Even though spin-echo sequences are well suited for imaging of trabecular bone, they are sensitive to the quality of the inversion pulse. The flip angle of the refocusing hard pulse may deviate from 180°, depending on the actual amplitude of the applied RF field.
In the case of a dedicated wrist transmit/receive coil, the problem of flip angle calibration is specific to the coil geometry rather than the particular scanner implementation. The custom-built, elliptical cross-section quadrature birdcage coil (12) used in our laboratory has been designed for optimum filling factor. It has high RF field homogeneity in most of its central region. However, near the coil conductors the field is greater and there is a transition region where it is relatively inhomogeneous. Depending on wrist size, the subcutaneous fat is located in this transition region. Since the flip angle in the transition region differs from that near the coil axis, automatic setting of the transmit gain on the basis of the total detected spectral signal (which is dominated by the signal from fat) may therefore fail to produce the correct flip angle in the volume of interest. Thus, although automatic optimization often gives good estimates of the transmit gain, the operator manually checks each estimate. Manual transmit gain adjustment has the advantage that it is based on a projection image, therefore allowing flip angle optimization in the volume of interest. Even though the projection contains signal from the proximity of the coil edges the central part of the projection, used for adjustment, is dominated by signal from the central region of the coil. Nonetheless, even with these precautions, slight misadjustments are usually unavoidable.
While these imperfections are generally small, in combination with the particularities of our sequence they can produce two noticeable artifacts. The first is a consequence of longitudinal magnetization being rotated into the transverse plane after the imperfect refocusing pulse. This signal is dephased by the trailing crusher gradient applied immediately after the refocusing pulse. The remaining unwanted signal is then “chopped” by alternating the phase of the refocusing pulse between 0° and 180°. In this manner, the unwanted signal is displaced to the end slices of the reconstructed image, which are subsequently discarded (8).
Another consequence of the imperfection of the phase-reversal pulse is that a portion of the transverse magnetization, which is phase-encoded before the refocusing pulse, is converted into longitudinal magnetization (coherence pathways II and III in Fig. 2). Because of the short repetition time (TR = 80 ms) relative to the longitudinal relaxation time (T1 = 300 ms in fatty bone marrow), the longitudinal magnetization created in this manner is not significantly attenuated by the end of the repetition period and is rotated back into the transverse plane by the excitation pulse of the subsequent pulse sequence cycle. It is then again phase-encoded and refocused by the 180° pulse at time TE/2 after the main echo, as shown in Fig. 2. This unwanted echo, labeled II in Fig. 2, is the source of the described banding artifact.
Coherence Pathway of Artifactual Signal
Inspection of the coherence pathways of the signals generating the artifact (pathway II in Fig. 2) and the main echo (pathway I in Fig. 2) clarifies the origin of the artifactual signal and allows characterization of its relationship to the main echo. We will only consider coherence pathways I, II, and III, since only effects stemming from coherence pathways connecting two adjacent repetition periods are relevant. There are three more coherence pathways that can produce echoes in the following TR period (pathways IV, V, and VI in Fig. 2). In all of these coherence pathways the magnetization is transverse, up to the point it forms its strongest echo in the next repetition period. Therefore, the magnetization amplitude is significantly attenuated by T2 decay (T2 = 60 ms, TR = 80 ms) such that its amplitude relative to that of the magnetization in coherence pathway II is negligible.
For simplicity, we assume that all phase encodings and readout dephasing occur before the refocusing pulse, as shown in Fig. 1a. It is noted that in the implementation used for imaging at very high resolution, the y-phase encoding is split such that some of the encoding is performed after the refocusing pulse (8) in order to shorten the echo time. However, the essence of our arguments does not change for this particular variant of FLASE.
Even though all gradients varying between excitations are balanced within one repetition period, the magnetization is never fully in the steady state. The gradients are only balanced if one considers all zeroth moments within a TR period. It is evident, however, that the moments are not fully balanced in the periods between the excitation and the refocusing pulses. As already indicated, an imperfect refocusing pulse converts the phase-encoded transverse magnetization into longitudinal magnetization with phase memory that causes leakage (13, 14) into the following repetition period. However, since this effect is small we shall assume that the difference in the initial magnetization for two adjacent repetitions is negligible, which will simplify the analysis.
