Towards predicting the encoding capability of MR fingerprinting sequences

Sequence optimization and appropriate sequence selection is still an unmet need in magnetic resonance fingerprinting (MRF). The main challenge in MRF sequence design is the lack of an appropriate measure of the sequence's encoding capability. To find such a measure, three different candidates for judging the encoding capability have been investigated: local and global dot-product-based measures judging dictionary entry similarity as well as a Monte Carlo method that evaluates the noise propagation properties of an MRF sequence. Consistency of these measures for different sequence lengths as well as the capability to predict actual sequence performance in both phantom and in vivo measurements was analyzed. While the dot-product-based measures yielded inconsistent results for different sequence lengths, the Monte Carlo method was in a good agreement with phantom experiments. In particular, the Monte Carlo method could accurately predict the performance of different flip angle patterns in actual measurements. The proposed Monte Carlo method provides an appropriate measure of MRF sequence encoding capability and may be used for sequence optimization.

Retrospective image correction in the presence of nonlinear temporal magnetic field changes using multichannel navigator echoes

Spatio-temporal magnetic field changes in the brain caused by breathing or body movements can lead to image artifacts. This is especially a problem in T(2)(*)-weighted sequences. With the acquisition of an extra echo (navigator), it is possible to measure the magnetic field change induced frequency offset for a given slice during image acquisition. However, substantial local variation across a slice can occur. This work describes an extension of the conventional navigator technique that improves the estimation of the magnetic field distribution in the brain during strong field fluctuations. This is done using the combination of signals from multiple coil elements, the coil sensitivity profiles, and frequency encoding: termed sensitivity-encoded navigator echoes. In vivo validation was performed in subjects who performed normal breathing, nose touching, and deep breathing during scanning. The sensitivity-encoded navigator technique leads to an error reduction in estimating the field distribution in the brain of 73% ± 16% compared with 56% ± 14% for conventional estimation. Image quality can be improved via incorporating this navigator information appropriately into the image reconstruction. When the sensitivity-encoded navigator technique was applied to a T(2)(*)-weighted sequence at 7 T, a ghosting reduction of 47% ± 13% was measured during nose touching experiments compared with no correction.

Free-breathing whole-heart coronary MRA with 3D radial SSFP and self-navigated image reconstruction

Respiratory motion is a major source of artifacts in cardiac magnetic resonance imaging (MRI). Free-breathing techniques with pencil-beam navigators efficiently suppress respiratory motion and minimize the need for patient cooperation. However, the correlation between the measured navigator position and the actual position of the heart may be adversely affected by hysteretic effects, navigator position, and temporal delays between the navigators and the image acquisition. In addition, irregular breathing patterns during navigator-gated scanning may result in low scan efficiency and prolonged scan time. The purpose of this study was to develop and implement a self-navigated, free-breathing, whole-heart 3D coronary MRI technique that would overcome these shortcomings and improve the ease-of-use of coronary MRI. A signal synchronous with respiration was extracted directly from the echoes acquired for imaging, and the motion information was used for retrospective, rigid-body, through-plane motion correction. The images obtained from the self-navigated reconstruction were compared with the results from conventional, prospective, pencil-beam navigator tracking. Image quality was improved in phantom studies using self-navigation, while equivalent results were obtained with both techniques in preliminary in vivo studies.

Free breathing 3D balanced FFE coronary magnetic resonance angiography with prolonged cardiac acquisition windows and intra-RR motion correction

A shortcoming of today's coronary magnetic resonance angiography (MRA) is its low total scan efficiency (<5%), as only small well-defined fractions of the respiratory (50%) and cardiac (10%) cycle are used for data acquisition. These precautions are necessary to prevent blurring and artifacts related to respiratory and cardiac motion. Hence, scan times range from 4 to 9 min, which may not be tolerated by patients. To overcome this drawback, an ECG-triggered, navigator-gated free breathing radial 3D balanced FFE sequence with intra-RR motion correction is investigated in this study. Scan efficiency is increased by using a long cardiac acquisition window during the RR interval. This allows the acquisition of a number of independent k-space segments during each cardiac cycle. The intersegment motion is corrected using a self-guided epicardial fat tracking procedure in a postprocessing step. Finally, combining the motion-corrected segments forms a high-resolution image. Experiments on healthy volunteers are presented to show the basic feasibility of this approach.

