Broadband population inversion by phase modulated pulses

Roadmap on nanoscale magnetic resonance imaging

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Adiabatic null passage for on-resonance magnetization transfer preparation

PURPOSE

We propose a novel RF pulse providing an adiabatic null passage (ANP) for magnetization transfer preparation with improved insensitivity toB 1 + $$ {\mathrm{B}}_1^{+} $$ and B0 inhomogeneities and mitigated direct saturation and T2 effects.

METHOD

The phase modulation function of a 6-ms time-resampled frequency offset-corrected pulse was modified to achieve zero flip angle at the end of the pulse. The spectral response was simulated, and its insensitivity to B0 andB 1 + $$ {\mathrm{B}}_1^{+} $$ was investigated and compared with a phase-inverted (12 ¯ $$ \overline{2} $$ 1-1 ¯ $$ \overline{1} $$ 21 ¯ $$ \overline{1} $$ ) binomial pulse. The proposed pulse was implemented in a 2D-EPI pulse sequence to generate magnetization transfer (MT) contrast and MT ratio (MTR) maps. In vivo experiments were performed on 3 healthy participants with power-matched settings for ANP and the binomial pulse with the following parameters: 6-ms binomial pulse with a flip angle of 107° (shortest element) and pulse repetition period (PRP) of TRslice  = 59 ms, three experiments with 6-ms ANP and constant MT used overdrive factor (OF)/PRP values of 1/TRslice ,2 $$ \sqrt{2} $$ /2TRslice , and3 $$ \sqrt{3} $$ /3TRslice .

RESULTS

At gray matter (white matter) in vivo, the MTR decreased from 61% (64%) at OF = 1 to 38% (42%) applying ANP with an OF =3 $$ \sqrt{\mathsf{3}} $$ and PRP = 3 TRslice , demonstrating the mitigation of T2 /direct effect by 22% (22%). Bloch-McConnell simulations gave similar values. In vivo experiments showed significant improvement in the MTR values for areas with high B0 inhomogeneity.

CONCLUSION

ANP pulse was shown to be advantageous over its binomial counterpart in providing MT contrast by mitigating the T2 effect and direct saturation of the liquid pool as well as reduced sensitivity toB 1 + $$ {\mathrm{B}}_1^{+} $$ and B0 inhomogeneity.

An improved algorithm for design of broadband excitation, inversion, and mixing pulse sequences by iterative optimization of phases: TOPS-2

This paper presents an improved iterative algorithm (TOPS-2) for the design of broadband inversion, excitation and coherent transfer mixing sequence (TOCSY) pulses. The evolution of the Bloch vector is presented as a sequence of small constant flip angle pulses with varying phases and constant amplitude. This paper describes an improved algorithm for iterative optimization of piece-wise constant phases as we incorporate the quadratic terms in the propagators. In our iterative optimization we obtain a closed-form expression for each phase, and these phases are optimized sequentially using the new improved algorithm. This paper compares the simulation results of the TOPS vs TOPS-2 and shows that TOPS-2 perform better. Experimental validation of excitation and inversion TOPS-2 pulse sequence is performed with .5% H2O in 99.5% D2O, and experimental validation of TOPS-2 mixing (TOCSY) pulse sequence is done with 0.1% of Ethylbenzene (EB) in CDCl3 solvent.

Improved design of frequency-swept pulse sequences

Frequency-swept pulses are extensively used in magnetic resonance spectroscopic techniques for the robust manipulation of spins across wide ranges of offset frequencies in the presence of B₁ field variations. Nevertheless, designing pulse sequences consisting of multiple frequency-swept pulses can be challenging, as they often require specific timings and parameter tweaking. In the present work we discuss a simple and general approach for constructing such sequences. We present new and improved pulse sequences for applications including broadband B₁-tolerant CPMG (CHORUS-CPMG), broadband chirped excitation with suppression of homonuclear J-modulation (PROCHORUS), and the further compression of frequency-swept pulse sequences by superposition of pulses which reduces pulse sequence durations by 25-40%. All sequence design strategies are accompanied by mathematical presentations, experimental results, and supporting simulations.

