A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity-correction step. Spatially varying resolution, signal-to-noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two-dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data.

An experimental implementation and first performance analysis of parallel spatially selective excitation with an array of transmit coils and simultaneous transmission of individual waveforms on multiple channels is presented. This technique, also known as Transmit SENSE, uses the basic idea of parallel imaging to shorten the k-space trajectories that accompany multidimensional excitation pulses, and hence shorten the duration of such pulses. So far, this concept has only been presented in simulations and semi-experimental studies since no hardware setup had been available for a full experimental realization. Interest in multidimensional, spatially selective excitation (1-3) is increasing in the field of MRI because it has a large number of useful applications. Simple slice selection is probably the most widely used form of selective excitation in one dimension, but there are also many applications that use localization in more than one dimension. These applications include volume-selective excitation for localized spectroscopy (4,5), reduced field of view (FOV) scanning of a region of interest (ROI) (6), imaging of specially shaped volumes following anatomical structures (7), or echo planar imaging (EPI) with reduced echo train lengths (8). With the trend in MRI to move continuously to higher field strengths, the possibility of compensating for transmit field inhomogeneities due to wave effects by means of spatially varying excitation is expected to gain great importance (9).Despite these numerous possible beneficial applications, the use of multidimensional, spatially selective excitation is restricted by technical limitations that arise when RF pulses are combined with gradient shapes for spatial selectivity. Since gradient performance is limited, the duration of such pulses becomes rather long because of the time required to traverse a certain k-space trajectory in order to achieve sufficient resolution and reasonably sized fields of excitation (FOXs). In general, these considerable pulse durations lead to undesirable effects, such as increased echo times (TEs), repetition times (TRs), and specific absorption rates (SARs), as well as sensitivity of the excitation profiles to off-resonance effects induced by main field inhomogeneities or varying susceptibility.To overcome these difficulties, the recently introduced concept of multiple-channel transmit (10) or Transmit Sensitivity Encoding (Transmit SENSE) (11,12) will most likely play an important role in the future. In Transmit SENSE the concept of parallel imaging is transferred from reception to transmission. The RF required for a spatially selective pulse is applied using a phased-array coil with spatially varying transmit sensitivities of the array elements. The array elements are driven by an equal number of independent RF channels with individual waveforms on each channel. In analogy to parallel reception, the spatial dependency of the sensitivities provides a localization effect that is complementary to the one induced by gradient action. This makes it...

Purpose:To evaluate an optimized k-t-space related reconstruction method for dynamic magnetic resonance imaging (MRI), a method called PEAK-GRAPPA (Parallel MRI with Extended and Averaged GRAPPA Kernels) is presented which is based on an extended spatiotemporal GRAPPA kernel in combination with temporal averaging of coil weights. Materials and Methods:The PEAK-GRAPPA kernel consists of a uniform geometry with several spatial and temporal source points from acquired k-space lines and several target points from missing k-space lines. In order to improve the quality of coil weight estimation sets of coil weights are averaged over the temporal dimension. Results:The kernel geometry leads to strongly decreased reconstruction times compared to the recently introduced k-t-GRAPPA using different kernel geometries with only one target point per kernel to fit. Improved results were obtained in terms of the root mean square error and the signal-to-noise ratio as demonstrated by in vivo cardiac imaging. Conclusion:Using a uniform kernel geometry for weight estimation with the properties of uncorrelated noise of different acquired timeframes, optimized results were achieved in terms of error level, signal-to-noise ratio, and reconstruction time. DYNAMIC MRI is an important foundation for many clinical applications such as time-resolved (Cine) cardiac imaging for the assessment of left ventricular function. To achieve sufficient spatial and temporal resolution fast data acquisition is essential, particularly for applications that require breath-holding. In order to reduce total acquisition time or to increase spatiotemporal resolution, parallel imaging techniques such as SENSE or GRAPPA have been introduced. By decreasing the number of phase-encoding steps by a reduction factor R, imaging can be substantially accelerated (1,2). Based on varying sensitivity in multiple receiver coil arrays, parallel imaging reconstruction algorithms remove resulting aliasing artifacts either in the image domain (2) or regenerate the missing data in k-space (1). For parallel imaging reconstruction using the kspace related GRAPPA technique the image reconstruction and the combination of images from different receiver coils are decoupled. Therefore, the process of unaliasing of the uncombined coil images (generated from each coil) can be optimized separately.For conventional parallel dynamic MRI using GRAPPA, the central k-space for each timeframe is fully sampled, forming the autocalibration signal (ACS) lines, while the outer k-space is undersampled in the phase-encoding (ky) direction according to a user-defined reduction factor R. All timeframes are reconstructed independently using a kernel with a certain extension in kx-and ky-direction. The kernel is shifted across the ACS lines in order to estimate the coil weights needed for the reconstruction (or interpolation) of the missing lines in outer k-space. For the reconstruction process of the missing k-space lines, the kernel is shifted by an increment of R in ky-direction over the undersampl...

