A global sampler of single particle tracking solutions for single molecule microscopy.

The dependence on model-fitting to evaluate particle trajectories makes it difficult for single particle tracking (SPT) to resolve the heterogeneous molecular motions typical of cells. We present here a global spatiotemporal sampler for SPT solutions using a Metropolis-Hastings algorithm. The sampler does not find just the most likely solution but also assesses its likelihood and presents alternative solutions. This enables the estimation of the tracking error. Furthermore the algorithm samples the parameters that govern the tracking process and therefore does not require any tweaking by the user. We demonstrate the algorithm on synthetic and single molecule data sets. Metrics for the comparison of SPT are generalised to be applied to a SPT sampler. We illustrate using the example of the diffusion coefficient how the distribution of the tracking solutions can be propagated into a distribution of derived quantities. We also discuss the major challenges that are posed by the realisation of a SPT sampler.

Analysis of heterogeneity in T2-weighted MR images can differentiate pseudoprogression from progression in glioblastoma.

PURPOSE: To develop an image analysis technique that distinguishes pseudoprogression from true progression by analyzing tumour heterogeneity in T2-weighted images using topological descriptors of image heterogeneity called Minkowski functionals (MFs). METHODS: Using a retrospective patient cohort (n = 50), and blinded to treatment response outcome, unsupervised feature estimation was performed to investigate MFs for the presence of outliers, potential confounders, and sensitivity to treatment response. The progression and pseudoprogression groups were then unblinded and supervised feature selection was performed using MFs, size and signal intensity features. A support vector machine model was obtained and evaluated using a prospective test cohort. RESULTS: The model gave a classification accuracy, using a combination of MFs and size features, of more than 85% in both retrospective and prospective datasets. A different feature selection method (Random Forest) and classifier (Lasso) gave the same results. Although not apparent to the reporting radiologist, the T2-weighted hyperintensity phenotype of those patients with progression was heterogeneous, large and frond-like when compared to those with pseudoprogression. CONCLUSION: Analysis of heterogeneity, in T2-weighted MR images, which are acquired routinely in the clinic, has the potential to detect an earlier treatment response allowing an early change in treatment strategy. Prospective validation of this technique in larger datasets is required.

Analysis of image heterogeneity using 2D Minkowski functionals detects tumor responses to treatment.

PURPOSE: The acquisition of ever increasing volumes of high resolution magnetic resonance imaging (MRI) data has created an urgent need to develop automated and objective image analysis algorithms that can assist in determining tumor margins, diagnosing tumor stage, and detecting treatment response. METHODS: We have shown previously that Minkowski functionals, which are precise morphological and structural descriptors of image heterogeneity, can be used to enhance the detection, in T1 -weighted images, of a targeted Gd(3+) -chelate-based contrast agent for detecting tumor cell death. We have used Minkowski functionals here to characterize heterogeneity in T2 -weighted images acquired before and after drug treatment, and obtained without contrast agent administration. RESULTS: We show that Minkowski functionals can be used to characterize the changes in image heterogeneity that accompany treatment of tumors with a vascular disrupting agent, combretastatin A4-phosphate, and with a cytotoxic drug, etoposide. CONCLUSIONS: Parameterizing changes in the heterogeneity of T2 -weighted images can be used to detect early responses of tumors to drug treatment, even when there is no change in tumor size. The approach provides a quantitative and therefore objective assessment of treatment response that could be used with other types of MR image and also with other imaging modalities.

A stochastic model for electron multiplication charge-coupled devices--from theory to practice.

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images.

Automated multidimensional single molecule fluorescence microscopy feature detection and tracking.

Characterisation of multi-protein interactions in cellular networks can be achieved by optical microscopy using multidimensional single molecule fluorescence imaging. Proteins of different species, individually labelled with a single fluorophore, can be imaged as isolated spots (features) of different colour light in different channels, and their diffusive behaviour in cells directly measured through time. Challenges in data analysis have, however, thus far hindered its application in biology. A set of methods for the automated analysis of multidimensional single molecule microscopy data from cells is presented, incorporating Bayesian segmentation-based feature detection, image registration and particle tracking. Single molecules of different colours can be simultaneously detected in noisy, high background data with an arbitrary number of channels, acquired simultaneously or time-multiplexed, and then tracked through time. The resulting traces can be further analysed, for example to detect intensity steps, count discrete intensity levels, measure fluorescence resonance energy transfer (FRET) or changes in polarisation. Examples are shown illustrating the use of the algorithms in investigations of the epidermal growth factor receptor (EGFR) signalling network, a key target for cancer therapeutics, and with simulated data.

Characterization of image heterogeneity using 2D Minkowski functionals increases the sensitivity of detection of a targeted MRI contrast agent.

A targeted Gd(3+)-based contrast agent has been developed that detects tumor cell death by binding to the phosphatidylserine (PS) exposed on the plasma membrane of dying cells. Although this agent has been used to detect tumor cell death in vivo, the differences in signal intensity between treated and untreated tumors was relatively small. As cell death is often spatially heterogeneous within tumors, we investigated whether an image analysis technique that parameterizes heterogeneity could be used to increase the sensitivity of detection of this targeted contrast agent. Two-dimensional (2D) Minkowski functionals (MFs) provided an automated and reliable method for parameterization of image heterogeneity, which does not require prior assumptions about the number of regions or features in the image, and were shown to increase the sensitivity of detection of the contrast agent as compared to simple signal intensity analysis.

