Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors

Deep learning-based fusion of widefield diffuse optical tomography and micro-CT structural priors for accurate 3D reconstructions

Widefield illumination and detection strategies leveraging structured light have enabled fast and robust probing of tissue properties over large surface areas and volumes. However, when applied to diffuse optical tomography (DOT) applications, they still require a time-consuming and expert-centric solving of an ill-posed inverse problem. Deep learning (DL) models have been recently proposed to facilitate this challenging step. Herein, we expand on a previously reported deep neural network (DNN) -based architecture (modified AUTOMAP - ModAM) for accurate and fast reconstructions of the absorption coefficient in 3D DOT based on a structured light illumination and detection scheme. Furthermore, we evaluate the improved performances when incorporating a micro-CT structural prior in the DNN-based workflow, named Z-AUTOMAP. This Z-AUTOMAP significantly improves the widefield imaging process's spatial resolution, especially in the transverse direction. The reported DL-based strategies are validated both in silico and in experimental phantom studies using spectral micro-CT priors. Overall, this is the first successful demonstration of micro-CT and DOT fusion using deep learning, greatly enhancing the prospect of rapid data-integration strategies, often demanded in challenging pre-clinical scenarios.

Indirect and direct estimation of pharmacokinetic parameters in dynamic diffuse fluorescence tomography by adaptive extended Kalman filtering

Pharmacokinetic parameter estimation with the support of dynamic diffuse fluorescence tomography (DFT) can provide helpful diagnostic information for tumor differentiation and monitoring. Adaptive extended Kalman filtering (AEKF) as a nonlinear filter method has the merits of high quantitativeness, noise robustness, and initialization independence. In this paper, indirect and direct AEKF schemes combining with a commonly used two-compartment model were studied to estimate the pharmacokinetic parameters based on our self-designed dynamic DFT system. To comprehensively compare the performances of both schemes, the selection of optimal noise covariance matrices affecting estimation results was first studied, then a series of numerical simulations with the metabolic time ranged from 4.16 min to 38 min was carried out and quantitatively evaluated. The comparison results show that the direct AEKF outperforms the indirect EKF in estimation accuracy at different metabolic velocity and demonstrates stronger stability at the large metabolic velocity. Furtherly, the in vivo experiment was conducted to achieve the indocyanine green pharmacokinetic-rate images in the mouse liver. The experimental results confirmed the capability of both schemes to estimate the pharmacokinetic-rate images and were in agreement with the theory predictions and the numerical simulation results.

Three Dimensional Lifetime-Multiplex Tomography Based on Time-Gated Capturing of Near-Infrared Fluorescence Images

We report a computed tomography (CT) technique for mapping near-infrared fluorescence (NIRF) lifetime as a multiplex three-dimensional (3D) imaging method, using a conventional NIR camera. This method is achieved by using a time-gated system composed of a pulsed laser and an NIR camera synchronized with a rotatable sample stage for NIRF-CT imaging. The fluorescence lifetimes in microsecond-order of lanthanides were mapped on reconstructed cross-sectional and 3D images, via back-projection of two-dimensional projected images acquired from multiple angles at each time point showing fluorescence decay. A method to select slopes (the observed decay rates in time-gated imaging) used for the lifetime calculation, termed as the slope comparison method, was developed for the accurate calculation of each pixel, resulting in reduction of image acquisition time. Time-gated NIRF-CT provides a novel choice for multiplex 3D observation of deep tissues in biology.

High-sensitivity dynamic diffuse fluorescence tomography system for fluorescence pharmacokinetics

SIGNIFICANCE

Dynamic diffuse fluorescence tomography (DFT) can recover the static distribution of fluorophores and track dynamic temporal events related to physiological and disease progression. Dynamic imaging indocyanine green (ICG) approved by the food and drug administration is still under-exploited because of its characteristics of low quantum yield and relatively rapid tissue metabolism.

AIM

In order to acquire the ICG tomographic image sequences for pharmacokinetic analysis, a dynamic DFT system was proposed.

APPROACH

A fiber-based dynamic DFT system adopts square-wave modulation lock-in photon-counting scheme and series-parallel measurement mode, which possesses high sensitivity, large dynamic range, high anti-ambient light ability in common knowledge, as well as good cost performance. In order to investigate the effectiveness of the proposed system, the measurement stability and the anti-crosstalk-a crucial factor affecting the system parallelization-were assessed firstly, then a series of static phantoms, dynamic phantoms and in vivo mice experiments were conducted to verify the imaging capability.