Efficient solvent suppression with adiabatic inversion for 1H-detected solid-state NMR

This study introduces a conceptually new solvent suppression scheme with adiabatic inversion pulses for ¹H-detected multidimensional solid-state NMR (SSNMR) of biomolecules and other systems, which is termed "Solvent suppression of Liquid signal with Adiabatic Pulse" (SLAP). ¹H-detected 2D ¹³C/¹H SSNMR data of uniformly ¹³C- and ¹⁵N-labeled GB1 sample using ultra-fast magic angle spinning at a spinning rate of 60 kHz demonstrated that the SLAP scheme showed up to 3.5-fold better solvent suppression performance over a traditional solvent-suppression scheme for SSNMR, MISSISSIPPI (Zhou and Rienstra, J Magn Reson 192:167-172, 2008) with 2/3 of the average RF power.

Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation

Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and in vivo MRS. In the present survey, a general expression for chirped pulses will be introduced, and some numerical approaches to calculate the spin dynamics during chirped pulses via solutions of the well-known Liouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebra along with comprehensive examples are presented. In both cases, spin state trajectories are calculated using the solution of differential equations. Additionally, applications of the proposed methods to study the spin dynamics during the PSYCHE pulse element for broadband homonuclear decoupling and the CHORUS sequence for broadband excitation will be presented.

The evolution of solution state NMR pulse sequences through the 'eyes' of triple-resonance spectroscopy

Careful pulse sequence design and optimization is critical to the success of a given NMR experiment. Over the past several decades the level of sophistication of NMR pulse sequences has increased tremendously, leading to large spectral sensitivity and resolution improvements, to data sets with far fewer artifacts, and to much more rapid acquisition times, opening up a wide range of applications. Here I briefly highlight how pulse sequence 'engineering' has evolved, focusing on liquid state NMR, and, in particular, on the HNCA-class of triple-resonance experiment. In many respects, the evolution of triple-resonance NMR mirrors the evolution of solution state NMR experiments in general, with 'tricks' that first appeared in triple-resonance pulse sequences or that were motivated by them now incorporated into a broad range of experiments.

Improved ultra-broadband chirp excitation

The design and application of ultra-broadband excitation pulses have been among the most interesting and timely areas in NMR and EPR methodology in recent years, due especially to advances in hardware design in EPR, the advent and popularity of high- and ultrahigh-field NMR, and the application of numerical methods like optimal control theory to the design and optimization of radiofrequency pulses and pulse sequences. In this communication, we present a short, robust, and flexible version of the CHORUS family of constant-phase, very broadband excitation sequences. We demonstrate that more than 0.5 MHz excitation with uniform amplitudes and phases can be achieved with this excitation sequence.

Rf-inhomogeneity compensation using method of Fourier synthesis

In this paper, we propose a new method for design of composite pulses that are robust to rf-amplitude (rf-inhomogeneity). We call this, the method of Fourier synthesis. The method is general enough to design excitation, inversion, refocusing or arbitary flip angle pulses that are robust to rf-amplitude. The method can be tailored to have amplitude selective excitation. We experimentally show rf-compensation over a order of magnitude (20db) variation in rf-amplitude. The method is expected to find use in invivo NMR studies using surface coils, where there is large dispersion in rf-amplitude over the sample.

