Constrained alternating minimization for parameter mapping (CAMP).

OBJECTIVE: To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images. APPROACH: In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12. MAIN RESULTS: CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias. SIGNIFICANCE: For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

A Physics-Based Algorithm to Universally Standardize Routinely Obtained Clinical T2-Weighted Images.

RATIONALE AND OBJECTIVES: MR images can be challenging for machine learning and other large-scale analyses because most clinical images, for example, T2-weighted (T2w) images, reflect not only the biologically relevant T2 of tissue but also hardware and acquisition parameters that vary from site to site. Quantitative T2 mapping avoids these confounds because it quantitatively isolates the biological parameter of interest, thus representing a universal standardization across sites. However, efforts to incorporate quantitative mapping sequences into routine clinical practice have seen slow adoption. Here we show, for the first time, that the routine T2w complex raw dataset can be successfully regarded as a quantitative mapping sequence that can be reconstructed with classical optimization methods and physics-based constraints. MATERIALS AND METHODS: While previous constrained reconstruction methods are unable to reconstruct a T2 map based on this data, the expanding-constrained alternating minimization for parameter mapping (e-CAMP), which employs stepwise initialization, a linearized version of the exponential model and a phase conjugacy constraint, is demonstrated to provide useful quantitative maps directly from a vendor T2w single image data. RESULTS: This paper introduces the method and demonstrates its performance using simulations, retrospectively undersampled brain images, and prospectively acquired T2w images taken on both phantom and brain. CONCLUSION: Because T2w scans are included in nearly every protocol, this approach could open the door to creating large, standardized datasets without requiring widespread changes in clinical protocols.

HIV-1 Env trimers asymmetrically engage CD4 receptors in membranes.

Human immunodeficiency virus 1 (HIV-1) infection is initiated by binding of the viral envelope glycoprotein (Env) to the cell-surface receptor CD41-4. Although high-resolution structures of Env in a complex with the soluble domains of CD4 have been determined, the binding process is less understood in native membranes5-13. Here we used cryo-electron tomography to monitor Env-CD4 interactions at the membrane-membrane interfaces formed between HIV-1 and CD4-presenting virus-like particles. Env-CD4 complexes organized into clusters and rings, bringing the opposing membranes closer together. Env-CD4 clustering was dependent on capsid maturation. Subtomogram averaging and classification revealed that Env bound to one, two and finally three CD4 molecules, after which Env adopted an open state. Our data indicate that asymmetric HIV-1 Env trimers bound to one and two CD4 molecules are detectable intermediates during virus binding to host cell membranes, which probably has consequences for antibody-mediated immune responses and vaccine immunogen design.

New measures of anisotropy of cryo-EM maps.

We propose two new measures of resolution anisotropy for cryogenic electron microscopy maps: Fourier shell occupancy (FSO), and the Bingham test (BT). FSO varies from 1 to 0, with 1 representing perfect isotropy, and lower values indicating increasing anisotropy. The threshold FSO = 0.5 occurs at Fourier shell correlation resolution. BT is a hypothesis test that complements the FSO to ensure the existence of anisotropy. FSO and BT allow visualization of resolution anisotropy. We illustrate their use with different experimental cryogenic electron microscopy maps.

Steerable Near-Quadrature Filter Pairs in Three Dimensions.

Steerable filter pairs that are near quadrature have many image processing applications. This paper proposes a new methodology for designing such filters. The key idea is to design steerable filters by minimizing a departure-from-quadrature function. These minimizing filter pairs are almost exactly in quadrature. The polar part of the filters is nonnegative, monotonic, and highly focused around an axis, and asymptotically the filters achieve exact quadrature. These results are established by exploiting a relation between the filters and generalized Hilbert matrices. These near-quadrature filters closely approximate three dimensional Gabor filters. We experimentally verify the asymptotic mathematical results and further demonstrate the use of these filter pairs by efficient calculation of local Fourier shell correlation of cryogenic electron microscopy.

Cryo-EM structure of the plant 26S proteasome.

Targeted proteolysis is a hallmark of life. It is especially important in long-lived cells that can be found in higher eukaryotes, like plants. This task is mainly fulfilled by the ubiquitin-proteasome system. Thus, proteolysis by the 26S proteasome is vital to development, immunity, and cell division. Although the yeast and animal proteasomes are well characterized, there is only limited information on the plant proteasome. We determined the first plant 26S proteasome structure from Spinacia oleracea by single-particle electron cryogenic microscopy at an overall resolution of 3.3 Å. We found an almost identical overall architecture of the spinach proteasome compared with the known structures from mammals and yeast. Nevertheless, we noticed a structural difference in the proteolytic active ß1 subunit. Furthermore, we uncovered an unseen compression state by characterizing the proteasome's conformational landscape. We suspect that this new conformation of the 20S core protease, in correlation with a partial opening of the unoccupied gate, may contribute to peptide release after proteolysis. Our data provide a structural basis for the plant proteasome, which is crucial for further studies.