Basic considerations on the impact of the coil array on the performance of Transmit SENSE

"Transmit SENSE" adapts the idea of parallel imaging to RF transmission. Using multiple independent transmit coils, the duration of a spatially selective RF pulse can be reduced. It is known from parallel imaging that a suboptimal coil-array geometry might lead to an ill-conditioned sensitivity matrix and, thus, to a non-homogenous noise amplification in the resulting image. The current paper investigates the consequences of suboptimal coil arrays for Transmit SENSE. Two possible consequences of a suboptimal coil array are studied in the framework of numerical simulations: the incorrect excitation of the desired spatial pattern and the increase of the specific energy absorption rate (SAR), i.e. the RF power required to excite the desired pattern. Incorrect pattern excitation occurs only in pathologic coil-array scenarios. The increase of the SAR is very moderate for a large range of coil-array geometries. Using spiral excitation k-space trajectories leads to superior results compared to Cartesian trajectories. The problem of an ill-conditioned matrix inversion does not seem to play a major role in Transmit SENSE. Consequently, the freedom in designing coil arrays seems to be much larger in Transmit SENSE than in SENSE in the receive mode.

Efficient foldover suppression using SENSE

Parallel imaging techniques, which in principle represent procedures of unfolding a reduced dataset, are well known and well established in MR imaging. This paper presents a further application of one particular reconstruction method, the SENSE algorithm, considered from a different point of view to remove potential foldover in conventional images acquired with multiple receive coils. Based on the coil sensitivity information, a body coverage map in the excited plane is calculated. This is used together with the measured raw data in a SENSE-type reconstruction to optimize the signal-to-noise ratio (SNR) as well as to remove foldover reliably by unfolding the image to a larger field of view. The reconstruction is performed automatically, without any user interaction, and does not affect data acquisition. Based on phantom and in vivo studies, which retain high image quality after the removal, the potential and limits of this approach are discussed, also taking into account future scanner hardware that will support a large number of parallel receiver channels.

Fast isotropic volumetric coronary MR angiography using free-breathing 3D radial balanced FFE acquisition

A shortcoming of current coronary MRA methods with thin-slab 3D acquisitions is the time-consuming examination necessitated by extensive scout scanning and precise slice planning. To improve ease of use and cover larger parts of the anatomy, it appears desirable to image the entire heart with high spatial resolution instead. For this purpose, an isotropic 3D-radial acquisition was employed in this study. This method allows undersampling of k-space in all three spatial dimensions, and its insensitivity to motion enables extended acquisitions per cardiac cycle. We present initial phantom and in vivo results obtained in volunteers that demonstrate large volume coverage with high isotropic spatial resolution. We were able to visualize all major parts of the coronary arteries retrospectively from the volume data set without compromising the image quality. The scan time ranged from 10 to 14 min during free breathing at a heart rate of 60 bpm, which is comparable to that of a thin-slab protocol comprising multiple scans for each coronary artery.

3D coronary vessel wall imaging utilizing a local inversion technique with spiral image acquisition

Current 2D black blood coronary vessel wall imaging suffers from a relatively limited coverage of the coronary artery tree. Hence, a 3D approach facilitating more extensive coverage would be desirable. The straightforward combination of a 3D-acquisition technique together with a dual inversion prepulse can decrease the effectiveness of the black blood preparation. To minimize artifacts from insufficiently suppressed blood signal of the nearby blood pools, and to reduce residual respiratory motion artifacts from the chest wall, a novel local inversion technique was implemented. The combination of a nonselective inversion prepulse with a 2D selective local inversion prepulse allowed for suppression of unwanted signal outside a user-defined region of interest. Among 10 subjects evaluated using a 3D-spiral readout, the local inversion pulse effectively suppressed signal from ventricular blood, myocardium, and chest wall tissue in all cases. The coronary vessel wall could be visualized within the entire imaging volume.

