Manual segmentation of the Left Ventricle (LV) is a tedious and meticulous task that can vary depending on the patient, the Magnetic Resonance Images (MRI) cuts and the experts. Still today, we consider manual delineation done by experts as being the ground truth for cardiac diagnosticians. Thus, we are reviewing the p…
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48 results for “left ventricle”
The morphological structure of left ventricle segmented from cardiac magnetic resonance images can be used to calculate key clinical parameters, and it is of great significance to the accurate and efficient diagnosis of cardiovascular diseases. Compared with traditional methods, the segmentation algorithms based on ful…
Non-invasive detection of cardiovascular disorders from radiology scans requires quantitative image analysis of the heart and its substructures. There are well-established measurements that radiologists use for diseases assessment such as ejection fraction, volume of four chambers, and myocardium mass. These measuremen…
LU-Net improves cardiac segmentation accuracy and robustness.
problem Robustness and accuracy of deep learning cardiac segmentation.
method Multi-task end-to-end network designed to improve cardiac segmentation.
result Outperforms current best deep learning solution, reducing outliers and improving clinical indices.
In the United States, heart disease is the leading cause of death for both men and women, accounting for 610,000 deaths each year [1]. Physicians use Magnetic Resonance Imaging (MRI) scans to take images of the heart in order to non-invasively estimate its structural and functional parameters for cardiovascular diagnos…
Deep learning models trained on adult cardiac MRI data struggle to accurately segment rare congenital heart diseases.
problem Accuracy of U-Net-based segmentation models trained on adult cardiac MRI data when applied to rare congenital heart diseases like Tetralogy of Fallot.
method Cross-validation with four-fold, evaluation on unseen data from different pathologies.
result Deep learning models overfit to the training data, leading to significant accuracy drops when applied to other pathologies.
Echocardiography (echo) is a common means of evaluating cardiac conditions. Due to the label scarcity, semi-supervised paradigms in automated echo analysis are getting traction. One of the most sought-after problems in echo is the segmentation of cardiac structures (e.g. chambers). Accordingly, we propose an echocardio…
Transthoracic echo is one of the most common means of cardiac studies in the clinical routines. During the echo exam, the sonographer captures a set of standard cross sections (echo views) of the heart. Each 2D echo view cuts through the 3D cardiac geometry via a unique plane. Consequently, different views share some l…
Cardiac motion modeling using LDDMM and shape splines.
problem Difficulties in probing cardiac function due to shape and deformation interactions.
method LDDMM framework, parallel transport, normalization, shape splines.
result Significant differences in model parameters between pathologies, revealing insights into disease dynamics.
In cardiac magnetic resonance imaging, fully-automatic segmentation of the heart enables precise structural and functional measurements to be taken, e.g. from short-axis MR images of the left-ventricle. In this work we propose a recurrent fully-convolutional network (RFCN) that learns image representations from the ful…
The segmentation of the left ventricle (LV) from CINE MRI images is essential to infer important clinical parameters. Typically, machine learning algorithms for automated LV segmentation use annotated contours from only two cardiac phases, diastole, and systole. In this work, we present an analysis work-flow for fully-…
Large prospective epidemiological studies acquire cardiovascular magnetic resonance (CMR) images for pre-symptomatic populations and follow these over time. To support this approach, fully automatic large-scale 3D analysis is essential. In this work, we propose a novel deep neural network using both CMR images and pati…
Volumetric analysis of brain ventricle (BV) structure is a key tool in the study of central nervous system development in embryonic mice. High-frequency ultrasound (HFU) is the only non-invasive, real-time modality available for rapid volumetric imaging of embryos in utero. However, manual segmentation of the BV from H…
The exploitation of large-scale population data has the potential to improve healthcare by discovering and understanding patterns and trends within this data. To enable high throughput analysis of cardiac imaging data automatically, a pipeline should comprise quality monitoring of the input images, segmentation of the …
Researchers use operator learning to predict cardiac activation and repolarization times.
problem Computational demands and need for clear, interpretable information in cardiac electrophysiology.
method Exploiting Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL) to learn operator mappings.
result Both FNO and KOL approaches are computationally efficient and robust to hyperparameters.
Background: Cardiac MRI derived biventricular mass and function parameters, such as end-systolic volume (ESV), end-diastolic volume (EDV), ejection fraction (EF), stroke volume (SV), and ventricular mass (VM) are clinically well established. Image segmentation can be challenging and time-consuming, due to the complex a…
Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
Framework for joint learning of tasks on dementia data with missing values.
problem Lack of multi-task learning, handling time-dependent data, and missing values in dementia forecasting.
method Proposes SSHIBA model using Bayesian variational inference for imputation and combined information from different views.
result SSHIBA model outperforms baselines in predicting diagnosis, ventricle volume, and clinical scores in dementia.
Linear ODEs are solved by geodesics in hyperbolic geometry.
problem Solving real linear second order ODEs.
method Defined a Riemannian hyperbolic geometry and showed that solutions to ODEs correspond to geodesics in this geometry.
result Local solutions to ODEs correspond to geodesics in a specific hyperbolic geometry.
Early diagnosis, playing an important role in preventing progress and treating the Alzheimer\{'}s disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocamp…
The paper revisits the -Yamabe problem and proves the existence of a conformal metric with constant -scalar curvature.
problem Finding a conformal metric with constant -scalar curvature on closed manifolds.
method Analyzing the -Yamabe constant and proving its achievability under certain conditions.
result The -Yamabe constant is achieved by a conformal metric, solving the -Yamabe problem on manifolds with positive Yamabe constant.
