Deep Learning Analysis of Polar Maps from SPECT Myocardial Perfusion Imaging for Prediction of Coronary Artery Disease

Purpose: This study aimed to investigate the diagnostic accuracy of deep convolutional neural networks for classifying the polar map images in Single-photon emission computed tomography (SPECT) myocardial perfusion imaging (MPI) by considering the physician’s diagnosis as reference.Methods: 3318 images of stress and rest polar maps related to patients (67% women and 33% men) who underwent 99mTc-sestamibi MPI were collected. The images were manually labeled with normal and abnormal labels according to the doctor’s diagnosis reports. The proposed deep learning model was trained using stress and rest polar maps and evaluated for prediction of obstructive disease in a stratified 5-fold cross-validation procedure.Results: The mean values of accuracy, sensitivity, accuracy, specificity, f1 score, and the area under the roc curve were 0.7562, 0.7856, 0.5748, 0.7434, 0.6646, and, 0.8450, respectively over 5 folds using both stress and rest scans. The inclusion of rest perfusion maps significantly improved AUC of the deep learning model (AUC: 0.845; 95% CI: 0.832-0.857), compared with using stress polar maps only (AUC: 0.827; 95% CI: 0.814-0.840); P < 0.05.Conclusion: The results of the present work reveal the possible applications of deep learning for polar map images classification in SPECT MPI.

Plane polar Cremona maps of arbitrarily large degree in positive characteristic

A result of I.V. Dolgachev states that the complex homaloidal polynomials in three variables, i.e. the complex homogeneous polynomials whose polar map is birational, are of degree at most three. In this note we describe homaloidal polynomials in three variables of arbitrarily large degree in positive characteristic. Using combinatorial arguments, we also classify line arrangements whose polar map is homaloidal in positive characteristic.

DeepStrain: A Deep Learning Workflow for the Automated Characterization of Cardiac Mechanics

Myocardial strain analysis from cinematic magnetic resonance imaging (cine-MRI) data could provide a more thorough characterization of cardiac mechanics than volumetric parameters such as left-ventricular ejection fraction, but sources of variation including segmentation and motion estimation have limited its wide clinical use. We designed and validated a deep learning (DL) workflow to generate both volumetric parameters and strain measures from cine-MRI data, including strain rate (SR) and regional strain polar maps, consisting of segmentation and motion estimation convolutional neural networks developed and trained using healthy and cardiovascular disease (CVD) subjects (n=150). DL-based volumetric parameters were correlated (>0.98) and without significant bias relative to parameters derived from manual segmentations in 50 healthy and CVD subjects. Compared to landmarks manually-tracked on tagging-MRI images from 15 healthy subjects, landmark deformation using DL-based motion estimates from paired cine-MRI data resulted in an endpoint-error of 2.9 (1.5) mm. Measures of end-systolic global strain from these cine-MRI data showed no significant biases relative to a tagging-MRI reference method. On 4 healthy subjects, intraclass correlation coefficient for intrascanner repeatability was excellent (>0.95) for strain, moderate to excellent for SR (0.690-0.963), and good to excellent (0.826-0.994) in most polar map segments. Absolute relative change was within ~5% for strain, within ~10% for SR, and <1% in half of polar map segments. In conclusion, we developed and evaluated a DL-based, end-to-end fully-automatic workflow for global and regional myocardial strain analysis to quantitatively characterize cardiac mechanics of healthy and CVD subjects based on ubiquitously acquired cine-MRI data.

Математическое моделирование нарушений перфузии миокарда, диагностируемых методом однофотонной эмиссионной компьютерной томографии

In this paper the results of studies aimed at the developing of mathematical model of the left ventricle myocardium of the heart in the polar map "bulleye" are presented. Comparison of images obtained as a result of numerical simulation with similar cases in clinical practice made it possible to assess the errors and inaccuracies of reconstruction in the method of SPECT.

Degenerations of the generic square matrix, the polar map and the determinantal structure

One studies certain degenerations of the generic square matrix over a field [Formula: see text] along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. The main tool comes from commutative algebra, with emphasis on ideal theory and syzygy theory. The structure of the polar map is completely identified and the main properties of the ideal of submaximal minors are determined. Cases where the degenerated determinant has non-vanishing Hessian determinant show that the former is a factor of the latter with the (Segre) expected multiplicity, a problem envisaged by Landsberg–Manivel–Ressayre by geometric means. Another byproduct is an affirmative answer to a question of F. Russo concerning the codimension in the polar image of the dual variety to a hypersurface.