Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation

Encoder-decoder deep learning network for simultaneous reconstruction of fluorescence yield and lifetime distributions

A time-domain fluorescence molecular tomography in reflective geometry (TD-rFMT) has been proposed to circumvent the penetration limit and reconstruct fluorescence distribution within a 2.5-cm depth regardless of the object size. In this paper, an end-to-end encoder-decoder network is proposed to further enhance the reconstruction performance of TD-rFMT. The network reconstructs both the fluorescence yield and lifetime distributions directly from the time-resolved fluorescent signals. According to the properties of TD-rFMT, proper noise was added to the simulation training data and a customized loss function was adopted for self-supervised and supervised joint training. Simulations and phantom experiments demonstrate that the proposed network can significantly improve the spatial resolution, positioning accuracy, and accuracy of lifetime values.

Depth-recognizable time-domain fluorescence molecular tomography in reflective geometry

Conventional fluorescence molecular tomography (FMT) reconstruction requires photons penetrating the whole object, which limits its applications to small animals. However, by utilizing reflective photons, fluorescence distribution near the surface could be reconstructed regardless of the object size, which may extend the applications of FMT to surgical navigation and so on. Therefore, time-domain reflective fluorescence molecular tomography (TD-rFMT) is proposed in this paper. The system excites and detects the emission light from the same angle within a field of view of 5 cm. Because the detected intensities of targets depend strongly on the depth, the reconstruction of targets in deep regions would be evidently affected. Therefore, a fluorescence yield reconstruction method with depth regularization and a weighted separation reconstruction strategy for lifetime are developed to enhance the performance for deep targets. Through simulations and phantom experiments, TD-rFMT is proved capable of reconstructing fluorescence distribution within a 2.5-cm depth with accurate reconstructed yield, lifetime, and target position(s).

Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

Role of late photons in diffuse optical imaging

The ability to image through turbid media, such as organic tissues, is a highly attractive prospect for biological and medical imaging. This is challenging, however, due to the highly scattering properties of tissues which scramble the image information. The earliest photons that arrive at the detector are often associated with ballistic transmission, whilst the later photons are associated with complex paths due to multiple independent scattering events and are therefore typically considered to be detrimental to the final image formation process. In this work, we report on the importance of these highly diffuse, "late" photons for computational time-of-flight diffuse optical imaging. In thick scattering materials, >80 transport mean free paths, we provide evidence that including late photons in the inverse retrieval enhances the image reconstruction quality. We also show that the late photons alone have sufficient information to retrieve images of a similar quality to early photon gated data. This result emphasises the importance in the strongly diffusive regime of fully time-resolved imaging techniques.

Reconstruction of high-resolution early-photon tomography based on the first derivative of temporal point spread function

For fluorescence molecular tomography, higher spatial resolution can be achieved using minimally scattered early photons. Conventional reconstruction methods of early photon tomography (EPT) are based on the integral of temporal point spread function (TPSF), which may lead to poor image quality due to systematic noise and time mismatch between the TPSF data and forward model. The derivative of the rising portion of TPSF is proposed to be used in EPT to increase the performance of reconstruction because the derivative is less sensitive to noise and time mismatch than the integral. A method based on projected Tikhonov regularization with the reconstructed result of steepest descent algorithm as a priori information is developed. Using the derivative of TPSF, the method can achieve high spatial resolution in phantom experiments and is capable of separating targets with an edge-edge distance of 1.5 mm.

Self-guided reconstruction for time-domain fluorescence molecular lifetime tomography

Fluorescence probes have distinct yields and lifetimes when located in different environments, which makes the reconstruction of fluorescence molecular lifetime tomography (FMLT) challenging. To enhance the reconstruction performance of time-domain (TD) FMLT with heterogeneous targets, a self-guided L 1 regularization projected steepest descent (SGL1PSD) algorithm is proposed. Different from other algorithms performed in time domain, SGL1PSD introduces a time-resolved strategy into fluorescence yield reconstruction. The algorithm consists of four steps. Step 1 reconstructs the initial yield map with full time gate strategy; steps 2–4 reconstruct the inverse lifetime map, the yield map, and the inverse lifetime map again with time-resolved strategy, respectively. The reconstruction result of each step is used as a priori for the reconstruction of the next step. Projected iterated Tikhonov regularization algorithm is adopted for the yield map reconstructions in steps 1 and 3 to provide a solution with iterative refinement and nonnegative constraint. The inverse lifetime map reconstructions in steps 2 and 4 are based on L 1 regularization projected steepest descent algorithm, which employ the L 1 regularization to reduce the ill-posedness of the high-dimensional nonlinear problem. Phantom experiments with heterogeneous targets at different edge-to-edge distances demonstrate that SG

