Time-gated perturbation Monte Carlo for whole body functional imaging in small animals

Unrolled-DOT: an interpretable deep network for diffuse optical tomography

SIGNIFICANCE

Imaging through scattering media is critical in many biomedical imaging applications, such as breast tumor detection and functional neuroimaging. Time-of-flight diffuse optical tomography (ToF-DOT) is one of the most promising methods for high-resolution imaging through scattering media. ToF-DOT and many traditional DOT methods require an image reconstruction algorithm. Unfortunately, this algorithm often requires long computational runtimes and may produce lower quality reconstructions in the presence of model mismatch or improper hyperparameter tuning.

AIM

We used a data-driven unrolled network as our ToF-DOT inverse solver. The unrolled network is faster than traditional inverse solvers and achieves higher reconstruction quality by accounting for model mismatch.

APPROACH

Our model "Unrolled-DOT" uses the learned iterative shrinkage thresholding algorithm. In addition, we incorporate a refinement U-Net and Visual Geometry Group (VGG) perceptual loss to further increase the reconstruction quality. We trained and tested our model on simulated and real-world data and benchmarked against physics-based and learning-based inverse solvers.

RESULTS

In experiments on real-world data, Unrolled-DOT outperformed learning-based algorithms and achieved over 10× reduction in runtime and mean-squared error, compared to traditional physics-based solvers.

CONCLUSION

We demonstrated a learning-based ToF-DOT inverse solver that achieves state-of-the-art performance in speed and reconstruction quality, which can aid in future applications for noninvasive biomedical imaging.

MCCL: an open-source software application for Monte Carlo simulations of radiative transport

The Monte Carlo Command Line application (MCCL) is an open-source software package that provides Monte Carlo simulations of radiative transport through heterogeneous turbid media. MCCL is available on GitHub through our virtualphotonics.org website, is actively supported, and carries extensive documentation. Here, we describe the main technical capabilities, the overall software architecture, and the operational details of MCCL.

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues.

Time-Domain Near-Infrared Spectroscopy and Imaging: A Review

This article reviews the past and current statuses of time-domain near-infrared spectroscopy (TD-NIRS) and imaging. Although time-domain technology is not yet widely employed due to its drawbacks of being cumbersome, bulky, and very expensive compared to commercial continuous wave (CW) and frequency-domain (FD) fNIRS systems, TD-NIRS has great advantages over CW and FD systems because time-resolved data measured by TD systems contain the richest information about optical properties inside measured objects. This article focuses on reviewing the theoretical background, advanced theories and methods, instruments, and studies on clinical applications for TD-NIRS including some clinical studies which used TD-NIRS systems. Major events in the development of TD-NIRS and imaging are identified and summarized in chronological tables and figures. Finally, prospects for TD-NIRS in the near future are briefly described.

Hyperspectral wide-field time domain single-pixel diffuse optical tomography platform

We present the design and comprehensive instrumental characterization of a time domain diffuse optical tomography (TD-DOT) platform based on wide-field illumination and wide-field hyperspectral time-resolved single-pixel detection for functional and molecular imaging in turbid media. The proposed platform combines two digital micro-mirror devices (DMDs) to generate structured light and a spectrally resolved multi-anode photomultiplier tube (PMT) detector in time domain for hyperspectral data acquisition over 16 wavelength channels based on the time-correlated single-photon counting (TCSPC) technique. The design of the proposed platform is described in detail and its characteristics in spatial, temporal and spectral dimensions are calibrated and presented. The performance of the system is further validated through a phantom study where two absorbers in glass tubes with spectral contrast are mapped in a turbid medium of ~20 mm thickness. The method presented here offers the potential of accelerating the imaging process and improving reconstruction results in TD-DOT and thus facilitates its wide spread use in preclinical and clinical in vivo imaging scenarios.

