Motion Vector Field Research Articles

Stability analysis of patient-specific 4DCT- and 4DCBCT-based correspondence models.

Surrogate-based motion compensation in stereotactic body radiation therapy (SBRT) strongly relies on a constant relationship between an external breathing signal and the internal tumor motion over the course of treatment, that is, a stable patient-specific correspondencemodel. This study aims to develop methods for analyzing the stability of correspondence models by integrating planning 4DCT and pretreatment 4D cone-beam computed tomography (4DCBCT) data and assessing the relation to patient-specific clinicalparameters. For correspondence modeling, a regression-based approach is applied, correlating patient-specific internal motion (vector fields computed by deformable image registration) and external breathing signals (recorded by Varian's RPM and RGSC system). To analyze correspondence model stability, two complementary methods are proposed. (1) Target volume-based analysis: 4DCBCT-based correspondence models predict clinical target volumes (GTV and internal target volume [ITV]) within the planning 4DCT, which are evaluated by overlap and distance measures (Dice similarity coefficient [DSC]/average symmetric surface distance [ASSD]). (2) System matrix-based analysis: 4DCBCT-based regression models are compared to 4DCT-based models using mean squared difference (MSD) and principal component analysis of the system matrices. Stability analysis results are correlated with clinical parameters. Both methods are applied to a dataset of 214 pretreatment 4DCBCT scans (Varian TrueBeam) from a cohort of 46 lung tumor patients treated with ITV-based SBRT (planning 4DCTs acquired with Siemens AS Open and SOMATOM go.OPEN Pro CT scanners). Consistent results across the two complementary analysis approaches (Spearman correlation coefficient of between system matrix-based MSD and GTV-based DSC/ASSD) were observed. Analysis showed that stability was not predominant, with 114/214 fraction-wise models not surpassing a threshold of for the GTV, and only 14/46 patients demonstrating a in all fractions. Model stability did not degrade over the course of treatment. The mean GTV-based DSC is (mean ASSD of ) and the respective ITV-based DSC is (mean ASSD of ). The clinical parameters showed a strong correlation between smaller tumor motion ranges and increasedstability. The proposed methods identify patients with unstable correspondence models prior to each treatment fraction, serving as direct indicators for the necessity of replanning and adaptive treatment approaches to account for internal-external motion variations throughout the course oftreatment.

Anomaly detection in structural dynamic systems via nonlinearity occurrence analysis using video data

Dynamic loads in disaster events, such as earthquakes, often cause structural damages that severely affect serviceability and even reduce the safety of civil structures or render them unsafe. Most of these damage scenarios can cause the transition from a linear to nonlinear behavior in structural dynamics. Therefore, extracting such nonlinear behaviors is an effective strategy for structural anomaly detection. In recent years, the rapid development of media devices has led to the widespread use of video data, primarily because of the ease of acquisition and lack of contact measurement. This study developed a novel method for detecting anomalies due to structural nonlinearity from video data that could capture target dynamic behaviors via non-contact measurement. The method is based on optical flow, extended repulsive force networks, and morphological operations for extracting singularities due to nonlinear events in the estimated motion vector field in video data. Subsequently, shaking table tests on a three-story shear building model containing a novel controllable hinge bearing verified the effectiveness of the developed method. The results of the feature enhancement process demonstrate the accurate localization of anomalous regions and effective mitigation of unwanted interference using the proposed method. The proposed method facilitates the use of video-based technology to evaluate rapid damage conditions post-earthquake.

