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Dynamic MRI is restricted due to the time required to obtain enough data to reconstruct the image sequence. Several undersampled reconstruction techniques have been proposed to reduce the acquisition time. In most of these techniques the nonacquired data are recovered by modeling the temporal information as varying pixel intensities represented in time or in temporal frequencies. Here we propose a new approach that recovers the missing data through a motion estimation of the object elements ("obels," or pieces of tissue) of the image. This method assumes that an obel displacement through the sequence has lower bandwidth than fluctuations in pixel intensities caused by the motion, and thus it can be modeled with fewer parameters. Preliminary results show that this technique can effectively reconstruct (with root mean square (RMS) errors below 4%) cardiac images and joints with undersampling factors of 8 and 4, respectively. Moreover, in the reconstruction process an approximation of the motion vectors is obtained for each obel, which can be used to quantify dynamic information. In this method the motion need not be confined to a part of the field of view (FOV) or to a portion of the temporal frequency. It is appropriate for dynamic studies in which the obels' motion model has fewer parameters than the number of acquired samples., ((c) 2007 Wiley-Liss, Inc.)

Magnetic resonance spectroscopic imaging (MRSI) is a noninvasive technique for producing spatially localized spectra. MRSI presents the important challenge of reducing the scan time while maintaining the spatial resolution. The preferred approach for this is to use time-varying readout gradients to collect the spatial and chemical-shift information. Fast, three-dimensional (3D) spatial encoded methods also reduce the scan time. Despite the existence of several new and faster 3D encoded methods, or k-space trajectories, for magnetic resonance imaging (MRI), only stack of spirals and echo planar have been studied in 3D MRSI. A novel formulation for designing fast, 3D k-space trajectory applicable to 3D MRSI is presented. This approach is simple and consists of rays expanding from the origin of k-space into a revolving sphere, collecting spectral data of all 3D spatial k-space at different times in the same scan. This article describes this new method and presents some results of its application to 3D MRSI. This technique allows some degree of undersampling; hence, it is possible to reconstruct high-quality undersampled spectroscopic imaging in order to recognize different compounds in short scan times. Additionally, the method is tested in regular 3D MRI. This proposed method can also be used for dynamic undersampled imaging.

In 3D MRI, sampling k-space with traditional trajectories can be excessively time-consuming. Fast imaging trajectories are used in an attempt to efficiently cover the k-space and reduce the scan time without significantly affecting the image quality. In many applications, further reductions in scan time can be achieved via undersampling of the k-space; however, no clearly optimal method exists. In most 3D trajectories the k-space is divided into regions that are sampled with shots that share a common geometry (e.g., spirals). A different approach is to design trajectories that gradually but uniformly cover the k-space. In the current work, successive shots progressively add sampled regions to the 3D frequency space. By cutting the sequence short, a natural undersampled method is obtained. This can be particularly efficient because in these types of trajectories the contribution of new information by later shots is less significant. In this work the performance of progressive trajectories for different degrees of undersampling is assessed with trajectories based on missile guidance (MG) ideas. The results show that the approach can be efficient in terms of reducing the scan time, and performs better than the stack of spirals (SOS) technique, particularly under nonideal conditions., (Copyright 2005 Wiley-Liss, Inc.)

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 degrees and 180 degrees 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 degrees pulses, reducing the excitation length in 4% and the RF pulse energy in 3%.

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.

This work explores the use of magnetic resonance imaging (MRI) for nondestructive determination of wood characteristics and for 3D wood modeling. In this context, one of the applications under development is the automatic recognition and reconstruction of rings from transversal images obtained from MRI scanners. The algorithm analyzes a set of transversal MRI images, detecting and reconstructing growth ring edges. The information generated is then interpolated in order to obtain an accurate 3D picture of the log and its fundamental constituents (individual rings, knots, defects, etc). Results also show that the technique has potential for defect recognition, providing a powerful tool for future developments in wood analysis. The results are encouraging and further research is needed to develop automatic detection not only of rings, but also of different types of defects that are of paramount importance in the sawmill and plywood industries.

Image quality and total scan time in MRI are determined in large part by the trajectory employed to sample the Fourier space. Each trajectory has different properties like coverage of k-space, scan time, sensitivity to off-resonance conditions, etc. These properties are often contradictory, therefore a universal optimal trajectory does not exist and ultimately, it will depend on the image characteristics sought. Most trajectories used today are designed based on intuition and k-space analysis more than with optimization methods. This work presents a 3D k-space trajectory design method based on Genetic Algorithm optimization. Genetic Algorithms have been chosen because they are particularly good for searching large solution spaces. They emulate the natural evolutionary process allowing better offsprings to survive. The objective function searches the maximum of the trajectory's k-space coverage subject to hardware constraints for a fixed scanning time using the trajectory's torsion as its optimization variable. The method proved to be effective for generating k-space trajectories. They are compared with well-established trajectories. The results of simulated experiments show that they can be appropriate for image acquisition under certain special conditions, like off-resonance and undersampling. This design method can be extended to include other objective functions for different behaviors.

Magnetic Resonance Imaging opens an alternative way to analyze wood structures using a non-destructive technology. It provides high resolution, compound-based contrast manipulation and increased data acquisition flexibility. The technique is particularly useful for tree logs, since they present several characteristics that can be used to reduce the long scan time. This study proposes a method that takes advantage of the log cylindrical symmetry, acquiring transverse 1-D projections with a helical and undersampled pattern. Linear interpolation is used to estimate the skipped data and slice images are reconstructed by filtered backprojection. The sequence is improved using selective multi-pass scanning, without major variations of the scan time. Computer simulations and experimental results show that the proposed technique can increase the scan speed by a factor of 6, while maintaining the ability to identify typical tree log characteristics.

A post-processing technique is presented for correcting images undersampled in k-space. The method works by taking advantage of the image's background zeros (dynamically segmented through the application of a threshold) to extrapolate the missing k-space samples. The algorithm can produce good quality images from a small set of k-space frequencies with only a few iterations of simple matrix operations, using the image entropy as the focus criterion. It does not require any special patient preparation, extra pulse sequences, complex gradient programming or specialized hardware. This makes it a good candidate for any application that requires short scan times or where only few frequencies can be sampled.