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Kluwer - Handbook of Biomedical Image Analysis Vol

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Rakesh Sharma and Avdhesh Sharma

velocity as a change of phase. The phase accumulation associated with such a gradient is expressed as:

φ = γ V · T · A

(3.14)

where φ is phase shift induced by flow in the transverse spin magnetization, γ is the gyromagnetic ratio of the spin, V is the component of the spin’s velocity in the applied gradient’s direction, T is the center-to-center time interval between the two gradient lobes, and A is the area of each gradient lobe. This equation describes only the phase shift induced by constant velocity flow when a bipolar gradient is applied and not phase shifts due to such higher orders of motion as acceleration or jerk. Since the flow-induced phase shift is directly proportional to velocity, a stationary spin with zero velocity will have no net phase accumulation. For subsequent acquisitions, this pulse sequence inverts the polarity of the bipolar flow-encoding gradients. The polarity of the gradient ( A) is now negative, giving the equation for the second acquisition as φ = −γ VTA. When the image data from the first acquisition is subtracted from the second acquisition, the remaining data is from the signal that is different in two acquisitions i.e., the intravascular signal from moving blood. The procedural difference in these two acquisitions is the negation of bipolar gradients. A stationary spin will have identical (zero) phase shifts for each polarity of the flow-encoding pulse, resulting in a zero net phase shift. So, the subtraction of two vectors result in zero. The vector subtraction of signals from the spins moving with constant velocity is quite different.

Suppose two signals have the same magnitude but different phases. Consequently, when the vectors are subtracted, the resulting vector is not zero. The result is signal originating from vascular structures with nearly complete elimination of stationary tissues from the MR angiogram. In MRA, the imager acquires the equivalent of three raw data sets for three flow-encoding directions. The magnitudes of these data sets are combined into a total flow angiogram.

3.2.4.2 Image Contrast

Image contrast in PC angiography is influenced by several factors such as flow direction, velocity encoding and aliasing, phase dispersion and flow compensation, and saturation effects.

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3.2.4.3 Flow-Encoding Gradients

In PC angiography, the bipolar flow-encoding gradients may be applied in a single direction (e.g. superior/inferior) or in all directions—S/I, A/P, and R/L. In some anatomic regions, the carotid bifurcation such as application of a single flowencoding axis may be sufficient. The resulting images represent flow direction by the sign of the pixel value in an S/I flow image, for example superior-to- inferior flow is represented by positive pixel values (brighter), while inferior- to-superior flow is represented by negative pixel values (darker). In such a case, single flow-encoding directions will not be adequate i.e., intracranial MRA shows blood flow components in all directions. However, the total flow image can be obtained by measurement of individual flow components and combining them mathematically into a composite image called “velocity image.” This image is made of flows in multiple directions and has magnitude (in cm/sec) but no specific direction. Velocity is defined as a vector with a magnitude (in cm/sec) and direction such as S/I, A/P, and R/L. The individual flow measurements can also generate a phase image with velocity and directional flow information. In the phase contrast angiograms, display pixel values are proportional to the product of image magnitude and velocity encoding. This relationship of velocity with image magnitude provides quantitative measurement of velocity.

3.2.4.4 Spatial Misregistration Effects

The reason for spatial misregistration artifacts can be understood with the pulse sequence. In this sequence, phase encoding fixes the position of an isochromat in the phase-encoding direction, which occurs shortly after the 90nutation pulse. This fixing of the isochromat position in the read-out direction is followed by read-out which occurs only at echo time (e.g. approximately at TE, 2TE, etc.) after phase encoding. If spin isochromats move between these two events in an oblique in-plane direction, their signal is misregistered. Spatial misregistration occurs because the position of the flowing isochromats is identified in the phase-encoding direction prior to the read-out direction. The result is a shift in intravascular signal intensity in the direction of flow along the read-out gradient. Measurements of the displacement of the signal delineating an apparent vessel and the angle between vessel and