Direct approach to compute Jacobians for diffuse optical tomography using perturbation Monte Carlo-based photon "replay"

Perturbation Monte Carlo (pMC) has been previously proposed to rapidly recompute optical measurements when small perturbations of optical properties are considered, but it was largely restricted to changes associated with prior tissue segments or regions-of-interest. In this work, we expand pMC to compute spatially and temporally resolved sensitivity profiles, i.e. the Jacobians, for diffuse optical tomography (DOT) applications. By recording the pseudo random number generator (PRNG) seeds of each detected photon, we are able to "replay" all detected photons to directly create the 3D sensitivity profiles for both absorption and scattering coefficients. We validate the replay-based Jacobians against the traditional adjoint Monte Carlo (aMC) method, and demonstrate the feasibility of using this approach for efficient 3D image reconstructions using in vitro hyperspectral wide-field DOT measurements. The strengths and limitations of the replay approach regarding its computational efficiency and accuracy are discussed, in comparison with aMC, for point-detector systems as well as wide-field pattern-based and hyperspectral imaging systems. The replay approach has been implemented in both of our open-source MC simulators - MCX and MMC (http://mcx.space).

Development of computational small animal models and their applications in preclinical imaging and therapy research

The development of multimodality preclinical imaging techniques and the rapid growth of realistic computer simulation tools have promoted the construction and application of computational laboratory animal models in preclinical research. Since the early 1990s, over 120 realistic computational animal models have been reported in the literature and used as surrogates to characterize the anatomy of actual animals for the simulation of preclinical studies involving the use of bioluminescence tomography, fluorescence molecular tomography, positron emission tomography, single-photon emission computed tomography, microcomputed tomography, magnetic resonance imaging, and optical imaging. Other applications include electromagnetic field simulation, ionizing and nonionizing radiation dosimetry, and the development and evaluation of new methodologies for multimodality image coregistration, segmentation, and reconstruction of small animal images. This paper provides a comprehensive review of the history and fundamental technologies used for the development of computational small animal models with a particular focus on their application in preclinical imaging as well as nonionizing and ionizing radiation dosimetry calculations. An overview of the overall process involved in the design of these models, including the fundamental elements used for the construction of different types of computational models, the identification of original anatomical data, the simulation tools used for solving various computational problems, and the applications of computational animal models in preclinical research. The authors also analyze the characteristics of categories of computational models (stylized, voxel-based, and boundary representation) and discuss the technical challenges faced at the present time as well as research needs in the future.

Development of perturbation Monte Carlo methods for polarized light transport in a discrete particle scattering model

We present a polarization-sensitive, transport-rigorous perturbation Monte Carlo (pMC) method to model the impact of optical property changes on reflectance measurements within a discrete particle scattering model. The model consists of three log-normally distributed populations of Mie scatterers that approximate biologically relevant cervical tissue properties. Our method provides reflectance estimates for perturbations across wavelength and/or scattering model parameters. We test our pMC model performance by perturbing across number densities and mean particle radii, and compare pMC reflectance estimates with those obtained from conventional Monte Carlo simulations. These tests allow us to explore different factors that control pMC performance and to evaluate the gains in computational efficiency that our pMC method provides.

Generalized mesh-based Monte Carlo for wide-field illumination and detection via mesh retessellation

Monte Carlo methods are commonly used as the gold standard in modeling photon transport through turbid media. With the rapid development of structured light applications, an accurate and efficient method capable of simulating arbitrary illumination patterns and complex detection schemes over large surface area is in great need. Here we report a generalized mesh-based Monte Carlo algorithm to support a variety of wide-field illumination methods, including spatial-frequency-domain imaging (SFDI) patterns and arbitrary 2-D patterns. The extended algorithm can also model wide-field detectors such as a free-space CCD camera. The significantly enhanced flexibility of source and detector modeling is achieved via a fast mesh retessellation process that combines the target domain and the source/detector space in a single tetrahedral mesh. Both simulations of complex domains and comparisons with phantom measurements are included to demonstrate the flexibility, efficiency and accuracy of the extended algorithm. Our updated open-source software is provided at http://mcx.space/mmc.

