Autonomous and self-sustained circadian oscillators displayed in human islet cells.

AIMS/HYPOTHESIS: Following on from the emerging importance of the pancreas circadian clock on islet function and the development of type 2 diabetes in rodent models, we aimed to examine circadian gene expression in human islets. The oscillator properties were assessed in intact islets as well as in beta cells. METHODS: We established a system for long-term bioluminescence recording in cultured human islets, employing lentivector gene delivery of the core clock gene Bmal1 (also known as Arntl)-luciferase reporter. Beta cells were stably labelled using a rat insulin2 promoter fluorescent construct. Single-islet/cell oscillation profiles were measured by combined bioluminescence-fluorescence time-lapse microscopy. RESULTS: Human islets synchronised in vitro exhibited self-sustained circadian oscillations of Bmal1-luciferase expression at both the population and single-islet levels, with period lengths of 23.6 and 23.9 h, respectively. Endogenous BMAL1 and CRY1 transcript expression was circadian in synchronised islets over 48 h, and antiphasic to REV-ERBα (also known as NR1D1), PER1, PER2, PER3 and DBP transcript circadian profiles. HNF1A and PDX1 exhibited weak circadian oscillations, in phase with the REV-ERBα transcript. Dispersed islet cells were strongly oscillating as well, at population and single-cell levels. Importantly, beta and non-beta cells revealed oscillatory profiles that were well synchronised with each other. CONCLUSIONS/INTERPRETATION: We provide for the first time compelling evidence for high-amplitude cell-autonomous circadian oscillators displayed in human pancreatic islets and in dispersed human islet cells. Moreover, these clocks are synchronised between beta and non-beta cells in primary human islet cell cultures.

3-D PSF fitting for fluorescence microscopy: implementation and localization application.

Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy is significantly improved when the localization is performed using a more realistic model. Here, we show how this can be achieved by considering three-dimensional (3-D) point spread function models for the wide field microscope. We introduce a least-squares point spread function fitting framework that utilizes the Gibson and Lanni model and propose a computationally efficient way for evaluating its derivative functions. We demonstrate the usefulness of the proposed approach with algorithms for particle localization and defocus estimation, both implemented as plugins for ImageJ.

Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy.

Mechanical properties of the adventitia are largely determined by the organization of collagen fibers. Measurements on the waviness and orientation of collagen, particularly at the zero-stress state, are necessary to relate the structural organization of collagen to the mechanical response of the adventitia. Using the fluorescence collagen marker CNA38-OG488 and confocal laser scanning microscopy, we imaged collagen fibers in the adventitia of rabbit common carotid arteries ex vivo. The arteries were cut open along their longitudinal axes to get the zero-stress state. We used semi-manual and automatic techniques to measure parameters related to the waviness and orientation of fibers. Our results showed that the straightness parameter (defined as the ratio between the distances of endpoints of a fiber to its length) was distributed with a beta distribution (mean value 0.72, variance 0.028) and did not depend on the mean angle orientation of fibers. Local angular density distributions revealed four axially symmetric families of fibers with mean directions of 0°, 90°, 43° and -43°, with respect to the axial direction of the artery, and corresponding circular standard deviations of 40°, 47°, 37° and 37°. The distribution of local orientations was shifted to the circumferential direction when measured in arteries at the zero-load state (intact), as compared to arteries at the zero-stress state (cut-open). Information on collagen fiber waviness and orientation, such as obtained in this study, could be used to develop structural models of the adventitia, providing better means for analyzing and understanding the mechanical properties of vascular wall.

Realistic analytical phantoms for parallel magnetic resonance imaging.

