Application of optimal control to CPMG refocusing pulse design

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.     

Categories of coherence pathways for the CPMG sequence

The CPMG sequence has been extremely useful for efficient measurements of NMR signal, spin-spin relaxation, and diffusion, particularly in inhomogeneous magnetic fields, such as when samples are outside the magnet and RF coil. Due to the inaccuracy of the pulses and the off-resonance effects, the CPMG echoes have contributions from the Hahn echo as well as signals that are similar to stimulated echoes. The systematic understanding of the CPMG pulse sequence requires decomposing the magnetization dynamics into different coherence pathways. In this paper, we describe a method to classify the CPMG coherence pathways and illustrate the nature of these types of pathways. This classification shows that direct echo and stimulated echoes are the major contribution to the CPMG signal. It also provides a clear understanding of the effect of restricted diffusion in porous media.     

Scaling of dynamical decoupling for spin qubits

We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.     

Simple two-pulse time-reversal sequence for dipolar and quadrupolar-coupled spin systems

We demonstrate, both theoretically and experimentally, that two-pulse sequence (2n+1) X 90 degrees(Y) - 90 degrees(X) -Acq(t) without delay between pulses, yields the reverse of time evolution of spin system with dipolar and quadrupole interactions. This process results in refocusing of the spin magnetization into magic echo at te = t1/2 after the second pulse, where t1 is the length of the first pulse.     

Spin-lock techniques and CPMG imaging sequences: a critical appraisal of T1p contrast at 0.15 T

The addition of a spin-lock preparatory sequence to a Carr-Purcell-Meiboom-Gill (CPMG) imaging sequence provides a method which allows an accurate and simple comparison of T1p and T2 contrast. Sagittal and axial brain images, produced with the application of a three pulse preparatory spin-lock sequence prior to a sixteen-echo CPMG imaging sequence, are compared with images acquired without the spin-lock sequence. The CPMG sequence uses non-selective refocusing pulses. Therefore, observed echo signals accurately reflect T2 relaxation. This allows a convenient method for assessing the degree to which T1p and T2 contrast differ. The spin-lock CPMG (SL-CPMG) images were acquired with a spin-locking field amplitude of 0.4 G and resemble heavily T2-weighted images at 0.15 T. Quantitative analyses of signal intensities from edema and normal brain tissue confirm the qualitative observations. This in vivo method should prove useful for determining when the additional RF power deposition associated with spin-locking techniques will provide an alternate form of tissue contrast than that available from additional echo collection.     

Quantitative evaluation of the lactate signal loss and its spatial dependence in press localized (1)H NMR spectroscopy

Localized (1)H NMR spectroscopy using the 90 degrees -t(1)-180 degrees -t(1)+t(2)-180 degrees -t(2)-Acq. PRESS sequence can lead to a signal loss for the lactate doublet compared with signals from uncoupled nuclei which is dependent on the choice of t(1) and t(2). The most striking signal loss of up to 78% of the total signal occurs with the symmetrical PRESS sequence (t(1)=t(2)) at an echo time of 2/J (approximately 290 ms). Calculations have shown that this signal loss is related to the pulse angle distributions produced by the two refocusing pulses which leads to the creation of single quantum polarization transfer (PT) as well as to not directly observable states (NDOS) of the lactate AX(3) spin system: zero- and multiple-quantum coherences, and longitudinal spin orders. In addition, the chemical shift dependent voxel displacement (VOD) leads to further signal loss. By calculating the density operator for various of the echo times TE=n/J, n=1, 2, 3,..., we calculated quantitatively the contributions of these effects to the signal loss as well as their spatial distribution. A maximum signal loss of 75% can be expected from theory for the symmetrical PRESS sequence and TE=2/J for Hamming filtered sinc pulses, whereby 47% are due to the creation of NDOS and up to 28% arise from PT. Taking also the VOD effect into account (2 mT/m slice selection gradients, 20-mm slices) leads to 54% signal loss from NDOS and up to 24% from PT, leading to a maximum signal loss of 78%. Using RE-BURP pulses with their more rectangular pulse angle distributions reduces the maximum signal loss to 44%. Experiments at 1.5 T using a lactate solution demonstrated a maximum lactate signal loss for sinc pulses of 82% (52% NDOS, 30% PT) at TE=290 ms using the symmetrical PRESS sequence. The great signal loss and its spatial distribution is of importance for investigations using a symmetrical PRESS sequence at TE=2/J.     

