Multi-component quantitative magnetic resonance imaging by phasor representation

Phasor Representation Approach for Rapid Exploratory Analysis of Large Infrared Spectroscopic Imaging Data Sets

Infrared (IR) spectroscopic imaging is potentially useful for digital histopathology as it provides spatially resolved molecular absorption spectra, which can subsequently yield useful information by powerful artificial intelligence methods. A typical analysis pipeline in using IR imaging data for chemical pathology often involves iterative processes of segmentation, evaluation, and analysis that necessitate rapid data exploration. Here, we present a fast, reliable, and intuitive method based on a phasor representation of spectra and discuss its unique applicability for IR imaging data. We simulate different features extant in IR spectra and discuss their influence on the phasor waveforms; similarly, we undertake IR image analysis in the transform space to understand spectral similarity and variance. We demonstrate the potential of phasor analysis for biomedical tissue imaging using a variety of samples, using fresh frozen surgical prostate resections and formalin-fixed paraffin-embedded breast cancer tissue microarray samples as model systems that span common histopathology practice. To demonstrate further generalizability of this approach, we apply the method to data from different experimental conditions─including standard (5.5 μm × 5.5 μm pixel size) and high-definition (1.1 μm × 1.1 μm pixel size) Fourier transform IR (FTIR) spectroscopic imaging using transmission and transflection modes. Quantitative segmentation results from our approach are compared to previous studies, showing good agreement and quick visualization. The presented method is rapid, easy to use, and highly capable of deciphering compositional differences, presenting a convenient tool for exploratory analysis of IR imaging data.

Model-free phasor image analysis of quantitative myocardial T1 mapping

Model-free phasor image analysis, well established in fluorescence lifetime imaging and only recently applied to qMRI [Formula: see text] data processing, is here adapted and validated for myocardial qMRI [Formula: see text] mapping. Contrarily to routine mono-exponential fitting procedures, phasor enables mapping the lifetime information from all image voxels to a single plot, without resorting to any regression fitting analysis, and describing multi-exponential qMRI decays without biases due to violated modelling assumptions. In this feasibility study, we test the performance of our recently developed full-harmonics phasor method for unravelling partial-volume effects, motion or pathological tissue alteration, respectively on a numerically-simulated dataset, a healthy subject scan, and two pilot patient datasets. Our results show that phasor analysis can be used, as alternative method to fitting analysis or other model-free approaches, to identify motion artifacts or partial-volume effects at the myocardium-blood interface as characteristic deviations, or delineations of scar and remote myocardial tissue in patient data.

A Weighted Stochastic Conjugate Direction Algorithm for Quantitative Magnetic Resonance Images—A Pattern in Ruptured Achilles Tendon T2-Mapping Assessment

This study presents an accurate biexponential weighted stochastic conjugate direction (WSCD) method for the quantitative T2-mapping reconstruction of magnetic resonance images (MRIs), and this approach was compared with the non-negative-least-squares Gauss–Newton (GN) numerical optimization method in terms of accuracy and goodness of fit of the reconstructed images from simulated data and ruptured Achilles tendon (AT) MRIs. Reconstructions with WSCD and GN were obtained from data simulating the signal intensity from biexponential decay and from 58 MR studies of postrupture, surgically repaired ATs. Both methods were assessed in terms of accuracy (closeness of the means of calculated and true simulated T2 values) and goodness of fit (magnitude of mean squared error (MSE)). The lack of significant deviation in correct T2 values for the WSCD method was demonstrated for SNR ≥ 20 and for GN–SNR ≥ 380. The MSEs for WSCD and GN were 287.52 ± 224.11 and 2553.91 ± 1932.31, respectively. The WSCD reconstruction method was better than the GN method in terms of accuracy and goodness of fit.

Method of transmission filters to measure emission spectra in strongly scattering media

We describe a method based on a pair of transmission filters placed in the emission path of a microscope to resolve the emission wavelength of every point in an image. The method can be applied to any type of imaging device that provides the light in the wavelength transmission range of the filters. Unique characteristics of the filter approach are that the light does not need to be collimated and the wavelength response does not depend on the scattering of the sample or tissue. The pair of filters are used to produce the spectral phasor of the transmitted light, which is sufficient to perform spectral deconvolution over a broad wavelength range. The method is sensitive enough to distinguish free and protein-bound NADH and can be used in metabolic studies.