Research on teaching basketball free throw action process based on motion vector field transformation

Research on teaching basketball free throw action process based on motion vector field transformation

Teaching the process of free throw action in basketball course based on motion vector field transformation

Abstract In order to improve the teaching quality of the free throw action process in basketball courses, this paper proposes research on the teaching of free throw action by integrating motion vector field transformation. Starting from the actual situation of the player’s free throw action, it describes the problems in the teaching process of free throw action. It elaborates on the structure and principle of the motion vector field transformation algorithm in depth. In video analysis teaching of free-throw shooting action processes, the player’s motion vectors can easily be interfered with by random noise, which needs to be optimized using smoothing processing and compensation models. Combined with the teaching objectives of free throw action, the design and development of the “basketball free throw action” microteaching by integrating the motion vector field transformation through the analysis of a university sports college basketball class of 2021 students found that from the seventh week and the eighth week of the experimental group and the control group, respectively, there is a difference of 7.8% and 13%. The ball-hitting rate is significantly different from that of the control group (<0.5). A significant difference occurred (<0.05). Although both methods have improved the free throw shooting rate of the athletes, the teaching of free throw shooting action in the basketball course integrating the motion vector field transformation performs better compared to the traditional free throw shooting action teaching mode. This study provides technical support and diversified media presentation methods for the design and development of basketball micro-courses. It constructs a feasible way to develop and innovate college basketball teaching.

Self-Attention Convolutional Long Short-Term Memory for Short-Term Arctic Sea Ice Motion Prediction Using Advanced Microwave Scanning Radiometer Earth Observing System 36.5 GHz Data

Over the past four decades, Arctic sea ice coverage has steadily declined. This loss of sea ice has amplified solar radiation and heat absorption from the ocean, exacerbating both polar ice loss and global warming. It has also accelerated changes in sea ice movement, posing safety risks for ship navigation. In recent years, numerical prediction models have dominated the field of sea ice movement prediction. However, these models often rely on extensive data sources, which can be limited in specific time periods or regions, reducing their applicability. This study introduces a novel approach for predicting Arctic sea ice motion within a 10-day window. We employ a Self-Attention ConvLSTM deep learning network based on single-source data, specifically optical flow derived from the Advanced Microwave Scanning Radiometer Earth Observing System 36.5 GHz data, covering the entire Arctic region. Upon verification, our method shows a reduction of 0.80 to 1.18 km in average mean absolute error over a 10-day period when compared to ConvLSTM, demonstrating its improved ability to capture the spatiotemporal correlation of sea ice motion vector fields and provide accurate predictions.

3D wind field profiles from hyperspectral sounders: revisiting optic-flow from a meteorological perspective

In this work, we present an efficient optic flow algorithm for the extraction of vertically resolved 3D atmospheric motion vector (AMV) fields from incomplete hyperspectral image data measures by infrared sounders. The model at the heart of the energy to be minimized is consistent with atmospheric dynamics, incorporating ingredients of thermodynamics, hydrostatic equilibrium and statistical turbulence. Modern optimization techniques are deployed to design a low-complexity solver for the energy minimization problem, which is non-convex, non-differentiable, high-dimensional and subject to physical constraints. In particular, taking advantage of the alternate direction of multipliers methods (ADMM), we show how to split the original high-dimensional problem into a recursion involving a set of standard and tractable optic-flow sub-problems. By comparing with the ground truth provided by the operational numerical simulation of the European Centre for Medium-Range Weather Forecasts (ECMWF), we show that the performance of the proposed method is superior to state-of-the-art optical flow algorithms in the context of real infrared atmospheric sounding interferometer (IASI) observations.

CT‐value conservation based spatial transformer network for cardiac motion correction

AbstractArtifact correction is a great challenge in cardiac imaging. During the correction of coronary tissue with motion‐induced artifacts, the spatial distribution of CT value not only shifts according to the motion vector field (MVF), but also shifts according to the volume change rate of the local voxels. However, the traditional interpolation method does not conserve the CT value during motion compensation. A new sample interpolation algorithm is developed based on the constraint of conservation of CT value before and after image deformation. This algorithm is modified on the existing interpolation algorithms and can be embedded into neural networks with deterministic back propagation. Comparative experimental results illustrate that the method can not only correct motion‐induced artifacts, but also ensure the conservation of CT value in the region of interest (ROI) area, so as to obtain corrected images with clinically recognized CT value. Both effectiveness and efficiency are proved in forward motion correction process and backward training steps in deep learning. Simultaneously, using the network to learn the MVF making this method more interpretable than the existing image‐based end‐to‐end deep learning method.