The purpose of this study was to combine a recently introduced spatiotemporal parallel imaging technique, PEAK-GRAPPA (parallel MRI with extended and averaged generalized autocalibrating partially parallel acquisition), with two-dimensional (2D) cine phase-contrast velocity mapping. Phase-contrast MRI was applied to measure the blood flow in the thoracic aorta and the myocardial motion of the left ventricle. To evaluate the performance of different reconstruction methods, fully acquired kspace data sets were used to compare conventional parallel imaging using GRAPPA with reduction factors of R ‫؍‬ 2-6 and PEAK-GRAPPA as well as sliding window reconstruction with reduction factors R ‫؍‬ 2-12 (net acceleration factors up to 5.2). PEAK-GRAPPA reconstruction resulted in improved image quality with considerably reduced artifacts, which was also supported by error analysis. To analyze potential blurring or low-pass filtering effects of spatiotemporal PEAK-GRAPPA, the velocity time courses of aortic flow and myocardial tissue motion were evaluated and compared with conventional image reconstructions. Quantitative comparisons of blood flow velocities and pixel-wise correlation analysis of velocities highlight the potential of PEAK-GRAPPA for highly accelerated dynamic phase-contrast velocity mapping.

This work describes the first experimental realization of three-dimensional spatially selective excitation using parallel transmission in vivo. For the design of three-dimensional parallel excitation pulses with short durations and high excitation accuracy, the choice of a suitable transmit k-space trajectory is crucial. For this reason, the characteristics of a stack-of-spirals trajectory and of a concentric-shells trajectory were examined in an initial simulation study. It showed that, especially when undersampling the trajectories in combination with parallel transmission, experimental parameters such as transmit-coil geometry and off-resonance conditions have an essential impact on the suitability of the selected trajectory and undersampling scheme. Both trajectories were applied in MR inner-volume imaging experiments which demonstrate that acceptably short and robust three-dimensional selective pulses can be achieved if the trajectory is temporally optimized and its actual path is measured and considered during pulse calculation. Pulse durations as short as 3.2 ms were realized and such pulses were appropriate to accurately excite arbitrarily shaped volumes in a corn cob and in a rat in vivo. Reduced field-of-view imaging of these selectively excited targets allowed high spatial resolution and significantly reduced measurement times and furthermore demonstrates the feasibility of three-dimensional parallel excitation in realistic MRI applications in vivo.