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read-out direction are used to determine flow velocity. In quantitative terms, the time difference t is the time between the phase-encoding and the readout events. The distance A is the measurement by which the signal is displaced outside a vessel. Measurement of the angle C is the angle between the vessel and the read-out direction, which permits determination of the flow velocity V :

V = A/( t cos C)

(3.15)

3.2.5 Velocity-Encoding and Aliasing

Flow encoding in a vessel can be called velocity encoding (VENC). It is a parameter that is selected by the MR operator when using PC MRA. VENC is the maximum velocity present in the imaging volume. Any velocity greater than VENC will be aliased according to the following formula: aliased velocity =

VENC − actual velocity. A small VENC is always more sensitive to slow flow (venous flow) and to smaller branches, but it causes more rapid (arterial) flow to get aliased. A larger VENC is more appropriate for arterial flow. So, small and large VENC are important for imaging all flow components. This method has several advantages. PC MRA is capable of generating magnitude and phase images with superior background suppression. VENC is less sensitive to intravoxel dephasing or saturation effects. On the other hand, this method suffers from several disadvantages such as long scan time, sensitivity to signal losses due to turbulence and dephasing on vessel turns (carotid siphon), and dependence on maximum flow velocity in order to select an optimum VENC. To provide quantitative information regarding velocity in PC angiography, the VENC should be selected to encompass the highest velocities that are likely to be encountered within the area of interest (see Fig. 3.21). The normal maximal flow velocities are likely to be encountered within the vessel region of interest. The normal maximal flow velocities of intracranial arteries do not exceed 80 cm/sec. So, the VENC of 80 cm/sec would encompass all flow velocities up to and including 80 cm/sec. When a velocity encoding is selected, the amplitude of the bipolar flow-encoding gradients is adjusted so that all velocities including the selected value can be imaged without aliasing. Aliasing in phase contrast occurs when high flow velocities are incorrectly represented in the velocity image as lower flow velocities.

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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 sphenoparietal 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.

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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 180or 180phase 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 +190phase shift is equivalent to a −170phase 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 frequencyencoding axis. The first half of the read-out gradient refocuses the magnetization, producing an echo at time TE.

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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 180for 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

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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

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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 of the 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 (M0) describes the effect of a gradient on the phase of stationary spins. Similarly, the

Figure 3.23: Gradient reversal.

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first moment (M1) 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 phaseencoding 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

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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.

3.2.6 MRA Image Reformation

The MR data from MRA images is reformatted and this reformatting plays a major role in vascular anatomy observed in the MRA imaging. The common method for reformatting TOF-MRA uses the technique known as MIP. This technique also generates 3D images of blood vessels with blood motion. The other method for reformatting MRA images is shaded surface display. This method reformats image data in such a way that it appears as if a light is thrown onto structures to generate 3D appearance of vasculature.

3.2.6.1 Maximum Intensity Projection

The method of reformatting based on ‘maximum intensity projection’ is known as ‘mipping.’ The mipping of blood can be done based upon the blood flow characteristics. Flowing blood in MRA techniques has a high intensity. The intensity of a pixel in a slice is compared with that of the corresponding pixels in all the other slices (as in a channel), and the one with maximum intensity is selected. For example, pixel (1, 1) in slice 1 is compared with other pixels (1, 1) of all other slices. For this, an internal threshold is used, below which no pixel in the channel falls. This threshold process is repeated for all the pixels in the slice to connect high intensity dots in space in order to generate an MRA image. Thus MRA image represents the highest intensities (caused by flowing blood) in the imaging volume. A major drawback of this method is that bright structures other than blood may be included in the mipped image i.e. fat, posterior pituitary glands and subacute hemorrhage. This problem is observed only with TOF MRA and not with PC MRA. PC MRA is a subtraction technique based on velocity-induced phase shifts rather than on tissue T1 and T2 relaxation times.

3.2.6.2 Saturation Effects

The saturation effects can minimize the loss in signal intensity if small (15–20) flip angles are used. The 3D phase contrast technique can image large volumes, such as the entire head, without serious signal loss due to saturation effects. As