Direct comparison of 3D spiral vs. Cartesian gradient-echo coronary magnetic resonance angiography

While 3D thin-slab coronary magnetic resonance angiography (MRA) has traditionally been performed using a Cartesian acquisition scheme, spiral k-space data acquisition offers several potential advantages. However, these strategies have not been directly compared in the same subjects using similar methodologies. Thus, in the present study a comparison was made between 3D coronary MRA using Cartesian segmented k-space gradient-echo and spiral k-space data acquisition schemes. In both approaches the same spatial resolution was used and data were acquired during free breathing using navigator gating and prospective slice tracking. Magnetization preparation (T(2) preparation and fat suppression) was applied to increase the contrast. For spiral imaging two different examinations were performed, using one or two spiral interleaves, during each R-R interval. Spiral acquisitions were found to be superior to the Cartesian scheme with respect to the signal-to-noise ratio (SNR) and contrast-to-noise-ratio (CNR) (both P < 0.001) and image quality. The single spiral per R-R interval acquisition had the same total scan duration as the Cartesian acquisition, but the single spiral had the best image quality and a 2.6-fold increase in SNR. The double-interleaf spiral approach showed a 50% reduction in scanning time, a 1.8-fold increase in SNR, and similar image quality when compared to the standard Cartesian approach. Spiral 3D coronary MRA appears to be preferable to the Cartesian scheme. The increase in SNR may be "traded" for either shorter scanning times using multiple consecutive spiral interleaves, or for enhanced spatial resolution.

Accelerated coronary MRA by simultaneous acquisition of multiple 3D stacks

The implementation and first in vivo results of a novel coronary magnetic resonance angiography (MRA) protocol allowing simultaneous acquisition of multiple geometrically independent 3D imaging stacks are presented. Each imaging stack is acquired in a separate cardiac phase using an individual magnetization preparation and navigator-based gating and prospective motion correction. Each stack covers one of the main coronary vessels. Thus, an improvement of scan efficiency was achieved, which was used in this study to reduce total scan time at standard image quality. Experiments performed in healthy volunteers and in patients using a two-stack approach yielded a total scan time reduction of 50% with an image quality equivalent to standard single-stack coronary MRA.

Advances in sensitivity encoding with arbitrary k-space trajectories

New, efficient reconstruction procedures are proposed for sensitivity encoding (SENSE) with arbitrary k-space trajectories. The presented methods combine gridding principles with so-called conjugate-gradient iteration. In this fashion, the bulk of the work of reconstruction can be performed by fast Fourier transform (FFT), reducing the complexity of data processing to the same order of magnitude as in conventional gridding reconstruction. Using the proposed method, SENSE becomes practical with nonstandard k-space trajectories, enabling considerable scan time reduction with respect to mere gradient encoding. This is illustrated by imaging simulations with spiral, radial, and random k-space patterns. Simulations were also used for investigating the convergence behavior of the proposed algorithm and its dependence on the factor by which gradient encoding is reduced. The in vivo feasibility of non-Cartesian SENSE imaging with iterative reconstruction is demonstrated by examples of brain and cardiac imaging using spiral trajectories. In brain imaging with six receiver coils, the number of spiral interleaves was reduced by factors ranging from 2 to 6. In cardiac real-time imaging with four coils, spiral SENSE permitted reducing the scan time per image from 112 ms to 56 ms, thus doubling the frame-rate.

Free-breathing cardiac MR imaging: study of implications of respiratory motion--initial results

The respiratory motion of several anatomic regions (right hemidiaphragm, left ventricle of the heart, chest wall, abdominal wall) was investigated during free breathing in 10 healthy volunteers by using multinavigator technology and real-time magnetic resonance (MR) imaging. The respiratory motion shows hysteretic effects, which are strongly subject dependent and might have some effect on the quality of cardiac MR images.

Interactive reduced FOV imaging for projection reconstruction and spiral acquisition

MR fluoroscopy is likely to gain increasing importance for the visualization of dynamic processes such as cardiac function and for the guidance of interventional procedures. In many applications the dynamic processes are restricted to a part of the object under study making reduced field of view (rFOV) imaging desirable. The restriction to a smaller FOV can either be used to increase the spatial or the temporal resolution. In projection reconstruction (PR) and spiral imaging severe backfolding artifacts occur if a rFOV is used. In this paper efficient suppression schemes are proposed for PR- and spiral imaging to avoid backfolding artifacts. Evaluation of the proposed schemes was done on an interactive real-time MR-scanner. Cardiac function studies clearly showed the potential of this technique for PR- and spiral imaging.