An Evaluation of Beam Configuration to Detect the Plasma Vector Velocity: A Simulation Method Based on the SYISR System

AbstractMeasuring the plasma motion vector field accurately is beneficial to understanding the physical processes in the ionosphere. As a newly built advanced modular phase array Incoherent Scatter Radar in Sanya (SYISR), SYISR can measure the line‐of‐sight (LOS) velocity of ion drift in multiple directions, potentially yielding the spatial distribution of ionospheric plasma drift at low latitudes in East Asia. Compared to the traditional ISR, it can operate continuously for a long‐time and perform with fast and flexible scanning. This paper evaluates different beam configurations and inversion methods for vector ion velocity detection by comparing the vector ion velocities input in the forward modeling and derived by inversion. For the mono‐static SYISR, the all‐sky scan mode is suitable for observing the distribution of vector ion velocity with height, and the fine scan mode is suitable for observing the spatial distribution of two components of vector ion drift perpendicular to the magnetic field in the northern region of SYISR's non‐grating lobe. For the future tri‐static SYISR, it could simultaneously observe the spatial distribution of all three components of the vector ion velocity. Besides, the inversion method based on Bayesian estimation shows good accuracy and stability in deriving the vector ion velocity, especially when the LOS ion velocity has a large error. These results will benefit the design and optimization of the actual experiments for the vector ion velocity measurement and inversion using the SYISR system.

Respiratory motion management using a single rapid MRI scan for a 0.35 T MRI-Linac system.

MRI has a rapidly growing role in radiation therapy (RT) for treatment planning, real-time image guidance, and beam gating (e.g., MRI-Linac). Free-breathing 4D-MRI is desirable in respiratory motion management for therapy. Moreover, high-quality 3D-MRIs without motion artifacts are needed to delineate lesions. Existing MRI methods require multiple scans with lengthy acquisition times or are limited by low spatial resolution, contrast, and signal-to-noise ratio. We developed a novel method to obtain motion-resolved 4D-MRIs and motion-integrated 3D-MRI reconstruction using a single rapid (35-45 s scan on a 0.35 T MRI-Linac. Golden-angle radial stack-of-stars MRI scans were acquired from a respiratory motion phantom and 12 healthy volunteers (n=12) on a 0.35 T MRI-Linac. A self-navigated method was employed to detect respiratory motion using 2000 (acquisition time=5-7 min) and the first 200 spokes (acquisition time=35-45 s). Multi-coil non-uniform fast Fourier transform (MCNUFFT), compressed sensing (CS), and deep-learning Phase2Phase (P2P) methods were employed to reconstruct motion-resolved 4D-MRI using 2000 spokes (MCNUFFT2000) and 200 spokes (CS200 and P2P200). Deformable motion vector fields (MVFs) were computed from the 4D-MRIs and used to reconstruct motion-corrected 3D-MRIs with the MOtion Transformation Integrated forward-Fourier (MOTIF) method. Image quality was evaluated quantitatively using the structural similarity index measure (SSIM) and the root mean square error (RMSE), and qualitatively in a blinded radiological review. Evaluation using the respiratory motion phantom experiment showed that the proposed method reversed the effects of motion blurring and restored edge sharpness. In the human study, P2P200 had smaller inaccuracy in MVFs estimation than CS200. P2P200 had significantly greater SSIMs (p<0.0001) and smaller RMSEs (p<0.001) than CS200 in motion-resolved 4D-MRI and motion-corrected 3D-MRI. The radiological review found that MOTIF 3D-MRIs using MCNUFFT2000 exhibited the highest image quality (scoring>8 out of 10), followed by P2P200 (scoring>5 out of 10), and then motion-uncorrected (scoring<3 out of 10) in sharpness, contrast, and artifact-freeness. We have successfully demonstrated a method for respiratory motion management for MRI-guided RT. The method integrated self-navigated respiratory motion detection, deep-learning P2P 4D-MRI reconstruction, and a motion integrated reconstruction (MOTIF) for 3D-MRI using a single rapid MRI scan (35-45 s) on a 0.35 T MRI-Linac system.

