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Matrix description of general motion correction applied to multishot images

Motion of an object degrades MR images, as the acquisition is time‐dependent, and thus k‐space is inconsistently sampled. This causes ghosts. Current motion correction methods make restrictive assumptions on the type of motions, for example, that it is a translation or rotation, and use special properties of k‐space for these transformations. Such methods, however, cannot be generalized easily to nonrigid types of motions, and even rotations in multiple shots can be a problem. Here, a method is presented that can handle general nonrigid motion models. A general matrix equation gives the corrupted image from the ideal object. Thus, inversion of this system allows us to get the ideal image from the corrupted one. This inversion is possible by efficient methods mixing Fourier transforms with the conjugate gradient method. A faster but empirical inversion is discussed as well as methods to determine the motion. Simulated three‐dimensional affine data and two‐dimensional pulsation data and in vivo nonrigid data are used for demonstration. All examples are multishot images where the object moves between shots. The results indicate that it is now possible to correct for nonrigid types of motion that are representative of many types of patient motion, although computation times remain an issue. Magn Reson Med, 2005.

Fast magnetic resonance coronary angiography with a three-dimensional stack of spirals trajectory.

In this work, three‐dimensional (3D) spiral imaging has been utilized for magnetic resonance coronary angiography. Spiral‐based 3D techniques can dramatically reduce imaging time requirements compared with 3D Fourier Transform imaging. The method developed here utilized a “stack of spirals” trajectory, to traverse 3D k‐space rapidly. Both thick‐slab volumes encompassing the entire coronary tree with isotropic resolution and thin‐slab volumes targeted to a particular vessel of interest were acquired. Respiratory compensation was achieved using the diminishing variance algorithm. T2‐prepared contrast was also applied in some cases to improve contrast between vessel and myocardium, while off‐resonance blurring was minimized by applying a linear correction to the acquired data. Images from healthy volunteers were displayed using a curved reformatting technique to view long segments of vessel in a single projection. The results demonstrate that this 3D spiral technique is capable of producing high‐quality coronary magnetic resonance angiograms. Magn Reson Med 41:1170–1179, 1999.

Assessment of normal flow patterns in the pulmonary circulation by using 4D magnetic resonance velocity mapping.

OBJECTIVE The purpose of this study was to analyze flow patterns in the pulmonary circulation of healthy volunteers by using 4D flow magnetic resonance imaging. MATERIALS AND METHODS The study was approved by the local ethics committee and all subjects gave written informed consent. Eighteen volunteers underwent a 4D flow scan of the whole-heart. Two patients with congenital heart disease were also included to detect possible patterns of flow abnormalities (Patient 1: corrected transposition of great arteries (TGA); Patient 2: partial anomalous pulmonary venous return and atrial septal defect). To analyze flow patterns, 2D planes were placed on the main pulmonary artery (PA), left and right PA. Flow patterns were assessed manually by two independent viewers using vector fields, streamlines and particle traces, and semi-automatically by vorticity quantification. RESULTS Two counter-rotating helices were found in the main PA of volunteers. Right-handed helical flow was detected in the right PA of 15 volunteers. Analysis of the helical flow by particles traces revealed that both helices contributed mainly to the flow in the right PA. In the patient with corrected TGA helical flow was not detected. Abnormal vortical flow was visualized in the main PA of patient 2, suggesting elevated mean PA pressure. CONCLUSIONS Helical flow is normally present in the main PA and right PA. 4D flow is an excellent tool to evaluate noninvasively complex blood flow patterns in the pulmonary circulation. Knowledge of normal and abnormal flow patterns might help to evaluate patients with congenital heart disease adding functional information undetectable with other imaging modalities.

Caval blood flow distribution in patients with Fontan circulation: quantification by using particle traces from 4D flow MR imaging.