Heteronuclear refocusing by nonlinear phase and amplitude modulation on a single transmitter channel

The application of low magnetic fields to heteronuclear NMR has expanded recently alongside the emergence of methods for achieving near unity polarization of spin ensembles, independent of magnetic field strength. The parahydrogen induced hyperpolarization methods in particular, often use a hybrid arrangement where a high field spectrometer is used to detect or image polarized molecules that have been conjured on a separate, dedicated polarizer instrument operating at fields in the mT regime where yields are higher. For controlling polarizer chemistry, spare TTL channels of portable NMR spectrometers can be used to pulse program reaction timings in synchrony with heteronuclear RF transformations. The use of a spectrometer as a portable polarizer control module has the advantage of allowing detection in situ, simplifying the process of optimizing polarization yields prior to in vivo experimental trials. Suitable heteronuclear spectrometers compatible with this application are becoming more common, but are still sparsely available in comparison to a large existing infrastructure of single channel NMR consoles. With the goal of expanding the range of these systems to multinuclear applications, the feasibility of rotating a pair of heteronuclear spins ((13)C and (1)H) at 12mT was investigated in this study. Nonlinear phase and amplitude modulated waveforms designed to simultaneously refocus magnetization at 128kHz ((13)C) and 510kHz ((1)H) were generated numerically with optimal control. Although precise quantitative comparisons were not attempted due to limitations of the experimental setup, signals refocused at heteronuclear frequencies with this PANORAMIC approach (Precession And Nutation for Observing Rotation At Multiple Intervals about the Carrier) yielded amplitudes comparable to signals which were refocused using traditional block pulses on heteronuclear channels. Using this PANORAMIC approach to heteronuclear NMR at low field would reduce expense as well as hardware complexity and bulk, weighed against the caveat that elaborate pulses are required. More work will be necessary to test this method on the targeted application of parahydrogen induced hyperpolarization as well as to quantify efficiency, but upon further development we anticipate that this method may offer a viable 'software' approach to heteronuclear manipulations of spins at low magnetic fields.

New strategies for designing robust universal rotation pulses: application to broadband refocusing at low power

Optimizing pulse performance often requires a compromise between maximizing signal amplitude and minimizing spectral phase errors. We consider methods for the de novo design of universal rotation pulses, applied specifically but not limited to refocusing pulses. Broadband inversion pulses that rotate all magnetization components 180° about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180° universal rotation pulses (180(UR)(°)) using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. Nearly ideal refocusing is possible over a resonance offset range of ± 170% relative to the nominal pulse B(1) field, concurrent with tolerance to B(1) inhomogeneity/miscalibration of ± 33%. We present new modifications of the optimal control algorithm that incorporate symmetry principles (S-BURBOP) and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of low-power 180(BURBOP)(°) pulses suitable for widespread use in (13)C spectroscopy on the majority of available probes. A quantitative measure for the reduced spectral phase error provided by these symmetry principles is also derived. For pulses designed according to this symmetry, refocusing phase errors are virtually eliminated upon application of EXORCYCLE or an equivalent G-180(S-BURBOP)(°)-G gradient sandwich, independent of resonance offset and RF inhomogeneity. The magnitude of the refocused component is not significantly compromised in achieving such ideal phase performance.

Constant amplitude broadband refocusing pulses from numerical optimization

Broadband refocusing pulses for high-field NMR can be constructed with broadband 90× pulses from numerical optimization of Bloch simulations concatenated with their time and phase reversed transformations. This work describes the search for minimal duration 18-kHz modulation frequency constant amplitude refocusing pulses made in this manner for bandwidths of 40, 60 and 80 kHz. Variants optimized at multiple frequencies and with sine squared amplitude truncation also are described. The resulting pulses are expected to have immediate application especially for (13)C refocusing in multidimensional experiments.

Slice with angulated non-parallel boundaries

Adiabatic pulses are widely used for spatial localization in magnetic resonance spectroscopy because of their high immunity to RF inhomogeneity and excellent slice profiles. Since non-rectangular volume is often preferred in localized spectroscopy, we propose a scheme for selecting a trapezoidal slice using adiabatic π pulses. In this scheme, a time-varying gradient orthogonal to a stationary slice selection gradient is used to change the boundaries of the slice profile from parallel to non-parallel. Numerical simulation results for the transverse and longitudinal magnetization using different RF and gradient waveforms are presented for non-parallel slice selection. Phantom imaging and in vivo(1)H MRS of rat brain using non-parallel slices are demonstrated.