优化重聚脉冲提高梯度场核磁共振信号强度

缩短射频脉冲宽度, 有助于解决脉冲电力消耗大、样品吸收率高、信噪比低等极端条件核磁共振探测的关键问题. 本文首先分析射频脉冲角度对核磁共振自旋回波信号强度的影响机理, 基于Bloch方程推导了回波信号幅度与扳转角、重聚角的关系. 在特制核磁共振分析仪上采用变脉冲角度技术, 分别在均匀磁场和梯度磁场条件下实现对扳转角和重聚角与回波信号强度关系的数值模拟和实验测量. 结果表明, 梯度场中, 扳转角为90°、重聚角为140°的射频脉冲组合获得最大首波信号强度, 比180°脉冲对应的回波幅值提高13%, 能耗降低至78%. 选用该重聚角(140°) 优化设计饱和恢复脉冲序列探测流体的纵向弛豫时间T₁特性, 准确获得 T₁分布.该结果对于低电力供应、且对信噪比有较高要求的核磁共振测量, 如随钻核磁共振测井和在线核磁共振快速检测等, 具有重要意义. 关键词： 核磁共振 信号强度 重聚脉冲角度 Bloch方程     

A comparison and evaluation of reduced-FOV methods for multi-slice 7 T human imaging

Eight different reduced field-of-view (FOV) MRI techniques suitable for high field human imaging were implemented, optimized, and evaluated at 7 T. These included selective Inner-Volume Imaging (IVI) based methods, and Outer-Volume Suppression (OVS) techniques, some of which were previously unexplored at ultra-high fields. Design considerations included use of selective composite excitation and adiabatic refocusing radio-frequency (RF) pulses to address B1 inhomogeneities, twice-refocused spin echo techniques, frequency-modulated pulses to sharply define suppressed regions, and pulse sequence designs to improve SNR in multi-slice scans. The different methods were quantitatively compared in phantoms and in vivo human brain images to provide measurements of relative signal to noise ratio (SNR), power deposition (specific absorption rate, SAR), suppression of signal, artifact strength and prevalence, and general image quality. Multi-slice signal losses in out-of-slice locations were simulated for IVI methods, and then measured experimentally across a range of slice numbers. Corrections for B1 nonuniformities demonstrated an improved SNR and a reduction in artifact power in the reduced-FOV, but produced an elevated SAR. Multi-slice sequences with reordering of pulses in traditional and twice-refocused IVI techniques demonstrated an improved SNR compared to conventional methods. The combined results provide a basis for use of reduced-FOV techniques for human imaging localized to a small FOV at 7 T.     

Comparison of electron spin relaxation times measured by Carr-Purcell-Meiboom-Gill and two-pulse spin-echo sequences

Electron spin relaxation times obtained by two-pulse spin-echo and Carr-Purcell-Meiboom-Gill (CPMG) experiments were compared for samples with: (i) low concentrations of nuclear spins, (ii) higher concentrations of nuclear spins and low concentrations of unpaired electrons, (iii) higher concentrations of nuclear spins and of electron spins, and (iv) dynamic averaging of inequivalent hyperfine couplings on the EPR timescale. In each case, the CPMG time constant decreased as the time between the refocusing pulses increased. For the samples with low concentrations of nuclear spins (the E' center in irradiated amorphous SiO2) the limiting value of the CPMG time constant at short interpulse spacings was similar to the Tm obtained by two-pulse spin echo at small turning angle. For the other samples, the time constants obtained by CPMG at short interpulse spacings were systematically longer than Tm obtained by two-pulse spin echo. For most of the samples, the CPMG time constant decreased with increasing electron spin concentration, which is consistent with the expectation that the CPMG sequence does not refocus dephasing due to electron-electron dipolar interaction between resonant spins. Dynamic processes that average inequivalent hyperfine couplings contributed less to the CPMG time constant than to the spin-echo decay time constant. The impact of nuclear echo envelope modulation on CPMG time constants also was examined. For a Nycomed trityl radical in glassy D2O:glycerol-d8 solution, the CPMG time constant was up to 20 times longer when the time between pulses was approximately equal to integer multiples of the reciprocal of the deuterium Larmor frequency than when the time between pulses was an odd multiple of half the reciprocal of the deuterium Larmor frequency.     