Coronary magnetic resonance angiography

Despite advances in both prevention and treatment, cardiovascular disease remains the leading cause of morbidity and mortality in the United States. The current gold standard for the diagnosis of coronary artery disease is the x-ray coronary angiogram, which is both costly and associated with a small risk of morbidity. More than 1 million Americans are referred for this test annually, and despite the availability of numerous noninvasive tests to identify patients with coronary artery disease, > or =35% of patients referred for this test are found not to have disease. It therefore would be beneficial to use a noninvasive test to allow the presence of coronary atherosclerosis to be determined directly. Coronary magnetic resonance angiography, a technique that is aimed at establishing a noninvasive test for the assessment of significant coronary stenoses, obviates the risks of patient exposure to radiation of x-ray angiography and therefore represents a major step forward in diagnostic cardiology.

Improved 3D spiral imaging for coronary MR angiography

Thin-slab 3D spiral imaging has been used for MR angiography to image selected coronary arteries. Improved scan efficiency was achieved using a train of multiple spiral interleaves within each single R-R interval acquired in the late diastole. Data acquisition was performed during free breathing, using navigator gating. Additionally, prospective slice tracking was applied to further reduce the sensitivity to motion. The application of a T(2)-preparation pulse and fat suppression increased the contrast between blood and myocardium. Experiments performed on healthy volunteers are presented to show the feasibility of this approach, which allows coronary artery imaging of selected vessels within a few minutes. Magn Reson Med 45:172-175, 2001.

Reversed spiral MR imaging

Reversed spiral imaging is discussed as an approach that provides strong intrinsic T *(2) contrast without the need for long repetition times. In comparison to the conventional forward spiral method, the T *(2) contrast achieved by reversing the spiral k-space trajectory is similar and differs only for very fast relaxing species. The flow and motion sensitivity of the reversed approach is the same if flow compensation is applied, except for a flow-dependent voxel shift and the sign of the artifact pattern. By simulations as well as phantom and in vivo experiments, it is shown that the image quality in reversed spiral imaging is comparable to that obtained with the forward spiral method.

On the performance and accuracy of 2D navigator pulses

The purpose of this study was to investigate and to optimize the performance of two-dimensional spatially selective excitation pulses used for navigator applications on a clinical scanner. The influence of gradient imperfections, off-resonance effects, and incomplete k-space covering on the pencil beam-shaped spatial excitation profile of the 2D RF pulse was studied. The studies involved experiments performed on phantoms and in vivo. In addition, simulations were carried out by numerical integration of the Bloch equations. The accuracy of positioning of the pencil beam was increased by a factor of three by employing a simple correction scheme for the compensation of gradient distortions. The spatial selectivity of the 2D RF pulse was improved by taking sampling density corrections into account. The 2D RF pulse performance was found to be sufficient to monitor the diaphragm motion even at moderate gradient strength. For applications, where a high spatial resolution is required or a less characteristic contrast is present a strong gradient system is recommended.

Improvements in spiral MR imaging

The basic principles of spiral MR image acquisition and reconstruction are summarised with the aim to explain how high quality spiral images can be obtained. The sensitivity of spiral imaging to off-resonance effects, gradient system imperfections and concomitant fields are outlined and appropriate measures for corrections are discussed in detail. Phantom experiments demonstrate the validity of the correction approaches. Furthermore, in-vivo results are shown to demonstrate the applicability of the corrections under in-vivo conditions. The spiral image quality thus obtained was found to be comparable to that obtainable with robust spin warp sequences.

Resampling of data between arbitrary grids using convolution interpolation

For certain medical applications resampling of data is required. In magnetic resonance tomography (MRT) or computer tomography (CT), e.g., data may be sampled on nonrectilinear grids in the Fourier domain. For the image reconstruction a convolution-interpolation algorithm, often called gridding, can be applied for resampling of the data onto a rectilinear grid. Resampling of data from a rectilinear onto a nonrectilinear grid are needed, e.g., if projections of a given rectilinear data set are to be obtained. In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another. The basic algorithm can be split into two steps. First, the data are resampled from the arbitrary input grid onto a rectilinear grid and second, the rectilinear data is resampled onto the arbitrary output grid. Furthermore, we like to introduce a new technique to derive the sampling density function needed for the first step of our algorithm. For fast, sampling-pattern-independent determination of the sampling density function the Voronoi diagram of the sample distribution is calculated. The volume of the Voronoi cell around each sample is used as a measure for the sampling density. It is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids. Furthermore, it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns. Examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral, radial, and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image.

