Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

Combined diffuse optical tomography and photoacoustic tomography for enhanced functional imaging of small animals: a methodological study on phantoms

Hybrid imaging methods combining diffuse optical tomography (DOT) and other anatomical or nonoptical functional modalities have been widely investigated to improve imaging performance degraded by the strong optical scattering of biological tissues, through constraining the reconstruction process by prior structures. However, these modalities with different contrast mechanisms may be ineffective in revealing early-staged lesions with high optical contrast but no morphological changes. Photoacoustic tomography (PAT) is particularly useful for visualizing light-absorbing structures embedded in soft tissues with high spatial resolution. Although it is still challenging for PAT to quantitatively disclose the absorption distribution, the modality does provide reliable and specific a priori information differentiating light-absorbing structures of soft tissues and might be more appropriate to guide DOT in lesion diagnosis, as compared with other anatomical or nonoptical functional modalities. In this study, a PAT-guided DOT approach is introduced with both soft- and hard-prior regularizations. The methodology is experimentally validated on small-animal-sized phantoms using a computed-tomography-analogous (CT-analogous) PAT/DOT dual-modality system, focusing on future whole-body applications. The results show that the proposed scheme is capable of effectively improving the quantitative accuracy and spatial resolution of DOT reconstruction.

Region-based diffuse optical tomography with registered atlas: in vivo acquisition of mouse optical properties

The reconstruction quality in the model-based optical tomography modalities can greatly benefit from a priori information of accurate tissue optical properties, which are difficult to be obtained in vivo with a conventional diffuse optical tomography (DOT) system alone. One of the solutions is to apply a priori anatomical structures obtained with anatomical imaging systems such as X-ray computed tomography (XCT) to constrain the reconstruction process of DOT. However, since X-ray offers low soft-tissue contrast, segmentation of abdominal organs from sole XCT images can be problematic. In order to overcome the challenges, the current study proposes a novel method of recovering a priori organ-oriented tissue optical properties, where anatomical structures of an in vivo mouse are approximately obtained by registering a standard anatomical atlas, i.e., the Digimouse, to the target XCT volume with the non-rigid image registration, and, in turn, employed to guide DOT for extracting the optical properties of inner organs. Simulative investigations have validated the methodological availability of such atlas-registration-based DOT strategy in revealing both a priori anatomical structures and optical properties. Further experiments have demonstrated the feasibility of the proposed method for acquiring the organ-oriented tissue optical properties of in vivo mice, making it as an efficient way of the reconstruction enhancement.

A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method is proposed to reconstruct the fluorescent target for FMT. The SCP-Kaczmarz method uses the preconditioning strategy to minimize the correlation between the rows of the forward matrix and constrains the Kaczmarz iteration results to be sparse. Numerical simulation and phantom and in vivo experiments were performed to test the efficiency of the proposed method. The results demonstrate that both the convergence and accuracy of the proposed method are improved compared with the classical memory-efficient low-cost Kaczmarz method.

Performance Enhancement of Pharmacokinetic Diffuse Fluorescence Tomography by Use of Adaptive Extended Kalman Filtering

Due to both the physiological and morphological differences in the vascularization between healthy and diseased tissues, pharmacokinetic diffuse fluorescence tomography (DFT) can provide contrast-enhanced and comprehensive information for tumor diagnosis and staging. In this regime, the extended Kalman filtering (EKF) based method shows numerous advantages including accurate modeling, online estimation of multiparameters, and universal applicability to any optical fluorophore. Nevertheless the performance of the conventional EKF highly hinges on the exact and inaccessible prior knowledge about the initial values. To address the above issues, an adaptive-EKF scheme is proposed based on a two-compartmental model for the enhancement, which utilizes a variable forgetting-factor to compensate the inaccuracy of the initial states and emphasize the effect of the current data. It is demonstrated using two-dimensional simulative investigations on a circular domain that the proposed adaptive-EKF can obtain preferable estimation of the pharmacokinetic-rates to the conventional-EKF and the enhanced-EKF in terms of quantitativeness, noise robustness, and initialization independence. Further three-dimensional numerical experiments on a digital mouse model validate the efficacy of the method as applied in realistic biological systems.

Temporal Unmixing of Dynamic Fluorescent Images by Blind Source Separation Method with a Convex Framework

By recording a time series of tomographic images, dynamic fluorescence molecular tomography (FMT) allows exploring perfusion, biodistribution, and pharmacokinetics of labeled substances in vivo. Usually, dynamic tomographic images are first reconstructed frame by frame, and then unmixing based on principle component analysis (PCA) or independent component analysis (ICA) is performed to detect and visualize functional structures with different kinetic patterns. PCA and ICA assume sources are statistically uncorrelated or independent and don't perform well when correlated sources are present. In this paper, we deduce the relationship between the measured imaging data and the kinetic patterns and present a temporal unmixing approach, which is based on nonnegative blind source separation (BSS) method with a convex analysis framework to separate the measured data. The presented method requires no assumption on source independence or zero correlations. Several numerical simulations and phantom experiments are conducted to investigate the performance of the proposed temporal unmixing method. The results indicate that it is feasible to unmix the measured data before the tomographic reconstruction and the BSS based method provides better unmixing quality compared with PCA and ICA.

Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization

Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.

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.

Enhancement of fluorescence molecular tomography with structural-prior-based diffuse optical tomography: combating optical background uncertainty

The common approach in fluorescence molecular tomography (FMT) assumes homogeneous distributions of the optical properties and normally results in reconstructions of low sensitivity. A natural enhancement is to incorporate diffuse optical tomography (DOT) to FMT. However, the traditional voxel-based DOT has been a severely ill-posed inverse problem and cannot retrieve the optical property distributions accurately. We present a structural-prior-based DOT method to effectively acquire the heterogeneous optical background with the aid of some imperfect structural priors from x-ray computed tomography and/or magnetic resonance imaging anatomical imaging modalities, and quantitatively compare its hard- and soft-prior schemes for achieving an improved recovery of the fluorescence distribution. Numerical simulations are conducted on a region-labeled three-dimensional (3D) digital mouse model to investigate the performance of this method. Physical experiments on a cylindrical phantom are also conducted to assess this methodology. Our simulated and experimental reconstruction results indicate that the structural-prior-based DOT guided FMT approach can significantly improve the sensitivity of FMT reconstruction, as well as its imaging resolution and quantitative accuracy.

Shape-parameterized diffuse optical tomography holds promise for sensitivity enhancement of fluorescence molecular tomography

A fundamental approach to enhancing the sensitivity of the fluorescence molecular tomography (FMT) is to incorporate diffuse optical tomography (DOT) to modify the light propagation modeling. However, the traditional voxel-based DOT has been involving a severely ill-posed inverse problem and cannot retrieve the optical property distributions with the acceptable quantitative accuracy and spatial resolution. Although, with the aid of an anatomical imaging modality, the structural-prior-based DOT method with either the hard- or soft-prior scheme holds promise for in vivo acquiring the optical background of tissues, the low robustness of the hard-prior scheme to the segmentation error and inferior performance of the soft-prior one in the quantitative accuracy limit its further application. We propose in this paper a shape-parameterized DOT method for not only effectively determining the regional optical properties but potentially achieving reasonable structural amelioration, lending itself to FMT for comparably improved recovery of fluorescence distribution.

Reconstruction of localized fluorescent target from multi-view continuous-wave surface images of small animal with lp sparsity regularization

Fluorescence diffuse optical tomography using a multi-view continuous-wave and non-contact measurement system and an algorithm incorporating the lp (0 < p ≤ 1) sparsity regularization reconstructs a localized fluorescent target in a small animal. The measurement system provides a total of 25 fluorescence surface 2D-images of an object, which are acquired by a CCD camera from five different angles of view with excitation from five different angles. Fluorescence surface emissions from five different angles of view are simultaneously imaged on the CCD sensor, thus leading to fast acquisition of the 25 images within three minutes. The distributions of the fluorophore are reconstructed by solving the inverse problem based on the photon diffusion equations. In the reconstruction process incorporating the lp sparsity regularization, the regularization term is reformulated as a differentiable function for gradient-based non-linear optimization. Numerical simulations and phantom experiments show that the use of the lp sparsity regularization improves the localization of the target and quantitativeness of the fluorophore concentration. A mouse experiment demonstrates that a localized fluorescent target in a mouse is successfully reconstructed.

A two-stage reconstruction of fluorescence molecular tomography based on sparse regularization

Fluorescence molecular tomography (FMT) is a promising imaging modality that offers the possibilities to monitor cellular and molecular function in vivo. However, accurate and stable reconstruction of fluorescence-labeled targets remains a challenging problem. In this contribution, a two-stage reconstruction algorithm that combines sparse regularization with adaptive finite element method is proposed, and two different inversion algorithms are employed separately on the initial coarse mesh and the second refined one. Numerical experiment results with a digital mouse model demonstrate the stability and computational efficiency of the proposed method for FMT.

Adaptive regularized method based on homotopy for sparse fluorescence tomography

Determining an appropriate regularization parameter is often challenging work because it has a narrow range and varies with problems, which is likely to lead to large reconstruction errors. In this contribution, an adaptive regularized method based on homotopy is presented for sparse fluorescence tomography reconstruction. Due to the adaptive regularization strategy, the proposed method is always able to reconstruct sources accurately independent of the estimation of the regularization parameter. Moreover, the proposed method is about two orders of magnitude faster than the two contrasting methods. Numerical and in vivo mouse experiments have been employed to validate the robustness and efficiency of the proposed method.

Normalized Born Approximation-Based Two-Stage Reconstruction Algorithm for Quantitative Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a promising technique forin vivosmall animal imaging. In this paper, a two-stage reconstruction method based on normalized Born approximation is developed for FMT, which includes two steps for quantitative reconstruction. First, the localization of fluorescent fluorophore is determined byl1-norm regularization method. Then, in the location region of fluorophore, which is provided by the first stage, algebraic reconstruction technique (ART) is utilized for the fluorophore concentration reconstruction. The validity of the two-stage quantitative reconstruction algorithm is testified by simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom. The results suggest that we are able to recover the fluorophore location and concentration.