Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit [1].

Long-term effects of Pfizer-BioNTech COVID-19 vaccinations on platelets.

There is a global concern about the safety of COVID-19 vaccines associated with platelet function. However, their long-term effects on overall platelet activity remain poorly understood. Here we address this problem by image-based single-cell profiling and temporal monitoring of circulating platelet aggregates in the blood of healthy human subjects, before and after they received multiple Pfizer-BioNTech (BNT162b2) vaccine doses over a time span of nearly 1 year. Results show no significant or persisting platelet aggregation trends following the vaccine doses, indicating that any effects of vaccinations on platelet turnover, platelet activation, platelet aggregation, and platelet-leukocyte interaction was insignificant.

Real-time intelligent classification of COVID-19 and thrombosis via massive image-based analysis of platelet aggregates.

Microvascular thrombosis is a typical symptom of COVID-19 and shows similarities to thrombosis. Using a microfluidic imaging flow cytometer, we measured the blood of 181 COVID-19 samples and 101 non-COVID-19 thrombosis samples, resulting in a total of 6.3 million bright-field images. We trained a convolutional neural network to distinguish single platelets, platelet aggregates, and white blood cells and performed classical image analysis for each subpopulation individually. Based on derived single-cell features for each population, we trained machine learning models for classification between COVID-19 and non-COVID-19 thrombosis, resulting in a patient testing accuracy of 75%. This result indicates that platelet formation differs between COVID-19 and non-COVID-19 thrombosis. All analysis steps were optimized for efficiency and implemented in an easy-to-use plugin for the image viewer napari, allowing the entire analysis to be performed within seconds on mid-range computers, which could be used for real-time diagnosis.

Enabling early detection of osteoarthritis from presymptomatic cartilage texture maps via transport-based learning.

Many diseases have no visual cues in the early stages, eluding image-based detection. Today, osteoarthritis (OA) is detected after bone damage has occurred, at an irreversible stage of the disease. Currently no reliable method exists for OA detection at a reversible stage. We present an approach that enables sensitive OA detection in presymptomatic individuals. Our approach combines optimal mass transport theory with statistical pattern recognition. Eighty-six healthy individuals were selected from the Osteoarthritis Initiative, with no symptoms or visual signs of disease on imaging. On 3-y follow-up, a subset of these individuals had progressed to symptomatic OA. We trained a classifier to differentiate progressors and nonprogressors on baseline cartilage texture maps, which achieved a robust test accuracy of 78% in detecting future symptomatic OA progression 3 y prior to symptoms. This work demonstrates that OA detection may be possible at a potentially reversible stage. A key contribution of our work is direct visualization of the cartilage phenotype defining predictive ability as our technique is generative. We observe early biochemical patterns of fissuring in cartilage that define future onset of OA. In the future, coupling presymptomatic OA detection with emergent clinical therapies could modify the outcome of a disease that costs the United States healthcare system $16.5 billion annually. Furthermore, our technique is broadly applicable to earlier image-based detection of many diseases currently diagnosed at advanced stages today.

Invariance encoding in sliced-Wasserstein space for image classification with limited training data.

Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the Radon Cumulative Distribution Transform (R-CDT), a recently introduced image transform. We demonstrate that for a particular type of learning problem, our mathematical solution has advantages over data augmentation with deep CNNs in terms of classification accuracy and computational complexity, and is particularly effective under a limited training data setting. The method is simple, effective, computationally efficient, non-iterative, and requires no parameters to be tuned. Python code implementing our method is available at https://github.com/rohdelab/mathematical augmentation. Our method is integrated as a part of the software package PyTransKit, which is available at https://github.com/rohdelab/PyTransKit.

Transport-based pattern recognition versus deep neural networks in underwater OAM communications.

Comparisons between machine learning and optimal transport-based approaches in classifying images are made in underwater orbital angular momentum (OAM) communications. A model is derived that justifies optimal transport for use in attenuated water environments. OAM pattern demultiplexing is performed using optimal transport and deep neural networks and compared to each other. Additionally, some of the complications introduced by signal attenuation are highlighted. The Radon cumulative distribution transform (R-CDT) is applied to OAM patterns to transform them to a linear subspace. The original OAM images and the R-CDT transformed patterns are used in several classification algorithms, and results are compared. The selected classification algorithms are the nearest subspace algorithm, a shallow convolutional neural network (CNN), and a deep neural network. It is shown that the R-CDT transformed images are more accurate than the original OAM images in pattern classification. Also, the nearest subspace algorithm performs better than the selected CNNs in OAM pattern classification in underwater environments.