Mesh Optimization for Monte Carlo-Based Optical Tomography

Mesh-based Monte Carlo techniques for optical imaging allow for accurate modeling of light propagation in complex biological tissues. Recently, they have been developed within an efficient computational framework to be used as a forward model in optical tomography. However, commonly employed adaptive mesh discretization techniques have not yet been implemented for Monte Carlo based tomography. Herein, we propose a methodology to optimize the mesh discretization and analytically rescale the associated Jacobian based on the characteristics of the forward model. We demonstrate that this method maintains the accuracy of the forward model even in the case of temporal data sets while allowing for significant coarsening or refinement of the mesh.

Hyperspectral time-resolved wide-field fluorescence molecular tomography based on structured light and single-pixel detection

We present a time-resolved fluorescence diffuse optical tomography platform that is based on wide-field structured illumination, single-pixel detection, and hyperspectral acquisition. Two spatial light modulators (digital micro-mirror devices) are employed to generate independently wide-field illumination and detection patterns, coupled with a 16-channel spectrophotometer detection module to capture hyperspectral time-resolved tomographic data sets. The main system characteristics are reported, and we demonstrate the feasibility of acquiring dense 4D tomographic data sets (space, time, spectra) for time domain 3D quantitative multiplexed fluorophore concentration mapping in turbid media.

High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing

Mesoscopic fluorescence molecular tomography (MFMT) is new imaging modality aiming at 3-D imaging of molecular probes in a few millimeter thick biological samples with high-spatial resolution. In this paper, we develop a compressive sensing-based reconstruction method with l1-norm regularization for MFMT with the goal of improving spatial resolution and stability of the optical inverse problem. Three-dimensional numerical simulations of anatomically accurate microvasculature and real data obtained from phantom experiments are employed to evaluate the merits of the proposed method. Experimental results show that the proposed method can achieve 80 μm spatial resolution for a biological sample of 3 mm thickness and more accurate quantifications of concentrations and locations for the fluorophore distribution than those of the conventional methods.

L(p) regularization for early gate fluorescence molecular tomography

Time domain fluorescence molecular tomography (TD-FMT) provides a unique dataset for enhanced quantification and spatial resolution. The time-gate dataset can be divided into two temporal groups around the maximum counts gate, which are early gates and late gates. It is well established that early gates allow for improved spatial resolution and late gates are essential for fluorophore unmixing and concentration quantification. However, the inverse problem of FMT is ill-posed and typically underdetermined, which makes image reconstruction highly susceptible to data noise. More specifically, photon counts are inherently very low at early gates due to high absorption and scattering of tissue, resulting in a low signal-to-noise ratio and unstable reconstructions. In this work, an L(p) regularization-based reconstruction algorithm was developed and tested with our wide-field mesh-based Monte Carlo simulation strategy. We compared the early time-gate reconstructions obtained with the different p (p∈{1/16,1/8,1/4,1/3,1/2,1,2}) from a synthetic murine model simulating the fluorophore uptake in the kidneys and preclinical data. The results from a 3D mouse atlas and a mouse experiment show that our L(1/4) regularization methods give the best performance for early time gates reconstructions.

Perturbation Monte Carlo methods for tissue structure alterations

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.

Adaptive wide-field optical tomography

We describe a wide-field optical tomography technique, which allows the measurement-guided optimization of illumination patterns for enhanced reconstruction performances. The iterative optimization of the excitation pattern aims at reducing the dynamic range in photons transmitted through biological tissue. It increases the number of measurements collected with high photon counts resulting in a dataset with improved tomographic information. Herein, this imaging technique is applied to time-resolved fluorescence molecular tomography for preclinical studies. First, the merit of this approach is tested by in silico studies in a synthetic small animal model for typical illumination patterns. Second, the applicability of this approach in tomographic imaging is validated in vitro using a small animal phantom with two fluorescent capillaries occluded by a highly absorbing inclusion. The simulation study demonstrates an improvement of signal transmitted (∼2 orders of magnitude) through the central portion of the small animal model for all patterns considered. A corresponding improvement in the signal at the emission wavelength by 1.6 orders of magnitude demonstrates the applicability of this technique for fluorescence molecular tomography. The successful discrimination and localization (∼1  mm error) of the two objects with higher resolution using the optimized patterns compared with nonoptimized illumination establishes the improvement in reconstruction performance when using this technique.

