Single-molecule localization microscopy (SMLM) describes a family of powerful imaging techniques that dramatically improve spatial resolution over standard, diffraction-limited microscopy techniques and can image biological structures at the molecular scale. In SMLM, individual fluorescent molecules are computationally localized from diffraction-limited image sequences and the localizations are used to generate a super-resolution image or a time course of super-resolution images, or to define molecular trajectories. In this Primer, we introduce the basic principles of SMLM techniques before describing the main experimental considerations when performing SMLM, including fluorescent labelling, sample preparation, hardware requirements and image acquisition in fixed and live cells. We then explain how low-resolution image sequences are computationally processed to reconstruct super-resolution images and/or extract quantitative information, and highlight a selection of biological discoveries enabled by SMLM and closely related methods. We discuss some of the main limitations and potential artefacts of SMLM, as well as ways to alleviate them. Finally, we present an outlook on advanced techniques and promising new developments in the fast-evolving field of SMLM. We hope that this Primer will be a useful reference for both newcomers and practitioners of SMLM. This Primer explains the central concepts of single-molecule localization microscopy (SMLM) before discussing experimental considerations regarding fluorophores, optics and data acquisition, processing and analysis. The Primer further describes recent high-impact discoveries made by SMLM techniques and concludes by discussing emerging methodologies.

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Single-molecule localization microscopy

Older adults who ultimately develop dementia experience accelerated cognitive decline long before diagnosis. A similar acceleration in cognitive decline occurs in the years before death as well. To evaluate preclinical and terminal cognitive decline, past researchers have incorporated change points in their analyses of longitudinal data, identifying point estimates of how many years prior to diagnosis or death that decline begins to accelerate. The current systematic review aimed to summarize the published literature on preclinical and terminal change points in relation to mild cognitive impairment (MCI), dementia, and death, identifying the order in which cognitive and neurological outcomes decline and factors that modify the onset and rate of decline. A systematic search protocol yielded 35 studies, describing 16 longitudinal cohorts, modeling change points for cognitive and neurological outcomes preceding MCI, dementia, or death. Change points for cognitive abilities ranged from 3-7 years prior to MCI diagnosis, 1-11 years prior to dementia diagnosis, and 3-15 years before death. No sequence of decline was observed preceding MCI or death, but the following sequence was tentatively accepted for Alzheimer's disease: verbal memory, visuospatial ability, executive functions and fluency, and last, verbal IQ. Some of the modifiers of the onset and rate of decline examined by previous researchers included gender, education, genetics, neuropathology, and personality. Change point analyses evidence accelerated decline preceding MCI, dementia, and death, but moderators of the onset and rate of decline remain ambiguous due to between-study modeling differences, and coordinated analyses may improve comparability across future studies. (PsycINFO Database Record

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When does cognitive decline begin? A systematic review of change point studies on accelerated decline in cognitive and neurological outcomes preceding mild cognitive impairment, dementia, and death.

Photoacoustic tomography (PAT), or optoacoustic tomography, has achieved remarkable progress in the past decade, benefiting from the joint developments in optics, acoustics, chemistry, computing and mathematics. Unlike pure optical or ultrasound imaging, PAT can provide unique optical absorption contrast as well as widely scalable spatial resolution, penetration depth and imaging speed. Moreover, PAT has inherent sensitivity to tissue's functional, molecular, and metabolic state. With these merits, PAT has been applied in a wide range of life science disciplines, and has enabled biomedical research unattainable by other imaging methods. This Review article aims at introducing state-of-the-art PAT technologies and their representative applications. The focus is on recent technological breakthroughs in structural, functional, molecular PAT, including super-resolution imaging, real-time small-animal whole-body imaging, and high-sensitivity functional/molecular imaging. We also discuss the remaining challenges in PAT and envisioned opportunities.

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Listening to tissues with new light: recent technological advances in photoacoustic imaging.

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical elements of our proposal are supported by various results from numerical simulations with synthetic and experimental data.

Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement

We propose a direct imaging method based on the reverse time migration method for finding extended obstacles with phaseless total field data in the half space. We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the obstacle is far away from the surface of the half-space where the measurement is taken. Numerical experiments are included to illustrate the powerful imaging quality.