Suppressing one-bond correlations in HMBC spectra: improved performance for the BIRD-HMBC pulse sequence

An improved version of the BIRD-HMBC experiment is proposed. In comparison to the original version, the filtering (suppression of (1) J(CH) signals) is accomplished using a double tuned G-BIRD filter positioned in the middle of the long-range correlations evolution period. Compensation of offset dependence by replacing the rectangular 180 degree pulses with the broadband inversion pulses (BIPs), with superior inversion performance and improved tolerance to B(1) field inhomogeneity, significantly improves the sensitivity of the original BIRD-HMBC experiment. For usual one-bond coupling constants ranges (115-180 Hz), optimal results are easily obtained by adjusting the delays, delta, of the BIRD elements to an average J value. For larger ranges (e.g. 110-260 Hz), the use of a double tuned G-BIRD filter allows excellent suppression degrees for all types of one-bond constants present in a molecule, superior to the original scheme and other purging schemes. These attributes make the improved version of the BIRD-HMBC experiment a valuable and robust tool for rapid spectral analysis and rapid checks of molecular skeletons with a minimum spectrometer time.

Doubly compensated multiplicity-edited HSQC experiments utilizing broadband inversion pulses

We propose a family of doubly compensated multiplicity-edited heteronuclear single quantum coherence (HSQC) pulse sequences. The key difference between our proposed sequences and the compensation of refocusing inefficiency with synchronized inversion sweeps (CRISIS)-HSQC experiments they are based on is that the conventional rectangular 180 degrees pulses on the proton channel in the latter have been replaced by the computer-optimized broadband inversion pulses (BIPs) with superior inversion performance as well as much improved tolerance to B(1) field inhomogeneity. Moreover, all adiabatic carbon 180 degrees pulses during the INEPT and reverse-INEPT periods in the CRISIS-HSQC sequences have also been replaced with the much shorter BIPs, while the adiabatic sweeps during the heteronuclear spin echo for multiplicity editing are kept in place in order to maintain the advantage of the CRISIS feature of the original sequences, namely J-independent refocusing of the one-bond (1)H--(13)C coupling constants. These modifications have also been implemented to the preservation of equivalent pathways (PEP)-HSQC experiments. We demonstrate through a detailed comparison that replacing the proton 180 degrees pulses with the BIPs provide additional sensitivity gain that can be mainly attributed to the improved tolerance to B(1) field inhomogeneity of the BIPs. The proposed sequences can be easily adapted for (19)F--(13)C correlations.

Frequency-swept HMQC sequences for high-throughput NMR analysis

We describe here new versions of the DEPT phase-encoded HMQC experiment that offer robust performance and improved sensitivity. The new sequences rely on frequency-swept proton and carbon pulses to minimize signal losses from miscalibrated pulses while providing 'J compensation' to optimize the signal strength over a range of heteronuclear coupling constants. By including both proton and carbon-swept pulses, the new sequences also offer an additional signal gain of roughly 10% over well-calibrated hard-pulse experiments. The new sequences also demonstrate that one can construct a sequence that incorporates both 90 degrees and 180 degrees frequency-swept pulses. Although individual pulses in the sequence cause severe phase roll, the phase roll can be eliminated by the proper choice of pulse lengths and sweep directions.

Simultaneous water and lipid suppression for in vivo brain spectroscopy in humans

A method to achieve simultaneous water and lipid suppression is described. The key feature of the new dual suppression technique is the use of the well-known hyperbolic secant (HS) waveform as a 90 degrees saturation pulse. Two HS pulses with opposite frequency offsets are employed either sequentially or simultaneously to saturate resonance frequencies corresponding to water and lipid, while leaving the target spins untouched. The excitation bandwidth is controlled by the frequency sweep and offset of each pulse, while varying the pulse length controls the transition bandwidth. An example of the use of the dual saturation method in in vivo magnetic resonance spectroscopic imaging of the human brain is presented.

