## Imperfect MRI Pulse Sequences

A class of image artifact exists that is caused by imperfect design or execution of the MRI pulse sequence. In a well-engineered scanner with carefully crafted pulse sequences that is operated by an expert technologist, few of these problems should arise. But inevitably there will be occasions when practical constraints require that compromises be made, and image artifacts of the sort described next can occur. The aim of this section is to briefly describe the origin of such artifacts and show examples that should enable their presence to be recognized.

### 6.1 Truncation Artifacts

Truncation of the MRI data may occur both in the extent to which k-space is sampled and in the way the signal is digitized by the scanner receiver. Examples of both types of truncation are shown in Fig. 8. Clearly, it is always necessary to truncate the coverage of k-space, since one cannot practically sample an infinite space! But if the number of lines of k-space sampled has been reduced and zero-filled in either the readout or phase-encode dimensions, then a ringing artifact will be observed in the image. An example of this is shown in Fig. 8b, which shows ringing in the vertical ( phase-encode) dimension. This is because only 128 lines were collected in the phase-encode dimension, whereas 256 points were collected in the readout dimension. Thus, in the phase-encode (vertical) dimension, the effect is to multiply the k-space data, S(kx, ky) by a top hat function, n(ky), in the ky dimension. Standard Fourier transform theory predicts that when the resulting k-space data are Fourier transformed one obtains FT{S(kx, ky)}® FT{n(ky)}. The Fourier transform of the ideal S(kx, ky) is p(x, y), and the Fourier transform of n(ky) is a sinc function. This results in a Gibbs ringing of the image in the undersampled dimension, an effect that is particularly prominent close to a sharp intensity transition in the data. Figure 8b

FIGURE 7 Images showing the chemical-shift artifact from superimposed lipid and water images, (a) A conventional 1.5-tesla image of the leg in which no fat suppression was employed. Note the horizontal misalignment of the surface fatty tissue and the bone marrow relative to the water signal from the muscle. (b) A 3-tesla spin-echo EPI image, also collected without fat saturation. The lipid image is shifted in the readout dimension by 7 pixels (220 Hz) in a 256-pixel matrix (8 kHz bandwidth) in (a) and in the phase-encode dimension by 20 pixels (410 Hz) in a 64-pixel matrix (1.29 kHz effective bandwidth) in (b).

clearly shows this Gibbs ringing in the vertical dimension when compared with an image of the ideal Shepp-Logan phantom shown in Fig. 8a. The intensity of the Gibbs ringing may be minimized by preapodization of the truncated fc-space data by a smoothly varying function (e.g., a Gaussian). This reduces the sharpness of the top-hat function, but degrades the point-spread function in the resulting image.

A truncation of the fc-space data can also be caused when the signal that is sent to the receiver is too large to be represented by the analog-to-digital converter (ADC). If the receiver gain has been correctly set up on the scanner, then this artifact

FIGURE 8 Rogues' gallery of acquisition artifacts. (a) The computergenerated 256 x 256 pixel Shepp-Logan head phantom. (b) Gibbs ringing caused by collecting only l28 lines of fc-space in the phase encode direction and zero-filling up to 256. (c) The effect of clipping the data in the ADC process (receiver overflow). The background has been intentionally raised. (d) The zipper artifact caused by adding an unwanted FID decay from a misset spin echo sequence. (e) Phase-encode direction aliasing resulting from an off-isocenter subject. (f) The aliasing effect of reducing the phase-encode direction field-of-view in a spin echo sequence. (g) How additional moire fringes are induced in the aliased regions of a gradient-echo sequence. (h) The effect of an unwanted phase-encoded echo (stimulated echo, etc.) that is predominantly shifted in fcx only. (i) The effect of an unwanted phase-encoded echo that is shifted both in fcx and fcy.