Quantitative tomographic imaging of intermolecular FRET in small animals

Forster resonance energy transfer (FRET) is a nonradiative transfer of energy between two fluorescent molecules (a donor and an acceptor) in nanometer range proximity. FRET imaging methods have been applied to proteomic studies and drug discovery applications based on intermolecular FRET efficiency measurements and stoichiometric measurements of FRET interaction as quantitative parameters of interest. Importantly, FRET provides information about biomolecular interactions at a molecular level, well beyond the diffraction limits of standard microscopy techniques. The application of FRET to small animal imaging will allow biomedical researchers to investigate physiological processes occurring at nanometer range in vivo as well as in situ. In this work a new method for the quantitative reconstruction of FRET measurements in small animals, incorporating a full-field tomographic acquisition system with a Monte Carlo based hierarchical reconstruction scheme, is described and validated in murine models. Our main objective is to estimate the relative concentration of two forms of donor species, i.e., a donor molecule involved in FRETing to an acceptor close by and a nonFRETing donor molecule.

Mesh-based Monte Carlo method in time-domain widefield fluorescence molecular tomography

We evaluated the potential of mesh-based Monte Carlo (MC) method for widefield time-gated fluorescence molecular tomography, aiming to improve accuracy in both shape discretization and photon transport modeling in preclinical settings. An optimized software platform was developed utilizing multithreading and distributed parallel computing to achieve efficient calculation. We validated the proposed algorithm and software by both simulations and in vivo studies. The results establish that the optimized mesh-based Monte Carlo (mMC) method is a computationally efficient solution for optical tomography studies in terms of both calculation time and memory utilization. The open source code, as part of a new release of mMC, is publicly available at http://mcx.sourceforge.net/mmc/.

Using graphics processing units to accelerate perturbation Monte Carlo simulation in a turbid medium

We report a fast perturbation Monte Carlo (PMC) algorithm accelerated by graphics processing units (GPU). The two-step PMC simulation [Opt. Lett. 36, 2095 (2011)] is performed by storing the seeds instead of the photon's trajectory, and thus the requirement in computer random-access memory (RAM) becomes minimal. The two-step PMC is extremely suitable for implementation onto GPU. In a standard simulation of spatially-resolved photon migration in the turbid media, the acceleration ratio between using GPU and using conventional CPU is about 1000. Furthermore, since in the two-step PMC algorithm one records the effective seeds, which is associated to the photon that reaches a region of interest in this letter, and then re-run the MC simulation based on the recorded effective seeds, radiative transfer equation (RTE) can be solved by two-step PMC not only with an arbitrary change in the absorption coefficient, but also with large change in the scattering coefficient.

Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency

PURPOSE

The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography.

METHODS

The methods investigated to generate time-gated Jacobians were the perturbation Monte Carlo (pMC) method, the adjoint Monte Carlo (aMC) method and the mid-way Monte Carlo (mMC) method. The effects of the different parameters that affect the computation time and statistics reliability were evaluated. Also, the methods were applied to a set of experimental data for tomographic application.

RESULTS

In silico results establish that, the investigated parameters affect the computational time for the three methods differently (linearly, quadratically, or not significantly). Moreover, the noise level of the Jacobian varies when these parameters change. The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours.

CONCLUSIONS

Among the three Monte Carlo methods, the mMC method is a computationally prohibitive technique that is not well suited for time-domain fluorescence tomography applications. The pMC method is advantageous over the aMC method when the early gates are employed and large number of detectors is present. Alternatively, the aMC method is the method of choice when a small number of source-detector pairs are used.

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.