Quantitation of cerebral oxygen tension using phasor analysis and phosphorescence lifetime imaging microscopy (PLIM)

Time-domain measurements for fluorescence lifetime imaging microscopy (FLIM) and phosphorescence lifetime imaging microscopy (PLIM) are conventionally computed by nonlinear curve fitting techniques to model the time-resolved profiles as mono- or multi-exponential decays. However, these techniques are computationally intensive and prone to fitting errors. The phasor or "polar plot" analysis method has recently gained attention as a simple method to characterize fluorescence lifetime. Here, we adapted the phasor analysis method for absolute quantitation of phosphorescence lifetimes of oxygen-sensitive phosphors and used the phasor-derived lifetime values to quantify oxygen partial pressure (pO2) in cortical microvessels of awake mice. Our results, both experimental and simulated, demonstrate that oxygen measurements obtained from computationally simpler phasor analysis agree well with traditional curve fitting calculations. To our knowledge, the current study constitutes the first application of the technique for characterizing microsecond-length, time-domain phosphorescence measurements and absolute, in vivo quantitation of a vital physiological parameter. The method shows promise for monitoring cerebral metabolism and pathological changes in preclinical rodent models.

Phasor-based image segmentation: machine learning clustering techniques

The phasor approach is a well-established method for data visualization and image analysis in spectral and lifetime fluorescence microscopy. Nevertheless, it is typically applied in a user-dependent manner by manually selecting regions of interest on the phasor space to find distinct regions in the fluorescence images. In this paper we present our work on using machine learning clustering techniques to establish an unsupervised and automatic method that can be used for identifying populations of fluorescent species in spectral and lifetime imaging. We demonstrate our method using both synthetic data, created by sampling photon arrival times and plotting the distributions on the phasor plot, and real live cells samples, by staining cellular organelles with a selection of commercial probes.

Untangling the diffusion signal using the phasor transform

Separating the decay signal from diffusion-weighted scans into two or more components can be challenging. The phasor technique is well established in the field of optical microscopy for visualization and separation of fluorescent dyes with different lifetimes. The use of the phasor technique for separation of diffusion-weighted decay signals was recently proposed. In this study, we investigate the added value of this technique for fitting decay models and visualization of decay rates. Phasor visualization was performed in five glioblastoma patients. Using simulations, the influence of incorrect diffusivity values and of the number of b-values on fitting a three-component model with fixed diffusivities (dubbed "unmixing") was investigated for both a phasor-based fit and a linear least squares (LLS) fit. Phasor-based intravoxel incoherent motion (IVIM) fitting was compared with nonlinear least squares (NLLS) and segmented fitting (SF) methods in terms of accuracy and precision. The distributions of the parameter estimates of simulated data were compared with those obtained in a healthy volunteer. In the phasor visualizations of two glioblastoma patients, a cluster of points was observed that was not seen in healthy volunteers. The identified cluster roughly corresponded to the enhanced edge region of the tumor of two glioblastoma patients visible on fluid-attenuated inversion recovery (FLAIR) images. For fitting decay models the usefulness of the phasor transform is less pronounced, but the additional knowledge gained from the geometrical configuration of phasor space can aid fitting routines. This has led to slightly improved fitting results for the IVIM model: phasor-based fitting yielded parameter maps with higher precision than the NLLS and SF methods for parameters f and D (interquartile range [IQR] for f: NLLS 27, SF 12, phasor 5.7%; IQR for D: NLLS 0.28, SF 0.18, phasor 0.10 μm² /s). For unmixing, LLS fitting slightly but consistently outperformed phasor-based fitting in all of the tested scenarios.

Full-Harmonics Phasor Analysis: Unravelling Multiexponential Trends in Magnetic Resonance Imaging Data

Phasor analysis is a robust, nonfitting, method for the study of multiexponential decays in lifetime imaging data, routinely used in Fluorescence Lifetime Imaging Microscopy (FLIM) and only recently validated for Magnetic Resonance Imaging (MRI). In the established phasor approach, typically only the first Fourier harmonic is used to unravel time-domain exponential trends and their intercorrelations across image voxels. Here, we demonstrate the potential of full-harmonics (FH) phasor analysis by using all frequency-domain data points in simulations and quantitative MRI (qMRI) T₂ measurements of phantoms with bulk liquids or liquid-filled porous particles and of a human brain. We show that FH analysis, while of limited advantage in FLIM due to the correlated nature of shot noise, in MRI outperforms single-harmonic phasor in unravelling multiple physical environments and partial-volume effects otherwise undiscernible. We foresee application of FH phasor to, e.g., big-data analysis in qMRI of biological or other multiphase systems, where multiparameter fitting is unfeasible.