Reconstruction of the Instantaneous Images Distorted by Surface Waves via Helmholtz–Hodge Decomposition

Imaging through water waves will cause complex geometric distortions and motion blur, which seriously affect the correct identification of an airborne scene. The current methods main rely on high-resolution video streams or a template image, which limits their applicability in real-time observation scenarios. In this paper, a novel recovery method for the instantaneous images distorted by surface waves is proposed. The method first actively projects an adaptive and adjustable structured light pattern onto the water surface for which random fluctuation will cause the image to degrade. Then, the displacement field of the feature points in the structured light image is used to estimate the motion vector field of the corresponding sampling points in the scene image. Finally, from the perspective of fluid mechanics, the distortion-free scene image is reconstructed based on the Helmholtz-Hodge Decomposition (HHD) theory. Experimental results show that our method not only effectively reduces the distortion to the image, but also significantly outperforms state-of-the-art methods in terms of computational efficiency. Moreover, we tested the real-scene sequences of a certain length to verify the stability of the algorithm.

Context-aware Pseudo-true Video Interpolation at 6G Edge

In the 6G network, lots of edge devices facilitate the low-latency transmission of video. However, with limited processing and storage capabilities, the edge devices cannot afford to reconstruct the vast amount of video data. On the condition of edge computing in the 6G network, this article fuses a self-similarity-based context feature into Frame Rate Up-Conversion (FRUC) to generate the pseudo-true video sequences at high frame rate, and its core is the extraction of the context layer for each video frame. First, we extract the patch centered at each pixel and use the self-similarity descriptor to generate the correlation surface. Then, the expectation or skewness of the correlation surface in statistics is computed to represent its context feature. By attaching an expectation or a skewness to each pixel, the context layer is constructed and added to the video frame as a new channel. According to the context layer, we predict the motion vector field of the absent frame by using the bidirectional context match and finally produce the interpolated frame. From the experimental results, it can be seen that by deploying the proposed FRUC algorithm on edge devices, the output pseudo-true video sequences have satisfying objective and subjective qualities.

Fast Deformable Image Registration for Real-Time Target Tracking During Radiation Therapy Using Cine MRI and Deep Learning

We developed a deep learning (DL) model for fast deformable image registration using 2-dimensional sagittal cine magnetic resonance imaging (MRI) acquired during radiation therapy and evaluated its potential for real-time target tracking compared with conventional image registration methods. Our DL model uses a pair of cine MRI images as input and provides a motion vector field (MVF) as output. The MVF is then applied to align the input images. A retrospective study was conducted to train and evaluate our model using cine MRI data from patients undergoing treatment for abdominal and thoracic tumors. For each treatment fraction, MR-linear accelerator delivery log files, tracking videos, and cine image files were analyzed. Individual MRI frames were temporally sampled to construct a large set of image registration pairs used to evaluate multiple methods. The DL model was optimized using 5-fold cross validation, and model outputs (transformed images and MVFs) using test set images were saved for comparison with 3 conventional registration methods (affine, b-spline, and demons). Evaluation metrics were 3-fold: (1) registration error, (2) MVF stability (both spatial and temporal), and (3) average computation time. We analyzed >21 hours of cine MRI (>629,000 frames) acquired during 86 treatment fractions from 21 patients. In a test set of 10,320 image registration pairs, DL registration outperformed conventional methods in both registration error (affine, b-spline, demons, DL; root mean square error: 0.067, 0.040, 0.036, 0.032; paired t test demons vs DL: t[20]=4.2, P < .001) and computation time per frame (51, 1150, 4583, 8 ms). Among deformable methods, spatial stability of resulting MVFs was comparable; however, the DL model had significantly improved temporal consistency. DL-based image registration can leverage large-scale MR cine data sets to outperform conventional registration methods and is a promising solution for real-time deformable motion estimation in radiation therapy.