Adiabatic pulses in 1H-15N direct and long-range heteronuclear correlations

The application of adiabatic inversion pulses to the detection of (1)H-(15)N heteronuclear correlations is described. The pulse sequences studied were gHSQC, CRISIS-gHSQC, gHMBC and CRISIS-gHMBC. The poor inversion quality of rectangular 180 degrees X pulses can lead to a loss of signal at the peripheries of the spectrum. Replacing these pulses with adiabatic sweeps significantly improves sensitivity across the potentially large (15)N spectral window. Satellite spectrum profiles are shown to demonstrate the increase in sensitivity when employing adiabatic pulses on wide spectral widths. Additionally, the active pharmaceutical nizatidine was used as a model compound to demonstrate the improvements in the long-range correlation data.

Near neighbor approximation in nuclear magnetic resonance

A new way to deal with the excitation by multiple effective RF fields with interference is presented using the coherent averaging theory. It significantly simplifies the calculation of the effect of RF interference that occurs in the excitations by periodic pulses and phase-incremented pulses (PIPs). This approach shows that each neighboring RF field contributes to an excitation profile an offset shift, which is termed the Bloch-Siegert offset shift (BSOS). The BSOS depends not only on the strengths of both RF fields that interfere with each other but also on their relative phase between the two RF fields. Consequently, it can be positive, negative, and zero. In addition, the BSOS is also inversely proportional to the frequency separation of the two RF fields. Therefore, only a few near neighbors need to be taken into account in most cases, resulting in a near neighbor approximation (NNA). The BSOS for two multiband excitation profiles, one by a periodic pulse and the other by a PIP, are calculated using the NNA. The results are in good agreement with the computer simulated ones.

Adjustable, broadband, selective excitation with uniform phase

An advance in the problem of achieving broadband, selective, and uniform-phase excitation in NMR spectroscopy of liquids is outlined. Broadband means that, neglecting relaxation, any frequency bandwidth may be excited even when the available radiofrequency (RF) field strength is strictly limited. Selective means that sharp transition edges can be created between pure-phase excitation and no excitation at all. Uniform phase means that, neglecting spin-spin coupling, all resonance lines have nearly the same phase. Conventional uniform-phase excitation pulses (e.g., E-BURP), mostly based on amplitude modulation of the RF field, are not broadband: they have an achievable bandwidth that is strictly limited by the peak power available. Other compensated pulses based on adiabatic half-passage, like BIR-4, are not selective. By contrast, inversion pulses based on adiabatic fast passage can be broadband (and selective) in the sense above. The advance outlined is a way to reformulate these frequency modulated (FM) pulses for excitation, rather than just inversion.

Sample restriction using radiofrequency field selective pulses in high-resolution solid-state NMR

In this article a method is suggested for restricting a sample (spatial localization) by preparing the magnetization with a phase-modulated radiofrequency pulse which inverts magnetization only over a very narrow range of radiofrequency field strengths. This is the most efficient method, in terms of sensitivity, of restricting the sample to improve rf homogeneity. The method is demonstrated by using it to improve the resolution obtained in a homonuclear dipolar decoupling experiment.

Coherent excitation with phase-incremented pulses

An outline is given for calculating the evolution of a spin system by a pulse sequence with phase-incremented pulses (PIPs). It is done in a frame with a speed of 2pideltaf=deltaphi/deltatau relative to the rotating frame, where deltaphi and deltatau are the phase- and time-increment of the PIP. This particular frame is defined as the eigenframe, in which the phase of the PIP for the center band is stationary and is subjected to a universal phase shift (UPS=-deltaphi/2), and the strength of the PIP is scaled by a factor of lambda=2[1-cos(deltaphi)]/(deltaphi). The phase differences between different eigenframes can be attributed to the initial phases of the PIPs, making it possible to use the Bloch vector model even in different eigenframes. A new way is provided to construct composite pulses with not only amplitude and phase modulations but also offset modulation. Several examples, including a broadband inversion pulse, a Hahn spin echo, and a selective inversion and null pulse, all composed of PIPs, are discussed in detail.