Left-symmetric algebroidsmath.DG
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from $\mathcal …
Early diagnosis, playing an important role in preventing progress and treating the Alzheimer's disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocampus …
In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a Manin triple for left-symmetric algebroids, which is equivalent to a left-symmet…
Use expert visualization or conventional clinical indices can lack accuracy for borderline classications. Advanced statistical approaches based on eigen-decomposition have been mostly concerned with shape and motion indices. In this paper, we present a new approach to identify CVDs from cine-MRI by estimating large poo…
The paper proves foliations of solutions to the minimal surface equation in exterior domains.
problem Existence and properties of foliations by solutions to the exterior Dirichlet problem for minimal surfaces.
method Analyzes a 1-parameter family of solutions to the minimal surface equation in exterior domains with specific boundary conditions.
result Foliation of the open subset in R^(n+1) by graphs of solutions, with bounds and asymptotic behavior.
The paper examines differentiability of horizons along their generators in Lorentz manifolds.
problem Analyzing the differentiability of horizons along their generators in Lorentz manifolds.
method Using a result that every mathematical horizon locally coincides with a Cauchy horizon, the paper proves conditions for differentiability of horizons.
result Horizons are either continuously differentiable or have differentiability jumping points.
A new matrix concentration inequality for random products of matrices.
problem Understanding the behavior of random matrix products under bounded independent positive semidefinite matrices.
method Developed a non-asymptotic concentration inequality for the product of matrices.
result The inequality provides a bound on the deviation of the matrix product from its expected value.
The paper proves conditions under which solutions to certain PDEs in Lie groups are constant.
problem Conditions for constant solutions to geometric PDEs in Lie groups.
method Analyzes left-invariant PDEs in Lie groups with specific decay conditions on gradients.
result If a solution to a geometric PDE in a Lie group satisfies a gradient decay condition, the solution is constant.
The study shows involutory quandles of certain links are not left-orderable.
problem Determining left-orderability of involutory quandles of links.
method Using a non-left-orderability criterion for involutory quandles of non-split links, the study improved previous results and introduced new families of links.
result The involutory quandles of non-trivial alternating links and certain augmented alternating links are not left-orderable.
Study proves all left-invariant contact structures on 3D Lie groups are tight.
problem Characterizing tightness of left-invariant contact structures on 3D Lie groups.
method Riemannian methods and unique factorization property for Lie groups.
result All left-invariant contact structures on 3D Lie groups are tight.
This paper studies moduli spaces of statistical structures on Lie groups.
problem Understanding statistical structures on Lie groups.
method Introduced and studied moduli spaces for left-invariant statistical structures on Lie groups.
result Moduli spaces of left-invariant Riemannian metrics are singletons for certain Lie groups.
Study on harmonic spinors on specific Lie groups.
problem Existence of left-invariant harmonic spinors on 3D Lie groups.
method Revised spin Dirac operator formula for left-invariant spinors, identified constraints on Lie algebras, and classified metrics with harmonic spinors.
result Identified conditions and metrics for left-invariant harmonic spinors on 3D Lie groups.
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore, thus there is a need for its fully automatic segmentation from clinical images. In …
A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this topological space is compact. Interesting examples of nonassociative magmas, whose spa…
Study on integrability of geodesic flows on Heisenberg group.
problem Integrability of geodesic flows on Heisenberg group.
method Investigation of two classes of normal geodesic flows associated with left-invariant sub-Riemannian metric.
result Left-left configuration is completely integrable in non-commutative sense, while left-right configuration exhibits non-commutative integrability in dimensions > 5.
The study characterizes spacetime and modified gravity models using projective curvature tensor.
problem Characterizing spacetime and modified gravity models with projective curvature tensor.
method Analyzing $f\left(R,G
ight)$, $f\left(R,T
ight)$, and $f\left(R,L_{m}
ight)$-gravity models.
result Projectively flat perfect fluid spacetimes represent dark energy era and are locally isometric to Minkowski or de-Sitter spacetimes.
The Jones polynomial for an oriented link is a one-variable Laurent polynomial link invariant discovered by Jones. For any integer , we show that: (1) the difference of Jones polynomials for two oriented links which are -equivalent is divisible by $\left(t-1\right)^{n}\left(t^{2}+t+1\right…
3D shape instantiation which reconstructs the 3D shape of a target from limited 2D images or projections is an emerging technique for surgical intervention. It improves the currently less-informative and insufficient 2D navigation schemes for robot-assisted Minimally Invasive Surgery (MIS) to 3D navigation. Previously,…
We call a connected Lie group endowed with a left-invariant Lorentzian flat metric Lorentzian flat Lie group. In this Note, we determine all Lorentzian flat Lie groups admitting a timelike left-invariant Killing vector field. We show that these Lie groups are 2-solvable and unimodular and hence geodesically complete. M…
In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics, and is based on the moduli space of left-invariant pseudo-Riemannian metrics. A…
K-theory of affine actionsmath.DG
For a Lie group and a vector bundle we study those actions of the Lie group on for which the action map is a morphism of vector bundles, and call those \emph{affine actions}. We prove that the category of such actions over a fixed …
Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be cla…
Left-invariant metrics force 2-step nilpotent groups, preserving Kähler-like conditions.
problem Existence of left-invariant pluriclosed Hermitian metrics on Lie groups.
method Analyzing left-invariant metrics on unimodular Lie groups with abelian complex structures.
result Pluriclosed flow preserves Strominger Kähler-like conditions on 2-step nilpotent Lie groups.
The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the os…
In this paper we determine the at least -dimensional affine reductive homogeneous manifolds for an at most -dimensional simple Lie group or an at most -dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable …
Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.
problem Determining the index of symmetry for solvable 3D Lie groups with left-invariant metrics.
method Examined all solvable three-dimensional Lie groups, combined with previous work on unimodular groups.
result Index of symmetry is positive for every solvable 3D Lie algebra with a left-invariant metric, and is never 2.