# Flow Phenomena

Flow Phenomena

Introduction

Unlike computerized tomography (CT) (with or without contrast), in which the appearance of flowing blood in a vessel is predictable, the appearance of flowing blood in MRI is much more complicated. Flowing blood or cerebrospinal fluid (CSF) can appear dark or bright depending on numerous factors, including, but not limited to, the following:

• Velocity

• Pulse sequence (e.g., spin echo [SE] vs. gradient echo [GRE])

• Position of the slice containing the vessel relative to the rest of the slices

• Contrast (TR and TE)

• Echo number (even or odd)

• Slice thickness

• Flip angle

• Gradient strength and rise time

• Use of gradient moment nulling techniques

• Use of spatial presaturation pulse

• Use of cardiac gating

• Chance of cardiac gating (pseudogating)

Types of Flow

In Chapter 18, we discussed two types of motion: random and periodic. Blood and CSF flow have a periodic-type motion. Furthermore, flow of blood can be divided into the following:

• Laminar flow

• Plug flow

• Turbulent flow

• Flow (stream) separation/vortex flow

These types of flow are depicted in Figure 26-1. Let’s discuss these separately.

Laminar Flow. This type of flow is seen in most normal vessels and has a parabolic profile. If the lumen radius is R, then the velocity v at position r would be

v(r) = Vmax (1 – r2/R2)

where Vmax is the maximum velocity in the center of the lumen. Therefore, the average velocity in the lumen is given by

Vave = Vmax/2

Plug Flow. This type of flow is usually seen only in large vessels (aorta) with high velocities. The velocity across the lumen is constant, thus yielding a flat velocity profile:

v(r) = Vmax = Vave = constant

Turbulence. This phenomenon is observed in abnormal vessels (e.g., distal to stenosis) or at bifurcations during which a random motion of fluid elements is observed. Vortex flow and large-scale recirculation zones (i.e., eddies) are other terms that refer to such random motions.

Flow (Stream) Separation. This phenomenon is observed near the wall of a vessel (e.g., in the proximal internal carotid artery) in which some of the flow is separated from the main streamline.

Question: What determines laminar versus turbulent flow? Figure 26-1. Types of flow. A: Laminar flow. B: Plug flow. C: Turbulent flow (distal to stenosis). D:Flow (stream) separation.

Answer: A dimensionless number called the Reynolds number (Re) can predict the type of flow. It is given by

Re = (density × velocity × diameter)/viscosity

where density is in g/cm3, velocity is in cm/sec, diameter is in cm, viscosity is in centipoise or g/cm-sec, and Re has no units. If Re < 2100, then flow is laminar. If Re > 2100, then flow is turbulent.

Question: What is a typical blood flow velocity?

Answer: It depends on the vessel. Table 26-1 gives some examples.

The blood velocity may be much higher in abnormal conditions, such as in an arteriovenous fistula (AVF).

Question: What is the difference between flow and velocity?

Answer: A mathematical relationship exists between bulk or volumetric flow in a vessel lumen and the velocity of flow:

v = Q/A

where v is the average velocity (in cm/sec), Q is the bulk or volumetric flow (in cm3/sec), and A is the cross-sectional area of the vessel (in cm2).

Normal Appearance of Flowing Blood. Most flow effects can be attributed to one of the following:

• Time-of-flight (TOF) effects

• Motion-induced phase changes

TOF effects can lead to the following:

• Signal loss (high-velocity signal loss or TOF loss)

• Signal gain (flow-related enhancement [FRE])

Flowing blood can appear bright or dark. Three main independent factors result in each case:

• ↓ SI of flowing blood

• high velocity

• turbulent flow

• dephasing

• ↑ SI of flowing blood

• even-echo rephasing

• diastolic pseudogating

• FRE

Let’s discuss each of these separately.

Table 26-1

 Vessel Blood Flow Velocity (cm/sec) Aorta 140 ± 40 Superficial femoral artery 90 ± 13 Vertebral artery 36 ± 9 Venous flow <20 Figure 26-2. To form an echo, protons must be exposed to both a 90° and a 180° pulse. As velocity increases, a larger portion of flowing protons is exposed only to the 90° but not the 180° pulse, thus causing signal loss.