Hierarchical Denoising of Ordinal Time Series of Clinical Scores.

Clinical scores (disease rating scales) are ordinal in nature. Longitudinal studies which use clinical scores produce ordinal time series. These time series tend to be noisy and often have a short-duration. This paper proposes a denoising method for such time series. The method uses a hierarchical approach to draw statistical power from the entire population of a study's patients to give reliable, subject-specific results. The denoising method is applied to MDS-UPDRS motor scores for Parkinson's disease.

Hierarchical MAP Denoising of Longitudinal Hamilton Depression Rating Scores.

The Hamilton Depression Rating Scale provides ordinal ratings for evaluating different aspects of depression. These ratings are usually quite noisy, and longitudinal patterns in the ratings can be difficult to discern. This paper proposes a hierarchical maximum-a-posteriori (MAP) method for denoising the ordinal time series of such ratings. Real-world data from a clinical trial are analyzed using the model. Denoising reveals subject-specific longitudinal patterns, predicts future ratings, and reveals progression patterns via principal component analysis.

Self-normalized Classification of Parkinson's Disease DaTscan Images.

Classifying SPECT images requires a preprocessing step which normalizes the images using a normalization region. The choice of the normalization region is not standard, and using different normalization regions introduces normalization region-dependent variability. This paper mathematically analyzes the effect of the normalization region to show that normalized-classification is exactly equivalent to a subspace separation of the half rays of the images under multiplicative equivalence. Using this geometry, a new self-normalized classification strategy is proposed. This strategy eliminates the normalizing region altogether. The theory is used to classify DaTscan images of 365 Parkinson's disease (PD) subjects and 208 healthy control (HC) subjects from the Parkinson's Progression Marker Initiative (PPMI). The theory is also used to understand PD progression from baseline to year 4.

Robust Bayesian Analysis of Early-Stage Parkinson's Disease Progression Using DaTscan Images.

This paper proposes a mixture of linear dynamical systems model for quantifying the heterogeneous progress of Parkinson's disease from DaTscan Images. The model is fitted to longitudinal DaTscans from the Parkinson's Progression Marker Initiative. Fitting is accomplished using robust Bayesian inference with collapsed Gibbs sampling. Bayesian inference reveals three image-based progression subtypes which differ in progression speeds as well as progression trajectories. The model reveals characteristic spatial progression patterns in the brain, each pattern associated with a time constant. These patterns can serve as disease progression markers. The subtypes also have different progression rates of clinical symptoms measured by MDS-UPDRS Part III scores.

Continuous flexibility analysis of SARS-CoV-2 spike prefusion structures.

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results.

Continuous flexibility analysis of SARS-CoV-2 Spike prefusion structures.

With the help of novel processing workflows and algorithms, we have obtained a better understanding of the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state. We have re-analyzed previous cryo-EM data combining 3D clustering approaches with ways to explore a continuous flexibility space based on 3D Principal Component Analysis. These advanced analyses revealed a concerted motion involving the receptor-binding domain (RBD), N-terminal domain (NTD), and subdomain 1 and 2 (SD1 & SD2) around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. We show that in this dataset there are not well-defined, stable, spike conformations, but virtually a continuum of states moving in a concerted fashion. We obtained an improved resolution ensemble map with minimum bias, from which we model by flexible fitting the extremes of the change along the direction of maximal variance. Moreover, a high-resolution structure of a recently described biochemically stabilized form of the spike is shown to greatly reduce the dynamics observed for the wild-type spike. Our results provide new detailed avenues to potentially restrain the spike dynamics for structure-based drug and vaccine design and at the same time give a warning of the potential image processing classification instability of these complicated datasets, having a direct impact on the interpretability of the results.

Measuring local-directional resolution and local anisotropy in cryo-EM maps.

The introduction of local resolution has enormously helped the understanding of cryo-EM maps. Still, for any given pixel it is a global, aggregated value, that makes impossible the individual analysis of the contribution of the different projection directions. We introduce MonoDir, a fully automatic, parameter-free method that, starting only from the final cryo-EM map, decomposes local resolution into the different projection directions, providing a detailed level of analysis of the final map. Many applications of directional local resolution are possible, and we concentrate here on map quality and validation.

Gaussian process post-processing for particle tracking velocimetry.