Enhanced detection of early photons in time-domain optical imaging by running in the "dead-time" regime

Optical tomography can yield anatomical and molecular information about biological tissue. However, its spatial resolution is poor in thick samples owing to high scatter. Early photon approaches, where photon arrival times are measured with time-resolved detectors, provide one means of improving spatial resolution through selection of photons that travel a straighter path. Here, a novel approach to significantly enhance detection of early photons in time-correlated single photon counting with avalanche photodiodes has been discussed. Results suggest that the early photon detection rate can be increased by about 10 orders of magnitude by running the detector in a dead-time regime.

Unmixing multiple adjacent fluorescent targets with multispectral excited fluorescence molecular tomography

Fluorescence molecular tomography (FMT) can visualize biological activities at cellular and molecular levels in vivo, and has been extensively used in drug delivery and tumor detection research of small animals. The ill-posedness of the FMT inverse problem makes it difficult to reconstruct and unmix multiple adjacent fluorescent targets that have different functional features but are labeled with the same fluorochrome. A method based on independent component analysis for multispectral excited FMT was proposed in our previous study. It showed that double fluorescent targets with certain edge-to-edge distance (EED) could be unmixed by the method. In this study, the situation is promoted to unmix multiple adjacent fluorescent targets (i.e., more than two fluorescent targets and EED=0). Phantom experiments on the resolving ability of the proposed algorithm demonstrate that the algorithm performs well in unmixing multiple adjacent fluorescent targets in both lateral and axial directions. And also, we recovered the locational information of each independent fluorescent target and described the variable trends of the corresponding fluorescent targets under the excitation spectrum. This method is capable of unmixing multiple fluorescent targets with small EED but labeled with the same fluorochrome, and may be used in imaging of nonspecific probe targeting and metabolism of drugs.

Nonlinear greedy sparsity-constrained algorithm for direct reconstruction of fluorescence molecular lifetime tomography

In order to improve the spatial resolution of time-domain (TD) fluorescence molecular lifetime tomography (FMLT), an accelerated nonlinear orthogonal matching pursuit (ANOMP) algorithm is proposed. As a kind of nonlinear greedy sparsity-constrained methods, ANOMP can find an approximate solution of L0 minimization problem. ANOMP consists of two parts, i.e., the outer iterations and the inner iterations. Each outer iteration selects multiple elements to expand the support set of the inverse lifetime based on the gradients of a mismatch error. The inner iterations obtain an intermediate estimate based on the support set estimated in the outer iterations. The stopping criterion for the outer iterations is based on the stability of the maximum reconstructed values and is robust for problems with targets at different edge-to-edge distances (EEDs). Phantom experiments with two fluorophores at different EEDs and in vivo mouse experiments demonstrate that ANOMP can provide high quantification accuracy, even if the EED is relatively small, and high resolution.

Time-domain geometrical localization of point-like fluorescence inclusions in turbid media with early photon arrival times

We introduce a novel approach for localizing a plurality of discrete point-like fluorescent inclusions embedded in a thick turbid medium using time-domain measurements. The approach uses early photon information contained in measured time-of-flight distributions originating from fluorescence emission. Fluorescence time point-spread functions (FTPSFs) are acquired with ultrafast time-correlated single photon counting after short pulse laser excitation. Early photon arrival times are extracted from the FTPSFs obtained from several source-detector positions. Each source-detector measurement allows defining a geometrical locus where an inclusion is to be found. These loci take the form of ovals in 2D or ovoids in 3D. From these loci a map can be built, with the maxima thereof corresponding to positions of inclusions. This geometrical approach is supported by Monte Carlo simulations performed for biological tissue-like media with embedded fluorescent inclusions. To validate the approach, several experiments are conducted with a homogeneous phantom mimicking tissue optical properties. In the experiments, inclusions filled with indocyanine green are embedded in the phantom and the fluorescence response to a short pulse of excitation laser is recorded. With our approach, several inclusions can be localized with low millimeter positional error. Our results support the approach as an accurate, efficient, and fast method for localizing fluorescent inclusions embedded in highly turbid media mimicking biological tissues. Further Monte Carlo simulations on a realistic mouse model show the feasibility of the technique for small animal imaging.