RESULTS

The system has the limited dynamic range of 100 dB, the fluctuation of photon counting within 3%, and channel-to-channel crosstalk ratio better than 1.35. Under the condition of a sufficient signal-to-noise ratio, a complete measurement time for one frame image was 10.08 s. The experimental results of static phantoms with a single target and three targets showed that this system can accurately obtain the positions, sizes, and shapes of the targets and the reconstructed images exhibited a high quantitativeness. Further, the self-designed dynamic phantom experiments demonstrated the capability of the system to capture fast changing fluorescence signals. Finally, the in vivo experiments validated the practical capability of the system to effectively track the ICG metabolism in living mice.

CONCLUSIONS

These results demonstrate that our proposed system can be utilized for assessing ICG pharmacokinetics, which may provide a valuable tool for tumor detection, drug assessment, and liver function evaluation.

Method for improving the accuracy of fluorescence molecular tomography based on multi-wavelength concurrent reconstruction

A Concurrent-wavelength Reconstruction Algorithm (CRA) based on multi-wavelength information fusion is proposed in this paper that aims to further improve the accuracy of Fluorescence Molecular Tomography (FMT) reconstruction. Combining multi-spectral data with FMT technology, the information of 650 and 750 nm wavelengths near-infrared was used to increase the feature information of the dominant 850 nm wavelength near-infrared effectively. Principal component analysis, which can remove redundant information and achieve data dimensionality reduction, was then utilized to extract the feature information. Finally, tomographic reconstruction of the anomalies was performed based on the stacked auto-encoder neural network model. The comparison results of numerical experiments showed that the reconstruction effect of CRA was superior to the performance of the single wavelength model. The correlation coefficient between CRA reconstructed anomalies' fluorescence yield values and the real fluorescence yield values remained at 0.95 or more under the noise of different levels of signal-to-noise ratios. Therefore, the CRA proposed in this paper could effectively improve on the ill-posedness of the inverse problem, which could further enhance the accuracy of FMT reconstruction.

Principal Component Analysis Based Dynamic Cone Beam X-Ray Luminescence Computed Tomography: A Feasibility Study

Cone beam X-ray luminescence computed tomography (CB-XLCT) is a promising imaging technique in studying the physiological and pathological processes in small animals. However, the dynamic bio-distributions of probes in small animal, especially in adjacent targets are still hard to be captured directly from dynamic CB-XLCT. In this paper, a 4D temporal-spatial reconstruction method based on principal component analysis (PCA) in the projection space is proposed for dynamic CB-XLCT. First, projections of angles in each 3D frame are compressed to reduce the noises initially. Then a temporal PCA is performed on the projection data to decorrelate the 4D problem into separate 3D problems in the PCA domain. In the PCA domain, the difference between dynamic behaviors of multiple targets can be reflected by the first several principal components which can be further used for fast and improved reconstruction by a restarted Tikhonov regularization method. At last, by discarding the principal components mainly reflecting noise, the concentration series of targets are recovered from the first few reconstruction results with a mask as the constraint. The numerical simulation and phantom experiment demonstrate that the proposed method can resolve multiple targets and recover the dynamic distributions with high computation efficiency. The proposed method provides new feasibility for imaging dynamic bio-distributions of probes in vivo.

Laplace-domain diffuse optical measurement

Time-domain diffuse optical measurement systems determine depth-resolved absorption changes by using the time of flight distribution of the detected photons. It is well known that certain feature data, such as the Laplace transform of the temporal point spread function, is sufficient for image reconstruction and diffuse optical sensing. Conventional time-domain systems require the acquisition of full temporal profiles of diffusive photons and then numerically compute the feature dataset, for example, Laplace transformed intensities for imaging applications. We have proposed a novel method for directly obtaining the Laplace transform data. Our approach can significantly improve the data acquisition speed for time-domain diffuse optical imaging. We also demonstrated that the use of negative Laplace parameters can provide enhanced sensitivity to perturbations located in deep regions.

Spectral-resolved cone-beam X-ray luminescence computed tomography with principle component analysis

Cone-beam X-ray luminescence computed tomography (CB-XLCT) has become a promising technique for its higher utilization of X-ray and shorter scanning time compared to the narrow-beam XLCT, but it suffers from the low-spatial resolution that results in the insufficiency to resolve the adjacent multiple probes. In multispectral CB-XLCT, multiple probes show different emission behaviors in the dimension of the spectrum. In this work, a spectral-resolved CB-XLCT method combining multispectral CB-XLCT with principle component analysis (PCA) was proposed to improve the imaging resolution. Results of digital simulation and the phantom experiment illustrated that the proposed method was capable of resolving adjacent multiple probes accurately and had better performance than the common multispectral CB-XLCT with spectrum information priori.