NMR spectroscopy in inhomogeneous B0 and B1 fields with non-linear correlation

Resolved NMR spectra from samples in inhomogeneous B0 and B1 fields can be obtained with the so-called "ex situ" methodology, employing a train of composite or adiabatic z-rotation RF pulses to periodically refocus the inhomogeneous broadening during the detection of the time-domain signal. Earlier schemes relied on a linear correlation between the inhomogeneous B0 and B1 fields. Here the pulse length, bandwidth, and amplitude of the adiabatic pulses of the hyperbolic secant type are adjusted to improve the refocusing for a setup with non-linear correlation. The field correlation is measured using a two-dimensional nutation experiment augmented with a third dimension with varying RF carrier frequency accounting for off-resonance effects. The pulse optimization is performed with a computer algorithm using the experimentally determined field correlation and a standard adiabatic z-rotation pulse as a starting point for the iterative optimization procedure. The shape of the z-rotation RF pulse is manipulated to provide refocusing for the conditions given by the sample-, magnet-, and RF-coil geometry.     

Use of Carr-Purcell pulse sequence with low refocusing flip angle to measure T₁ and T₂ in a single experiment

The Carr-Purcell pulse sequence, with low refocusing flip angle, produces echoes midway between refocusing pulses that decay to a minimum value dependent on T(2). When the refocusing flip angle was π/2 (CP(90)) and τ>T(2), the signal after the minimum value, increased to reach a steady-state free precession regime (SSFP), composed of a free induction decay signal after each pulse and an echo, before the next pulse. When τ相似文献   

Diffusion in porous building materials with high internal magnetic field gradients

An algorithm to calculate NMR signals of a multi-echo pulse sequence with arbitrary position dependent B0 and B1 fields taking into account relaxation and spin-diffusion is presented. The multi-echo pulse sequence consists of an initial RF pulse ("90 degrees " RF pulse) and a series of L refocusing RF pulses with arbitrary phases and flip-angles. The calculation is exact and takes into account all the magnetization pathways that contribute to the signal on a predefined spatial grid. The theoretical prediction is verified experimentally using a high field NMR microscopy system. The algorithm was implemented in a simulation program in order to optimize the design of an inside-out MR intra-vascular catheter that is used for characterization of vessel wall tissue. Measured data obtained with the catheter are in good agreement with the theoretical prediction of the simulation.     

Lactate quantification by means of press spectroscopy—Influence of refocusing pulses and timing scheme

The quantitative assessment of lactic acid in tissue is an important goal for in vivo volume-selective NMR spectroscopy to aid in the noninvasive diagnosis of oxygen deficiency or other metabolic disorders. PRESS localized ¹H spectra provide comparatively high signal-to-noise ratio from small volume elements in a single acquisition mode. The quantification of lactate after multipulse excitation is not trivial due to the J-coupling characteristics which do not occur for the substances serving as references. The influence of the timing scheme and of the quality of the refocusing pulses was systematically evaluated for the lactate resonances by volume-selective measurements. Gaussian pulses, Hanning-filtered sinc pulses, and numerically optimized RE-BURP-pulses were applied for refocusing the magnetization in the PRESS sequence and the effects on the lactate AX₃ spin system were compared. For these pulses, sequence parameters are presented providing high sensitivity to lactate signals. Timing schemes are shown which provide good quantification of lactate, even in cases with B₁-inhomogeneities or slight misadjustment of the transmitter amplitude. The combination of both echo times in the double-echo sequences clearly influences the signal characteristics of lactate at overall echo times near TE = 145 and 290 ms, which may result in pure in-phase magnetization for this weakly coupled homonuclear system. Numerically optimized refocusing pulses (RE-BURP) provided up to 50% higher signal ratio of the methyl protons of lactate to uncoupled nuclei than the often used Hanning-filtered sinc pulses.     

Encoding of diffusion and T1 in the CPMG echo shape: single-shot D and T1 measurements in grossly inhomogeneous fields

We present a new approach of NMR measurements in the presence of grossly inhomogeneous fields where information is encoded in the echo shape of CPMG trains. The method is based on sequences that consist of an initial encoding sequence that generates echoes with contributions from at least two different coherence pathways that are then both refocused many times by a long string of closely spaced identical pulses. The generated echoes quickly assume an asymptotic shape that encodes the information of interest. High signal-to-noise ratios can be achieved by averaging the large number of echoes. We demonstrate this approach with different implementations of the measurements of longitudinal relaxation time, T(1), and diffusion coefficient, D. It is shown that the method can be used for novel single-shot measurements.     

Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.     