CIRCOAST: a statistical hypothesis test for cellular colocalization with network structures.

Motivation: Colocalization of structures in biomedical images can lead to insights into biological behaviors. One class of colocalization problems is examining an annular structure (disk-shaped such as a cell, vesicle or molecule) interacting with a network structure (vascular, neuronal, cytoskeletal, organellar). Examining colocalization events across conditions is often complicated by changes in density of both structure types, confounding traditional statistical approaches since colocalization cannot be normalized to the density of both structure types simultaneously. We have developed a technique to measure colocalization independent of structure density and applied it to characterizing intercellular colocation with blood vessel networks. This technique could be used to analyze colocalization of any annular structure with an arbitrarily shaped network structure. Results: We present the circular colocalization affinity with network structures test (CIRCOAST), a novel statistical hypothesis test to probe for enriched network colocalization in 2D z-projected multichannel images by using agent-based Monte Carlo modeling and image processing to generate the pseudo-null distribution of random cell placement unique to each image. This hypothesis test was validated by confirming that adipose-derived stem cells (ASCs) exhibit enriched colocalization with endothelial cells forming arborized networks in culture and then applied to show that locally delivered ASCs have enriched colocalization with murine retinal microvasculature in a model of diabetic retinopathy. We demonstrate that the CIRCOAST test provides superior power and type I error rates in characterizing intercellular colocalization compared to generic approaches that are confounded by changes in cell or vessel density. Availability and implementation: CIRCOAST source code available at: https://github.com/uva-peirce-cottler-lab/ARCAS. Supplementary information: Supplementary data are available at Bioinformatics online.

Cell Image Classification: A Comparative Overview.

Cell image classification methods are currently being used in numerous applications in cell biology and medicine. Applications include understanding the effects of genes and drugs in screening experiments, understanding the role and subcellular localization of different proteins, as well as diagnosis and prognosis of cancer from images acquired using cytological and histological techniques. The article also reviews three main approaches for cell image classification most often used: numerical feature extraction, end-to-end classification with neural networks (NNs), and transport-based morphometry (TBM). In addition, we provide comparisons on four different cell imaging datasets to highlight the relative strength of each method. The results computed using four publicly available datasets show that numerical features tend to carry the best discriminative information for most of the classification tasks. Results also show that NN-based methods produce state-of-the-art results in the dataset that contains a relatively large number of training samples. Data augmentation or the choice of a more recently reported architecture does not necessarily improve the classification performance of NNs in the datasets with limited number of training samples. If understanding and visualization are desired aspects, TBM methods can offer the ability to invert classification functions, and thus can aid in the interpretation of results. These and other comparison outcomes are discussed with the aim of clarifying the advantages and disadvantages of each method. © 2020 International Society for Advancement of Cytometry.

Parametric Signal Estimation Using the Cumulative Distribution Transform.

We present a new method for estimating signal model parameters using the Cumulative Distribution Transform (CDT). Our approach minimizes the Wasserstein distance between measured and model signals. We derive some useful properties of the CDT and show that the resulting estimation problem, while nonlinear in the original signal domain, becomes a linear least squares problem in the transform domain. Furthermore, we discuss the properties of the estimator in the presence of noise and present a novel approach for mitigating the impact of the noise on the estimates. The proposed estimation approach is evaluated by applying it to a source localization problem and comparing its performance against traditional approaches.

Methods to label, image, and analyze the complex structural architectures of microvascular networks.

Microvascular networks play key roles in oxygen transport and nutrient delivery to meet the varied and dynamic metabolic needs of different tissues throughout the body, and their spatial architectures of interconnected blood vessel segments are highly complex. Moreover, functional adaptations of the microcirculation enabled by structural adaptations in microvascular network architecture are required for development, wound healing, and often invoked in disease conditions, including the top eight causes of death in the Unites States. Effective characterization of microvascular network architectures is not only limited by the available techniques to visualize microvessels but also reliant on the available quantitative metrics that accurately delineate between spatial patterns in altered networks. In this review, we survey models used for studying the microvasculature, methods to label and image microvessels, and the metrics and software packages used to quantify microvascular networks. These programs have provided researchers with invaluable tools, yet we estimate that they have collectively attained low adoption rates, possibly due to limitations with basic validation, segmentation performance, and nonstandard sets of quantification metrics. To address these existing constraints, we discuss opportunities to improve effectiveness, rigor, and reproducibility of microvascular network quantification to better serve the current and future needs of microvascular research.