Particle tracking velocimetry (PTV) gives quantitative estimates of fluid flow velocities from images. But particle tracking is a complicated problem, and it often produces results that need substantial post-processing. We propose a novel Gaussian process regression-based post-processing step for PTV: The method smooths ("denoises") and densely interpolates velocity estimates while rejecting track irregularities. The method works under a large range of particle densities and fluid velocities. In addition, the method calculates standard deviances (error bars) for the velocity estimates, opening the possibility of propagating the standard deviances through subsequent processing and analysis. The accuracy of the method is experimentally evaluated using Optical Coherence Tomography images of particles in laminar flow in a pipe phantom. Following this, the method is used to quantify cilia-driven fluid flow and vorticity patterns in a developing Xenopus embryo.

Bayesian Longitudinal Modeling of Early Stage Parkinson's Disease Using DaTscan Images.

This paper proposes a disease progression model for early stage Parkinson's Disease (PD) based on DaTscan images. The model has two novel aspects: first, the model is fully coupled across the two caudates and putamina. Second, the model uses a new constraint called model mirror symmetry (MMS). A full Bayesian analysis, with collapsed Gibbs sampling using conjugate priors, is used to obtain posterior samples of the model parameters. The model identifies PD progression subtypes and reveals novel fast modes of PD progression.

Voxel-based logistic analysis of PPMI control and Parkinson's disease DaTscans.

A comprehensive analysis of the Parkinson's Progression Markers Initiative (PPMI) Dopamine Transporter Single Photon Emission Computed Tomography (DaTscan) images is carried out using a voxel-based logistic lasso model. The model reveals that sub-regional voxels in the caudate, the putamen, as well as in the globus pallidus are informative for classifying images into control and PD classes. Further, a new technique called logistic component analysis is developed. This technique reveals that intra-population differences in dopamine transporter concentration and imperfect normalization are significant factors influencing logistic analysis. The interactions with handedness, sex, and age are also evaluated.

Broadband multimode fiber spectrometer.

A general-purpose all-fiber spectrometer is demonstrated to overcome the trade-off between spectral resolution and bandwidth. By integrating a wavelength division multiplexer with five multimode optical fibers, we have achieved 100 nm bandwidth with 0.03 nm resolution at wavelength 1500 nm. An efficient algorithm is developed to reconstruct the spectrum from the speckle pattern produced by interference of guided modes in the multimode fibers. Such an algorithm enables a rapid, accurate reconstruction of both sparse and dense spectra in the presence of noise.

Robust w-Estimators for Cryo-EM Class Means.

A critical step in cryogenic electron microscopy (cryo-EM) image analysis is to calculate the average of all images aligned to a projection direction. This average, called the class mean, improves the signal-to-noise ratio in single-particle reconstruction. The averaging step is often compromised because of the outlier images of ice, contaminants, and particle fragments. Outlier detection and rejection in the majority of current cryo-EM methods are done using cross-correlation with a manually determined threshold. Empirical assessment shows that the performance of these methods is very sensitive to the threshold. This paper proposes an alternative: a w-estimator of the average image, which is robust to outliers and which does not use a threshold. Various properties of the estimator, such as consistency and influence function are investigated. An extension of the estimator to images with different contrast transfer functions is also provided. Experiments with simulated and real cryo-EM images show that the proposed estimator performs quite well in the presence of outliers.

Why Does Mutual-Information Work for Image Registration? A Deterministic Explanation.

This paper proposes a deterministic explanation for mutual-information-based image registration (MI registration). The explanation is that MI registration works because it aligns certain image partitions. This notion of aligning partitions is new, and is shown to be related to Schur- and quasi-convexity. The partition-alignment theory of this paper goes beyond explaining mutual- information. It suggests other objective functions for registering images. Some of these newer objective functions are not entropy-based. Simulations with noisy images show that the newer objective functions work well for registration, lending support to the theory. The theory proposed in this paper opens a number of directions for further research in image registration. These directions are also discussed.

Directly reconstructing principal components of heterogeneous particles from cryo-EM images.

Structural heterogeneity of particles can be investigated by their three-dimensional principal components. This paper addresses the question of whether, and with what algorithm, the three-dimensional principal components can be directly recovered from cryo-EM images. The first part of the paper extends the Fourier slice theorem to covariance functions showing that the three-dimensional covariance, and hence the principal components, of a heterogeneous particle can indeed be recovered from two-dimensional cryo-EM images. The second part of the paper proposes a practical algorithm for reconstructing the principal components directly from cryo-EM images without the intermediate step of calculating covariances. This algorithm is based on maximizing the posterior likelihood using the Expectation-Maximization algorithm. The last part of the paper applies this algorithm to simulated data and to two real cryo-EM data sets: a data set of the 70S ribosome with and without Elongation Factor-G (EF-G), and a data set of the influenza virus RNA dependent RNA Polymerase (RdRP). The first principal component of the 70S ribosome data set reveals the expected conformational changes of the ribosome as the EF-G binds and unbinds. The first principal component of the RdRP data set reveals a conformational change in the two dimers of the RdRP.