Motion pattern adapted real-time respiratory gating

The information about the current respiratory motion state used in conventional gating to accept or to reject data can further be used to obtain motion statistics during an MR scan. This can serve to monitor changes in the respiratory pattern of the patient by comparison of motion statistics subsequently obtained during scanning. Two indicators are introduced: first a parameter that registers changes of the motion pattern, and second an indicator that expresses the quality of the data set already obtained. Based on these indicators, the gating algorithm decides to change gating parameters during scanning automatically. This new approach has the potential to increase the scan efficiency considerably without the need of operator interaction and/or significant patient cooperation. The basic principle is described and illustrated for the motion-adapted gating technique, and first in vivo results are presented to underline the feasibility of this concept.

On spatially selective RF excitation and its analogy with spiral MR image acquisition

The basic principles of the design of spatially selective RF pulses are described, and their analogy with MR image acquisition and reconstruction is shown. The paper focuses on RF-pulse design and imaging schemes in which spiral k-space trajectories are used. The sensitivity of RF excitation to gradient-system imperfections and to spatially varying off-resonance are analyzed, and suitable measures of correction are discussed. The spatial resolution obtainable with selective RF pulses and the consequences of the linearity of the pulse-design problem are examined. Phantom experiments showing the performance of multidimensional spatially selective RF pulses further illustrate the analogy with MR image acquisition.

Fast 1H spectroscopic imaging using a multi-element head-coil array

Fast proton magnetic resonance spectroscopic imaging (MRSI) using a multi-element head-coil array is examined with respect to three aspects: the coil design, the use of an appropriate signal combination method, and the design of the MRSI pulse sequence itself. An eight-element head-coil array has been developed to increase the signal-to-noise ratio (SNR) of MRSI in the human brain. The flexible wraparound design optimally fits different head sizes and thus provides high sensitivity. The signal combination of the individual coil elements is based on the approach proposed by Roemer et al. (Magn. Reson. Med. 16, 192 (1990)). An additional short prescan is performed to provide a good estimate of the complex coil sensitivity profiles, which are used in the signal combination procedure to correct the spectroscopic imaging data for the spatially varying intensity. The use of coil arrays in MRSI has some effect on the requirements for both water and lipid suppression. These techniques and a MRSI pulse sequence that provides a high spectroscopic resolution are described and discussed. Experimental results at 1.5 T show that metabolite maps of N-acetylaspartate (NAA), choline (Cho), phosphocreatine (PCr)/creatine (Cr) can be obtained within a 5-min acquisition time.

Effects of gradient anisotropy in MRI

A gradient system is anisotropic if the impulse responses of at least two of the gradient channels, x, y, or z, differ from each other. Such an undesired condition may arise, for example, from differences between the gradient channels with respect to eddy currents or from unbalanced time delays in the electronic components. Depending on the degree of anisotropy, the actual gradient then deviates from the nominal, desired gradient under certain oblique orientations during the transient periods of gradient switching. The adverse consequence is degradation of image quality, such as distortion, ghosting, and blurring. In this paper, a theoretical analysis is given of the basic effects. Furthermore, the implications for the MRI process and possible correction methods are described. The effects of anisotropy are shown experimentally for echo-planar imaging and two-dimensional selective RF excitation with spiral gradient pulses.

Motion-adapted gating based on k-space weighting for reduction of respiratory motion artifacts

A new modified type of gating is presented that shows the ability to reduce the total scan time with almost conserved image quality compared with conventional gating. This new motion-adapted gating approach is based on a k-space-dependent gating threshold function. MR data acquired are only accepted if the motion-induced displacements measured from a reference position are below the chosen gating threshold function. During the MR measurement the scanner analyses respiratory motion decides in real-time which data in k-space could be measured according to the gating threshold function and performs data acquisition. In the present paper the approach will be described and discussed. Simulations based on in vivo data and initial in vivo experiments are presented to compare different variants of the new approach mutually and to the conventional technique. The analysis given is focused on spin warp type sequences, which are the best candidates for this approach.