Discovery and visualization of structural biomarkers from MRI using transport-based morphometry.

Disease in the brain is often associated with subtle, spatially diffuse, or complex tissue changes that may lie beneath the level of gross visual inspection, even on magnetic resonance imaging (MRI). Unfortunately, current computer-assisted approaches that examine pre-specified features, whether anatomically-defined (i.e. thalamic volume, cortical thickness) or based on pixelwise comparison (i.e. deformation-based methods), are prone to missing a vast array of physical changes that are not well-encapsulated by these metrics. In this paper, we have developed a technique for automated pattern analysis that can fully determine the relationship between brain structure and observable phenotype without requiring any a priori features. Our technique, called transport-based morphometry (TBM), is an image transformation that maps brain images losslessly to a domain where they become much more separable. The new approach is validated on structural brain images of healthy older adult subjects where even linear models for discrimination, regression, and blind source separation enable TBM to independently discover the characteristic changes of aging and highlight potential mechanisms by which aerobic fitness may mediate brain health later in life. TBM is a generative approach that can provide visualization of physically meaningful shifts in tissue distribution through inverse transformation. The proposed framework is a powerful technique that can potentially elucidate genotype-structural-behavioral associations in myriad diseases.

De-multiplexing vortex modes in optical communications using transport-based pattern recognition.

Free space optical communications utilizing orbital angular momentum beams have recently emerged as a new technique for communications with potential for increased channel capacity. Turbulence due to changes in the index of refraction emanating from temperature, humidity, and air flow patterns, however, add nonlinear effects to the received patterns, thus making the demultiplexing task more difficult. Deep learning techniques have been previously been applied to solve the demultiplexing problem as an image classification task. Here we make use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation to describe a method that utilizes a "shallow" learning method instead. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain similar classification accuracies (bit error ratio) at a small fraction (1/90) of the computational cost, thus enabling higher bit rates.

Analysis of live cell images: Methods, tools and opportunities.

Advances in optical microscopy, biosensors and cell culturing technologies have transformed live cell imaging. Thanks to these advances live cell imaging plays an increasingly important role in basic biology research as well as at all stages of drug development. Image analysis methods are needed to extract quantitative information from these vast and complex data sets. The aim of this review is to provide an overview of available image analysis methods for live cell imaging, in particular required preprocessing image segmentation, cell tracking and data visualisation methods. The potential opportunities recent advances in machine learning, especially deep learning, and computer vision provide are being discussed. This review includes overview of the different available software packages and toolkits.

Detecting and visualizing cell phenotype differences from microscopy images using transport-based morphometry.

Modern microscopic imaging devices are able to extract more information regarding the subcellular organization of different molecules and proteins than can be obtained by visual inspection. Predetermined numerical features (descriptors) often used to quantify cells extracted from these images have long been shown useful for discriminating cell populations (e.g., normal vs. diseased). Direct visual or biological interpretation of results obtained, however, is often not a trivial task. We describe an approach for detecting and visualizing phenotypic differences between classes of cells based on the theory of optimal mass transport. The method is completely automated, does not require the use of predefined numerical features, and at the same time allows for easily interpretable visualizations of the most significant differences. Using this method, we demonstrate that the distribution pattern of peripheral chromatin in the nuclei of cells extracted from liver and thyroid specimens is associated with malignancy. We also show the method can correctly recover biologically interpretable and statistically significant differences in translocation imaging assays in a completely automated fashion.

Optimal Mass Transport: Signal processing and machine-learning applications.

Transport-based techniques for signal and data analysis have received increased attention recently. Given their ability to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications including content-based retrieval, cancer detection, image super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art results in several applications. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here we provide a practical overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications. Software accompanying this tutorial is available at [43].

Valproic Acid Limits Pancreatic Recovery after Pancreatitis by Inhibiting Histone Deacetylases and Preventing Acinar Redifferentiation Programs.