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

Direct reconstruction in CT-analogous pharmacokinetic diffuse fluorescence tomography: two-dimensional simulative and experimental validations

We present a generalized strategy for direct reconstruction in pharmacokinetic diffuse fluorescence tomography (DFT) with CT-analogous scanning mode, which can accomplish one-step reconstruction of the indocyanine-green pharmacokinetic-rate images within in vivo small animals by incorporating the compartmental kinetic model into an adaptive extended Kalman filtering scheme and using an instantaneous sampling dataset. This scheme, compared with the established indirect and direct methods, eliminates the interim error of the DFT inversion and relaxes the expensive requirement of the instrument for obtaining highly time-resolved date-sets of complete 360 deg projections. The scheme is validated by two-dimensional simulations for the two-compartment model and pilot phantom experiments for the one-compartment model, suggesting that the proposed method can estimate the compartmental concentrations and the pharmacokinetic-rates simultaneously with a fair quantitative and localization accuracy, and is well suitable for cost-effective and dense-sampling instrumentation based on the highly-sensitive photon counting technique.

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.

Direct reconstruction method for time-domain fluorescence molecular lifetime tomography

For the reconstruction of time-domain fluorescence molecular lifetime tomography, conventional methods based on the Laplace or Fourier transform utilize only part of the information from the measurement data, and rely on the selection of transformation factors. To make the best of all the measurement data, a direct reconstruction algorithm is proposed. The fluorescence yield map is first reconstructed with a full-time gate, and then an objective function for the inverse lifetime tomography (instead of the lifetime) is developed so as to avoid dealing with the singularity of the zero points in the lifetime image. Through simulations and physical phantom experiments, the proposed algorithm is demonstrated to have high localization accuracy for fluorescent targets, high quantification accuracy for fluorescence lifetime, and good contrast between different fluorescence targets.

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.

Spatial-frequency-compression scheme for diffuse optical tomography with dense sampling dataset

Dense sampling of illumination and detection offers an effective way of improving the image-reconstruction performance of near-infrared diffuse optical tomography (DOT) at a cost of lengthy computation times. In this paper, we describe a fast DOT scheme for reconstructing the absorption coefficient image of a slab medium from dense sampling of both illumination and detection in the noncontact DOT. The proposed method is carried out with spatial-frequency encoding in both the source and detection spaces, and involves a spatial-frequency-compression (SFC) strategy for selecting the useful spatial frequency based on the tissue transfer function. The method is expected to considerably reduce the calculation time for reconstruction while improving the quality of the reconstructed images. Results from the simulated data show that the speed for absorption reconstruction with the proposed SFC method is more than 400 times faster than that with the conventional one. A noncontact DOT system for dense sampling of both illumination and detection is developed by using laser raster scanning and CCD-based data acquisition. Experimental measurements on several solid phantoms demonstrate that a high quantitativeness ratio can be obtained from the proposed method thanks to reduction of the ill-posedness of the inverse calculation. It takes less than 20 s for the proposed method to experimentally reconstruct one absorption image from a 256×256-sized dataset, which would take a few hours with the conventional method.

Perturbative forward solver software for small localized fluorophores in tissue

In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green's functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated.

Depth resolution and multiexponential lifetime analyses of reflectance-based time-domain fluorescence data

Time-domain fluorescence imaging is a powerful new technique that adds a rich amount of information to conventional fluorescence imaging. Specifically, time-domain fluorescence can be used to remove autofluorescence from signals, resolve multiple fluorophore concentrations, provide information about tissue microenvironments, and, for reflectance-based imaging systems, resolve inclusion depth. The present study provides the theory behind an improved method of analyzing reflectance-based time-domain data that is capable of accurately recovering mixed concentration ratios of multiple fluorescent agents while also recovering the depth of the inclusion. The utility of the approach was demonstrated in a number of simulations and in tissuelike phantom experiments using a short source-detector separation system. The major findings of this study were (1) both depth of an inclusion and accurate ratios of two-fluorophore concentrations can be recovered accurately up to depths of approximately 1 cm with only the optical properties of the medium as prior knowledge, (2) resolving the depth and accounting for the dispersion effects on fluorescent lifetimes is crucial to the accuracy of recovered ratios, and (3) ratios of three-fluorophore concentrations can be resolved at depth but only if the lifetimes of the three fluorophores are used as prior knowledge. By accurately resolving the concentration ratios of two to three fluorophores, it may be possible to remove autofluorescence or carry out quantitative techniques, such as reference tracer kinetic modeling or ratiometric approaches, to determine receptor binding or microenvironment parameters in point-based time-domain fluorescence applications.

Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates

Time-resolved fluorescence optical tomography allows 3-dimensional localization of multiple fluorophores based on lifetime contrast while providing a unique data set for improved resolution. However, to employ the full fluorescence time measurements, a light propagation model that accurately simulates weakly diffused and multiple scattered photons is required. In this article, we derive a computationally efficient Monte Carlo based method to compute time-gated fluorescence Jacobians for the simultaneous imaging of two fluorophores with lifetime contrast. The Monte Carlo based formulation is validated on a synthetic murine model simulating the uptake in the kidneys of two distinct fluorophores with lifetime contrast. Experimentally, the method is validated using capillaries filled with 2.5nmol of ICG and IRDye™800CW respectively embedded in a diffuse media mimicking the average optical properties of mice. Combining multiple time gates in one inverse problem allows the simultaneous reconstruction of multiple fluorophores with increased resolution and minimal crosstalk using the proposed formulation.

Fluorescence lifetime optical tomography with Discontinuous Galerkin discretisation scheme

We develop discontinuous Galerkin framework for solving direct and inverse problems in fluorescence diffusion optical tomography in turbid media. We show the advantages and the disadvantages of this method by comparing it with previously developed framework based on the finite volume discretization. The reconstruction algorithm was used with time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Optical parameters, quantum yield and lifetime were simultaneously reconstructed. Reconstruction results are presented and discussed.

Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm

A depth compensation algorithm (DCA) can effectively improve the depth localization of diffuse optical tomography (DOT) by compensating the exponentially decreased sensitivity in the deep tissue. In this study, DCA is investigated based on computer simulations, tissue phantom experiments, and human brain imaging. The simulations show that DCA can largely improve the spatial resolution of DOT in addition to the depth localization, and DCA is also effective for multispectral DOT with a wide range of optical properties in the background tissue. The laboratory phantom experiment demonstrates that DCA can effectively differentiate two embedded objects at different depths in the medium. DCA is further validated by human brain imaging using a finger-tapping task. To our knowledge, this is the first demonstration to show that DCA is capable of accurately localizing cortical activations in the human brain in three dimensions.

Reconstruction of fluorescence/bioluminescence sources in biological medium with spatial filter

We propose a new method for reconstruction of emitting source distributions by use of a spatial filter and a successive updating process of the forward model for fluorescence/bioluminescence diffuse optical tomography. The spatial filter transforms a set of the measurement data to a single source strength at a position of interest, and the forward model is updated by use of the estimated source strengths. This updating process ignores the dispensable source positions from reconstruction according to the reconstructed source distribution, and the spatial resolution of the reconstructed image is improved. The estimated sources are also used for the reduction of artifacts induced by noises based on the singular value decomposition. Some numerical experiments show the advantages of the proposed method by comparing the present results with those obtained by the conventional methods of the least squares method nd Algebraic Reconstruction Technique. Finally the criteria for practical use of the method are quantitatively presented by the simulations for 2D and 3D geometries.

Simultaneous fluorescence yield and lifetime tomography from time-resolved transmittances of small-animal-sized phantom

There has been recently a considerable interest in simultaneously reconstructing yield and lifetime distributions of fluorescent imaging agents inside a bulky tissue, since combined monitoring of these two parameters provides a potential means of in vivo interrogating quantitative and environmental information of specific molecules, as well as accessing interactions among them. It is widely accepted that an advantageous way of accomplishing the task in the context of small-animal imaging is to use a time-domain (TD) modality. In this paper, we present a full three-dimensional, featured-data algorithm for TD diffuse fluorescence tomography, which inverts the Laplace-transformed TD coupled photon diffusion equations and employs a pair of real-domain transform-factors to effectively separate the fluorescent yield and lifetime parameters. By use of a specifically designed 16x16 channel time-correlated single photon counting system and a normalized Born formulation for the inversion, the proposed scheme in a transmission mode is experimentally validated to achieve simultaneous reconstruction of the fluorescent yield and lifetime distributions with reasonable accuracy.

Combined reconstruction of fluorescent and optical parameters using time-resolved data

We present an algorithm for simultaneous reconstruction of optical parameters, quantum yield, and lifetime in turbid media with embedded fluorescent inclusions. This algorithm is designed in the Fourier domain as an iterative solution of a system of differential equations of the Helmholtz type and does not involve full ill-conditioned matrix computations. The approach is based on allowing the unknown optical parameters, quantum yield, and lifetime to depend on the Fourier spectral parameter. The algorithm was applied to a time-gated experimental data set acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Relatively accurate reconstruction demonstrates the potential of the method.