Curved slice imaging

Curved slice imaging based on multidimensional RF pulses is introduced and discussed. This new approach makes it possible to image curved anatomical structures by using MRI. The 2D RF or 3D RF pulses used can be tailored to excite or refocus transverse magnetization of a previously defined arbitrarily curved slice profile in a 3D space. These RF pulses can be integrated into all standard MRI sequences to perform slice selection. The final curved slice image is obtained as a projection of the curved slice magnetization onto a selected imaging plane. The problem of ambiguities arising due to this projection process is addressed. Phantom and in vivo experiments were performed to illustrate the advantages and limitations of this approach.

Coronary artery imaging at 0.5 T using segmented 3D echo planar imaging

The application of segmented 3D gradient echo EPI at 0.5 T for coronary artery imaging is described. Experiments were performed using fat suppression, ECG triggering, and a patient-controlled breath-holding scheme. This approach provides a sufficient signal-to-noise ratio for thin contiguous slices in conjunction with a phased array cardiac receive coil. Wide 3D volumes, covering the proximal branches of the coronary tree, were measured with a high spatial resolution. Such data sets can be used for subsequent vessel segmentation. Furthermore, data out of narrow 3D volumes were obtained containing fewer slices angulated in the direction of a selected coronary artery. This provides a good visualization of the selected vessel over several centimeters without the need for segmentation.

Single-shot-double-echo EPI

Echo planar imaging (EPI) was extended for the acquisition of both, the spin-echo (SE) and the stimulated echo in a stimulated echo sequence after one excitation from thermal equilibrium. The two independent EPI images reflect different states of the transverse magnetization excited and measured almost simultaneously. This single-shot-double-echo EPI approach offers a variety of useful applications such as varying image contrast, obtaining flow or diffusion information, improving image resolution or circumventing T*2 requirements in single shot EPI. Benefits and limits of this technique are discussed.

Fast perfluorocarbon imaging using 19F U-FLARE

The application of an ultra-fast low angle RARE technique for the 19F imaging of perfluorocarbons (PFCs) used as temporary blood substitutes is described. This sequence is attractive for fast 19F imaging studies that measure the biodistribution of PFCs in vivo, due to its high signal-to-noise ratio. Extensions of this technique for the chemical shift selective measurement of fluorine T1 values are presented. Using the linear dependence between the oxygen partial pressure (pO2) and the T1 relaxation rate of PFC resonances this technique makes possible the fast in vivo measurement of oxygen tension. Using the sequence in a diffusion sensitized form 19F measurements of the diffusion constants of PFCs are also presented. Phantom experiments to test the methods, and in vivo images obtained in rat studies are given and discussed.

On the application of ultra-fast RARE experiments

The ultra-fast application of the RARE experiment is described in detail, with special emphasis on its multifarious applications with preparation experiments that produce transverse magnetization. The factors affecting the temporal evolution of the magnetization during the experiment are described, and the implications for the slice profile when using a Gaussian refocusing pulse are experimentally examined. The choice of phase-encoding scheme for use with preparation experiments is discussed, as is the use of various phase-encoding schemes to reduce line broadening in the phase-encoding direction if a number of averages are acquired. An explanation for the decomposition of the echo are into two components if the read gradient is imbalanced is given, and the experimental conditions necessary for the coherent addition of these two echo groups are described. An alternative sequence that removes one of these groups from the acquisition window is proposed. The sensitivity of the sequence to flow and motion is investigated, and the drastic loss of signal in this situation explained. The in vivo and in vitro application of preparation experiments leading to the accurate measurement of T1, T2, diffusion constant, and magnetization transfer characteristics is presented. The implementation of zoom-imaging using spin- and stimulated-echo preparation is described, and 3D in vivo spin-echo zoom images are presented. Simple phantom experiments demonstrating the feasibility of chemical-shift selective and spectroscopic imaging are also given.

Pulse sequence and parameter choice in NMR imaging as a problem of constrained multidimensional nonlinear optimization

The advantage of the multiparametric nature of NMR imaging is connected with the problem of finding optimum pulse sequences and sequence parameters, which ensure a high contrast-to-noise ratio. For a given imaging task with m (m greater than or equal to 2) regions characterized by sets of NMR parameters (e.g., rho, T1, T2) two functions are proposed, which can be used to transform the search for an optimum pulse sequence into a problem of constrained multidimensional nonlinear optimization. The numerical algorithm is described and the results of two examples are presented and discussed. A short description of useful extensions of the proposed optimization approach, which are currently implemented, is given.