The return of the frequency sweep: designing adiabatic pulses for contemporary NMR

Frequency-modulated (FM) pulses that function according to adiabatic principles are becoming increasingly popular in many areas of NMR. Often adiabatic pulses can extend experimental capabilities and minimize annoying experimental imperfections. Here, adiabatic principles and some of the current methods used to create these pulses are considered. The classical adiabatic rapid passage, which is a fundamental element upon which all adiabatic pulses and sequences are based, is analyzed using vector models in different rotating frames of reference. Two methods to optimize adiabaticity are described, and ways to tailor modulation functions to best satisfy specific experimental needs are demonstrated. Finally, adiabatic plane rotation pulses and frequency-selective multiple spin-echo sequences are considered.

Carr-Purcell sequences with composite pulses

We present novel Carr-Purcell-like sequences using composite pulses that exhibit improved performance in strongly inhomogeneous fields. The sequences are designed to retain the intrinsic error correction of the standard Carr-Purcell-Meiboom-Gill (CPMG) sequence. This is achieved by matching the excitation pulse with the refocusing cycle such that the initial transverse magnetization lies along the axis n(Beta) characterizing the overall rotation of the refocusing cycle. Such sequences are suitable for relaxation measurements. It is shown that in sufficiently inhomogeneous fields, the echo amplitudes have an initial transient modulation that is limited to the first few echoes and then decay with the intrinsic relaxation time of the sample. We show different examples of such sequences that are constructed from simple composite pulses. Sequences of the form 90 degrees (0)-(90 degrees (90-theta/2)-theta(180-theta/2)-90 degrees (90-theta/2))(n) with theta approximately 90 degrees and 270 degrees generate signal over a bandwidth larger than that of the conventional CPMG sequence, resulting in an improved signal-to-noise ratio in inhomogeneous fields. The new sequence 127 degrees (x,y)-(127 degrees (x)-127 degrees (-x))(n) only excites signal off-resonance with a spectrum that is bimodal, peaking at Delta omega(0)=+/-omega(1). Depending on the phase and exact timing of the first pulse, symmetric or antisymmetric excitation is obtained. We also demonstrate several new sequences with improved dependence on the RF field strength. The sequence (22.5 degrees (67.5)-90 degrees (-22.5))-(90 degrees (67.5)-45 degrees (157.5)-90 degrees (67.5))(n) has the property that the phase of the signal depends on B(1), allowing coarse B(1) imaging in a one-dimensional experiment.

An adiabatic multiple spin-echo pulse sequence: removal of systematic errors due to pulse imperfections and off-resonance effects

Application of AFP (adiabatic fast passage) pulses for removal of systematic errors associated with multiple spin-echo sequences is demonstrated. The adiabatic fast passage pulses facilitate minimization of cumulative pulse errors for all three components of magnetization. It is also shown that off-resonance effects present in conventional CPMG sequences which degrade image quality in magnetic resonance imaging and introduce systematic errors in measured T2 relaxation time peak amplitudes can be suppressed by introduction of AFP pulses without any degradation of overall signal intensity. The technique has been tested on the 15N spin-spin relaxation time measurements of a 110 amino acid domain of the F-actin cross-linking protein.