Tissue-Specific T2 * Biomarkers in Patellar Tendinopathy by Subregional Quantification Using 3D Ultrashort Echo Time MRI

Background

Quantitative MRI of patellar tendinopathy (PT) can be challenging due to spatial variation of T₂* relaxation times.

Purpose

1) To compare T₂* quantification using a standard approach with analysis in specific tissue compartments of the patellar tendon. 2) To evaluate test–retest reliability of different methods for fitting ultrashort echo time (UTE)‐relaxometry data.

Study Type

Prospective.

Subjects

Sixty‐five athletes with PT.

Field Strength/Sequence

3D UTE scans covering the patellar tendon were acquired using a 3.0T scanner and a 16‐channel surface coil.

Assessment

Voxelwise median T₂* was quantified with monoexponential, fractional‐order, and biexponential fitting. We applied two methods for T₂* analysis: first, a standard approach by analyzing all voxels covering the proximal patellar tendon. Second, within subregions of the patellar tendon, by using thresholds on biexponential fitting parameter percentage short T₂* (0–30% for mostly long T₂*, 30–60% for mixed T₂*, and 60–100% for mostly short T₂*).

Statistical Tests

Average test–retest reliability was assessed in three athletes using coefficients‐of‐variation (CV) and coefficients‐of‐repeatability (CR).

Results

With standard image analysis, we found a median [interquartile range, IQR] monoexponential T₂* of 6.43 msec [4.32–8.55] and fractional order T₂* 4.39 msec [3.06–5.78]. The percentage of short T₂* components was 52.9% [35.5–69.6]. Subregional monoexponential T₂* was 13.78 msec [12.11–16.46], 7.65 msec [6.49–8.61], and 3.05 msec [2.52–3.60] and fractional order T₂* 11.82 msec [10.09–14.44], 5.14 msec [4.25–5.96], and 2.19 msec [1.82–2.64] for 0–30%, 30–60%, and 60–100% short T₂*, respectively. Biexponential component short T₂* was 1.693 msec [1.417–2.003] for tissue with mostly short T₂* and long T₂* of 15.79 msec [13.47–18.61] for mostly long T₂*. The average CR (CV) was 2 msec (15%), 2 msec (19%) and 10% (22%) for monoexponential, fractional order and percentage short T₂*, respectively.

Data Conclusion

Patellar tendinopathy is characterized by regional variability in binding states of water. Quantitative multicompartment T₂* analysis in PT can be facilitated using a voxel selection method based on using biexponential fitting parameters.

Level of Evidence

1

Technical Efficacy Stage

1 J. Magn. Reson. Imaging 2020;52:420–430.

Pre-processing visualization of hyperspectral fluorescent data with Spectrally Encoded Enhanced Representations

Hyperspectral fluorescence imaging is gaining popularity for it enables multiplexing of spatio-temporal dynamics across scales for molecules, cells and tissues with multiple fluorescent labels. This is made possible by adding the dimension of wavelength to the dataset. The resulting datasets are high in information density and often require lengthy analyses to separate the overlapping fluorescent spectra. Understanding and visualizing these large multi-dimensional datasets during acquisition and pre-processing can be challenging. Here we present Spectrally Encoded Enhanced Representations (SEER), an approach for improved and computationally efficient simultaneous color visualization of multiple spectral components of hyperspectral fluorescence images. Exploiting the mathematical properties of the phasor method, we transform the wavelength space into information-rich color maps for RGB display visualization. We present multiple biological fluorescent samples and highlight SEER’s enhancement of specific and subtle spectral differences, providing a fast, intuitive and mathematical way to interpret hyperspectral images during collection, pre-processing and analysis.

Spectral phasor analysis allows unmixing fluorescence microscopy images, but it requires user involvement and has a limited number of labels that can be analyzed and displayed. Here the authors present a semi-automated solution to visualise multiple spectral components of hyperspectral fluorescence images, simultaneously.