A direct imaging method for the half-space inverse scattering problem with phaseless data

Motivated by the problem of the detection of a change point in the mean structure of yield curves, we introduce several methods to test the null hypothesis that the mean structure of a time series of curves does not change. The mean structure does not refer merely to the level of the curves, but also to their range and other aspects of their shape, most prominently concavity. The performance of the tests depends on whether possible break points in the error structure, which refers to the random variability in the aspects of the curves listed above, are taken into account or not. If they are not taken into account, an existing change point in the mean structure may fail to be detected with a large probability. The paper contains a complete asymptotic theory, a simulation study and illustrative data examples, as well as details of the numerical implementation of the testing procedures.

This article is protected by copyright. All rights reserved

/pdf/change-point-tests-in-functional-factor-models-with-2y34979xv8.pdf

Change point tests in functional factor models with application to yield curves

Photoacoustic tomography (PAT) is a hybrid imaging modality where we intend to reconstruct optical properties of heterogeneous media from measured ultrasound signals generated by the photoacoustic effect. In recent years, there have been considerable interests in using PAT to image two-photon absorption, in addition to the usual single-photon absorption, inside diffusive media. We present a mathematical model for quantitative image reconstruction in two-photon photoacoustic tomography (TP-PAT). We propose a computational strategy for the reconstruction of the optical absorption coefficients and provide some numerical evidences based on synthetic photoacoustic acoustic data to demonstrate the feasibility of quantitative reconstructions in TP-PAT.

Quantitative photoacoustic imaging of two-photon absorption.

— A central problem of microstructure is to develop technologies capable of producing an arrangement, or ordering, of a polycrystalline material, in terms of mesoscopic parameters, like geometry and crystallography, appropriate for a given application. Is there such an order in the first place? Our goal is to describe the emergence of the grain boundary character distribution (GBCD), a statistic that details texture evolution discovered recently, and to illustrate why it should be considered a material property. For the GBCD statistic, we have developed a theory that relies on mass transport and entropy. The focus of this paper is its identification as a gradient flow in the sense of De Giorgi, as illustrated by Ambrosio, Gigli, and Savaré. In this way, the empirical texture statistic is revealed as a solution of a Fokker–Planck type equation whose evolution is determined by weak topology kinetics and whose limit behavior is a Boltzmann distribution. The identification as a gradient flow by our method is tantamount to exhibiting the harvested statistic as the iterates in a JKO implicit scheme. This requires several new ideas. The development exposes the question of how to understand the circumstances under which a harvested empirical statistic is a property of the underlying process.

Towards a gradient flow for microstructure

Convergence and stability results for the inverse Born series [Moskow and Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings between Banach spaces. We show that by restarting the inverse Born series one obtains a class of iterative methods containing the Gauss-Newton and Chebyshev-Halley methods. We use the generalized inverse Born series results to show convergence of the inverse Born series for the Schr\"odinger problem with discrete internal measurements. In this problem, the Schr\"odinger potential is to be recovered from a few measurements of solutions to the Schr\"odinger equation resulting from a few different source terms. An application of this method to a problem related to transient hydraulic tomography is given, where the source terms model injection and measurement wells.

Restarted inverse Born series for the Schr\"odinger problem with discrete internal measurements

We present a simple, frequency domain, preprocessing step to Kirchhoff migration that allows the method to image scatterers when the wave field phase information is lost at the receivers, and only intensities are measured. The resulting imaging method does not require knowing the phases of the probing field or manipulating the phase of the wave field at the receivers. In a regime where the scattered field is small compared to the probing field, the problem of recovering the full-waveform scattered field from intensity data can be formulated as an embarrassingly simple least-squares problem. Although this only recovers the projection (on a known subspace) of the full-waveform scattered field, we show that, for high frequencies, this projection gives Kirchhoff images asymptotically identical to the images obtained with full waveform data. Our method can also be used when the source is modulated by a Gaussian process and autocorrelations are measured at an array of receivers.

Patrick Bardsley

Papers

Change point tests in functional factor models with application to yield curves

Quantitative photoacoustic imaging of two-photon absorption.

Towards a gradient flow for microstructure

Restarted inverse Born series for the Schr\"odinger problem with discrete internal measurements

Kirchhoff migration without phases