Sequence parameters of double spin-echo sequences affect quantification of citrate

Quantification of citrate by localized ¹H spectroscopy is usually performed using the water signal as reference, but the signal behavior of the J-coupled AB spin system of citrate after multipulse excitation is not as trivial as for uncoupled substances. The influence of the timing scheme of double spin-echo sequences and of the spatial flip angle distribution of (nonideal) refocusing pulses was analyzed systematically for the citrate resonances. Both single echo times of the double spin-echo sequence were varied between 20 ms and 250 ms in theoretical and experimental approaches. Relatively long total echo times (TE > 120 ms) provide high selectivity to citrate signals, since signals from triglycerides at 2.6 ppm are markedly reduced. Asymmetrical timing schemes of the double spin-echo sequence with one short single echo time of 20 ms and one longer single echo time of about 120 ms result in high integral signal from the central lines of citrate, whereas symmetrical timing leads to high sensitivity for total echo times TE near 100 ms. The integral citrate signals in spectra with relatively long echo times (TE > 120 ms) were found to depend markedly on the type of the refocusing pulses, affecting quantitative citrate measurements in vitro and in vivo.     

Selective saturation in strongly inhomogeneous magnetic fields

The possibility to produce selective saturation by nuclear magnetic resonance (NMR) sequences of low-power radio-frequency pulses in strongly inhomogeneous magnetic fields is explored. The saturation of parts of the sensitive volume is produced by a particular pulse sequence with reduced amplitude distribution and the spectrum of the recorded signal is compared with the simulated spectrum. The spectra of the recorded free induction decays and echo signals are in good agreement with the simulated spectra of the pulse sequence, which demonstrates the effect of the selective saturation. The results obtained are an important step towards the development of new mobile and lowpower NMR equipments operating with inhomogeneous magnetic fields.     

The effects of slice-selective excitation/refocusing in localized spectral editing with gradient-selected double-quantum coherence transfer

Spectral editing using gradient-selected double-quantum filtering (DQF) with PRESS localization has been used for selective observation of metabolites in vivo. In previous studies using localized DQF sequences, it is generally assumed that the slice-selective pulses used in the sequence have no roles in coherence transfer, and do not interfere with DQF. To validate this assumption, the effects of slice-selective excitation/refocusing on DQF were investigated in DQF lactate editing sequences combined with PRESS localization. Contrary to the previous assumption, the results show that, due to chemical shift displacement artifact and J coupling, slice selection in DQF does interfere with coherence transfer, affecting both the accuracy of spatial localization and the detection sensitivity adversely. In the case of lactate editing, the effects of this interference can be accounted for simply by adjusting the strength of the slice-selection gradients and by using narrowband slice-selective refocusing pulses.     

The generating functions formalism for the analysis of spin response to the periodic trains of RF pulses. Echo sequences with arbitrary refocusing angles and resonance offsets

The generating functions (GF) formalism was applied for calculation of spin density matrix evolution under the influence of periodic trains of RF pulses. It was shown that in a general case, closed expression for the generating function can be found that allows in many cases to derive analytical expressions for the generating function of spin density matrix (magnetization, coherences). This approach was shown to be particularly efficient for the analysis of multi-echo sequences, where one has to average over various frequency isochromats. The explicit analytical expressions for the generating function for echo amplitudes in a Carr–Purcell–Meiboom–Gill (CPMG) echo sequence, a multiecho sequence with incremental phase of refocusing pulse, a gradient echo sequence including transient period were obtained for an arbitrary flip angle and an arbitrary resonance offset. Comparison of the theory and the spin-echo experiments was done, demonstrating a good agreement.     

Partial angle inversion recovery (PAIR) MR imaging: spin-echo and snapshot implementation.

The effects of varying the inversion or excitation RF pulse flip angles on image contrast and imaging time have been investigated in IR imaging theoretically, with phantoms and with normal volunteers. Signal intensity in an IR pulse sequence as a function of excitation, inversion and refocusing pulse flip angles was calculated from the solution to the Bloch equations and was utilized to determine the contrast behavior of a lesion/liver model. Theoretical and experimental results were consistent with each other. With the TI chosen to suppress the fat signal, optimization of the excitation pulse flip angle results in an increase in lesion/liver contrast or allows reduction in imaging time which, in turn, can be traded for an increased number of averages. This, in normal volunteers, improved spleen/liver contrast-to-noise ratio (9.0 vs. 5.7, n = 8, p less than 0.01) and suppressed respiratory ghosts by 33% (p less than 0.01). Reducing or increasing the inversion pulse from 180 degrees results in shorter TI needed to null the signal from the tissue of interest. Although this decreases the contrast-to-noise ratio, it can substantially increase the number of sections which can be imaged per given TR in conventional IR imaging or during breathold in the snapshot IR (turboFLASH) technique. Thus, the optimization of RF pulses is useful in obtaining faster IR images, increasing the contrast and/or increasing the number of imaging planes.