Adiabatic pulses

Adiabatic pulses are sometimes considered to be mysterious and exotic entities which are difficult to understand, complex to generate and impractical to implement. This work is an attempt to bring familiarity and to fulfill the preliminary needs of anyone interested in learning more about this subject. The response of magnetization to stimuli produced by adiabatic pulses is analyzed using vector representations in a frequency modulated rotating frame. The first section deals with basic principles of amplitude and frequency modulated pulses and a vector representation in a second rotating frame is used to explain how the adiabatic condition can be satisfied. The subsequent section explains the principles of offset independent adiabaticity. These principles are then used to design optimal functions for the amplitude, frequency, and magnetic field gradient modulations for adiabatic inversion pulses. The last section considers some practical aspects for those who want to develop methodologies involving adiabatic pulses.

A model of the inversion process in an arterial inversion experiment

A model of the behavior of spins moving through spatially varying gradient and B1 fields is presented. The model simulates the adiabatic behavior of flowing arterial water during a two-coil arterial inversion experiment. Predictions of the degree of inversion generated by the model are compared with flow phantom results for a wide range of gradient magnitudes, nominal B1 magnitudes, and flow velocities. The high level of agreement between the model and the flow phantom results indicates that the model can be used to help select efficient pulse sequence parameters when setting up an in vivo arterial inversion experiment. In addition, the model provides valuable insights into the adiabatic behavior of arterial spins. These insights could be useful in selecting an efficient surface coil geometry which achieves maximum inversion with a minimum B1 magnitude.

Localized 31P MR spectroscopy of the transplanted human kidney in situ shows altered metabolism in rejection and acute tubular necrosis

The purpose of this study was to investigate the function of transplant kidneys in situ, and to detect pathologic changes, using volume-selective phosphorous NMR spectroscopy (31P MRS). Localized 31P MR spectra were obtained from 37 patients using a whole-body MR scanner with a combination of surface coils, adiabatic excitation pulses, and a modified image-selected in vivo spectroscopy (ISIS) sequence. Seventeen patients with pathologic changes after renal transplant were compared with a control group of 20 patients with no evidence of transplant dysfunction. The transplant kidneys with rejection reaction showed higher ratios of inorganic phosphate (P2i) to adenosine triphosphate-alpha (ATP-alpha) than the normal control group (.4 +/- .16 compared with .22 +/- .11, P = .01) and reduced pH. The spectra of transplant kidneys with tubular necrosis had lower phosphomonoester (PME)/phosphodiester (PDE) ratios than the control group (.65 +/- .35 compared with .96 +/- .5, P = .04). The pathologies of rejection and tubular necrosis could be differentiated from each other by pH (6.93 +/- .1 in rejection versus 7.14 +/- .19 in tubular necrosis, P = .04). Preliminary results indicate that localized image-guided 31P MR spectroscopy of transplant kidneys in situ can detect rejection reactions and acute tubular necrosis noninvasively, providing an incentive for further research.

Single-shot, B1-insensitive slice selection with a gradient-modulated adiabatic pulse, BISS-8

An adiabatic pulse has been developed to accomplish uniform slice-selective excitation with a spatially inhomogeneous B1. This new pulse can generate a uniform, arbitrary flip angle that is determined by four adjustable phase shifts in the pulse. Self-refocused slice selection is achieved by modulating a B(O) gradient in concert with the pulse frequency (or phase) modulation. B1-compensated, self-refocused slice selection is demonstrated in computer simulations and phantom experiments using a surface transmitter/receiver coil. This adiabatic pulse can provide optimal performance in multislice MRI and localized spectroscopy when transmitting with an inhomogeneous B1.

A reduced power selective adiabatic spin-echo pulse sequence

We introduce a selective adiabatic pulse sequence suitable for generating selective spin-echoes for both MR imaging and spectroscopy. The technique is simple; one uses the echo generated by any pair of identical selective adiabatic inversion pulses. The nonlinear phase across the slice is compensated perfectly by the second pi pulse. This compensation is immune to RF inhomogeneity and nonlinearity. For imaging applications, we concentrate on a reduced-power version of the pulse sequence in which time is traded off variably for RF amplitude in the presence of a time-varying gradient. This technique, known as variable-rate excitation, mildly degrades the off-resonant slice profile when applied to amplitude-modulated pulses. We present theoretical explanations and experimental results that show that the variable-rate adiabatic pulses are immune to off-resonant degradation of the magnitude normally encountered in MR imaging.

