Magnetic Resonance Imaging

Dr. Rafiqul Islam

 Introduction
o Magnetic resonance imaging (MRI) is an imaging
technique used primarily in medical settings to
produce high quality images of the soft tissues of
the human body.
o It is based on the principles of nuclear magnetic
resonance (NMR), a spectroscopic technique to
obtain microscopic chemical and physical
information about molecules
o MRI has advanced beyond a tomographic imaging
technique to a volume imaging technique
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 Timeline of MR Imaging
1972 – Damadian
patents idea for large
NMR scanner to 1985 – Insurance
detect malignant reimbursements for
tissue. MRI exams begin.

1973 – Lauterbur MRI scanners

publishes method for
1924 - Pauli suggests 1937 – Rabi measures become clinically
generating images prevalent.
that nuclear particles magnetic moment of
using NMR gradients.
may have angular nucleus. Coins
momentum (spin). “magnetic resonance”.
NMR renamed MRI

1920 1930 1940 1950 1960 1970 1980 1990 2000

1990 – Ogawa and
1946 – Purcell shows 1973 – Mansfield
colleagues create
that matter absorbs independently
functional images
energy at a resonant 1959 – Singer publishes gradient
using endogenous,
frequency. measures blood flow approach to MR.
blood-oxygenation
using NMR (in
contrast.
mice).
1946 – Bloch demonstrates 1975 – Ernst
that nuclear precession can be develops 2D-Fourier
measured in detector coils. transform for MR.

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Nobel Prizes for Magnetic Resonance
• 1944: Rabi
Physics (Measured magnetic moment of nucleus)

• 1952: Felix Bloch and Edward Mills Purcell

Physics (Basic science of NMR phenomenon)

• 1991: Richard Ernst

Chemistry (High-resolution pulsed FT-NMR)

• 2002: Kurt Wüthrich

Chemistry (3D molecular structure in solution by NMR)

• 2003: Paul Lauterbur & Peter Mansfield

Physiology or Medicine (MRI technology)

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Main Components of a Scanner
• Static Magnetic Field Coils
• Gradient Magnetic Field Coils
• Magnetic shim coils
• Radiofrequency Coil
• Subsystem control computer

• Data transfer and storage computers

• Physiological monitoring, stimulus display, and behavioral
recording hardware

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 MRI Hardware
RF Coil
B0

Magnet Gradient Coil RF Coil

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 MRI Component
ShimmingRF RF gradient
coil coil
main main
magnet magnet

Transmit Receive

Control
Computer

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 Main Magnet Field
• Purpose is to align H protons in H2O (little magnets)

[Main magnet and some of its lines of force]

[Little magnets lining up with external lines of force]

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 MRI Basics
• Nuclear Magnetic Resonance (NMR) (or Magnetic
Resonance Imaging - MRI)
• most detailed anatomical information
• high-energy radiation is not used, i.e. “save”
• based on the principle of nuclear resonance
• (medicine) uses resonance properties of protons
 MRI Basics: polarized

• all atoms (core) with an

odd number of protons
have a ‘spin’, which leads to
a magnetic behavior
• Hydrogen (H) - very
common in human body +
very well magnetizing
• Stimulate to form a
macroscopically
measurable magnetic field
 MRI Basics: Signal to Noise Ratio
• proton density pictures - measures H
MRI is good for tissues, but not for bone
• signal recorded in Frequency domain!!
• Noise - the more protons per volume unit, the more
accurate the measurements - better SNR through
decreased resolution
 MRI Principles
o The composition of the human body is primarily
fat and water
o Fat and water have many hydrogen atoms
o 63% of human body is hydrogen atoms
o Hydrogen nuclei have an NMR signal
o MRI uses hydrogen because it has only one
proton and it aligns easily with the MRI magnet.
o The hydrogen atom’s proton, possesses a
property called spin
o A small magnetic field
o Will cause the nucleus to produce an NMR signal

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 MRI Principles
o The spinning hydrogen protons act like small ,
weak magnets.
o They align with an external magnetic field (Bø).
o There is a slight excess of protons aligned with
the field. (for 2 million , 9 excess)
~6 million billion/voxel at 1.5T
o The # of protons that align with the field is so
very large that we can pretty much ignore
quantum mechanics and focus on classical
mechanics.

