Visualizing Slice Selection and Shaped Pulse Excitation profiles

What is slice selection?

Routinely used in MRI, slice-selection refers to the excitation and observation of signals from only a specific, well-defined ‘slice’ of the sample, instead of the whole sample. In MRI, this could be a ‘slice’ of the human brain:

Magnetic field gradient causes the center frequency (Fc) of each slice to vary by position. The range of frequencies (ΔF) contained in a slice depends on slice thickness (ΔF) and the strength of the gradient (Gss).

Source: https://mriquestions.com/slice-selective-excitation.html 

From an high-resolution NMR perspective, it most often refers to selectively observing different parts of the typical NMR tube, as described here in Glenn Facey’s blog. 

As also described in Facey’s blog, slice-selection is achieved by applying a linear gradient simultaneously with the excitation pulse, which is usually a shaped RF pulse. A key difference between slice selection in imaging applications vs high-resolution NMR is that imaging applications normally use 3-axes (x,y,z) gradients while most NMR slice selection is done via a single-axis gradient, which is usually along the main magnetic (B0) field (z-axis). 

A gradient (G) along z creates a linear magnetic field distribution as a function of the z position (see illustration below). Thus, the Larmor frequency also acquires a dependence on the spatial position, as given by Equation 1, which reduces to ν(z) = ν0 at the isocenter of the magnet. 

Equation 1

With this linear gradient on, the application of a frequency selective RF pulse excites only a selective range of frequencies, and hence only selective spatial positions.

The thickness of the slice is dependent on the strength of the magnetic field gradient (G) and the bandwidth of the RF pulse. With the pulse bandwidth kept constant, a stronger gradient selects a thinner slice. The same can also be achieved by decreasing the RF bandwidth (increasing the pulse duration) while keeping the gradient strength constant. While on-resonance, both approaches lead to the same spatial slice, but the former approach is preferred as it leads to a smaller chemical shift displacement [1].

The spatial position of the slice is determined by the gradient strength and the transmitter frequency of the RF pulse (νRF). While the gradient creates the spatial distribution of frequencies, the RF transmitter frequency and RF bandwidth determines which frequencies will be excited. When νRF = ν0 (Larmor frequency), the spins in the middle (isocenter) of the magnet are excited. To excite a slice at a distance from the isocenter, νRF needs to be adjusted according to Eq. 1.

The gradient strength (Gz) required to select a particular slice thickness (Dslice) for a given RF pulse duration (thus bandwidth, BW) can be calculated using Equation 2.

Equation 2

The gradient unit of kHz.cm-1 can be converted to the more familiar Gauss(G).cm-1 or mT.m-1 by using the Proton gyromagnetic ratio 4257.6 Hz.Gauss-1.

Once the gradient strength is determined, the slice position can be adjusted by changing the transmitter frequency according to Eq. 1 as follows:

Why can’t we just use a hard pulse for slice-selection?

While performing slice-selection, it is important that the slices have well-defined boundaries, such that there is minimal out-of-slice excitation. The shape of the slice, thus the boundaries, is defined by the excitation profile of the RF pulse. The excitation profile of a hard/square/rectangular pulse has a ‘sinc’ shape with ill-defined boundaries, while commonly used shaped pulses are designed to produce well-defined transition and suppression bands. For instance, compare the frequency profile of a rectangular pulse vs that of a commonly used sinc-3 (time-bandwidth=6) pulse, both of 1-ms duration.

Waveforms

Excitation profile

It is easy to see that the sinc pulse has a sharper transition between the excitation and suppression bands, and is more suitable for slice selection.

Visualizing Slice Selection

The shape of a slice can be visualized experimentally by employing a ‘gradient-echo imaging’ pulse-sequence shown below:

The rephasing gradient following the slice-selection gradient/pulse pair refocuses the dephasing of magnetization that occurs during the excitation. The gradient just preceding the readout /acquisition prepares the transverse magnetization for encoding of spatial information during acquisition. The ‘readout’ gradient enables acquisition of spatially dependent frequencies, which gives the spatial spin distribution upon Fourier transformation. For more details on slice-selection experiments, please see Chapter 4 of Reference [1].

Let us look at some real ‘1D images’ of slice selection acquired using the above sequence on a 1.04 Tesla NMR spectrometer (Spinsolve, Magritek), with a standard 5-mm NMR tube. Note that on this magnet, the B0 (z) direction is horizontal in the laboratory frame and thus perpendicular to the NMR tube axis, and it is equipped with a z-gradient of ~200 mT/m peak amplitude. We will compare two different RF pulses - a standard 5-lobe sinc pulse and a Shinnar-Le Roux (SLR) optimized excitation pulse -  both 1-ms long with time-bandwidth product (R) = 6. The RF waveforms and their respective simulated excitation profiles are shown below:

And here are the experimental gradient-echo images of a ~0.78-mm slice obtained using the two pulses above. The slice-selection gradient for this slice-thickness was ~180 mT/m (90% of peak amplitude). Notice how the slice profile closely matches the simulated excitation profile above.

We can also vary the gradient strength to select different slice thicknesses, as illustrated below, where the gradient strength was varied from 10% (thickest slice) to 90% (thinnest slice). The outermost envelope represents the non-slice selective version of the same experiment, using a hard pulse for excitation.

Thus we can see that the choice of the excitation pulse had a significant effect on the shape of the slice, which is a direct reflection of the RF pulse’s excitation profile. While the sinc pulse has a marginally more narrow transition band, it has significantly more out of band excitation, which is not desirable. A lot of work in NMR literature has been dedicated to designing RF pulses with very well-defined excitation profiles - narrow transition bands, a flat top, and minimal out of band excitation - but that is a topic for another day. 

References

1. De Graaf, R. A. (2019). In vivo NMR spectroscopy: principles and techniques. John Wiley & Sons.