Dual-mode emission and transmission microscopy for virtual histochemistry using hematoxylin- and eosin-stained tissue sections

In the clinical practice of pathology, trichrome stains are commonly used to highlight collagen and to help evaluate fibrosis. Such stains do delineate collagen deposits but are not molecularly specific and can suffer from staining inconsistencies. Moreover, performing histochemical stain evaluation requires the preparation of additional sections beyond the original hematoxylin- and eosin-stained slides, as well as additional staining steps, which together add cost, time, and workflow complications. We have developed a new microscopy approach, termed DUET (DUal-mode Emission and Transmission) that can be used to extract signals that would typically require special stains or advanced optical methods. Our preliminary analysis demonstrates the potential of using the resulting signals to generate virtual histochemical images that resemble trichrome-stained slides and can support clinical evaluation. We demonstrate advantages of this approach over images acquired from conventional trichrome-stained slides and compare them with images created using second harmonic generation microscopy.

In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging

We introduce a simple new approach for time-resolved multiplexed analysis of complex systems using near-infrared (NIR) dyes, applicable to in vitro and in vivo studies. We show that fast and precise in vitro quantification of NIR fluorophores' short (subnanosecond) lifetime and stoichiometry can be done using phasor analysis, a computationally efficient and user-friendly representation of complex fluorescence intensity decays obtained with pulsed laser excitation and time-gated camera imaging. We apply this approach to the study of binding equilibria by Förster resonant energy transfer using two different model systems: primary/secondary antibody binding in vitro and ligand/receptor binding in cell cultures. We then extend it to dynamic imaging of the pharmacokinetics of transferrin engagement with the transferrin receptor in live mice, elucidating the kinetics of differential transferrin accumulation in specific organs, straightforwardly differentiating specific from nonspecific binding. Our method, implemented in a freely-available software, has the advantage of time-resolved NIR imaging, including better tissue penetration and background-free imaging, but simplifies and considerably speeds up data processing and interpretation, while remaining quantitative. These advances make this method attractive and of broad applicability for in vitro and in vivo molecular imaging and could be extended to applications as diverse as image-guided surgery or optical tomography.

Use of the NESMA Filter to Improve Myelin Water Fraction Mapping with Brain MRI

BACKGROUND AND PURPOSE

Myelin water fraction (MWF) mapping permits direct visualization of myelination patterns in the developing brain and in pathology. MWF is conventionally measured through multiexponential T₂ analysis which is very sensitive to noise, leading to inaccuracies in derived MWF estimates. Although noise reduction filters may be applied during postprocessing, conventional filtering can introduce bias and obscure small structures and edges. Advanced nonblurring filters, while effective, exhibit a high level of complexity and the requirement for supervised implementation for optimal performance. The purpose of this paper is to demonstrate the ability of the recently introduced nonlocal estimation of multispectral magnitudes (NESMA) filter to greatly improve the determination of MWF parameter estimates from gradient and spin echo (GRASE) imaging data.

METHODS

We evaluated the performance of the NESMA filter for MWF mapping from clinical GRASE imaging data of the human brain, and compared the results to those calculated from unfiltered images. Numerical and in vivo analyses of the brains of three subjects, representing different ages, were conducted.

RESULTS

Our results demonstrated the potential of the NESMA filter to permit high-quality in vivo MWF mapping. Indeed, NESMA permits substantial reduction of random variation in derived MWF estimates while preserving accuracy and detail.

CONCLUSIONS

In vivo estimation of MWF in the human brain from GRASE imaging data was markedly improved through use of the NESMA filter. The use of NESMA may contribute to the goal of high-quality MWF mapping in clinically feasible imaging times.

μMAPPS: a novel phasor approach to second harmonic analysis for in vitro-in vivo investigation of collagen microstructure

Second Harmonic Generation (SHG) is a label-free imaging method used to monitor collagen organization in tissues. Due to its sensitivity to the incident polarization, it provides microstructural information otherwise unreachable by other intensity based imaging methods. We develop and test a Microscopic Multiparametric Analysis by Phasor projection of Polarization-dependent SHG (μMAPPS) that maps the features of the collagen architecture in tissues at the micrometer scale. μMAPPS retrieves pixel-by-pixel the collagen fibrils anisotropy and orientation by operating directly on two coupled phasor spaces, avoiding direct fitting of the polarization dependent SHG signal. We apply μMAPPS to fixed tissue sections and to the study of the collagen microscopic organization in tumors ex-vivo and in-vivo. We develop a clustering algorithm to automatically group pixels with similar microstructural features. μMAPPS can perform fast analyses of tissues and opens to future applications for in-situ diagnosis of pathologies and diseases that could assist histo-pathological evaluation.