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 More MRI Principles
• The spinning protons wobble or “precess”
about that axis of the external Bø field at the
precessional, Larmor or resonance frequency.
• Magnetic resonance imaging frequency
n = g Bo
where g is the gyromagnetic ratio
The resonance frequency n of a spin is
proportional to the magnetic field, Bo.
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 More MRI Principles
o Now if an electromagnetic radio frequency
(RF) pulse is applied at the resonance (Larmor,
precession, wobble) frequency, then the
protons can absorb that energy, and (at the
quantum level) jump to a higher energy state.

o At the macro level, the magnetization vector,

Mø, (6 million billion protons) spirals down
towards the XY plane.

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 MRI Details: Magnet
• The most expensive component of
the imaging system.
• Most magnets are of the
superconducting type. This is a
picture of a 1.5 Tesla
• A superconducting magnet is an
electromagnet made of
superconducting wire.
• Superconducting wire has a
resistance close to zero when it is
cooled to a zero temperature (-
273.15o C or 0 K, by emersion in
liquid helium).
• Once current flows in the coil, it
will continue to flow as long as the
coil is kept at liquid helium
temperatures.

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MRI Details: Gradient Coils

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 Gradient Coils Principles
o These are room temperature coils
o A gradient in Bo in the Z direction is achieved with an
antihelmholtz type of coil.
o Current in the two coils flow in opposite directions creating
a magnetic field gradient between the two coils.
o The B field at one coil adds to the Bo field while the B field
at the center of the other coil subtracts from the Bo field
o The X and Y gradients in the Bo field are created by a pair of
figure-8 coils. The X axis figure-8 coils create a gradient in
Bo in the X direction due to the direction of the current
through the coils.
o The Y axis figure-8 coils provides a similar gradient in Bo
along the Y axis.

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RF Coils

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 RF Coils
o RF coils create the B1 field which rotates the
net magnetization in a pulse sequence.
o RF coils can be divided into three general
categories
o transmit and receive coils
o receive only coils
o transmit only coils

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 MRI Image Example: Knee

Coronal Sagittal
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MRI Image Example: Brain

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MRI Image Formation

K-space data MRI Image

 MRI Image Formation
• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts
 MR imaging is based on precession
z

[courtesy William Overall]

Spins precess at the Larmor rate:

 = g (B0 + DB)

field strength field offset

2D Imaging via 2D Fourier Transform

1DFT

1D Signal 1D “Image”

2DFT
ky y

kx x
2D Signal 2D Image
K-space (raw data) Image space
(spatial frequency domain) FT

Measured MRI signal (k-space)

i2 kx t x i2 ky t y
S kx t ,ky t M x,y e e dx dy

Magnetization at each voxel (= image): M x, y M xy0 x , y , z dz

MRI Reconstruction Examples
Effects of Sampling the K-space
Partial k-space coverage
IFT IFT
 Gradients and image acquisition
• Magnetic field gradients encode spatial
position in precession frequency
• Signal is acquired in the frequency domain (k-
space)
• To get an image, acquire spatial frequencies
along both x and y
• Image is recovered from k-space data using a
Fourier transform
 Sampling k-space
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x FT
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x

o Perfect reconstruction of an object would require

measurement of all locations in k-space (infinite!)
o Data is acquired point-by-point in k-space (sampling)
 Sampling k-space
o highest frequency we Dkx ky
need to sample in k-
space (kmax)?
o How close should the
samples be in k-
space (Dk)? kx

2 kxmax
2D Extension
kymax

1 2 3 4

kxmax 5 6 kx
7
max
8

9 10 11 12

kymax
2 kxmax
13image resolution
kmax determines 14 15 16
Large kmax means high resolution ! increasing kmax
 Nyquist Sampling Theorem
• A given frequency must be sampled at least twice per cycle in
order to reproduce it accurately
1 samp/cyc 2 samp/cyc

Cannot distinguish Upper waveform is

between waveforms resolved!
Nyquist Sampling Theorem

increasing field

Insufficient sampling
forces us to interpret
that both samples are
at the same location:
aliasing
Aliasing (ghosting): inability to differentiate between 2 frequencies makes
them appear to be at same location

x x

Applied FOV Aliased image

max ive max ive
frequency frequency
 k-space relations:
FOV and Resolution
Dkx ky

