Scan Parameters and Image Optimization

Introduction

In this chapter, we will discuss all the important parameters in MR imaging that the operator can control and adjust. We will then see how these changes influence the image quality. Every radiologist is comfortable with a particular set of techniques; therefore, “custom-made” techniques can be achieved only if the radiologist is aware of the parameters and trade-offs involved.

Primary and Secondary Parameters

Primary parameters are those that are set directly:

From the primary parameters above, we can get the secondary parameters (which are also used to describe the image):

S/N ratio (SNR)
Scan time
Coverage
Resolution
Image contrast

Unfortunately, optimization of these parameters may involve some trade-offs. To gain some advantage with one parameter, we might have to sacrifice another parameter. Let’s start out with the concept of signal-to-noise ratio (SNR).

Signal-to-Noise Ratio. What we want is signal. What we don’t want is noise. Although we can’t completely eliminate noise, there are ways to maximize the SNR. SNR is given by

which makes sense because N_y × NEX × T_s is the total time the machine is “listening” to the spin echoes.

Since T_s = N_x · ΔT_s and ΔT_s = 1/BW, then T_s = N_x/BW.

Therefore, SNR depends on

Voxel volume = Δx · Δy · Δz
Number of excitations (NEX)
Number of phase-encoding steps (N_y)
Number of frequency-encoding steps (N_x)
Full bandwidth (BW)

Let’s go through each parameter and see how SNR is affected.

Voxel Volume

If we increase the voxel size, we increase the number of proton spins in the voxel and, therefore, increase the signal coming out of the voxel (Fig. 17-1). The voxel volume is given by Voxel volume = Δx · Δy · Δz where Δx = pixel size in the x direction, Δy = pixel size in the y direction, and Δz = slice thickness.

NEX (Number of Excitations or Acquisitions). NEX stands for the number of times the scan is repeated. Let’s say we have two signals (S₁ and S₂), corresponding to the same slice (with the same G_y). There is constant noise (N) associated with each signal (N₁ = N₂ = N). If we add up the signals (assuming S₁ = S₂ = S), we get S₁ + S₂ = 2S However, if we add up the noise, we get

This formula does not make sense at first glance. Why do we get

N and not 2N? The answer has to do with a somewhat complicated statistical concept and the so-called random Brownian motion theory, which deals with the spectral density of the noise.

Figure 17-1. A voxel is a three-dimensional volume element with dimensions Δx, Δy, and Δz. The more spins in a voxel, the more signal. Therefore, increasing voxel size increases SNR.

In a simplistic approach, think of the noise as the variance (σ²) of a Gaussian distribution (σ = standard deviation). Then, for the sum of the two noise distributions, the variance is additive and given by σ₁² + σ₂² = σ² + σ² = 2σ² from which the standard deviation is calculated to be

This is where the

factor comes from. However, you don’t need to know the underlying math—you just need to understand the concept. In summary:

The resulting signal will be twice the original signal. The resulting noise, however, will be less—it will be the square root of 2 multiplied by the noise

In other words, if we increase the number of acquisitions by a factor of 2, the signal doubles and noise increases by

, for a net 2/

; thus, SNR increases by a factor of

Therefore, ↑ NEX by a factor of 2 → ↑ SNR by a factor of

Think of the NEX as an averaging operation that causes “smoothing” and improvement in the image quality by increasing the signal to a greater degree (e.g., factor 2) relative to the increase in the noise (e.g., factor

). As another example, increasing NEX by a factor of 4 results in an increase of signal by 4 and an increase of noise by

or 2. Thus, SNR increases by 4/2 or twofold.

N_y (Number of Phase-Encoding Steps). The same concept holds for N_y. That is, similar to NEX, there is a 41% (

) increase in SNR when N_y is doubled. As with NEX, when the number of phase-encode steps doubles, signal doubles and noise increases (randomly) by

(for a net

increase in SNR).

Bandwidth. An inverse relationship exists between BW and SNR. If we go to a wider bandwidth, we include more noise, and the SNR decreases. If we decrease the bandwidth, we
allow less noise to come through, and the SNR increases.

↓ BW → ↑ SNR To be exact, decreasing the BW by a factor of 2 causes the SNR to improve by a factor of

In general, decreased bandwidth causes the following:

Increased SNR
Increased chemical shift artifact (more on this later)
Longer minimum TE (which means less signal due to more T2 decay). Remember that Bandwidth = 1/ΔT_s = N_x/T_s

Therefore, a longer sampling time (T_s), which is necessary for a decreased bandwidth, results in a longer minimum TE. With a long TE, increased T2 dephasing results in decreased signal. However, the contribution from reduced noise due to a lower bandwidth outweighs the deleterious effect of reduced signal due to greater T2 decay from increased TE.
Decreased number of slices. This decrease is caused by the longer TE. Remember, number of slices = TR/(TE + T_s/2 + T_o) where T_s is the total sampling (readout) time and T_o is the “overhead” time. A narrower bandwidth is usually used on the second echo of a T2-weighted dual-echo image because, with the second echo, we have a longer TE and we are able to afford the longer sampling time. On the first echo, however, we can’t afford to use a narrower bandwidth because we can’t afford to lengthen the TE. However, we probably don’t need the smaller bandwidth anyway because we already have enough SNR on the proton density-weighted first echo of a long T2, double-echo image. A typical T_s for a 1.5-T scanner is 8 msec, resulting in a BW (for a 256 matrix) of BW = N_x/T_s = 256/8 = 32 kHz = ± 16 kHz = 125 Hz/pixel

Note that BW can be described as “full bandwidth” (32 kHz in example above), ± the Nyquist frequency (which is ± 16 kHz above and defines the FOV) or “bandwidth per pixel” (which is unambiguous if you forget the ±).

A typical “variable bandwidth” option includes

A wide bandwidth (±16 kHz) on the first echo, and
A narrow bandwidth (±4 kHz) on the second echo, thus increasing SNR and counteracting T2 decay effects.

Question: How does the gradient affect the BW?

Answer: Recall from Chapter 15 that the field of view (FOV) is given by FOV = BW/γG_x or G_x = BW/γFOV

For a given FOV, increasing the gradient G_x causes increased BW and, therefore, decreased SNR.

SNR in 3D Imaging

In 3D imaging, we have the same factors contributing to SNR, plus an additional phaseencoding step in the z direction (N_z):

From this equation, you can see why SNR in 3D imaging is higher than that in 2D imaging. Specifically,

Another way to look at SNR is to say that SNR depends on only two factors:

Voxel size
Total sampling time

Sampling time (T_s) is the time that we sample the signal. Therefore, it makes sense that the more time we spend sampling the signal, the higher the SNR will be. Let’s look again at the formula for SNR (in 2D imaging):

Recall that T_s = N_x/BW or 1/BW = T_s/N_x
so

We know that N_y is the number of phase-encoding steps, which is the number of times we sample the echo corresponding to a particular phaseencoding gradient G_y, and that NEX is the number of times we repeat each phase-encoding step. In essence, the factor T = T_s · N_y · NEX is the total sampling time of all the echoes received for a particular slice. Thus,

In summary, SNR can be increased by doing the following:

Increasing TR
Decreasing TE
Using a lower BW
Using volume (i.e., 3D) imaging
Increasing NEX
Increasing N_y
Increasing N_x
Increasing the voxel size

Resolution. Spatial resolution (or pixel size) is the minimum distance that we can distinguish between two points on an image. It is determined by Pixel size = FOV/number of pixels ↑ N_y → better resolution If we increase the number of phase-encoding steps, what happens to SNR? Obviously, better resolution usually means poorer SNR. However, if we look at Equation 17-2, it appears that by increasing N_y, the SNR should increase! What’s the catch? The catch is, we are keeping the FOV constant while increasing N_y. Take, for example, Pixel size along y-axis = Δ_y = FOV_y

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