Acceleration of early-photon fluorescence molecular tomography with graphics processing units

Fluorescence molecular tomography (FMT) with early-photons can improve the spatial resolution and fidelity of the reconstructed results. However, its computing scale is always large which limits its applications. In this paper, we introduced an acceleration strategy for the early-photon FMT with graphics processing units (GPUs). According to the procedure, the whole solution of FMT was divided into several modules and the time consumption for each module is studied. In this strategy, two most time consuming modules (G_d and W modules) were accelerated with GPU, respectively, while the other modules remained coded in the Matlab. Several simulation studies with a heterogeneous digital mouse atlas were performed to confirm the performance of the acceleration strategy. The results confirmed the feasibility of the strategy and showed that the processing speed was improved significantly.

Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion

Fluorescence molecular tomography (FMT) is a promising imaging modality that enables three-dimensional visualization of fluorescent targets in vivo in small animals. L2-norm regularization methods are usually used for severely ill-posed FMT problems. However, the smoothing effects caused by these methods result in continuous distribution that lacks high-frequency edge-type features and hence limits the resolution of FMT. In this paper, the sparsity in FMT reconstruction results is exploited via compressed sensing (CS). First, in order to ensure the feasibility of CS for the FMT inverse problem, truncated singular value decomposition (TSVD) conversion is implemented for the measurement matrix of the FMT problem. Then, as one kind of greedy algorithm, an ameliorated stagewise orthogonal matching pursuit with gradually shrunk thresholds and a specific halting condition is developed for the FMT inverse problem. To evaluate the proposed algorithm, we compared it with a TSVD method based on L2-norm regularization in numerical simulation and phantom experiments. The results show that the proposed algorithm can obtain higher spatial resolution and higher signal-to-noise ratio compared with the TSVD method.

Seeing through turbidity with harmonic holography [Invited]

The ability to see inside the body noninvasively is indispensable in modern biology and medicine. Optical approaches to such abilities are of rapidly growing interest because of their nonionizing nature and low cost. However, the problem of opacity due to the optical turbidity of tissues must be addressed before optical means become practical. Harmonic holography amalgamates the capability of holographic phase conjugation with the contrast-forming mechanism of second-harmonic generation, which provides a unique opportunity for imaging through a turbid medium. In this review we give accounts of the effort of imaging through turbid media using harmonic holographic phase conjugation.

The effect of temporal impulse response on experimental reduction of photon scatter in time-resolved diffuse optical tomography

New fast detector technology has driven significant renewed interest in time-resolved measurement of early photons in improving imaging resolution in diffuse optical tomography and fluorescence mediated tomography in recent years. In practice, selection of early photons results in significantly narrower instrument photon density sensitivity functions (PDSFs) than the continuous wave case, resulting in a better conditioned reconstruction problem. In this work, we studied the quantitative impact of the instrument temporal impulse response function (TIRF) on experimental PDSFs in tissue mimicking optical phantoms. We used a multimode fiber dispersion method to vary the system TIRF over a range of representative literature values. Substantial disagreement in PDSF width--by up to 40%--was observed between experimental measurements and Monte Carlo (MC) models of photon propagation over the range of TIRFs studied. On average, PDSFs were broadened by about 0.3 mm at the center plane of the 2 cm wide imaging chamber per 100 ps of the instrument TIRF at early times. Further, this broadening was comparable on both the source and detector sides. Results were confirmed by convolution of instrument TIRFs with MC simulations. These data also underscore the importance of correcting imaging PDSFs for the instrument TIRF when performing tomographic image reconstruction to ensure accurate data-model agreement.

Weighted depth compensation algorithm for fluorescence molecular tomography reconstruction

In fluorescence molecular tomography (FMT), diffuse-light measurements are obtained from a series of source-detector pairs placed on the boundary of the medium. The sensitivity of measurements deteriorates quickly with increased distance from the sources and detectors and therefore yields poor depth quantitative recovery. A depth compensation algorithm is presented in this paper to reconstruct fluorescent inclusions in deep tissues. Two weight matrixes are employed to level off sensitivity differences and enhance prominent elements of the solution. Results of numerical and phantom experiments demonstrate that both relative quantitation and spatial resolution of FMT are improved for inclusions at different depths.