Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials

Building Fluorescence Lifetime Maps Photon-by-Photon by Leveraging Spatial Correlations

Fluorescence lifetime imaging microscopy (FLIM) has become a standard tool in the quantitative characterization of subcellular environments. However, quantitative FLIM analyses face several challenges. First, spatial correlations between pixels are often ignored as signal from individual pixels is analyzed independently thereby limiting spatial resolution. Second, existing methods deduce photon ratios instead of absolute lifetime maps. Next, the number of fluorophore species contributing to the signal is unknown, while excited state lifetimes with <1 ns difference are difficult to discriminate. Finally, existing analyses require high photon budgets and often cannot rigorously propagate experimental uncertainty into values over lifetime maps and number of species involved. To overcome all of these challenges simultaneously and self-consistently at once, we propose the first doubly nonparametric framework. That is, we learn the number of species (using Beta-Bernoulli process priors) and absolute maps of these fluorophore species (using Gaussian process priors) by leveraging information from pulses not leading to observed photon. We benchmark our framework using a broad range of synthetic and experimental data and demonstrate its robustness across a number of scenarios including cases where we recover lifetime differences between species as small as 0.3 ns with merely 1000 photons.

High Resolution Fluorescence Lifetime Maps from Minimal Photon Counts

Fluorescence lifetime imaging microscopy (FLIM) may reveal subcellular spatial lifetime maps of key molecular species. Yet, such a quantitative picture of life necessarily demands high photon budgets at every pixel under the current analysis paradigm, thereby increasing acquisition time and photodamage to the sample. Motivated by recent developments in computational statistics, we provide a direct means to update our knowledge of the lifetime maps of species of different lifetimes from direct photon arrivals, while accounting for experimental features such as arbitrary forms of the instrument response function (IRF) and exploiting information from empty laser pulses not resulting in photon detection. Our ability to construct lifetime maps holds for arbitrary lifetimes, from short lifetimes (comparable to the IRF) to lifetimes exceeding interpulse times. As our method is highly data efficient, for the same amount of data normally used to determine lifetimes and photon ratios, working within the Bayesian paradigm, we report direct blind unmixing of lifetimes with subnanosecond resolution and subpixel spatial resolution using standard raster scan FLIM images. We demonstrate our method using a wide range of simulated and experimental data.

Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach

The deconvolution process is a key step for quantitative evaluation of fluorescence lifetime imaging microscopy (FLIM) samples. By this process, the fluorescence impulse responses (FluoIRs) of the sample are decoupled from the instrument response (InstR). In blind deconvolution estimation (BDE), the FluoIRs and InstR are jointly extracted from a dataset with minimal a priori information. In this work, two BDE algorithms are introduced based on linear combinations of multi-exponential functions to model each FluoIR in the sample. For both schemes, the InstR is assumed with a free-form and a sparse structure. The local perspective of the BDE methodology assumes that the characteristic parameters of the exponential functions (time constants and scaling coefficients) are estimated based on a single spatial point of the dataset. On the other hand, the same exponential functions are used in the whole dataset in the global perspective, and just the scaling coefficients are updated for each spatial point. A least squares formulation is considered for both BDE algorithms. To overcome the nonlinear interaction in the decision variables, an alternating least squares (ALS) methodology iteratively solves both estimation problems based on non-negative and constrained optimizations. The validation stage considered first synthetic datasets at different noise types and levels, and a comparison with the standard deconvolution techniques with a multi-exponential model for FLIM measurements, as well as, with two BDE methodologies in the state of the art: Laguerre basis, and exponentials library. For the experimental evaluation, fluorescent dyes and oral tissue samples were considered. Our results show that local and global perspectives are consistent with the standard deconvolution techniques, and they reached the fastest convergence responses among the BDE algorithms with the best compromise in FluoIRs and InstR estimation errors.

Large field-of-view nanometer-sectioning microscopy by using metal-induced energy transfer and biexponential lifetime analysis

Total internal reflection fluorescence (TIRF) microscopy, which has about 100-nm axial excitation depth, is the method of choice for nanometer-sectioning imaging for decades. Lately, several new imaging techniques, such as variable angle TIRF microscopy, supercritical-angle fluorescence microscopy, and metal-induced energy transfer imaging, have been proposed to enhance the axial resolution of TIRF. However, all of these methods use high numerical aperture (NA) objectives, and measured images inevitably have small field-of-views (FOVs). Small-FOV can be a serious limitation when multiple cells need to be observed. We propose large-FOV nanometer-sectioning microscopy, which breaks the complementary relations between the depth of focus and axial sectioning by using MIET. Large-FOV imaging is achieved with a low-magnification objective, while nanometer-sectioning is realized utilizing metal-induced energy transfer and biexponential fluorescence lifetime analysis. The feasibility of our proposed method was demonstrated by imaging nanometer-scale distances between the basal membrane of human aortic endothelial cells and a substrate.

