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Figure 3.21: Three-Dimensional PC angiogram at multiple velocity encoding (VENC) shows the effect of high velocity encoding (cm/sec) at 80° (left panel), 40° (right panel) on top row and 20° (left panel), 10° (right panel) on bottom row to emphasize the better venous anatomical appearance with clear spheno-parietal sinus at low VENC.

3.2.5.1 Aliasing in Speed Images

When the velocity-encoding set below the peak velocities is encountered within the vessel lumen, the higher velocities will be aliased and appear as lower signal intensities from the lower velocities. Since the highest velocities are usually present at the center of the vessel, aliasing may result in a decrease in signal intensity within the center of the vessel. If a very low velocity encoding (VENC = 20 cm/sec) is used, the higher flow velocities will be aliased and the slower velocities will have greater signal intensity. The advantage of aliasing in magnitude and velocity images is also noticeable to bring out slower flow along the walls of arteries, structures, or to emphasize venous anatomy. VENC may be set lower than the peak velocity. Aliasing artifacts makes the flow information at the center of the artery meaningless but this part of the vessel is often not seen in the MIP projection images.

3.2.5.2 Aliasing in Phase Images

When peak velocity in a vessel is equal to the VENC value, the bipolar gradients give either a 180° or 180° phase shift, depending on the direction of flow. When velocity exceeds the VENC value and the phase shift exceeds 180°, it becomes indistinguishable from the phase shift produced by flow in the opposite direction. The result is phase aliasing. Here aliasing flow seems to change direction, since the +190° phase shift is equivalent to a —170° phase shift (see Fig. 3.22). For this reason, aliasing in individual flow-axis images is often recognized by adjacent white and black pixels. In addition, the measured phase shift increases with velocity up to a value of 180°, at which point it is aliased with an equal negative velocity. This sets a limit on the usable degree of flow encoding for quantitative

Figure 3.22: Phase plot shows the effect of a gradient on transverse magnetization at three different locations along the frequency axis. The gradient echo is formed by first dephasing the transverse magnetization along the frequency-encoding axis. The first half of the read-out gradient refocuses the magnetization, producing an echo at time TE.

Figure 3.22: Phase plot shows the effect of a gradient on transverse magnetization at three different locations along the frequency axis. The gradient echo is formed by first dephasing the transverse magnetization along the frequency-encoding axis. The first half of the read-out gradient refocuses the magnetization, producing an echo at time TE.

studies. With higher velocity encoding, pulse is wrapped. Magnitude and speed images show a drop in signal intensity with increasing velocity.

For quantitative studies, one sets the flow encoding to produce a phase shift just below 180° for the highest velocities present. The quantitative relationship between velocity and phase shift reduces the detectability of small vessels and some aneurysms and reduces the apparent diameter of large vessels.

3.2.5.3 Phase Dispersion and Flow Compensation

Intravoxel spin-phase dispersion is called intravoxel incoherence or loss of spinphase coherence. It imposes a limitation for vascular MRI. This loss of signal intensity can occur whenever any of the three conditions exists: (1) A wide spectrum of flow velocities exists within an imaging voxel; (2) higher orders of motion, such as acceleration and jerk, are not compensated; and (3) local variations in magnetic field homogeneity are present, such as those produced by magnetic susceptibility effects. In a long straight vessel with no bifurcation, blood flow is typically laminar flow. That is, the velocity profile across the vessel is not constant, but varies across the vessel lumen. The flow at the center of the lumen of the vessel is faster than that at the vessel wall, where resistance slows down the blood flow. As a result, the blood velocity is almost zero near the wall, and increases toward the center of the vessel. The velocity profile becomes more complicated when the flow is pulsatile and the vessel curves or bifurcates. In general, shear rate increases near the vessel wall, resulting in greater velocity variations, intravoxel phase dispersion, and loss of signal intensity. Decreasing the voxel size is one important strategy for minimizing intravoxel dephasing in vascular MRI studies. Smaller voxels encompass a smaller range of flow velocities. This reduced size of voxel also reduces SNR in a linear fashion. The loss of SNR can be offset by the use of long acquisition times. SNR is proportional to the square root of the imaging time. The other alternative is employing the stronger magnetic fields, as SNR is proportional to magnetic field strength. Thus, voxel-size reduction will improve nonturbulent flow only such as vascular structures with well-characterized distribution of velocities within a vessel. It will not eliminate signal loss due to true turbulence. The reason for this is that turbulence flow has randomly oriented the velocity vectors. The lower voxel-size strategy offers similar improvements in the regions with magnetic susceptibility changes due to magnetic field gradients. Phase shift induced by flowing blood in the presence of a flow-encoding gradient is directly proportional to the velocity. A dispersion of velocities in a vessel, therefore, results in a dispersion of phase shifts. Consequently, a projection measurement of phase through a vessel with laminar flow will represent the average velocity provided that the flow-encoding gradient is not too strong. If the flow becomes complex or turbulent, the dispersion of velocity components along the projection may cause an attenuation of the signal, or even zero signal. Turbulent flow is the flows with different velocities that fluctuate randomly. The difference in velocities across the vessel changes erratically.

