Spiral MRI

In Chapter 18 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss a type of magnetic resonance imaging called echo-planar imaging.

In EPI the echoes are not created using π pulses. Instead, they are created by dephasing the spins at different positions along the x axis using a G_x gradient, and then reversing that gradient to rephase the spins, as shown in Fig. 18.32. Whenever the integral of G_x(t) is zero, the spins are all in phase and the signal appears. A large negative G_y pulse sets the initial value of k_y to be negative; small positive G_y pulses (“blips”) then increase the value of k_y for each successive k_x readout. Echo-planar imaging requires strong gradients—at least five times those for normal studies—so that the data can be acquired quickly. Moreover, the rise and fall-times of these pulses are short, which induces large voltages in the coils. Eddy currents are also induced in the patient, and it is necessary to keep these below the threshold for neural activation. These problems can be reduced by using sinusoidally-varying gradient currents. The engineering problems are discussed in Schmitt et al. (1998); in Vlaardingerbroek and den Boer (2004); and in Bernstein et al. (2004).

Echo-Planar Imaging:
Theory, Technique and Application,
edited by Schmitt, Stehling, and Turner.

To learn more about “sinusoidally-varying gradient currents,” I consulted the first of the three references, Echo-Planar Imaging: Theory, Technique and Application, edited by Franz Schmitt, Michael Stehling, and Robert Turner (Springer, 1998). In his chapter on the “Theory of Echo-Planar Imaging,” Mark Cohen discusses a spiral echo-planar pulse sequence in which the gradient fields have the unusual form G_x = G_o t sin(ωt) and G_y = G_o t cos(ωt).

Below I show the pulse sequence, which you can compare with the echo-planar imaging sequence in Fig. 18.32 of IPMB if you have the book by your side (don’t you always keep IPMB by your side?). The top two curves are the conventional slice selection sequence: a gradient G_z (red) in the z direction is applied during a radiofrequency π/2 pulse B_x (black), which rotates the spins into the x-y plane. The unconventional readout gradient G_x (blue) varies as an increasing sine wave. It produces a gradient echo at times corresponding approximately to the extrema of the G_x curve (excluding the first small positive peak). The phase encoding gradient G_y (green), an increasing cosine wave, is approximately zero at the echo times, but will shift the phase and therefore impact the amplitude of the echo.

A pulse sequence for spiral echo-planar imaging,
based on Fig. 14 of “Theory of Echo-Planar Imaging,”
by Mark Cohen.

If you look at the output in terms of spatial frequencies (k_x, k_y), you find that the echos correspond to points along an Archimedean spiral.

The spiral echo-planar imaging technique as viewed in frequency space,
based on Fig. 13 of “Theory of Echo-Planar Imaging,” by Mark Cohen.

Spiral echo-planar imaging has some drawbacks. Data in k-space is not collected over a uniform array, so you need to interpolate onto a square grid before performing a numerical two-dimensional inverse Fourier transform to produce the image. Moreover, you get blurring from chemical shift and susceptibility artifacts. The good news is that you eliminate the rapid turning on and off of gradient pulses, which reduces eddy currents that can cause their own image distortions and possibly neural stimulation. So, spiral imaging has advantages, but the pulse sequence sure looks weird.

Echo-planar imaging in general, and spiral imaging in particular, are very fast. In his chapter on “Spiral Echo-Planar Imaging,” Craig Meyer discusses his philosophy about using EPI.

Spiral scanning is a promising alternative to traditional EPI. The properties of spiral scanning stem from the circularly symmetric nature of the technique. Among the attractive properties of spiral scanning are its efficiency and its good behavior in the presence of flowing material; the most unattractive property is uncorrected inhomogeneity leads to image blurring. Spiral image reconstruction can be performed rapidly using gridding, and there are a number of techniques for compensating for inhomogeneity. There are good techniques for generating efficient spiral gradient waveforms. Among the growing number of applications of spiral scanning are cardiac imaging, angiography, abdominal tumor imaging, functional imaging, and fluoroscopy.

Spiral scanning is a promising technique, but at the present it is still not in routine clinical use. There are many theoretical reasons why spiral scanning may be advantageous for a number of clinical problems, and initial volunteer and clinical studies have yielded very promising results for a number of applications. Still, until spiral scanning is established in routine clinical use, some caution is warranted about proclaiming it to be the answer for any particular question.