FIGURE 8 Rogues' gallery of acquisition artifacts. (a) The computergenerated 256 x 256 pixel Shepp-Logan head phantom. (b) Gibbs ringing caused by collecting only l28 lines of fc-space in the phase encode direction and zero-filling up to 256. (c) The effect of clipping the data in the ADC process (receiver overflow). The background has been intentionally raised. (d) The zipper artifact caused by adding an unwanted FID decay from a misset spin echo sequence. (e) Phase-encode direction aliasing resulting from an off-isocenter subject. (f) The aliasing effect of reducing the phase-encode direction field-of-view in a spin echo sequence. (g) How additional moire fringes are induced in the aliased regions of a gradient-echo sequence. (h) The effect of an unwanted phase-encoded echo (stimulated echo, etc.) that is predominantly shifted in fcx only. (i) The effect of an unwanted phase-encoded echo that is shifted both in fcx and fcy.

should never be seen in the image data. But it is surprising how often this artifact ¿5 seen. An example of ADC overflow is shown in Fig. 8c. The image background has been intentionally raised to reveal the presence of a slowly modulating pattern in the background of the image (and also in the image itself). The artifact is easily understood as a misrepresentation of the low spatial frequency regions of fc-space. This is because the low spatial frequencies (around the center of fc-space) contain the bulk of the signal and are, therefore, those regions most likely to be clipped by an incorrectly set ADC gain. Once it is present in the data, this is a difficult artifact to correct.

### 6.2 Non-Steady-State Effects

The purpose of magnetic resonance imaging is to obtain spatially determined information on some contrast mechanism of interest. The contrast may simply be the spin density of the nucleus, p(x, y), or some manipulation to the spin density may

FIGURE 7 Images showing the chemical-shift artifact from superimposed lipid and water images, (a) A conventional 1.5-tesla image of the leg in which no fat suppression was employed. Note the horizontal misalignment of the surface fatty tissue and the bone marrow relative to the water signal from the muscle. (b) A 3-tesla spin-echo EPI image, also collected without fat saturation. The lipid image is shifted in the readout dimension by 7 pixels (220 Hz) in a 256-pixel matrix (8 kHz bandwidth) in (a) and in the phase-encode dimension by 20 pixels (410 Hz) in a 64-pixel matrix (1.29 kHz effective bandwidth) in (b).

be made to induce some other contrast mechanism of interest (e.g., T1 weighting, T2 weighting, diffusion weighting). Regardless, it is vital in a modern scanning environment to optimize the quality of data at acquisition and to minimize the duration of the scan itself. To this end, many pulse sequences are run in a partially saturated state — in other words, a state in which only partial recovery of longitudinal magnetization is allowed between subsequent excitations of the spin system. When this is the case, any variation in the repeat time between spin excitations, TR, will lead to varying amounts of longitudinal magnetization recovery. It is this longitudinal magnetization that is tipped into the transverse observation plane for detection. Hence, any line-to-line fluctuations in k-space in the amplitude of the signal that are not related to the applied field gradients will generate Fourier noise in the image. Since any given readout row in k-space is generated from a single spin excitation, there should be no artifact in the readout dimension of the image. However, in the phase-encode direction, where any given column in k-space is generated from M different excitations of the spins, substantial artifact can result if the TR time varies randomly. Under these conditions, the available longitudinal magnetization available for the jth excitation of the spins (and hence the jth row in k-space) will be given by

Mz = M°0 + [M°>-1 cos6 - Mz0] exp( - TR_i/T1), (11)

where Mz0 is the equilibrium longitudinal magnetization of the spins, 6 is the excitation flip angle, and TR;-1 is the duration of the (j - 1)th TR delay. (Note that when TR ^ T1 the exponential term is close to zero, and so MZ is always given by Mz°). Normally the TR period is accurately controlled and does not vary. However, if some form of gating is used, particularly cardiac gating, then the starting longitudinal magnetization can be modulated in concert with the varying duration of the cardiac period. This will lead to randomly appearing phase-encode noise.

Another implication of Eq. (11) is that if a very short TR time is to be used, even when the TR time is rigorously constant, then enough "dummy" excitations of the spin system should be allowed that the spins attain a steady-state starting magnetization. If the spin system starts from complete equilibrium (M(t = 0)= Mz°), then

The initial longitudinal magnetization will oscillate according to Eq. (12) until eventually a steady-state longitudinal magnetization is reached in which M° = M° 1. The steady-

state longitudinal magnetization will thus be given by (c.f. Eq. (5))

Mz = M°°[1 - exp(-TR/T1)]/[1 - cos 6 exp( - TR/T1)].

