Optimal transport features for morphometric population analysis.

Brain pathologies often manifest as partial or complete loss of tissue. The goal of many neuroimaging studies is to capture the location and amount of tissue changes with respect to a clinical variable of interest, such as disease progression. Morphometric analysis approaches capture local differences in the distribution of tissue or other quantities of interest in relation to a clinical variable. We propose to augment morphometric analysis with an additional feature extraction step based on unbalanced optimal transport. The optimal transport feature extraction step increases statistical power for pathologies that cause spatially dispersed tissue loss, minimizes sensitivity to shifts due to spatial misalignment or differences in brain topology, and separates changes due to volume differences from changes due to tissue location. We demonstrate the proposed optimal transport feature extraction step in the context of a volumetric morphometric analysis of the OASIS-1 study for Alzheimer's disease. The results demonstrate that the proposed approach can identify tissue changes and differences that are not otherwise measurable.

NousNav: A low-cost neuronavigation system for deployment in lower-resource settings.

PURPOSE: NousNav is a complete low-cost neuronavigation system that aims to democratize access to higher-quality healthcare in lower-resource settings. NousNav's goal is to provide a model for local actors to be able to reproduce, build and operate a fully functional neuronavigation system at an affordable cost. METHODS: NousNav is entirely open source and relies on low-cost off-the-shelf components, which makes it easy to reproduce and deploy in any region. NousNav's software is also specifically devised with the low-resource setting in mind. RESULTS: It offers means for intuitive intraoperative control. The designed interface is also clean and simple. This allows for easy intraoperative use by either the practicing clinician or a nurse. It thus alleviates the need for a dedicated technician for operation. CONCLUSION: A prototype implementation of the design was built. Hardware and algorithms were designed for robustness, ruggedness, modularity, to be standalone and data-agnostic. The built prototype demonstrates feasibility of the objectives.

Image-Based Methods for Phase Estimation, Gating, and Temporal Superresolution of Cardiac Ultrasound.

OBJECTIVE: Ultrasound is an effective tool for rapid noninvasive assessment of cardiac structure and function. Determining the cardiorespiratory phases of each frame in the ultrasound video and capturing the cardiac function at a much higher temporal resolution are essential in many applications. Fulfilling these requirements is particularly challenging in preclinical studies involving small animals with high cardiorespiratory rates, requiring cumbersome and expensive specialized hardware. METHODS: We present a novel method for the retrospective estimation of cardiorespiratory phases directly from the ultrasound videos. It transforms the videos into a univariate time series preserving the evidence of periodic cardiorespiratory motion, decouples the signatures of cardiorespiratory motion with a trend extraction technique, and estimates the cardiorespiratory phases using a Hilbert transform approach. We also present a robust nonparametric regression technique for respiratory gating and a novel kernel-regression model for reconstructing images at any cardiac phase facilitating temporal superresolution. RESULTS: We validated our methods using two-dimensional echocardiography videos and electrocardiogram (ECG) recordings of six mice. Our cardiac phase estimation method provides accurate phase estimates with a mean-phase-error range of 3%-6% against ECG derived phase and outperforms three previously published methods in locating ECGs R-wave peak frames with a mean-frame-error range of 0.73-1.36. Our kernel-regression model accurately reconstructs images at any cardiac phase with a mean-normalized-correlation range of 0.81-0.85 over 50 leave-one-out-cross-validation rounds. CONCLUSION AND SIGNIFICANCE: Our methods can enable tracking of cardiorespiratory phases without additional hardware and reconstruction of respiration-free single cardiac-cycle videos at a much higher temporal resolution.

Exploratory Population Analysis with Unbalanced Optimal Transport.

The plethora of data from neuroimaging studies provide a rich opportunity to discover effects and generate hypotheses through exploratory data analysis. Brain pathologies often manifest in changes in shape along with deterioration and alteration of brain matter, i.e., changes in mass. We propose a morphometry approach using unbalanced optimal transport that detects and localizes changes in mass and separates them from changes due to the location of mass. The approach generates images of mass allocation and mass transport cost for each subject in the population. Voxelwise correlations with clinical variables highlight regions of mass allocation or mass transfer related to the variables. We demonstrate the method on the white and gray matter segmentations from the OASIS brain MRI data set. The separation of white and gray matter ensures that optimal transport does not transfer mass between different tissues types and separates gray and white matter related changes. The OASIS data set includes subjects ranging from healthy to mild and moderate dementia, and the results corroborate known pathology changes related to dementia that are not discovered with traditional voxel-based morphometry. The transport-based morphometry increases the explanatory power of regression on clinical variables compared to traditional voxel-based morphometry, indicating that transport cost and mass allocation images capture a larger portion of pathology induced changes.

Automatic Estimation of the Optic Nerve Sheath Diameter from Ultrasound Images.

We present an algorithm to automatically estimate the diameter of the optic nerve sheath from ocular ultrasound images. The optic nerve sheath diameter provides a proxy for measuring intracranial pressure, a life threating condition frequently associated with head trauma. Early treatment of elevated intracranial pressures greatly improves outcomes and drastically reduces the mortality rate. We demonstrate that the proposed algorithm combined with a portable ultrasound device presents a viable path for early detection of elevated intracranial pressure in remote locations and without access to trained medical imaging experts.