3.2.5.4 Flow Compensation

Spin echoes recover the loss of signal because of magnetic field inhomogeneity or susceptibility gradients. However, these spin echoes with longer echo times are less effective in overcoming the phase dispersion due to spins moving at different velocities. Flow compensation is a first-order gradient moment nulling. It employs the refocusing gradients to re-establish phase coherence. For this, lobes are added to the read-out and slice-select gradient waveforms. As a result, the loss of phase coherence due to different velocity distributions is minimized and velocity-induced phase shifts are canceled. This strategy results in an acquisition at constant velocity. However, high-order motions such as acceleration and jerks are compensated by the use of waveform complexity. As a result of additional lobes of gradient waveforms, the echo time and degrade image quality are increased.

3.2.5.5 First-Order Gradient Moment Nulling

It means that the system applies gradient pulses so that constant velocity spins and stationary spins have no net phase accumulation at each echo time. For stationary spins, the signs of the gradients are reversed so that the phase advance experienced at a given location is compensated by appropriate phase retardation. The first-order gradient moment nulling balances the phase for both stationary spins and spins moving with constant velocity. This can be accomplished with the application of a gradient sequence in which the strength and duration of the gradient pulses have a 1:2:1 ratio (see Fig. 3.22). Vascular blood flow is pulsatile and velocity is not constant between excitation and detection. However, some phase dispersion will normally occur. In addition, in some anatomic regions the effects of acceleration become prominent and "acceleration drop out" signal loss becomes apparent in the resulting images. In peripheral vascular studies, pulsatile motion and jerk are significant causes of artifacts. Although acceleration compensation schemes exist, the inevitable trade-off of increased echo time can make them impractical.

3.2.5.6 Phase Dispersion

When magnetic field gradient is applied to a spin system, the spins within the voxel accumulate a phase angle in relation to one another. This phase angle difference is known as "phase dispersion." To correct for this phase dispersion, the gradient is typically reversed to rephase the spins. This technique is used frequently in imaging sequences to refocus stationary spins. These "bipolar" gradient lobes are of equal strength and duration but have opposite signs (see Fig. 3.23). Spins that are moving in the direction ofthe magnetic field gradient are not refocused and are left with some residual phase. The motion-induced phase shifts occurring in the presence of magnetic field gradients are arithmetically defined by position/time derivatives called "moments." The zeroth moment (Mo) describes the effect of a gradient on the phase of stationary spins. Similarly, the

first moment (Mi) describes its effect on the phase of a spin with constant velocity. The second moment (M2) describes the gradient's relationship to the phase of spins experiencing acceleration. The third moment (M3) defines the effect of jerk on spin phase. Even higher order moments exist, but they are usually less important.

3.2.5.7 Shorter Echo Times

Shorter echo times (TE) may also reduce the problem of signal loss due to phase dispersion. Short TE reduces the time for spins to dephase after the RF pulse. Short TE thereby reduces the signal loss arising from susceptibility gradients, velocity distributions, and higher orders of motion. For all VMRI techniques, flow-related phase errors accumulate as a function of TE(n + 1), where n is the moment (i.e., n = 1 for velocity and n = 2 for acceleration). Phase error is, proportional to TE(n + 1).

The effects of higher order moments become more significant for long echo delays. This is because the second moment (acceleration) has a cubic dependence on echo time, while the third moment (jerk) has fourth-power dependence. Using the shortest possible TE can therefore minimize signal loss due to these higher order moments. For example, a VMRI exam obtained with TE = 3 msec will have approximately one-half the velocity-related phase errors of the same study performed with TE = 4 msec.

3.2.5.8 Complex Flow

To minimize the problem of signal loss due to complex flow, several strategies may be employed. The dispersion of velocities along a projection can be greatly reduced by obtaining vessel images in thin cross-sections rather than in full projection. 3D data acquisition overcomes the problem of velocity dispersion within a voxel. Since the phase contrast technique relies on the phase shift induced in moving spins, conventional flow compensation techniques cannot be used on flow-encoding axis. To minimize phase dispersion, the bipolar phase-encoding gradient is placed symmetrically around the first moment (called PC flow compensation). However, a slightly shorter echo time can be achieved by placing this gradient asymmetrically in relation to the first moment. The resulting technique may be called "minimum TE." It produces the shortest possible TE with the PC sequence, and is selected by not choosing the flow compensation.

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