The quantitative validation of reconstruction algorithms requires reliable data. Rasterized simulations are popular but they are tainted by an aliasing component that impacts the assessment of the performance of reconstruction. We introduce analytical simulation tools that are suited to parallel magnetic resonance imaging and allow one to build realistic phantoms. The proposed phantoms are composed of ellipses and regions with piecewise-polynomial boundaries, including spline contours, Bézier contours, and polygons. In addition, they take the channel sensitivity into account, for which we investigate two possible models. Our analytical formulations provide well-defined data in both the spatial and k-space domains. Our main contribution is the closed-form determination of the Fourier transforms that are involved. Experiments validate the proposed implementation. In a typical parallel magnetic resonance imaging reconstruction experiment, we quantify the bias in the overly optimistic results obtained with rasterized simulations-the inverse-crime situation. We provide a package that implements the different simulations and provide tools to guide the design of realistic phantoms.

A fast wavelet-based reconstruction method for magnetic resonance imaging.

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.

Model-based estimation of 3-D stiffness parameters in photonic-force microscopy.

We propose a system to characterize the 3-D diffusion properties of the probing bead trapped by a photonic-force microscope. We follow a model-based approach, where the model of the dynamics of the bead is given by the Langevin equation. Our procedure combines software and analog hardware to measure the corresponding stiffness matrix. We are able to estimate all its elements in real time, including off-diagonal terms. To achieve our goal, we have built a simple analog computer that performs a continuous preprocessing of the data, which can be subsequently digitized at a much lower rate than is otherwise required. We also provide an effective numerical algorithm for compensating the correlation bias introduced by a quadrant photodiode detector in the microscope. We validate our approach using simulated data and show that our bias-compensation scheme effectively improves the accuracy of the system. Moreover, we perform experiments with the real system and demonstrate real-time capabilities. Finally, we suggest a simple adjunction that would allow one to determine the mass matrix as well.

Intracellular nanomanipulation by a photonic-force microscope with real-time acquisition of a 3D stiffness matrix.

A traditional photonic-force microscope (PFM) results in huge sets of data, which requires tedious numerical analysis. In this paper, we propose instead an analog signal processor to attain real-time capabilities while retaining the richness of the traditional PFM data. Our system is devoted to intracellular measurements and is fully interactive through the use of a haptic joystick. Using our specialized analog hardware along with a dedicated algorithm, we can extract the full 3D stiffness matrix of the optical trap in real time, including the off-diagonal cross-terms. Our system is also capable of simultaneously recording data for subsequent offline analysis. This allows us to check that a good correlation exists between the classical analysis of stiffness and our real-time measurements. We monitor the PFM beads using an optical microscope. The force-feedback mechanism of the haptic joystick helps us in interactively guiding the bead inside living cells and collecting information from its (possibly anisotropic) environment. The instantaneous stiffness measurements are also displayed in real time on a graphical user interface. The whole system has been built and is operational; here we present early results that confirm the consistency of the real-time measurements with offline computations.

Laser Doppler imaging for intraoperative human brain mapping.

The identification and accurate location of centers of brain activity are vital both in neuro-surgery and brain research. This study aimed to provide a non-invasive, non-contact, accurate, rapid and user-friendly means of producing functional images intraoperatively. To this end a full field Laser Doppler imager was developed and integrated within the surgical microscope and perfusion images of the cortical surface were acquired during awake surgery whilst the patient performed a predetermined task. The regions of brain activity showed a clear signal (10-20% with respect to the baseline) related to the stimulation protocol which lead to intraoperative functional brain maps of strong statistical significance and which correlate well with the preoperative fMRI and intraoperative cortical electro-stimulation. These initial results achieved with a prototype device and wavelet based regressor analysis (the hemodynamic response function being derived from MRI applications) demonstrate the feasibility of LDI as an appropriate technique for intraoperative functional brain imaging.

Coupled tomography and distinct-element-method approach to exploring the granular media microstructure in a jamming hourglass.

