MRI Physics: Flow Related Effects in MRI

Flow Voids | Flow-Related Enhancement | Phase Shifts | Flow-Related Dephasing | Go Home

Flow Voids

The first flow-related phenomenon we'll discuss is the flow void. This only occurs in spin-echo (and fast spin echo) sequences, typically with T2 weighting. Fast moving blood experiences the 90-degree pulse but misses the 180-degree rephasing pulse, so its signal decays before the echo is read out.

Flow Void Phenomenon

Blood moving through the slice experiences the 90 degree pulse but most of it exits before the 180-degree pulse. Only blood that is present for both pulses contributes to signal. Gray represents unexited or dephased tissue.

The time between the 90 and 180-degree RF pulses is TE/2, so if the blood flows through the slice (with thickness Δz) faster than TE/2, no signal will be obtained. As an equation, a signal void will be seen if, for blood velocity v,

v ≥ Δz / (TE/2)

Velocity:

Aorta, 100 cm/s
SMA, 120 cm/s
SFA, 70 cm/s
Vertebral Artery, 40 cm/s
Portal Vein, 20 cm/s
Superior Sagittal Sinus, 10 cm/s
Stationary Tissue, 0 cm/s

Velocity: cm/s

TE:

T1 at 1.5T, 15 ms
T2 at 1.5T, 100 ms

TE ms

Slice thickness, Δz mm

Signal remaining: %

Flow void

Some things to remember:


Flow-Related Enhancement

In many ways, this is the opposite of the flow void phenomenon. Flow-related enhancement is typically seen in gradient echo sequences (which do not have the 180-degree rephasing pulse and typically use very short TEs, making any flow void effect negligible). When an MR scanner images a slice of tissue, it subjects the tissue to multiple 90-degree pulses to flip the magnetization into the transverse plane and also cause T1 weighting. Remember that after the first 90 degree pulse, the tissue is only allowed to recover a certain fraction of its longitudinal magnetization - determined by TR - in order to give T1 weighting to the image. The longer the TR, the more recovery occurs, and the less T1 weighting.

Of course, this only happens if the tissue stays put and is subjected to these multiple pulses. If fresh blood flows into the slice, it will start out with all of its longitudinal magnetization. Therefore, after a 90-degree pulse, it will have a lot more transverse magnetization than the surrounding tissues. This will make it bright on the images (seeming like it has a short T1).

Flow-Related Enhancement Flow-Related Enhancement

The animation shows the effect of successive 90 degree RF pulses on static and flowing tissue. Fresh blood (red) that flows into the slice will not have experienced prior RF pulses, so its longitudinal magnetization is at maximum. Any moving blood still in the slice (orange) acts just like static tissue (yellow). The plot on the right shows the same phenomenon numerically. Remember that the signal in the transverse plane depends on the 'stored' longitudinal magnetization that has recovered since the prior pulse.

The degree to which this effect occurs depends on the velocity of the blood and the TR of the sequence. It also depends on the direction of scanning - if the scanner has already saturated the blood entering the slice because it came from the slice just before, then this effect will be less or nonexistant.

In order for new blood to replace old blood in the slice, it has to come in after one 90 degree pulse and before the next one, i.e. it must flow through the slice faster than TR. If it is slower than TR, it will get hit with a 90 degree pulse at some point during the imaging. So for blood velocity v, flow-related enhancement will occur if:

v ≥ Δz / TR

Velocity:

Aorta, 100 cm/s
SMA, 120 cm/s
SFA, 70 cm/s
Vertebral Artery, 40 cm/s
Portal Vein, 20 cm/s
Superior Sagittal Sinus, 10 cm/s
Stationary Tissue, 0 cm/s

Velocity: cm/s

TR:

T1 at 1.5T, 400 ms
T2 at 1.5T, 2500 ms

TR ms

Slice thickness, Δz mm

Signal gained: %

Maximal enhancement

A couple of points to remember:


Phase Shifts

Let's first review how radiofrequency (magnetic field) gradients cause phase shifts in precessing protons. (For more details about how gradients are used for phase encoding, see the section on Spatial Localization.) Remember that when a magnetic field gradient is on, the protons precess with a slightly different frequency since they experience a magnetic field slightly greater or lesser than B0 (the amount depends on their position and gradient strength).

After the gradient is turned off, they revert to the same frequency as all the other protons, precessing in the uniform magnetic field of the magnet. But, they 'remember' their experience in the gradient by keeping a phase shift. In other words, they rotate 'off cycle' from the other protons. The picture below illustrates this point.