Morse-Smale Regression.

This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduce a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by a discrete approximation of the Morse-Smale complex. This yields a segmentation with partitions corresponding to regions of the function with a single minimum and maximum that are often well approximated by a linear model. This approach yields regression models that are amenable to interpretation and have good predictive capacity. Typically, regression estimates are quantified by their geometrical accuracy. For the proposed regression, an important aspect is the quality of the segmentation itself. Thus, this paper introduces a new criterion that measures the topological accuracy of the estimate. The topological accuracy provides a complementary measure to the classical geometrical error measures and is very sensitive to over-fitting. The Morse-Smale regression is compared to state-of-the-art approaches in terms of geometry and topology and yields comparable or improved fits in many cases. Finally, a detailed study on climate-simulation data demonstrates the application of the Morse-Smale regression. Supplementary materials are available online and contain an implementation of the proposed approach in the R package msr, an analysis and simulations on the stability of the Morse-Smale complex approximation and additional tables for the climate-simulation study.

Visualization of uncertainty without a mean.

As dataset size and complexity steadily increase, uncertainty is becoming an important data aspect. So, today's visualizations need to incorporate indications of uncertainty. However, characterizing uncertainty for visualization isn't always straightforward. Entropy, in the information-theoretic sense, can be a measure for uncertainty in categorical datasets. The authors discuss the mathematical formulation, interpretation, and use of entropy in visualizations. This research aims to demonstrate entropy as a metric and expand the vocabulary of uncertainty measures for visualization.

Fast shape-based nearest-neighbor search for brain MRIs using hierarchical feature matching.

This paper presents a fast method for quantifying shape differences/similarities between pairs of magnetic resonance (MR) brain images. Most shape comparisons in the literature require some kind of deformable registration or identification of exact correspondences. The proposed approach relies on an optimal matching of a large collection of features, using a very fast, hierarchical method from the literature, called spatial pyramid matching (SPM). This paper shows that edge-based image features in combination with SPM results in a fast similarity measure that captures relevant anatomical information in brain MRI. We present extensive comparisons against known methods for shape-based, k-nearest-neighbor lookup to evaluate the performance of the proposed method. Finally, we show that the method compares favorably with more computation-intensive methods in the construction of local atlases for use in brain MR image segmentation.

Visual exploration of high dimensional scalar functions.

An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a high-dimensional function. Such data sets arise, for instance, in large numerical simulations, as energy landscapes in optimization problems, or in the analysis of image data relating to biological or medical parameters. This paper proposes an approach to analyze and visualizing such data sets. The proposed method combines topological and geometric techniques to provide interactive visualizations of discretely sampled high-dimensional scalar fields. The method relies on a segmentation of the parameter space using an approximate Morse-Smale complex on the cloud of point samples. For each crystal of the Morse-Smale complex, a regression of the system parameters with respect to the output yields a curve in the parameter space. The result is a simplified geometric representation of the Morse-Smale complex in the high dimensional input domain. Finally, the geometric representation is embedded in 2D, using dimension reduction, to provide a visualization platform. The geometric properties of the regression curves enable the visualization of additional information about each crystal such as local and global shape, width, length, and sampling densities. The method is illustrated on several synthetic examples of two dimensional functions. Two use cases, using data sets from the UCI machine learning repository, demonstrate the utility of the proposed approach on real data. Finally, in collaboration with domain experts the proposed method is applied to two scientific challenges. The analysis of parameters of climate simulations and their relationship to predicted global energy flux and the concentrations of chemical species in a combustion simulation and their integration with temperature.

Manifold modeling for brain population analysis.

This paper describes a method for building efficient representations of large sets of brain images. Our hypothesis is that the space spanned by a set of brain images can be captured, to a close approximation, by a low-dimensional, nonlinear manifold. This paper presents a method to learn such a low-dimensional manifold from a given data set. The manifold model is generative-brain images can be constructed from a relatively small set of parameters, and new brain images can be projected onto the manifold. This allows to quantify the geometric accuracy of the manifold approximation in terms of projection distance. The manifold coordinates induce a Euclidean coordinate system on the population data that can be used to perform statistical analysis of the population. We evaluate the proposed method on the OASIS and ADNI brain databases of head MR images in two ways. First, the geometric fit of the method is qualitatively and quantitatively evaluated. Second, the ability of the brain manifold model to explain clinical measures is analyzed by linear regression in the manifold coordinate space. The regression models show that the manifold model is a statistically significant descriptor of clinical parameters.

A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI.

This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.

On the manifold structure of the space of brain images.

This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the set of images. The approach builds on recent advances in manifold learning that allow to uncover nonlinear trends in data. We combine this manifold learning with distance measures between images that capture shape, in order to learn the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed manifold model to the data and we can compute statistical properties of the data using this manifold structure. We demonstrate this technology on a database of 436 MR brain images.