To propagate the amplitude of the magnetization of interest we use a standard form for the change in magnetization after a rotation by angle an θ about the x axis at time t (15):
where, M+(t+) (M+(t−)) is the complex transverse magnetization just after (before) time t and, analogously, Mz(t+) (Mz(t−)) is the real amplitude of the longitudinal magnetization immediately after (before) time t, while * denotes complex conjugation. We first follow coherence pathway II marked by the bold line in Fig. 2. The angle of the SLR pulse will be denoted by θ and the deviation of the refocusing pulse flip angle from π will be denoted by Δϕ. We set the amplitude of the transverse magnetization just after the SLR pulse to 1, since we are interested only in relative amplitudes. Under this assumption the transverse magnetization has the following amplitude just before the refocusing pulse
where ϕ is the phase imparted by phase encoding and readout prephasing, and ϕc is the phase due to the crusher prior to the phase-reversal pulse. All times referred to further in the text are labeled in Fig. 2. The part of the longitudinal magnetization that is produced by the refocusing pulse in coherence pathway II has the following magnitude and phase at the end of the first repetition period
The phase imparted by the crusher gradient is now stored in the longitudinal magnetization and is not affected by the trailing crusher gradient. After the excitation pulse in the next repetition this magnetization is rotated back into the transverse plane and phase encoded again
The artifactual echo is formed after the refocusing pulse with amplitude
at a point in k-space determined by the phase factor in Eq.  and the phase rewound by the trailing crusher. After this refocusing pulse the artifactual magnetization is in the transverse plane and the phase accumulated from the application of the left crusher gradient in this repetition is rephased by the trailing crusher; however, the phase encoding imparted by the leading crusher in the previous repetition persists.
The amplitude of the main echo originating from coherence pathway I is
Note that the T2 decay is less for the main echo since the magnetization generating it spends half as much time in the transverse plane as the magnetization forming the artifactual echo. The magnitude, ϵ, of the latter relative to the main echo is the absolute value of the ratio of expression  over :
Using values for the parameters given earlier and TE = 9 ms, we infer that the relative magnitude of the artifact is given as:
Using Eq.  and measuring the height of the main and artifact echoes in the raw k-space data, we estimate an average imperfection angle of 25° for the extreme case shown in Fig. 1b. In clinical scans banding stemming from imperfection angles of about 4° is noticeable, while pronounced banding occurs with imperfection angles of about 10°. These angles correspond to relative amplitude values of ε = 1.5% and ε = 3.8%.
We also note that coherence pathway III shown in Fig. 2 produces an echo simultaneous with the primary echo, thus increasing the amplitude of the main signal.
k-Space Analysis of Image Artifact
From Eq.  we see that the artifactual signal was phase encoded twice in y and z and also prephased twice in x. Thus, the nonbalanced phase imparted by the leading crusher before the first refocusing pulse moves the center of the echo along the kz axis by Δkz. In the readout direction the artifactual spin echo will appear TE/2 later than the main echo (t5 in Fig. 2) since this is the time needed for the stimulated echo to occur (see Fig. 2). The artifactual gradient echo in the readout direction occurs slightly earlier than t5 because the readout does not start immediately after the refocusing pulse due to the trailing crusher. In this manner, the center of the artifactual echo is translated by kpre in the kx direction. The magnitude of kpre is determined by the fractional echo dephasing and sets the spatial period of the banding in the readout direction, as will be shown further in the text. The artifactual signal sa can be written as:
where s is the pristine signal of the main echo and ε is the amplitude of the artifactual echo relative to the amplitude of the main echo. The total signal stotal is then given by:
To analyze the effect of the spurious echo on the reconstructed magnitude image, we calculate the magnitude of the corrupted image using Eq. . We first calculate the Fourier transform of the total signal ρtotal(x,y,z) = F[stotal(kx,ky,kz)] that gives the following complex image:
where ρ = F[s] is the image that would be obtained from the pristine data s. The magnitude image is:
where we have assumed that ρ(x,y,z) is real. The first term under the square root of Eq.  is the pristine image. The next two terms describe the image degradation due to the artifact. It would be desirable to expand Eq.  into a Taylor series since this would produce additive corruption terms. Even though ε is small, we cannot do this for all points. The ratio of the “stretched out” image ρ(x,y/2,z/2) and the pristine image can become much larger than ε if ρ(x,y,z) is very small in some region of the image. Because of this we shall consider only the full expression and resort to numerical calculations to compare with the experimental results.
The term of Eq.  that is linear in ε produces the main banding artifact observed in clinical scans. This term becomes noticeable only where the pristine image has sufficiently high intensity since it scales as ρ(x,y,z). It is also modulated by the stretched-out image ρ(x,y/2,z/2) and the cosine banding factor. In clinical scans the modulation from the two image terms appears as inhomogeneities in the cosine banding. Due to the small magnitude of the artifact signal and complicated shape of the image modulation, other details are not discernable. The banding modulation occurs in both readout and slice directions, as shown in Fig. 1b. This was observed in clinical scans as a translation of the banding along the readout direction as one would cycle through slices. Also, for a fixed field of view kpre is smaller for lower readout resolutions, leading to a longer period of the banding in the readout direction, as observed. Finally, the third term of Eq.  is quadratic in ε and appears as a faint ghost of the pristine image, stretched out by a factor of two in the y and z phase-encoding directions. One should also note that, since, as mentioned before, the stimulated secondary echo at t5 is not exactly coincident with the gradient echo, the artifactual signal may carry some extraneous phase (from background gradients) relative to the main signal. This phase can lead to curvature of the banding, as seen in the upper portion of Fig. 1b.