In vivo monitoring of fructose metabolism in the human liver by means of 31P magnetic resonance spectroscopy

It has been shown that fructose metabolism in the human liver can be monitored quantitatively by means of 1H image-guided 31P MRS, implemented on a clinical MR imaging system equipped with surface coils and with appropriate data processing software. Temporal resolution of the 31P MRS measurements is of the order of 2 min.

The design of practical selective pulses for magnetic resonance imaging and spectroscopy using SPINCALC

Recently, we introduced a new numerical approach to the design and optimization of NMR selective pulses, which we have christened "SPINCALC" (J. T. Ngo and P. G. Morris, Biochem. Soc. Trans. 14, 1271 (1986); J. T. Ngo and P. G. Morris, Magn. Reson. Med. 5, 217 (1987]. The first practical application of pulses generated by SPINCALC is demonstrated on a standard 0.5-T clinical MRI system. Results are shown for single phase pi pulses suitable both for selective inversion and for selective refocusing. The extension of SPINCALC to multidimensional pulses is illustrated by the design of a two-dimensional pi pulse.

1H image-guided localized 31P MR spectroscopy of human brain: quantitative analysis of 31P MR spectra measured on volunteers and on intracranial tumor patients

1H image-guided 31P MR spectra of normal human brain and of intracranial tumors have been analyzed quantitatively. Tumor types examined include prolactinoma, lymphoma, and various grade gliomas. The experimental signals were processed by means of a time-domain least-square fitting procedure, which yields the spectral parameters, as well as a prediction of the standard deviations. Significant spectral variations are observed within both populations of normal brain and of intracranial tumor 31P MR spectra. The metabolic ratios derived from the glioma 31P MR spectra and from corresponding uninfiltrated brain tissue do not differ significantly. Significant differences are, however, observed between the metabolic ratios of prolactinoma and uninfiltrated tissue 31P MR spectra. Alkaline pH values are found for the prolactinoma and the high-grade gliomas. Furthermore, spectral differences are observed between the patient's uninfiltrated tissue 31P MR spectra and those of an unmatched population of volunteers. This underscores the necessity for control measurements on the uninfiltrated tissue of the patient and for controls from a matched population of healthy individuals.

Experimental approaches to image localized human 31P NMR spectroscopy

Experimental procedures for obtaining localized 31P NMR spectra of humans by means of the ISIS sequence are discussed in detail. The technique is optimized for use with volume coils and with surface coils in order to measure localized 31P NMR spectra of different tissues and organs. Selective frequency-modulated (FM) inversion and excitation pulses are applied for optimal inversion or excitation despite B1 inhomogeneity. Pulse imperfection may lead to spurious signal contributions from outside the selected volume; this contamination is reduced by using long pulse intervals, by properly ordering the ISIS acquisitions, and by using FM excitation pulses. Simultaneous measurement of multiple volumes was implemented by including an additional selective inversion pulse, and an extension of the ISIS addition/subtraction scheme. Localized T1 measurements with surface coils are implemented by using a B1-insensitive inversion pulse in the inversion recovery sequence. The quantitative reproducibility of localized 31P NMR spectra was verified. Absolute metabolite concentration can be determined after a suitable calibration of the 31P NMR spectrum. Localized shimming is required to obtain localized 31P NMR spectra of excellent spectral resolution. This is done by monitoring the 1H NMR signal from water by a single-shot localization technique. The techniques discussed can be applied to obtain spectra of brain, liver, heart, and other organs. 31P NMR spectra of intracranial tumors demonstrate its applicability in the examination of patients.