% setup MRI-education-resources path and requirements
cd ../
startup

loading image
loading signal

Artifacts

This notebook includes a simulation of various MRI artifacts, as well as a high-level Artifact Comparison below. The wikipedia entry https://en.wikipedia.org/wiki/MRI_artifact is also very comprehensive.

Learning Goals

1. Identify artifacts and how to mitigate them

Introduction

Many of the artifacts that occur in MRI can be understood and analyzed using the k-space perspective. In particular, they can be understood as the k-space data being modified by some function. This is described mathematically in MRI Signal Equation and K-space in the K-space Data Weighting section.

Artifact Comparison

MRI artifacts can generally be categorized as originating from the sample, the sequence, or the system (Source in table below). The table below provides a high-level comparison of these artifacts.

Artifact Name	Source	Appearance	What to do?	Frequency or Phase encoding
Aliasing	Sequence - FOV too small	Signal folds across image	Increase FOV, swap PE/FE	Phase encoding
Gibbs Ringing/Truncation	Sequence - due to Fourier encoding of edges	Ripples/ringing at sharp edges	Filtering of data	N/A
Boundary Artifacts/Partial Volume	Sequence and Sample - opposite \(M_{XY}\) phases with a voxel due to inversion or chemical shift	Artificial dark lines at tissue boundaries	fat suppresion, fat/water imaging	N/A
Motion/Flow	Sample - signal modulated during spatial encoding	Copies or “Ghosts” of image regions that are changing due to motion or flow	Breath-hold, gating, triggering, flow compensation, swap PE/FE	Phase encoding
Image Displacement/Distortion	Sample - chemical shift (fat) and off-resonance (e.g. magnetic susceptibility differences)	Shifts in image	Increase bandwidths, shimming, fat suppression, fat/water imaging, swap PE/FE	Frequency encoding (2DFT), Phase encoding (EPI)
Slice Displacement	Sample chemical shift (fat) and off-resonance (e.g. magnetic susceptibility differences)	Slice location shifts	Increase RF bandwidth, shimming, 3D	N/A
T2*	Sample - magnetic suscpetibility differences (e.g. implants, air)	Signal loss	Spin-echo, shimming	N/A
Dielectric Shading	System - RF propogates unevenly, creating B1 inhomogeneity	Shading across entire image, particularly large FOV, higher B0	B1-insensitive pulse sequences (e.g. adiabatic pulses), image bias correction	N/A
RF interference/Zipper	System - unwanted RF signal in data	Line of noisy signal on top of image	RF shielding (close door), check RF hardware, check room lights	At a specific frequency encoding location
Gradient non-linearity	System - magnetic field gradients are not linear, especially away from isocenter	Distortion of subject, particularly near edges of large FOV	Gradient warping correction	N/A
Spike Noise	System - intermittent unwanted signal	Specific spatial frequency on top of entire image	check RF hardware (loose connections, broken components)	N/A

Displacement Artifacts

Since MRI relies on frequency to encode spatial information, unknown frequency shifts can lead to disortions of the image. These frequency shifts are due to chemical shift (e.g. fat) and/or off-resonance (e.g. main field inhomogeneities, susceptibility differences).

There will be a shift during frequency encoding of

\[\Delta_{FE} = \frac{\Delta f}{RBW} FOV_{FE}\]

where \(\Delta f\) is the frequency shift, \(RBW\) is the receiver bandwidth, and \(FOV_{FE}\) is the field of view in the frequency encoding direction.

During EPI, there is typically a much larger shift in the phase encoding direction that depends on the echo spacing, \(t_{esp}\). For simplicity, I convert the echo spacing into a “phase encoding bandwidth”, \(BW_{PE} = 1/t_{esp}\):

\[\Delta_{PE} = \frac{\Delta f}{BW_{PE} N_{interleaves}} FOV_{PE}\]

where \(N_{interleaves}\) is the number of interleaves that can be used to reduce the displacement.

Finally, there will also be a displacement of the slice selection, and this will be

\[\Delta_{SS} = \frac{\Delta f}{BW_{rf}} \Delta_z\]

where \(BW_{rf}\) is the slice select pulse bandwidth.

Motion and Flow Artifacts

Motion, including flow, can result in artifacts in MRI if it leads to inconsistency in the data.

