Gradient Spin Echoes for Selective Excitation

Shaped excitation pulses can replace the non-selective hard pulses typically used in a one-pulse measurement to achieve selective excitation. Another method of achieving selective excitation is the gradient spin echo using a selective 180° pulse. This technique is demonstrated in the figure below. A non-selective hard 90°_x pulse is first given followed by a pair of identical pulsed field gradients sandwiching a soft selective 180° pulse about the y axis. The hard 90° pulse rotates all spin vectors onto the -y axis. During the first gradient pulse the spin vectors dephase and evolve according to their offset frequencies. The soft 180°_y pulse flips a single resonance 180° about the y axis leaving all other resonances untouched. During the second gradient pulse, the "selected" resonance is rephased and its offset frequency evolution is refocused. The unselected resonances dephase more and continue to evolve according to their offset frequencies. The receiver is then turned on to collect the FID of the "selected" resonance, all others are dephased and therefore suppressed. This is demonstrated in the figure below which shows ¹H NMR spectra for a mixture of methylence chloride and acetone. The bottom trace shows a standard one-pulse measurement. The middle and top traces show results from a selective gradient spin echo measurement with the selective 180° pulse set for methylene chloride and acetone, respectively.

The Dephasing Power of Pulsed Field Gradients

Pulsed field gradients are used in many modern NMR measurements to select specific coherence pathways and eliminate (or at least minimize) the need for time consuming pulse and receiver phase cycles. The gradients are most often used in conjunction with spin echos such that unwanted coherences can be dephased and the desired coherences can be rephased. They are also used to measure diffusion constants or collect DOSY data. It is instructive to examine the magnetization vectors in the active volume of an NMR tube as a function of the gradient strength after the delivery of a 90° pulse. While a gradient is applied, the magnetization vectors precess at frequencies in the rotating frame which depend on their position in the NMR tube along the axis of the gradient. When the gradient is turned off, all of the magnetization vectors again precess at the same frequency however the phases of the vectors remain as they were at the end of the gradient. The top part of the first figure shows a series of 6 cases where z gradients of increasing strength are delivered after a 90°_-x pulse. Each case shows 8 equally spaced slices of the NMR tube on the z axis (the center of the sample is between the 4th and 5th slices). The stronger the gradient the larger the dephasing angle between slices. In this figure, the receiver is assumed to be on the y axis. From left to right, the number of degrees of dephasing between slices are 0° (no gradient), 22.5°, 45°, 67.5°, 90° and 112.5°. The y components of all the vectors are added and the sum is shown in blue below. One can see the the y magnetization decreases and oscillates about zero as a function of the gradient strength. This is illustrated more clearly in the bottom part of the figure which shows a plot of y magnetization as a function of gradient strength for a numerical calculation done using 50 slices. The second figure demonstrates this experimentally. It shows the 500 MHz ¹H NMR spectrum of HDO using the pulse sequence shown in the figure as a function of the % gradient strength (100% ~ 0.5 T/m). The gradient pulses were 1 msec in duration and rectangular in shape. One can see that the intensity profile matches closely to that predicted in the bottom of the first figure. The sample is almost entirely dephased using only 2% of the maximum gradient strength.

Gradient Recovery Times

Many pulse sequences employ pulsed field gradients for coherence selection thereby minimizing or eliminating the need for phase cycling. The routine use of pulsed field gradients has dramatically reduced the data collection times needed for many 2D experiments and therefore increased the throughput and productivity of NMR spectrometers. The field gradient coils in modern high resolution NMR probes surround the rf coils and are powered by an amplifier in the NMR spectrometer console. When a pulsed field gradient (typically 1 -2 msec in duration) is applied, the sample is no longer in a homogeneous magnetic field. When the gradient is turned off, the system must recover from the disturbance. This recovery is not instantaneous. Pulse sequences typically have delays of 50 - 200 μsec following a gradient pulse to allow for recovery of field homogeneity. The time for recovery after a gradient pulse depends on the design of the NMR probe, the strength and shape of the gradient pulse as well as the shielding between the gradient coils and the shim coils. One can measure the time required for recovery by applying a gradient pulse, and then collecting an NMR spectrum after a variable delay. In the figures below, the gradient recovery time was measured using a console equipped with gradients of maximum strength 50 G/cm, and a narrow bore 500 MHz broadband probe adapted to fit in a wide bore magnet. The duration of the gradient pulses was set to 1 msec. The first figure below shows the proton NMR data for a sample of doped 1% H₂O in D₂O with a line width of approximately 4 Hz with short term recovery times from 1 to 20 µsec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine bell shaped gradient pulse of 100 % strength. One can see that for the rectangular gradients the full intensity of the line is recovered in as little as 10 µsec. When the sine bell shaped gradient pulse is used, the full intensity of the line is recovered in less than 1 microsecond. This faster recovery is the result of the gradual rise and fall of the gradient strength in the sine bell shaped pulse.

A 4 Hz line is not a very sensitive gauge for the measurement of recovery times, so the experiments were repeated for a sample with a line of ~0.3 Hz in width where the line shape could be examined in detail at longer recovery times. The second figure shows the proton NMR data for a sample of 1% CHCl₃ in acetone-d₆ with a line width of approximately 0.3 Hz with long term recovery times from 50 to 800 msec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine shaped gradient pulse of 100 % strength. One can see that in all cases a reasonable line shape is recovered in ~ 400 msec. The shape of the gradient pulse does not seem to influence the time required to recover a good line shape.

Gradient Calibration - 1D MRI

When people think about magnetic resonance imaging (MRI), they often think about the huge whole body imagers in hospitals. NMR spectroscopists use one dimensional MRI in a specially prepared sample to calibrate the Z gradient strength of their spectrometers. The sample consists of a plastic disk with a precisely known thickness immersed in a column of water (see the figure below). 1D MRI is conceptually quite simple - a linear field gradient is applied during the collection of an FID. Since the magnetic field varies across the sample and the NMR frequency is proportional to the magnetic field strength, the resulting NMR spectrum represents a one dimensional image of the sample. The spectrum has a "notch" missing as a result of the plastic disk. The width of the "notch" is proportional to the applied gradient strength and the thickness of the plastic disk. If the thickness of the plastic disk is precisely known, then the strength of the applied gradient can be calculated. The spectrum is rounded at the edges as a result of the gradient strength falling off away from the center of the sample. A modified version of this experiment using an echo is used as a routine method of calibrating gradient strengths.