PURPOSE To validate the use of particle traces derived from four-dimensional (4D) flow magnetic resonance (MR) imaging to quantify in vivo the caval flow contribution to the pulmonary arteries (PAs) in patients who had been treated with the Fontan procedure. MATERIALS AND METHODS The institutional review boards approved this study, and informed consent was obtained. Twelve healthy volunteers and 10 patients with Fontan circulation were evaluated. The particle trace method consists of creating a region of interest (ROI) on a blood vessel, which is used to emit particles with a temporal resolution of approximately 40 msec. The flow distribution, as a percentage, is then estimated by counting the particles arriving to different ROIs. To validate this method, two independent observers used particle traces to calculate the flow contribution of the PA to its branches in volunteers and compared it with the contribution estimated by measuring net forward flow volume (reference method). After the method was validated, caval flow contributions were quantified in patients. Statistical analysis was performed with nonparametric tests and Bland-Altman plots. P < .05 was considered to indicate a significant difference. RESULTS Estimation of flow contributions by using particle traces was equivalent to estimation by using the reference method. Mean flow contribution of the PA to the right PA in volunteers was 54% ± 3 (standard deviation) with the reference method versus 54% ± 3 with the particle trace method for observer 1 (P = .4) and 54% ± 4 versus 54% ± 4 for observer 2 (P = .6). In patients with Fontan circulation, 87% ± 13 of the superior vena cava blood flowed to the right PA (range, 63%-100%), whereas 55% ± 19 of the inferior vena cava blood flowed to the left PA (range, 22%-82%). CONCLUSION Particle traces derived from 4D flow MR imaging enable in vivo quantification of the caval flow distribution to the PAs in patients with Fontan circulation. This method might allow the identification of patients at risk of developing complications secondary to uneven flow distribution. SUPPLEMENTAL MATERIAL http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.12120778/-/DC1.

Congenital Heart Disease in Children: Coronary MR Angiography during Systole and Diastole with Dual Cardiac Phase Whole-Heart Imaging

PURPOSE To assess the optimal timing for coronary magnetic resonance (MR) angiography in children with congenital heart disease by using dual cardiac phase whole-heart MR imaging. MATERIALS AND METHODS The local institutional review board approved this study, and informed consent was obtained from parents or guardians. Thirty children (13 girls; overall mean age, 5.01 years) were examined with a 1.5-T MR system. A free-breathing three-dimensional steady-state free precession dual cardiac phase sequence was used to obtain MR angiographic data during end-systolic and middiastolic rest periods. Vessel length, diameter, and sharpness, as well as image quality of the coronary artery segments, were analyzed and compared by using Bland-Altman plots, linear regression analysis, the t test, and Wilcoxon signed rank tests. RESULTS Optimal coronary artery imaging timing was patient dependent and different for each coronary artery segment (36 segments favored end systole, 28 favored middiastole). In 15 patients (50%), different segments favored different cardiac phases within the same patient. Image quality and vessel sharpness degraded with higher heart rates, with a similar correlation for end systole (right coronary artery [RCA], 0.39; left main [LM] coronary artery, 0.46; left anterior descending [LAD] artery, 0.51; and left circumflex [LCX] artery, 0.50) and middiastole (RCA, 0.34; LM, 0.45; LAD, 0.48; and LCx, 0.55). Mean image quality difference or mean vessel sharpness difference showed no indication to prefer a specific cardiac phase. CONCLUSION The optimal cardiac rest period for coronary MR angiography in children with congenital heart disease is specific for each coronary artery segment. Dual cardiac phase whole-heart coronary MR angiography enables optimal coronary artery visualization by retrospectively choosing the optimal imaging rest period.

Adipose Tissue MRI for Quantitative Measurement of Central Obesity

To validate adipose tissue magnetic resonance imaging (atMRI) for rapid, quantitative volumetry of visceral adipose tissue (VAT) and total adipose tissue (TAT).

Sensitivity analysis of geometric errors in additive manufacturing medical models.