Hwang et al. demonstrate that a high axial resolution can be achieved even with low numerical aperture (NA) objectives. They show the nano-profile of a basal cell membrane using metal-induced energy transfer and biexponential fluorescence lifetime analysis. The low-NA objective provides a larger field-of-view (FOV), thereby overcoming the limitations of a small FOV of the usually used high-NA objectives.

Fluorescence lifetime imaging microscopy: fundamentals and advances in instrumentation, analysis, and applications

SIGNIFICANCE

Fluorescence lifetime imaging microscopy (FLIM) is a powerful technique to distinguish the unique molecular environment of fluorophores. FLIM measures the time a fluorophore remains in an excited state before emitting a photon, and detects molecular variations of fluorophores that are not apparent with spectral techniques alone. FLIM is sensitive to multiple biomedical processes including disease progression and drug efficacy.

AIM

We provide an overview of FLIM principles, instrumentation, and analysis while highlighting the latest developments and biological applications.

APPROACH

This review covers FLIM principles and theory, including advantages over intensity-based fluorescence measurements. Fundamentals of FLIM instrumentation in time- and frequency-domains are summarized, along with recent developments. Image segmentation and analysis strategies that quantify spatial and molecular features of cellular heterogeneity are reviewed. Finally, representative applications are provided including high-resolution FLIM of cell- and organelle-level molecular changes, use of exogenous and endogenous fluorophores, and imaging protein-protein interactions with Förster resonance energy transfer (FRET). Advantages and limitations of FLIM are also discussed.

CONCLUSIONS

FLIM is advantageous for probing molecular environments of fluorophores to inform on fluorophore behavior that cannot be elucidated with intensity measurements alone. Development of FLIM technologies, analysis, and applications will further advance biological research and clinical assessments.

Image Restoration for Fluorescence Planar Imaging with Diffusion Model

Fluorescence planar imaging (FPI) is failure to capture high resolution images of deep fluorochromes due to photon diffusion. This paper presents an image restoration method to deal with this kind of blurring. The scheme of this method is conceived based on a reconstruction method in fluorescence molecular tomography (FMT) with diffusion model. A new unknown parameter is defined through introducing the first mean value theorem for definite integrals. System matrix converting this unknown parameter to the blurry image is constructed with the elements of depth conversion matrices related to a chosen plane named focal plane. Results of phantom and mouse experiments show that the proposed method is capable of reducing the blurring of FPI image caused by photon diffusion when the depth of focal plane is chosen within a proper interval around the true depth of fluorochrome. This method will be helpful to the estimation of the size of deep fluorochrome.

Temporal binning of time-correlated single photon counting data improves exponential decay fits and imaging speed

Time-correlated single photon counting (TCSPC) enables acquisition of fluorescence lifetime decays with high temporal resolution within the fluorescence decay. However, many thousands of photons per pixel are required for accurate lifetime decay curve representation, instrument response deconvolution, and lifetime estimation, particularly for two-component lifetimes. TCSPC imaging speed is inherently limited due to the single photon per laser pulse nature and low fluorescence event efficiencies (<10%) required to reduce bias towards short lifetimes. Here, simulated fluorescence lifetime decays are analyzed by SPCImage and SLIM Curve software to determine the limiting lifetime parameters and photon requirements of fluorescence lifetime decays that can be accurately fit. Data analysis techniques to improve fitting accuracy for low photon count data were evaluated. Temporal binning of the decays from 256 time bins to 42 time bins significantly (p<0.0001) improved fit accuracy in SPCImage and enabled accurate fits with low photon counts (as low as 700 photons/decay), a 6-fold reduction in required photons and therefore improvement in imaging speed. Additionally, reducing the number of free parameters in the fitting algorithm by fixing the lifetimes to known values significantly reduced the lifetime component error from 27.3% to 3.2% in SPCImage (p<0.0001) and from 50.6% to 4.2% in SLIM Curve (p<0.0001). Analysis of nicotinamide adenine dinucleotide-lactate dehydrogenase (NADH-LDH) solutions confirmed temporal binning of TCSPC data and a reduced number of free parameters improves exponential decay fit accuracy in SPCImage. Altogether, temporal binning (in SPCImage) and reduced free parameters are data analysis techniques that enable accurate lifetime estimation from low photon count data and enable TCSPC imaging speeds up to 6x and 300x faster, respectively, than traditional TCSPC analysis.