Real-Time Internal Motion Monitoring during Radiation Therapy Using Cine MRI and Deep Learning

<h3>Purpose/Objective(s)</h3> Fast and accurate internal motion estimation is fundamental to enabling real-time MRI-guided radiation therapy (RT). We hypothesized that a deep learning (DL) model for fast deformable image registration using 2D sagittal cine MRI is feasible. Herein, we report performance of a DL-based image registration model as compared to conventional image registration methods. <h3>Materials/Methods</h3> Our DL model uses a pair of cine MRI images acquired using an MR-LINAC as inputs and outputs a motion vector field (MVF) which is applied to align the images. Cine delivery data for patients (pts) undergoing treatment for abdominal and thoracic tumors were retrospectively analyzed. Cine MRI scans were sampled, constructing a large set of image registration pairs capturing pt respiratory motion to train the DL model. Data were partitioned by pt using five-fold cross validation. Model outputs (transformed images and MVFs) on test set images were saved for comparison with three conventional registration methods (affine, b-spline, and demons). Performance was quantified via average registration error and computation time. Paired t-tests determined whether differences in performance were statistically significant. <h3>Results</h3> We analyzed >21 hours of cine MRI (>629,000 frames) acquired during 86 treatment fractions from 21 pts. In a test set of 10,320 image registration pairs, DL registration outperformed conventional methods in both registration error (affine, b-spline, demons vs. DL; RMSE: 0.067, 0.040, 0.036 vs. 0.032; paired t-test demons vs DL: t(20) = 4.2, p<0.001) and computation time per frame (51 ms, 1150 ms, 4583 ms vs. 8 ms). <h3>Conclusion</h3> DL-based image registration can leverage large-scale cine MRI datasets to learn to predict pt internal motion fields using a single reference and a single moving frame as inputs. Low registration error and fast computation speed indicate that DL-based registration is a promising solution for real-time deformable motion tracking in RT. Further inter-institutional validation is underway.

Hybrid-driven structural modal shape visualization using subtle variations in high-speed video.

The phase-based motion magnification technique can exaggerate specific structural vibrations and obtain potential applications in visualizing and understanding modal shapes. However, the quality of motion magnification is affected by noise and clipping artifacts, especially in large amplifications. We propose a hybrid-driven motion magnification framework that combines Eulerian and Lagrangian motion processing. Since the structural global spatial vibration corresponding to different modal shapes usually accumulates energy differences in the timeline, from a Eulerian perspective, temporal intensity variations are denoised and separated according to the energy distribution to control spatial motions. Meanwhile, from a Lagrangian perspective, the motion magnification is realized by compensating spatial motion according to the magnified inter-frame motion vector field. By utilizing both Eulerian and Lagrangian motion processing, the proposed framework supports a larger amplification factor and achieves better performance in perceiving subtle vibrations in controlled modal tests.

Anatomical validation of automatic respiratory motion correction for coronary 18F-sodium fluoride positron emission tomography by expert measurements from four-dimensional computed tomography.