A well-designed pulse sequence will incorporate enough "dummy scan" acquisitions that when the image signal is detected, the spins have reached a steady state. This may not always be the case, though.

### 6.3 Unwanted NMR Echoes

Another implication of repeatedly exciting the spins, or of invoking multiple "spin echoes" from a single excitation, is that unwanted echoes may be generated in the signal. The details of how these unwanted signal echoes are generated are beyond the scope of this article. Further details maybe found in the papers of Crawley et al. [10], Majumdar etal. [27], and Liu etal. [26]. However, it is possible to categorize the artifacts into two broad classes. In the first class the unwanted echo is induced after the phase-encode field gradient has been played out, implying that the unwanted signal is not spatially encoded in y. In the second class the unwanted echo is induced before the phase-encode gradient has been played out, implying that the unwanted signal is spatially encoded in y. The resulting artifacts will be commensurately different. Figure 8d shows a simulated dataset indicating the appearance of an image in which an artifactual signal was generated by an imperfect 180° refocusing pulse in a spin-echo sequence. This caused additional signal to be tipped into the transverse plane, which occurs after the phase encode gradient has been played out. The image is thus formed by the desired signal, S(kx, ky), given by Eq. (4) plus an unwanted signal S'(kx, 0), given by

S'(kx, 0) = aj J P(x, y) exp[-2ni(kx + kmax)x]dxdy. (14)

The extra term kmax is included because the signal from the unwanted magnetization is a maximum at the edge of k-space rather than in the center ofk-space. The term a is a scaling term to account for the different intensity of the artifactual signal. When the two complex signals are Fourier transformed, they add to give the true image plus a band of artifactual signal through the center of the image in the readout direction. Close inspection of the artifactual band in Fig. 8 reveals an alteration in signal intensity in adjacent pixels (the so-called zipper artifact). This is simply caused by the kmax term in Eq. (12), which shifts the center of the unwanted "echo" (actually a free induction decay) to the edge of k-space, thus leading to a firstorder phase shift of 180° per point in the Fourier transformed data for the unwanted echo. The presence of such "zipper" artifacts through the center of the image is indicative of poor refocusing pulse behavior. This can be ameliorated either by accurate setting of the radio-frequency pulse power, or by employment of crusher field gradient pulses on either side of the radio-frequency refocusing pulse, designed to reject any spuriously induced transverse magnetization.

The second class of unwanted echo artifact can be recognized by its different appearance. For this class of unwanted echo the signal has been spatially encoded by the phase-encode pulse, with the resulting effect of mixing the desired signal, S(fcx, fcy), with an artifactual signal, S"(fcx, fcy), given by

The terms dfcx and dfc^ account for the slightly different gradient histories of the unwanted signal relative to the desired signal. If dfcx and dfc^ happen to be zero, then no artifact will be observed in the image, but the signal intensity will be enhanced by a factor (1 + a). Generally, however, the effect of the complex addition of S(fcx, fc^) + S"(fcx, fc^) is to cause interference fringes to be generated in the image, as is shown in Figs 8h and 8i. Once again, appropriate use of crusher field gradients can help to suppress such undesired effects.

Note that if the ripples are absolutely straight (corduroy) or checked, rather than slightly curved as schematically shown in Figs 8h and 8i, then hardware "spiking" should be suspected. This is caused by static electric discharges occurring in the magnet room, leading to a high spike in the fc-space data. Analysis of the raw fc-space data should reveal if this is the case. A field engineer should be contacted if spiking is present.

Fig. 8f shows a simulated spin-echo image in which the folded signal simply adds to the main image. In the case of gradientecho sequences, the phase of the aliased signal will generally be different to the phase of the main image, because of different shim environments in the sample. Interference (moiré) fringes will therefore be induced in the image, the severity of which will increase with gradient-echo time (TE). An example of moiré fringes is shown in Fig. 8g. Spatial saturation of signal from outside the field of view (with special spatial saturation pulses) can help to avoid phase-encode aliasing.

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