moreover, the experiments for sensitivity to the measurement errors of tissue optical properties demonstrate that, the reconstruction quality is not much affected by mismatch of parameters. In what follows, in vivo mouse BLT reconstructions further demonstrated the potential and effectiveness of the generalized graph cut based reconstruction method.

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.

Experimental Bioluminescence Tomography with Fully Parallel Radiative-transfer-based Reconstruction Framework

Bioluminescence imaging is a very sensitive imaging modality, used in preclinical molecular imaging. However, in its planar projection form, it is non-quantitative and has poor spatial resolution. In contrast, bioluminescence tomography (BLT) promises to provide three dimensional quantitative source information. Currently, nearly all BLT reconstruction algorithms in use employ the diffusion approximation theory to determine light propagation in tissues. In this process, several approximations and assumptions that are made severely affect the reconstruction quality of BLT. It is therefore necessary to develop novel reconstruction methods using high-order approximation models to the radiative transfer equation (RTE) as well as more complex geometries for the whole-body of small animals. However, these methodologies introduce significant challenges not only in terms of reconstruction speed but also for the overall reconstruction strategy. In this paper, a novel fully-parallel reconstruction framework is proposed which uses a simplified spherical harmonics approximation (SPN). Using this framework, a simple linear relationship between the unknown source distribution and the surface measured photon density can be established. The distributed storage and parallel operations of the finite element-based matrix make SPN-based spectrally resolved reconstruction feasible at the small animal whole body level. Performance optimization of the major steps of the framework remarkably improves reconstruction speed. Experimental reconstructions with mouse-shaped phantoms and real mice show the effectiveness and potential of this framework. This work constitutes an important advance towards developing more precise BLT reconstruction algorithms that utilize high-order approximations, particularly second-order self-adjoint forms to the RTE for in vivo small animal experiments.

Differential Evolution Approach for Regularized Bioluminescence Tomography

Bioluminescence tomography (BLT) is an inverse source problem that localizes and quantifies bioluminescent probe distribution in 3-D. The generic BLT model is ill-posed, leading to nonunique solutions and aberrant reconstruction in the presence of measurement noise and optical parameter mismatches. In this paper, we introduce the knowledge of the number of bioluminescence sources to stabilize the BLT problem. Based on this regularized BLT model, we develop a differential evolution-based reconstruction algorithm to determine the source locations and strengths accurately and reliably. Then, we evaluate this novel approach in numerical, phantom, and mouse studies.

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.

A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography

In this paper, we consider 3D Bioluminescence tomography (BLT) source reconstruction from Poisson data in three dimensional space. With a priori information of sources sparsity and MAP estimation of Poisson distribution, we study the minimization of Kullback-Leihbler divergence with ℓ1 and ℓ0 regularization. We show numerically that although several ℓ1 minimization algorithms are efficient for compressive sensing, they fail for BLT reconstruction due to the high coherence of the measurement matrix columns and high nonlinearity of Poisson fitting term. Instead, we propose a novel greedy algorithm for ℓ0 regularization to reconstruct sparse solutions for BLT problem. Numerical experiments on synthetic data obtained by the finite element methods and Monte-Carlo methods show the accuracy and efficiency of the proposed method.

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.