The mechanisms by which drugs induce pancreatitis are unknown. A definite cause of pancreatitis is due to the antiepileptic drug valproic acid (VPA). On the basis of three crucial observations-that VPA inhibits histone deacetylases (HDACs), HDACs mediate pancreas development, and aspects of pancreas development are recapitulated during recovery of the pancreas after injury-we hypothesized that VPA does not cause injury on its own, but it predisposes patients to pancreatitis by inhibiting HDACs and provoking an imbalance in pancreatic recovery. In an experimental model of pancreatic injury, we found that VPA delayed recovery of the pancreas and reduced acinar cell proliferation. In addition, pancreatic expression of class I HDACs (which are the primary VPA targets) increased in the midphase of pancreatic recovery. VPA administration inhibited pancreatic HDAC activity and led to the persistence of acinar-to-ductal metaplastic complexes, with prolonged Sox9 expression and sustained ß-catenin nuclear activation, findings that characterize a delay in regenerative reprogramming. These effects were not observed with valpromide, an analog of VPA that lacks HDAC inhibition. This is the first report, to our knowledge, that VPA shifts the balance toward pancreatic injury and pancreatitis through HDAC inhibition. The work also identifies a new paradigm for therapies that could exploit epigenetic reprogramming to enhance pancreatic recovery and disorders of pancreatic injury.

A supervised learning framework for pancreatic islet segmentation with multi-scale color-texture features and rolling guidance filters.

Islet cell quantification and function is important for developing novel therapeutic interventions for diabetes. Existing methods of pancreatic islet segmentation in histopathological images depend strongly on cell/nuclei detection, and thus are limited due to a wide variance in the appearance of pancreatic islets. In this paper, we propose a supervised learning pipeline to segment pancreatic islets in histopathological images, which does not require cell detection. The proposed framework firstly partitions images into superpixels, and then extracts multi-scale color-texture features from each superpixel and processes these features using rolling guidance filters, in order to simultaneously reduce inter-class ambiguity and intra-class variation. Finally, a linear support vector machine (SVM) is trained and applied to segment the testing images. A total of 23 hematoxylin-and-eosin-stained histopathological images with pancreatic islets are used for verifying the framework. With an average accuracy of 95%, training time of 20 min and testing time of 1 min per image, the proposed framework outperforms existing approaches with better segmentation performance and lower computational cost. © 2016 International Society for Advancement of Cytometry.

Automated Learning of Subcellular Variation among Punctate Protein Patterns and a Generative Model of Their Relation to Microtubules.

Characterizing the spatial distribution of proteins directly from microscopy images is a difficult problem with numerous applications in cell biology (e.g. identifying motor-related proteins) and clinical research (e.g. identification of cancer biomarkers). Here we describe the design of a system that provides automated analysis of punctate protein patterns in microscope images, including quantification of their relationships to microtubules. We constructed the system using confocal immunofluorescence microscopy images from the Human Protein Atlas project for 11 punctate proteins in three cultured cell lines. These proteins have previously been characterized as being primarily located in punctate structures, but their images had all been annotated by visual examination as being simply "vesicular". We were able to show that these patterns could be distinguished from each other with high accuracy, and we were able to assign to one of these subclasses hundreds of proteins whose subcellular localization had not previously been well defined. In addition to providing these novel annotations, we built a generative approach to modeling of punctate distributions that captures the essential characteristics of the distinct patterns. Such models are expected to be valuable for representing and summarizing each pattern and for constructing systems biology simulations of cell behaviors.

A continuous linear optimal transport approach for pattern analysis in image datasets.

We present a new approach to facilitate the application of the optimal transport metric to pattern recognition on image databases. The method is based on a linearized version of the optimal transport metric, which provides a linear embedding for the images. Hence, it enables shape and appearance modeling using linear geometric analysis techniques in the embedded space. In contrast to previous work, we use Monge's formulation of the optimal transport problem, which allows for reasonably fast computation of the linearized optimal transport embedding for large images. We demonstrate the application of the method to recover and visualize meaningful variations in a supervised-learning setting on several image datasets, including chromatin distribution in the nuclei of cells, galaxy morphologies, facial expressions, and bird species identification. We show that the new approach allows for high-resolution construction of modes of variations and discrimination and can enhance classification accuracy in a variety of image discrimination problems.