Respiratory motion correction is of importance in studies of coronary plaques employing 18 F-NaF; however, the validation of motion correction techniques mainly relies on indirect measures such as test-retest repeatability assessments. In this study, we aim to compare and, thus, validate the respiratory motion vector fields obtained from the positron emission tomography (PET) images directly to the respiratory motion observed during four-dimensional cine-computed tomography (CT) by an expert observer. To investigate the accuracy of the motion correction employed in a software (FusionQuant) used for evaluation of 18 F-NaF PET studies by comparing the respiratory motion of the coronary plaques observed in PET to the respiratory motion observed in 4D cine-CT images. This study included 23 patients who undertook thoracic PET scans for the assessment of coronary plaques using 18 F-sodium fluoride (18 F-NaF). All patients underwent a 5-s cine-CT (4D-CT), a coronary CT angiography (CTA), and 18 F-NaF PET. The 4D-CT and PET scan were reconstructed into 10 phases. Respiratory motion was estimated for the non-contrast visible coronary plaques using diffeomorphic registrations (PET) and compared to respiratory motion observed on 4D-CT. We report the PET motion vector fields obtained in the three principal axes in addition to the 3D motion. Statistical differences were examined using paired t-tests. Signal-to-noise ratios (SNR) are reported for the single-phase images (end-expiratory phase) and for the motion-corrected image-series (employing the motion vector fields extracted during the diffeomorphic registrations). In total, 19 coronary plaques were identified in 16 patients. No statistical differences were observed for the maximum respiratory motion observed in x, y, and the 3D motion fields (magnitude and direction) between the CT and PET (X direction: 4D CT=2.5±1.5mm, PET=2.4±3.2mm; Y direction: 4D CT=2.3±1.9mm, PET=0.7±2.9mm, 3D motion: 4D CT=6.6±3.1mm, PET=5.7±2.6mm, all p≥0.05). Significant differences in respiratory motion were observed in the systems' Z direction: 4D CT=4.9±3.4mm, PET=2.3±3.2mm, p=0.04. Significantly improved SNR is reported for the motion corrected images compared to the end-expiratory phase images (end-expiratory phase=6.8±4.8, motion corrected=12.2±4.5, p=0.001). Similar respiratory motion was observed in two directions and 3D for coronary plaques on 4D CT as detected by automatic respiratory motion correction of coronary PET using FusionQuant. The respiratory motion correction technique significantly improved the SNR in the images.

Parameter Evaluation in Motion Estimation for Forecasting Multiple Photovoltaic Power Generation

The power-generation capacity of grid-connected photovoltaic (PV) power systems is increasing. As output power forecasting is required by electricity market participants and utility operators for the stable operation of power systems, several methods have been proposed using physical and statistical approaches for various time ranges. A short-term (30 min ahead) forecasting method had been proposed previously for multiple PV systems using motion estimation. This method forecasts the short time ahead PV power generation by estimating the motion between two geographical images of the distributed PV power systems. In this method, the parameter λ, which relates the smoothness of the resulting motion vector field and affects the accuracy of the forecasting, is important. This study focuses on the parameter λ and evaluates the effect of changing this parameter on forecasting accuracy. In the periods with drastic power output changes, the forecasting was conducted on 101 PV systems. The results indicate that the absolute mean error of the proposed method with the best parameter is 10.3%, whereas that of the persistence forecasting method is 23.7%. Therefore, the proposed method is effective in forecasting periods when PV output changes drastically within a short time interval.

MR-assisted PET respiratory motion correction using deep-learning based short-scan motion fields.

We evaluated the impact of PET respiratory motion correction (MoCo) in a phantom and patients. Moreover, we proposed and examined a PET MoCo approach using motion vector fields (MVFs) from a deep-learning reconstructed short MRI scan. The evaluation of PET MoCo was performed in a respiratory motion phantom study with varying lesion sizes and tumor to background ratios (TBRs) using a static scan as the ground truth. MRI-based MVFs were derived from either 2000 spokes (MoCo2000 , 5-6 min acquisition time) using a Fourier transform reconstruction or 200 spokes (MoCoP2P200 , 30-40 s acquisition time) using a deep-learning Phase2Phase (P2P) reconstruction and then incorporated into PET MoCo reconstruction. For six patients with hepatic lesions, the performance of PET MoCo was evaluated using quantitative metrics (SUVmax , SUVpeak , SUVmean , lesion volume) and a blinded radiological review on lesion conspicuity. MRI-assisted PET MoCo methods provided similar results to static scans across most lesions with varying TBRs in the phantom. Both MoCo2000 and MoCoP2P200 PET images had significantly higher SUVmax , SUVpeak , SUVmean and significantly lower lesion volume than non-motion-corrected (non-MoCo) PET images. There was no statistical difference between MoCo2000 and MoCoP2P200 PET images for SUVmax , SUVpeak , SUVmean or lesion volume. Both radiological reviewers found that MoCo2000 and MoCoP2P200 PET significantly improved lesion conspicuity. An MRI-assisted PET MoCo method was evaluated using the ground truth in a phantom study. In patients with hepatic lesions, PET MoCo images improved quantitative and qualitative metrics based on only 30-40 s of MRI motion modeling data.

Motion compensation for aortic valves using partial angle CT reconstructions.

A motion compensation method that is aimed at correcting motion artifacts of cardiac valves is proposed. The primary focus is the aorticvalve. The method is based around partial angle reconstructions and a cost function including the image entropy. A motion model is applied to approximate the cardiac motion in the temporal and spatial domain. Based on characteristic values for velocities and strain during cardiac motion, penalties for the velocity and spatial derivatives are introduced to maintain anatomically realistic motion vector fields and avoid distortions. The model addresses global elastic deformation, but not the finer and more complicated motion of the valve leaflets. The method is verified based on clinical data. Image quality was improved for most artifact-impaired reconstructions. An image quality study with Likert scoring of the motion artifact severity on a scale from 1 (highest image quality) to 5 (lowest image quality/extreme artifact presence) was performed. The biggest improvements after applying motion compensation were achieved for strongly artifact-impaired initial images scoring 4 and 5, resulting in an average change of the scores by and , respectively. In the case of artifact-free images, a chance to introduce blurring was observed and their average score was raised by 0.42 ± 0.03. Motion artifacts were consistently removed and image qualityimproved.

Motion-compensated fat-water imaging for 3D cardiac MRI at ultra-high fields.

Respiratory motion-compensated (MC) 3D cardiac fat-water imaging at 7T. Free-breathing bipolar 3D triple-echo gradient-recalled-echo (GRE) data with radial phase-encoding (RPE) trajectory were acquired in 11 healthy volunteers (7M\4F, 21-35 years, mean: 30 years) with a wide range of body mass index (BMI; 19.9-34.0 kg/m2 ) and volunteer tailored shimming. The bipolar-corrected triple-echo GRE-RPE data were binned into different respiratory phases (self-navigation) and were used for the estimation of non-rigid motion vector fields (MF) and respiratory resolved (RR) maps of the main magnetic field deviations (ΔB0 ). RR ΔB0 maps and MC ΔB0 maps were compared to a reference respiratory phase to assess respiration-induced changes. Subsequently, cardiac binned fat-water images were obtained using a model-based, respiratory motion-corrected image reconstruction. The 3D cardiac fat-water imaging at 7T was successfully demonstrated. Local respiration-induced frequency shifts in MC ΔB0 maps are small compared to the chemical shifts used in the multi-peak model. Compared to the reference exhale ΔB0 map these changes are in the order of 10 Hz on average. Cardiac binned MC fat-water reconstruction reduced respiration induced blurring in the fat-water images, and flow artifacts are reduced in the end-diastolic fat-water separated images. This work demonstrates the feasibility of 3D fat-water imaging at UHF for the entire human heart despite spatial and temporal and B0 variations, as well as respiratory and cardiac motion.

Характеристический вектор почти контактной метрической структуры как аффинное движение

Smooth manifold with almost contact metric structure (i. e., almost contact metric manifold) was considered in this paper. We used a modern version of Cartan’s method of external forms to conduct our study. We assume that its Reeb vector field is affine motion. We got formulas for components of second covariant differential of contact form for an arbi­trary almost contact metric manifold. Criterion for affine motion of Reeb vector field has been obtained for arbitrary almost contact metric mani­fold in this paper. It is proved that if Reeb vector field of almost contact structure is affine motion then sixth structural tensor of almost contact metric structure is vanishing. It is proved that if Reeb vector field is affine motion and torse-forming vector field then Reeb vector field is Killing vector field. It is proved that if Reeb vector field of almost contact metric structure is torse-forming vector field and it is not Killing vector field then it is not affine motion.