Simulations of astronomical imaging phased arrays.

We describe a theoretical procedure for analyzing astronomical phased arrays with overlapping beams and apply the procedure to simulate a simple example. We demonstrate the effect of overlapping beams on the number of degrees of freedom of the array and on the ability of the array to recover a source. We show that the best images are obtained using overlapping beams, contrary to common practice, and show how the dynamic range of a phased array directly affects the image quality.

Coupled-mode theory for infrared and submillimeter wave detectors.

We present a comprehensive, spatiotemporal, modal theory of submillimeter-wave and far-infrared power detectors. The theory is based on the contraction of the coherence tensor of the light with another coherence tensor that incorporates all of the physics of the detector. The theory is extremely general and applies to detectors of any bandwidth, with light in any state of polarization and spatiotemporal coherence. The theory applies equally to quasi-monochromatic and pulsed systems. We show that the tensor associated with the detector is a measureable quantity and outline a procedure for its experimental determination. We derive expressions for the statistical properties of a detector's output, including the correlations between the outputs of different detectors, say, in an array or interferometer. The theory provides a clear conceptual understanding of how any general detector couples to the modes of an optical system and thereby provides a powerful and flexible way of modeling the behavior of detectors and instruments.

Partially coherent analysis of imaging and interferometric phased arrays: noise, correlations, and fluctuations.

Phased arrays are of considerable importance for far-infrared, submillimeter-wave, and microwave astronomy; they are also being developed for areas as diverse as optical switching, radar, and radio communications. We present a discretized, modal theory of imaging and interferometric phased arrays. It is shown that the average powers, field correlations, power fluctuations, and correlations between power fluctuations at the output ports of an imaging, or interferometric, phased array can be determined for a source in any state of spatial coherence and polarization, once the synthesized beam patterns are known. It is not necessary to know anything about the internal construction of the beam-forming networks; indeed, the beam patterns can be taken from experimental data. The synthesized beams can be nonorthogonal and even linearly dependent. Our theory leads to many conceptual insights and opens the way to a range of new design and simulation techniques.

Quantum-statistical analysis of multimode far-infrared and submillimeter-wave astronomical interferometers.

We present a detailed quantum-statistical model of multimode far-infrared and submillimeter-wave astronomical interferometers. The scheme identifies explicitly the optical modes associated with each telescope and uses these to trace the quantum-statistical properties of the field from a source through the telescopes, through the beam combiners, and onto the detectors. The scheme can be used with any optical configuration, and elegant expressions result for the average rate at which photons are detected by the pixels of an imaging array, the mean-square fluctuations in the rates, and the correlations between the fluctuations in the rates of different pixels. Numerous extensions to the basic technique are possible.

Modal analysis of astronomical bolometric interferometers.

A procedure is described for modeling the behavior of astronomical bolometric interferometers. The scheme is based on the notion of eigenfields. The input and output eigenfields are those field distributions on the sky and at the detector to which the individual telescopes of an interferometer can couple. Eigenfields are more fundamental than eigenmodes and provide, regardless of optical configuration, an orthogonal basis for propagating the second-order statistical properties of a field from a source through the telescopes, through the beam combiners, and onto the detectors. With our scheme, it is possible to calculate the power coupled into coherent, partially coherent, and incoherent imaging arrays and to include the spatially distributed noise sources of the telescopes themselves.

Markov-chain Monte Carlo approach to the design of multilayer thin-film optical coatings.

We reconsider the problem of locating the globally optimal solution of a multilayer-optical-coating design problem, within some predetermined space of parameters, with the aim of obtaining a robust technique that requires a minimum of user intervention. The approach we adopt centers on exploring the space of the parameters of interest by using a Markov-chain Monte Carlo sampling algorithm. This technique enables one to locate the global optimum automatically with high confidence and without the need for a good starting design. It also allows the trivial inclusion of prior constraints on the variables and provides a natural means for investigating the robustness of the optimal solution.

General approach for representing and propagating partially coherent terahertz fields with application to Gabor basis sets.

We discuss a general theoretical framework for representing and propagating fully coherent, fully incoherent, and the intermediate regime of partially coherent submillimeter-wave fields by means of general sampled basis functions, which may have any degree of completeness. Partially coherent fields arise when finite-throughput systems induce coherence on incoherent fields. This powerful extension to traditional modal analysis methods by using undercomplete Gaussian-Hermite modes can be employed to analyze and optimize such Gaussian quasi-optical techniques. We focus on one particular basis set, the Gabor basis, which consists of overlapping translated and modulated Gaussian beams. We present high-accuracy numerical results from field reconstructions and propagations. In particular, we perform one-dimensional analyses illustrating the Van Cittert-Zernike theorem and then extend our simulations to two dimensions, including simple models of horn and bolometer arrays. Our methods and results are of practical importance as a method for analyzing terahertz fields, which are often partially coherent and diffraction limited so that ray tracing is inaccurate and physical optics computationally prohibitive.

Representing the behavior of partially coherent optical systems by using overcomplete basis sets.

A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S = EE(dagger) and R = E(dagger)E. For overcomplete sets, S can be inverted to give a dual basis set, E = S(-1)E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, Pt = Tr[RA]; (iii) the power coupled between two fields, A and B, that are in different states of coherence, Pc = Tr[RARB]; and (iv) the entropy of a field, Q = Tr[Zsigmar(I-Z)r/r], where Z = RA/Tr[RA].