Periodic motion such as breathing, heart beating, and pulsatile flow will lead to distinct ghosting artifacts in the phase encoding direction. The location of ghosting artifacts in sequential phase encoding, will be at predictable intervals in the phase encoding direction:

\[\Delta_{PE} = \frac{TR}{T_{motion}} FOV_{PE}\]

where \(T_{motion}\) is the period of the motion (e.g. \(T_{motion} = 1 s\) for a heart rate of 60 beats per minute ).

Incoherent or more random motion such as irregular breathing, arrhytthmias, coughing, bulk motion will lead to more diffuse ghosting artifacts.

Simulations of Artifacts

% load k-space data
dataname = 'Data/se_t1_sag_data';
load(dataname)
kdata = data;
S = size(kdata);

im_original = ifft2c(kdata);

subplot(121)
imagesc(log(abs(kdata)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_original), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off

warning: load: 'C:\Users\PLarson\Documents\GitHub\MRI-education-resources\Data\se_t1_sag_data.mat' found by searching load path

%% aliasing
N_undersamp = 2;  % >= 1
data_undersamp = zeros(size(kdata));
Iundersamp = 1:N_undersamp:S(1);
data_undersamp(round(Iundersamp),:) = kdata(round(Iundersamp),:);
im_undersamp = ifft2c(data_undersamp);


subplot(121)
imagesc(log(abs(data_undersamp)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_undersamp), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off

%% spike noise
spike_location = [.6 .53];

data_spike = zeros(size(kdata));
data_spike(round(S(1)*spike_location(1)), round(S(2)*spike_location(2))) = max(kdata(:))/1.5;
im_spike = ifft2c(kdata + data_spike);


subplot(121)
imagesc(log(abs(kdata + data_spike)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_spike), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off

%% Ringing (with rect object)
N = 32;
kx = [-N/2:N/2-1]/N;
N_rect = N/2+2;
kdata = sinc(kx *N_rect).' * sinc(kx *N_rect);

rect_ringing = ifft2c(kdata);

subplot(221)
imagesc((abs(kdata)), [0 (1)])
colormap(gray), axis equal tight off
subplot(222)
imagesc(abs(rect_ringing), [0 max(abs(rect_ringing(:)))])
colormap(gray), axis equal tight off
ylabel('Ringing')

kdata_windowed = kdata .* (hamming(N) * hamming(N).');
rect_windowed = ifft2c(kdata_windowed);


subplot(223)
imagesc((abs(kdata_windowed)), [0 (1)])
colormap(gray), axis equal tight off
subplot(224)
imagesc(abs(rect_windowed), [0 max(abs(rect_windowed(:)))])
colormap(gray), axis equal tight off
ylabel('Windowed')

%% RF interference
relative_RF_frequency = 0.6;

%single frequency, phase modulated
ph_int = pi*rand(S(1),1);
rfint = exp(i*2*pi* [1:S(1)] *relative_RF_frequency/2 ) *  max(abs(kdata(:)))/S(1)/1.5;
data_rfint = repmat(rfint, [S(1), 1]) .* repmat(exp(i*ph_int), [1, S(2)]);
im_rfint = ifft2c(kdata + data_rfint);

figure
subplot(121)
imagesc(log(abs(kdata + data_rfint)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_rfint), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off

% RF interference -simulate amplitude modulated interference
relative_RF_frequency = 0.2;
rfint = exp(i*2*pi* [1:S(1)]/S(1) * S(1)*relative_RF_frequency/2) *  max(abs(kdata(:)))/S(1)/3;
data_rfint = randn(S(1),1) * rfint;
im_rfint = ifft2c(kdata + data_rfint);

figure
subplot(121)
imagesc(log(abs(kdata + data_rfint)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_rfint), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off

% RF interference - simulate frequency modulated interference
relative_RF_frequency = 1;
f = randn(S(1),1)*relative_RF_frequency/2;
data_rfint = exp(i*2*pi* f*[1:S(1)]/S(1)  ) *  max(abs(kdata(:)))/S(1)/1.5;
im_rfint = ifft2c(kdata + data_rfint);

figure
subplot(121)
imagesc(log(abs(kdata + data_rfint)), [0 max(log(abs(kdata(:))))])
colormap(gray), axis equal tight off
subplot(122)
imagesc(abs(im_rfint), [0 max(abs(im_original(:)))])
colormap(gray), axis equal tight off