High-Velocity Signal Loss

In SE imaging, the protons must be exposed to both a 90° and a 180° radio frequency (RF) pulse to give off a signal. High-velocity signal loss or TOF loss occurs when flowing protons do not remain within the selected slice long enough to be exposed to both RF pulses.

Figure 26-2 illustrates how the magnitude of signal loss is a function of the velocity. To see how this works, first recall the simple relationship among time, distance, and velocity:

Velocity = distance/time

or

v = d/t

The distance each proton in flowing blood has to travel within a slice is the slice thickness δz. The time between a 90° pulse and a 180° pulse is one-half TE.

Thus, if the velocity of flowing blood is

v = δz/(1/2 TE)

then protons flowing into the slice would be exposed only to the 90° pulse, and not to the 180° pulse, thus forming no signal or SE. Let’s give this velocity an arbitrary name vm, that is,

vm = δz/(1/2 TE)

However, if the velocity were 0 (i.e., for stagnant blood), then an SE would be formed. If the velocity falls in between, only a fraction of the protons would form an SE. The fraction of protons escaping the 180° pulse is given by

v/vm = v(1/2 TE)/δz

Thus, the fraction of protons receiving both RF pulses is

1-v/vm = 1-v(1/2 TE)/δz

The signal intensity is, therefore, proportional to

I α 1-v(1/2 TE)/δz

Figure 26-3 illustrates the linear relationship between signal intensity (I) and velocity v. It is clear from this graph that if the velocity of flowing blood is at least equal to vm (i.e., vvm), then a flow void is observed. Figure 26-3. A plot of signal intensity versus velocity. The higher the velocity, the more the signal loss. Figure 26-4. Axial PD image shows TOF losses in the right internal carotid and basilar arteries (black arrows); however, no TOF loss or “flow void” is seen in the left internal carotid artery (white arrow). Patient had left internal carotid artery occlusion.

Example

Suppose that the slice thickness δz = 1 cm and TE = 50 msec. What is the velocity at which flow void is observed?

Using the above formula, the velocity should be at least

vm = Δz/(1/2 TE) = 1 cm/(25 msec) = 1000 cm/25 sec = 40 cm/sec

which is seen in an artery.

Therefore, vm is larger for thicker slices and smaller TEs, and vice versa (see Fig. 26-4 for an example).

N.B.: Remember that TOF losses only apply to SE imaging and not to GRE imaging
because, in GRE, the echo is formed via a single RF pulse and refocusing gradients (without a 180° pulse). Figure 26-5. Sagittal 1.5-mm T2 image of the brain shows signal loss inferior to the aqueduct of Sylvius (arrow). This was due to high velocity of CSF and subsequent turbulent flow resulting in intravoxel dephasing. Patient had normal pressure hydrocephalus (NPH).

Turbulent Flow

In turbulent flow (with Re>2100), random flow exists that contains different velocity components (i.e., with different speed and direction of flow). Consequently, each of these components has different phases that tend to cancel each other out and result in no signal (flow void). This result can occur with low- or high-velocity flow (Fig. 26-5).

Dephasing

There are many causes of dephasing. One important cause is the so-called odd-echo dephasing. This phenomenon results in signal void on the first and other odd echoes. The protons in a voxel do not move at the same velocity across the lumen in laminar flow; thus, each precesses at a different frequency and accumulates a different phase. (Also see the discussion below on evenecho rephasing.)

Another cause of dephasing is intravoxel dephasing. Because of laminar flow, different velocities may exist within a voxel, thus leading to phase dispersion (incoherence) and signal loss. How to decrease intravoxel dephasing and increase SNR:

• Decrease the voxel size (increase spatial resolution), either by increasing the matrix (trade-off: will reduce signal-to-noise ratio [SNR]) or by reducing the FOV (trade-off: may cause wraparound).

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