Multidimensional spatially selective excitation (SSE) has stimulated a variety of useful applications in magnetic resonance imaging and magnetic resonance spectroscopy, which have regained considerable interest after the recent introduction of parallel excitation. For SSE, radiofrequency pulses are designed specifically for certain time-courses of spatially encoding magnetic fields (SEM) which are applied simultaneously with the radiofrequency pulses. However, experimental imperfections of gradient-systems and undesired SEM field contributions often prevent the correct co-action of radiofrequency pulses and gradient-waveforms and therefore degrade the fidelity of excitation patterns, especially for parallel excitation. To cope with such imperfections, a classical measurement of k-space-trajectories can be performed followed by an adaptation of the SSE-pulses. However, this method is limited to linear SEM field distributions, which are describable in the k-space-formalism. Hence, this work presents a more sophisticated method consisting in a spatially resolved measurement of the temporal phase evolution of the transverse magnetization. This exhaustive phase information can be incorporated into pulse-design algorithms to compensate even for undesired spatially nonlinear, dynamic SEM field contributions. Both approaches are assessed in various experimental scenarios and individual benefits and limitations are discussed. The adaptation of SSE-pulses to experimentally achieved calibration data turned out to be very beneficial, and especially the novel spatially resolved method exhibited high potential for robust SSE even in adverse experimental setups. Magn Reson Med 65:409-421,

With the recent proposal of using magnetic fields that are nonlinear by design for spatial encoding, new flexibility has been introduced to MR imaging. The new degrees of freedom in shaping the spatially encoding magnetic fields (SEMs) can be used to locally adapt the imaging resolution to features of the imaged object, e.g., anatomical structures, to reduce peripheral nerve stimulation during in vivo experiments or to increase the gradient switching speed by reducing the inductance of the coils producing the SEMs and thus accelerate the imaging process. In this work, the potential of nonlinear and nonbijective SEMs for spatial encoding during transmission in multidimensional spatially selective excitation is explored. Methods for multidimensional spatially selective excitation radiofrequency pulse design based on nonlinear encoding fields are introduced, and it is shown how encoding ambiguities can be resolved using parallel transmission. In simulations and phantom experiments, the feasibility of selective excitation using nonlinear, nonbijective SEMs is demonstrated, and it is shown that the spatial resolution with which the target distribution of the transverse magnetization can be realized varies locally. Thus, the resolution of the target pattern can be increased in some regions compared with conventional linear encoding. Furthermore, experimental proof of principle of accelerated two-dimensional spatially selective excitation using nonlinear SEMs is provided in this study.

Purpose Degeneration of the cartilage after anterior cruciate ligament reconstruction (ACL-R) is known, and further deterioration can be expected in patients with tunnel malplacement or partial meniscal resection. It was hypothesized that there is a significant increase in cartilage degeneration after failed ACL-R. Material and methods Isolated ACL revision surgery was performed in 154 patients at an interval of 46 ± 33 months (5–175 months) between primary and revision surgery. Cartilage status at the medial, lateral femorotibial, and patellofemoral compartments were assessed arthroscopically during primary and revision ACL-R in accordance with the Outerbridge classification. Tunnel placement, roof angle, and tibial slope was measured using anteroposterior and lateral radiographic views. Results Cartilage degeneration increased significantly in the medial femorotibial compartment, followed by the lateral and patellofemoral compartments. There was a correlation between both cartilage degeneration in the patellofemoral compartment (PFC) (rs = 0.28, p = 0.0012) and medial tibial plateau (Rs = 0.24, p = 0.003) in relation to the position of tibial tunnel in the frontal plane. Worsening of the cartilage status in the medial femorotibial compartment, either femoral or tibial, was correlated with the tibial aperture site in the lateral view (Rs = 0.28, p < 0.001). Cartilage degeneration in the lateral compartment of the knee, on both femoral or tibial side, was inversely correlated with the femoral roof angle (Rs = −0.1985, p = 0.02). Meniscal tears, either at the medial or lateral site or at both, were found in 93 patients (60%) during primary ACL-R and increased to 132 patients (86%) during revision ACL-R. Discussion Accelerated cartilage degeneration and high prevalence of meniscal lesions are seen in failed ACL-R. Tunnel placement showed significant impact on cartilage degeneration and may partially explain the increased risk of an inferior outcome when revision surgery is required after failed primary ACL-R. Level of evidence: Level IV—retrospective cohort study.