We describe an approach for exploring microscopic properties of granular media that couples x-ray microtomography and distinct-element-method (DEM) simulations through image analysis. We illustrate it via the study of the intriguing phenomenon of instant arching in an hourglass (in our case a cylinder filled with a polydisperse mixture of glass beads that has a small circular shutter in the bottom). X-ray tomography provides three-dimensional snapshots of the microscopic conditions of the system both prior to opening the shutter, and thereafter, once jamming is completed. The process time in between is bridged using DEM simulation, which settles to positions in remarkably good agreement with the x-ray images. Specifically designed image analysis procedures accurately extract the geometrical information, i.e., the positions and sizes of the beads, from the raw x-ray tomographs, and compress the data representation from initially 5 gigabytes to a few tens of kilobytes per tomograph. The scope of the approach is explored through a sensitivity analysis to input data perturbations in both bead sizes and positions. We establish that accuracy of size--much more than position--estimates is critical, thus explaining the difficulty in considering a mixture of beads of different sizes. We further point to limits in the replication ability of granular flows away from equilibrium; i.e., the difficulty of numerically reproducing chaotic motion.

Quantitative morphometrical characterization of human pronuclear zygotes.

BACKGROUND: Identification of embryos with high implantation potential remains a challenge in in vitro fertilization (IVF). Subjective pronuclear (PN) zygote scoring systems have been developed for that purpose. The aim of this work was to provide a software tool that enables objective measuring of morphological characteristics of the human PN zygote. METHODS: A computer program was created to analyse zygote images semi-automatically, providing precise morphological measurements. The accuracy of this approach was first validated by comparing zygotes from two different IVF centres with computer-assisted measurements or subjective scoring. Computer-assisted measurement and subjective scoring were then compared for their ability to classify zygotes with high and low implantation probability by using a linear discriminant analysis. RESULTS: Zygote images coming from the two IVF centres were analysed with the software, resulting in a series of precise measurements of 24 variables. Using subjective scoring, the cytoplasmic halo was the only feature which was significantly different between the two IVF centres. Computer-assisted measurements revealed significant differences between centres in PN centring, PN proximity, cytoplasmic halo and features related to nucleolar precursor bodies distribution. The zygote classification error achieved with the computer-assisted measurements (0.363) was slightly inferior to that of the subjective ones (0.393). CONCLUSIONS: A precise and objective characterization of the morphology of human PN zygotes can be achieved by the use of an advanced image analysis tool. This computer-assisted analysis allows for a better morphological characterization of human zygotes and can be used for classification.

A fast thresholded landweber algorithm for wavelet-regularized multidimensional deconvolution.

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the l(1)-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.

Snakuscules.

A snakuscule (a minuscule snake) is the simplest active contour that we were able to design while keeping the quintessence of traditional snakes: an energy term governed by the data, and a regularization term. Our construction is an area-based snake, as opposed to curve-based snakes. It is parameterized by just two points, thus further easing requirements on the optimizer. Despite their ultimate simplicity, snakuscules retain enough versatility to be employed for solving various problems such as cell counting and segmentation of approximately circular features. In this paper, we detail the design process of a snakuscule and illustrate its usefulness through practical examples. We claim that our didactic intentions are well served by the simplicity of snakuscules.

An Optimized Spline-Based Registration of a 3D CT to a Set of C-Arm Images.

We have developed an algorithm for the rigid-body registration of a CT volume to a set of C-arm images. The algorithm uses a gradient-based iterative minimization of a least-squares measure of dissimilarity between the C-arm images and projections of the CT volume. To compute projections, we use a novel method for fast integration of the volume along rays. To improve robustness and speed, we take advantage of a coarse-to-fine processing of the volume/image pyramids. To compute the projections of the volume, the gradient of the dissimilarity measure, and the multiresolution data pyramids, we use a continuous image/volume model based on cubic B-splines, which ensures a high interpolation accuracy and a gradient of the dissimilarity measure that is well defined everywhere. We show the performance of our algorithm on a human spine phantom, where the true alignment is determined using a set of fiducial markers.

Spline-based image-to-volume registration for three-dimensional electron microscopy.