Additive manufacturing (AM) models are used in medical applications for surgical planning, prosthesis design and teaching. For these applications, the accuracy of the AM models is essential. Unfortunately, this accuracy is compromised due to errors introduced by each of the building steps: image acquisition, segmentation, triangulation, printing and infiltration. However, the contribution of each step to the final error remains unclear. We performed a sensitivity analysis comparing errors obtained from a reference with those obtained modifying parameters of each building step. Our analysis considered global indexes to evaluate the overall error, and local indexes to show how this error is distributed along the surface of the AM models. Our results show that the standard building process tends to overestimate the AM models, i.e. models are larger than the original structures. They also show that the triangulation resolution and the segmentation threshold are critical factors, and that the errors are concentrated at regions with high curvatures. Errors could be reduced choosing better triangulation and printing resolutions, but there is an important need for modifying some of the standard building processes, particularly the segmentation algorithms.

Flow properties of fast three-dimensional sequences for MR angiography

To reduce the scan time of time of flight or phase contrast angiography sequences, fast three-dimensional k-space trajectories can be employed. The best 3D trajectory depends on tolerable scan time, readout time, geometric flexibility, flow/motion properties and others. A formalism for flow/motion sensitivity comparison based on the velocity k-space behavior is presented. It consists in finding the velocity k-space position as a function of the spatial k-space position. The trajectories are compared graphically by their velocity k-space maps, with simulations and with an objective computed index. The flow/motion properties of various 3D trajectories (cones, spiral-pr hybrid, spherical stack of spirals, 3DFT, 3D echo-planar, and shells) were determined. In terms of flow/motion sensitivity the cones trajectory is the best, however, it is difficult to use it for anisotropic resolutions or fields of view. Tolerating more flow sensitivity, the stack of spirals trajectory offers more geometric flexibility.

Chebyshev series for designing RF pulses employing an optimal control approach

Magnetic resonance imaging (MRI) provides bidimensional images with high definition and selectivity. Selective excitations are achieved applying a gradient and a radio frequency (RF) pulse simultaneously. They are modeled by the Bloch differential equation, which has no closed-form solution. Most methods for designing RF pulses are derived from approximation of this equation or are based on iterative optimization methods. The approximation methods are only valid for small tip angles and the optimization-based algorithms yield better results, but they are computationally intensive. To improve the solutions and to reduce processing time, a method for designing RF pulses using a pseudospectral approach is presented. The Bloch equation is expanded in Chebyshev series, which can be solved using a sparse linear algebraic system. The method permits three different formulations derived from the optimal control theory, minimum distance, minimum energy, or minimum time, which are solved as algebraic constrained minimization problems. The results were validated through simulated and real experiments of 90/spl deg/ and 180/spl deg/ RF pulses. They show improvements compared to the corresponding solutions obtained using the Shinnar-Le Roux method. The minimum time formulation produces the best performance for 180/spl deg/ pulses, reducing the excitation length in 4% and the RF pulse energy in 3%.

Fast three-dimensional k-space trajectory design using missile guidance ideas

Three‐dimensional (3D) k‐space trajectories are needed to acquire volumetric images in MRI. While scan time is determined by the trajectory efficiency, image quality and distortions depend on the shape of the trajectories. There are several 3D trajectory strategies for sampling the k‐space using rectilinear or curve schemes. Since there is no evidence about their optimality in terms of image quality and acquisition time, a new design method based on missile guidance ideas is explored. Since air‐to‐air missile guidance shares similar goals and constraints with the problem of k‐space trajectory design, a control approach for missiles is used to design a 3D trajectory. The k‐space is divided into small cubes, and each one is treated as a target to be sampled. The main goal is to cover the entire space as quickly and efficiently as possible, with good performance under different conditions. This novel design method is compared to other trajectories using simulated and real data. As an example, a trajectory that requires 0.11 times the number of shots needed by the cylindrical 3DFT acquisition was designed. This trajectory requires more shots (1.66 times) than the stack of spirals, but behaves better under nonideal conditions, such as off‐resonance and motion. Magn Reson Med 52:329–336, 2004.