FOV = 1/Dkx
kx
Dx = 1/(2*kxmax)

2 kxmax
 k-space relations:
FOV and Resolution
Dkx ky

xmax = 1/Dkx
kx
2 kxmax = 1/Dx

2 kxmax

k-space and image-space are inversely related: resolution in one domain

determines extent in other
 k-space Image

Full sampling Full-FOV,

high-res

2DFT Full-FOV,
Reduce kmax low-res:
blurred

Low-FOV,
high-res:
Increase Dk may be aliased
 Visualizing k-space trajectories


kx(t) = g Gx(t) dt

k (t) = g G (t) dt
y y

k-space location is proportional to accumulated area under

gradient waveforms
Gradients move us along a trajectory through k-space !
Raster-scan (2DFT) Acquisition

Acquire k-space line-by-line (usually called “2DFT”)

Gx causes frequency shift along x: “frequency encode” axis
Gy causes phase shift along y: “phase ecode” axis
Echo-planar Imaging (EPI) Acquisition

Single-shot (snap-shot): acquire all data at once

Many possible trajectories through k-space…
 Trajectory considerations

• Longer readout = more image artifacts

– Single-shot (EPI & spiral) warping or blurring
– PR & 2DFT have very short readouts and few artifacts

• Cartesian (2DFT, EPI) vs radial (PR, spiral)

– 2DFT & EPI = ghosting & warping artifacts
– PR & spiral = blurring artifacts

• SNR for N shots with time per shot Tread :

SNR   Ttotal =  N  Tread

 Partial k-space
If object is entirely real, quadrants of k-space
contain redundant information

2 1

c+id a+ib

ky aib cid
3 4

kx
 Partial k-space
Idea: just acquire half of k-space and “fill in” missing data
Symmetry isn’t perfect, so must get slightly more than half

c+id a+ib

measured data
ky a ib c id missing data

kx
 Multiple approaches

ky ky

kx kx

Acquire half of each Reduced phase

frequency encode encode steps
 Parallel imaging
(SENSE, SMASH, GRAPPA, iPAT, etc)
Surface
coils

Object in Single coil

8-channel array sensitivity

Multi-channel coils: Array of RF receive coils

Each coil is sensitive to a subset of the object
 Parallel imaging
(SENSE, SMASH, GRAPPA, iPAT, etc)
Surface
coils

Object in Single coil

8-channel array sensitivity

Coil sensitivity to encode additional information

Can “leave out” large parts of k-space (more than 1/2!)
Similar uses to partial k-space (faster imaging, reduced distortion, etc),
but can go farther
 Slice Selection
RF

0 frequency

Gz gradient

excited slice
 2D Multi-slice Imaging

excited slice

t1
t2
t3
t4
t5
t6

All slices excited and acquired sequentially (separately)

Most scans acquired this way (including FMRI, DTI)
 “True” 3D imaging

excited volume

excited volume

Repeatedly excite all slices simultaneously, k-space acquisition extended

from 2D to 3D
Higher SNR than multi-slice, but may take longer
Typically used in structural scans
 Motion Artifacts

PE

o Motion causes inconsistencies between readouts in multi-

shot data (structurals)
o Usually looks like replication of object edges along phase
encode direction
 Gibbs Ringing (Truncation)

Abruptly truncating signal in k-space introduces “ringing” to

the image
 EPI distortion (warping)
field offset image distortion

Field map EPI image

(uncorrected)

Magnetization precesses at a different rate than expected

Reconstruction places the signal at the wrong location
 EPI unwarping (FUGUE)

field map uncorrected corrected

Field map tells us where there are problems

Estimate distortion from field map and remove it
 EPI Trajectory Errors

Left-to-right lines offset from right-to-left lines

Many causes: timing errors, eddy currents…
 EPI Ghosting
Shifted trajectory is sum of 2 shifted
undersampled trajectories
Causes aliasing (“ghosting”)
To fix: measure shifts with reference
scan, shift back in reconstruction

= +

undersampled
 Thank you
• Question?

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