Hybrid use of early and quasi-continuous wave photons in time-domain tomographic imaging for improved resolution and quantitative accuracy

Measurement of early-photons (EPs) from a pulsed laser source has been shown to improve imaging resolution versus continuous wave (CW) systems in diffuse optical tomography (DOT) and fluorescence mediated tomography (FMT). However, EP systems also have reduced noise performance versus CW systems since EP measurements require temporal rejection of large numbers of transmitted photons. In this work, we describe a 'hybrid data set' (HDS) image reconstruction approach, the goal of which was to produce a final image that retained the resolution and noise advantages of EP and CW data sets, respectively. Here, CW data was first reconstructed to produce a quantitatively accurate 'initial guess' intermediate image, and then this was refined with EP data to yield a higher resolution final image. We performed a series of studies with simulated data to test the resolution, quantitative accuracy and detection sensitivity of the approach. We showed that in principle it was possible to produce final images that retained the bulk of the resolution and quantitative accuracy of EP and CW images, respectively, but the HDS approach did not improve the instrument sensitivity compared to EP data alone.

Full-field time-resolved fluorescence tomography of small animals

In this experimental investigation, we explore the feasibility of using wide-field illumination for time-resolved fluorescence molecular tomography. The performance of wide-field patterns with a time-resolved imaging platform is investigated in vitro and in a small animal model. A Monte Carlo-based forward model is employed to reconstruct fluorescence yield based on time-gated datasets. An improvement in resolution and quantification when using the time-gate data type compared to the commonly used cw data type is demonstrated in vitro. Furthermore, the feasibility of wide-field strategies for fluorescence preclinical applications is established by an accurate localization of a fluorescent inclusion implanted in the chest cavity of a murine model.

Development of an optical imaging platform for functional imaging of small animals using wide-field excitation

The design and characterization of a time-resolved functional imager using a wide-field excitation scheme for small animal imaging is described. The optimal operation parameters are established based on phantom studies. The performance of the platform for functional imaging and the simultaneous 3D reconstruction of absorption and scattering coefficients is investigated in vitro.

Time-resolved diffuse optical tomography with patterned-light illumination and detection

This investigation explores the feasibility of performing diffuse optical tomography based on time-domain wide-field illumination and detection strategies. Wide-field patterned excitation and detection schemes are investigated in transmittance geometry with time-gated detection channels. A Monte Carlo forward model is employed to compute the time-resolved Jacobians for rigorous light propagation modeling. We demonstrate both in silico and experimentally that reconstructions of absorption structures based on wide-field patterned-light strategies are feasible and outperform classical point excitation schemes for similar data set sizes. Moreover, we demonstrate that time-domain information is retained even though large spatial areas are illuminated. The enhanced time-domain data set allows for quantitative three-dimensional imaging in thick tissue based on relatively small data sets associated with much shorter acquisition times.

Illumination pattern optimization for fluorescence tomography: theory and simulation studies

Fluorescence molecular tomography is a powerful tool for 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degrees of absorption and scattering of light through tissue, the fluorescence tomographic inverse problem is inherently ill-posed. In order to improve source localization and the conditioning of the light propagation model, multiple sets of data are acquired by illuminating the animal surface with different spatial patterns of near-infrared light. However, the choice of these patterns in most experimental setups is ad hoc and suboptimal. This paper presents a systematic approach for designing efficient illumination patterns for fluorescence tomography. Our objective here is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. We achieve this by improving the conditioning of the Fisher information matrix. We parameterize the spatial illumination patterns and formulate our problem as a constrained optimization problem that, for a fixed number of illumination patterns, yields the optimal set of patterns. For geometric insight, we used our method to generate a set of three optimal patterns for an optically homogeneous, regular geometrical shape and observed expected symmetries in the result. We also generated a set of six optimal patterns for an optically homogeneous cuboidal phantom set up in the transillumination mode. Finally, we computed optimal illumination patterns for an optically inhomogeneous realistically shaped mouse atlas for different given numbers of patterns. The regularized pseudoinverse matrix, generated using the singular value decomposition, was employed to reconstruct the point spread function for each set of patterns in the presence of a sample fluorescent point source deep inside the mouse atlas. We have evaluated the performance of our method by examining the singular value spectra as well as plots of average spatial resolution versus estimator variance corresponding to different illumination schemes.