Phase Shift

Example of a Phase Shift. The dashed blue line is the original precession plot. A gradient is applied (gray line), and the precession speeds up briefly (solid blue line). Note that even after the gradient is off, the two plots are out of sync.

Mathematically, we can look at it like this: The signal we measure - transverse magnetization - depends on the angle of the precessing proton. This angle changes over time in a constant motion depending on the Larmor frequency (designated here by ω): angle = ω * t . We can describe a phase shift by just imagining that we bump up the angle by a certain constant (designated here by φ), so that

angle = ω * t + φ

Now, let's say that we speed up the frequency for a short while to F1, so

angle = F1 * t + φ

And now we turn off the gradient after some time T1. The angle now measures F1 * T1 + φ. As the proton continues to precess at its native frequency ω, its angle then measures

angle = ω * t + F1 * T1 + φ

As you can see, the angle remembers each of its phase shifts. Of course, angles can only measure up to 360 degrees - after that, it wraps around from 0 again.

Phase Shift

Effects of a Phase Shift on Precession Angles. The gray line shows a magnetic field gradient turned on for a brief time. The solid blue line represents the angle of the proton, which is constantly increasing - and it increases more rapidly when the gradient is on. The dashed blue line is also the angle - but it wraps back to 0 at 360 degrees.

Flow-Related Dephasing

Protons that are moving (e.g. in blood) experience different magnetic field strengths, as gradients vary in space. While they will precess at the same frequency as the stationary protons around them when they're in the slice, they will still 'remember' the phase shifts from those earlier different frequencies. This phenomenon is called flow-related dephasing.

Flow-Related Dephasing

Illustration of flow-related dephasing. Moving (blue) and stationary (orange) protons in the presence of a constant gradient Gx (red). Dashed lines show the phase φ of the two protons over time, while solid lines show position.

You can see that moving protons accumulate an additional phase shift when compared to stationary protons. However, flow-related dephasing is actually helpful sometimes:

But let's say we want to neutralize these effects (actually, we need to do this to properly calibrate both phase-contrast MRA and bright-blood cardiac MRI). We need to change our gradients so that they 'balance out' - and protons moving with constant speed end up without a phase shift. Let's first try a biphasic gradient - half of the time it will give a positive phase shift, while the other half of the time it will give a negative phase shift:

Biphasic Gradient

Moving (blue) and stationary (orange) protons in the presence of a biphasic gradient Gx (red). Dashed lines show the phase φ of the two protons over time, while solid lines show position.

The stationary protons end up with no net phase shift at the end, but the moving protons do have a phase shift. Why is that? Well, as you can see, the gradient is stronger as the proton moves farther out - therefore, while the amount of time is balanced, the second half of the gradient pulse actually causes a greater phase shift. This biphasic gradient is exactly what we want for Phase-Contrast MR Angiography; if we measure the phase shift, we know how far - and therefore how fast - the proton was moving.

In order to fully compensate for moving protons, we need to add another phase (or "lobe") to the gradient pulse. Remember that the gradient is stronger as the proton moves out, so we need an extra 'kick' at the end. The gradient also has to balance out overall so that stationary protons do not end up with a phase shift. We can use a triphasic gradient, as you see below; the ratio of the lobes is 1:-2:1 (which adds up to 0).

Triphasic Gradient

Moving (blue) and stationary (orange) protons in the presence of a triiphasic gradient Gx (red). Dashed lines show the phase φ of the two protons over time, while solid lines show position.

In this example, the phase shift of both moving and stationary protons is zero at the end. Thus, moving protons will end up with the same amount of signal as stationary protons. This is what is done to create a control image for phase-contrast MRA (for background subtraction). It's also what happens in bright-blood cardiac MRI sequences, so that you can see the blood without all sorts of dephasing artifacts as it moves through the heart.

Now, one thing we haven't focused on is the dynamics of the proton motion. It turns out that the triphasic gradient only works if the proton moves at a constant speed. If it's accelerating or decelerating - things that often happen in stenotic jets, for example - then you will get dephasing. You can add extra lobes to the flow-compensation gradient (e.g. 5 lobes instead of 3), but the more lobes you add the longer it takes to make the gradient.

Some things to remember:


References

  1. Hashemi, R. H., Bradley, W. G. & Lisanti, C. J. MRI: the basics. (Lippincott Williams & Wilkins, 2010).

Copyright 2013 Mark Hammer. All rights reserved.