This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of standard quantized-parameter methods by registering the images to a reference 3D particle model. We achieve the registration by employing a gradient-based iterative minimization of a least-squares measure of dissimilarity between an image and a projection of the volume in the Fourier transform (FT) domain. We compute the FT of the projection using the central-slice theorem (CST). To compute the gradient accurately, we take advantage of a cubic B-spline model of the data in the frequency domain. To improve the robustness of the algorithm, we weight the cost function in the FT domain and apply a "mixed" strategy for the assignment based on the minimum value of the cost function at registration for several different initializations. We validate our algorithm in a fully controlled simulation environment. We show that the mixed strategy improves the assignment accuracy; on our data, the quality of the angular and translational assignment was better than 2 voxel (i.e., 6.54 angstroms). We also test the performance of our algorithm on real EM data. We conclude that our algorithm outperforms a standard projection-matching refinement in terms of both consistency of 3D reconstructions and speed.

Spectral signal-to-noise ratio and resolution assessment of 3D reconstructions.

Measuring the quality of three-dimensional (3D) reconstructed biological macromolecules by transmission electron microscopy is still an open problem. In this article, we extend the applicability of the spectral signal-to-noise ratio (SSNR) to the evaluation of 3D volumes reconstructed with any reconstruction algorithm. The basis of the method is to measure the consistency between the data and a corresponding set of reprojections computed for the reconstructed 3D map. The idiosyncrasies of the reconstruction algorithm are taken explicitly into account by performing a noise-only reconstruction. This results in the definition of a 3D SSNR which provides an objective indicator of the quality of the 3D reconstruction. Furthermore, the information to build the SSNR can be used to produce a volumetric SSNR (VSSNR). Our method overcomes the need to divide the data set in two. It also provides a direct measure of the performance of the reconstruction algorithm itself; this latter information is typically not available with the standard resolution methods which are primarily focused on reproducibility alone.

Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images.

BACKGROUND: For the investigation of the molecular mechanisms involved in neurite outgrowth and differentiation, accurate and reproducible segmentation and quantification of neuronal processes are a prerequisite. To facilitate this task, we developed a semiautomatic neurite tracing technique. This article describes the design and validation of the technique. METHODS: The technique was compared to fully manual delineation. Four observers repeatedly traced selected neurites in 20 fluorescence microscopy images of cells in culture, using both methods. Accuracy and reproducibility were determined by comparing the tracings to high-resolution reference tracings, using two error measures. Labor intensiveness was measured in numbers of mouse clicks required. The significance of the results was determined by a Student t-test and by analysis of variance. RESULTS: Both methods slightly underestimated the true neurite length, but the differences were not unanimously significant. The average deviation from the true neurite centerline was a factor 2.6 smaller with the developed technique compared to fully manual tracing. Intraobserver variability in the respective measures was reduced by a factor 6.0 and 23.2. Interobserver variability was reduced by a factor 2.4 and 8.8, respectively, and labor intensiveness by a factor 3.3. CONCLUSIONS: Providing similar accuracy in measuring neurite length, significantly improved accuracy in neurite centerline extraction, and significantly improved reproducibility and reduced labor intensiveness, the developed technique may replace fully manual tracing methods.

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles.

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.

MOMS: maximal-order interpolation of minimal support.

We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function phi(x). We first give the expression for the cases of phi's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions, which we call maximal-order-minimal-support functions (MOMS) is made of linear combinations of the B-spline of the same order and of its derivatives. We provide an explicit form of the MOMS that maximizes the approximation accuracy when the step-size is small enough. We compute the sampling gain obtained by using these optimal basis functions over the splines of the same order. We show that it is already substantial for small orders and that it further increases with the approximation order L. When L is large, this sampling gain becomes linear; more specifically, its exact asymptotic expression is 2/(pie)L. Since the optimal functions are continuous, but not differentiable, for even orders, and even only piecewise continuous for odd orders, our result implies that regularity has little to do with approximating performance. These theoretical findings are corroborated by experimental evidence that involves compounded rotations of images.

Least-squares image resizing using finite differences.

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.

Interpolation revisited.

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims.