MRI Physics: MRI Image Formation Parameters, SNR, and Artifacts

Image Formation Parameters & SNR | Artifacts | Go Home

This MRI simulation shows you how changes in scanner parameters affect the image, aliasing, and SNR. Change the numbers in the boxes to see the effects. Green = higher value; Red = lower value. If your browser does not support Java, use the examples to see the image change.

Some examples:


γ = 42.6 MHz/T

Gx mT/m

BW* kHz = ± kHz

Matrix Size:
N Scan percentage %
Nx x Ny

Δz mm

Δtx ms = 1/BW

tx ms = Δtx * Nx

Assume FSE with TR = 1000 ms, ETL = 8.
Scan time s

Scan time Unchanged.

K Space

Δkx cm-1 = 1/FOVx = γ * Gx * Δtx

kx cm-1 = Δkx * Nx = 1/Δx

Δky cm-1 = 1/FOVy

ky cm-1 = Δkx * Nx = 1/Δy

Chemical Shift

At B0 = 1.5 T,
Δf(fat-water) = 3.5E-6 * γ * B0 = 220 Hz.

BW/pixel Hz/pixel

Misregistration by


Δx mm = FOVx / Nx

FOVx* cm = BW / (γ * Gx)

Δy mm = FOVy / Ny

Rectangular FOV %

FOVy cm = FOVx * RFOV

Resolution Unchanged.

FOV Unchanged.

2D SNR relative to baseline
SNR ∝ (voxel volume) * sqrt(sampling time)
= Δx * Δy * Δz * sqrt(Ny * NEX / BW)
= FOVx/Nx * FOVy * Δz * sqrt(NEX / (Ny * BW))

SNR Unchanged.

MRI Simulation

Explanations of Bandwidth and Reduced K-Space Acquisition


Just like in radio, bandwidth refers to the range of frequencies that a receiver listens to. Remember than in MRI, the frequencies encode one spatial dimension (for sake of discussion, the x-axis). (Of course, these are on top of the 'carrier frequency' which is the precession rate of a proton in the main magnetic field B0 as given by the Larmor equation.)

There are several important things to know about bandwidth. The first is its relationship to the frequency encoding gradient strength (Gx) and field of view (FOV). As mentioned, the gradient field sets up a relationship between frequency and position along the x-axis. Thus, since the bandwidth determines the range of frequencies we receive, it determines our FOV.

Bandwidth and Gradient strength

The second important thing to know about bandwidth is that it impacts the time required for the acquisition of the echo. Wider bandwidth means more high frequencies, and high frequencies are faster to acquire (though your sampling frequency has to be higher as well, per the Nyquist theorem). Thus, higher bandwidth takes less time to acquire. This is important for fast gradient echo sequences (e.g. 3D GRE), though less important for many standard FSE sequences (since TR is so long). A more detailed discussion on this subject can be found in the separate section on K-space.

Thirdly, bandwidth affects signal-to-noise (SNR). One major source of noise in MRI is electronic noise in the circuits. This noise is relatively evenly spread across all frequencies. As mentioned, increasing bandwidth means increasing the range of frequencies that you are acquiring for your signal. More frequencies means you are capturing more of the noise. The overall signal does not change, it is just spread across more frequencies. Thus, same signal and increased noise means that SNR goes down with higher bandwidth.

As a final point, bandwidth also impacts the prominence of chemical shift artifact, which is the difference between the precessional speed of fat and water protons. For a full discussion, see the separate section on Chemical Shift Artifact, but remember that the gradient sets up a frequency differential along the x-axis. The bigger the gradient, the more adjacent pixels are separated in frequency (big gradient => wide bandwidth for the same FOV, since our frequency range has to increase).

Low versus high bandwidth

Graph illustrating the difference between a low BW = low gradient (blue) and a high BW = high gradient (red). Obviously, the frequency difference between pixel 0 and pixel 10 is bigger with the higher gradient, which is why a larger bandwidth is needed. The graph also shows how each pixel (e.g. pixels 3 and 4) are more separated in frequency with the higher bandwidth.

Thus, the bigger the gradient, the better fat and water, with their slightly different precessional frequencies, will fit into the same pixel bin. In other words, increasing bandwidth reduces chemical shift artifact. Artifacts from metal implants are related to the susceptibility of the implants, i.e. how they change the local magnetic field. Near the implants, the magnetic field will be off by a bit, meaning that the precession frequency f = γ * B will be slightly off. Thus, for the same reasons as with chemical shift artifact, metal artifacts will decrease with higher bandwith.

K Space

K space is a very confusing concept to wrap your mind around fully. The easiest aspect to think about is the concept of frequency data (K space) as compared to pixel data (image or real space). Higher frequency waves are narrower, so they represent the finest details in an image. Think about a sharp edge - the color changes very fast as you cross an edge, i.e. the frequency of change is high. Thus, as you know, the perimeter of K space, which is the high frequency data, represents fine details. The center of K space - low frequency information - represents the smoother parts of the image, like major organs (people refer to this as the contrast in the image). K-Space is discussed in more detail in the section on Spatial Localization in MRI.

Often we want to speed up our scan by decreasing the number of phase encoding steps. One way to do this is simply not acquire some parts of K space. There are several different ways to do this:

The more confusing concept having to do with K space is spatial frequency. This represents converting the pixel-based frequency data that we acquire into millimeter- or distance-based frequency data. The MR machine knows how to do this because it knows how strong the frequency and phase-encoding gradients are, per millimeter. The confusing aspecct is that spatial frequency is expressed in units of inverse distance.




RF Contamination


MRI Artifact Simulation

Try the above MRI artifact simulation to see how different artifacts appear in the image and in K-space. All MR artifacts follow from how MR images are acquired. Thus, if you understand K space and how an MR scanner works, you should be able to figure out the artifacts.


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

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