MRI Physics 2: Introduction to Magnetic Resonance...

MRI Physics 2: Introduction to Magnetic

Resonance Imaging (MRI) Gareth J. Barker

Department of Neuroimaging

Terminology - Recap Nuclear Magnetic Resonance

– Property of (some) Nuclei – Magnetic effect – Resonance (i.e. matching) effect of some

property of nucleus to magnetic field MRS (Magnetic Resonance Spectroscopy) MRI (Magnetic Resonance Imaging)

More in later lectures … This lecture …

Terminology

sMRI •  structural MRI

–  Investigates physical appearance of brain

–  measurement of physical properties of brain structures

•  e.g. volumes, shapes, lengths = morphology

fMRI •  functional-MRI:

–  indirect measurement of brain activity related to function

–  extremely subtle changes in tissue appearance related to changes in blood oxygenation (BOLD)

–  requires detailed comparison of rapidly acquired “structural” scans

Basic principles of MRI apply to both sMRI and fMRI; application specific details in later lectures …

Magnetic Resonance Imaging

•  … can create images of many parts of the body –  Both structural &

functional •  How?

Learning Objectives •  To be aware of the basic concepts of

Magnetic Resonance Imaging (MRI), including: – Magnetic field gradients – Spin echoes and gradient echoes –  “Spin Warp” imaging:

•  Slice selection, frequency encoding and phase encoding

•  Multi-slice, 2D and 3D sequences – K-space

GRADIENTS AND ECHOES MRI Physics

•  By convention, the main magnetic field, B0, is aligned with z

Field Gradients

•  A field gradient along x, for example, means that magnetic field (in z direction) varies with position along x.

-x x

y z B 0

B0 + Gxx

B0 - Gxx

Colour Gradient

From lecture 1– More Units •  Magnetic field strength

is measured in Tesla

•  Older unit, Gauss, is still occasionally used –  10kG=1T –  10G=1mT

•  We will discuss magnetic field gradients in a later lecture

•  Gradient strength is measured in mTesla per metre (mT/m) –  1mT/m = 10 G/cm

From lecture 1– More Units •  Magnetic field strength

is measured in Tesla

•  Older unit, Gauss, is still occasionally used –  10kG=1T –  10G=1mT

•  We will discuss magnetic field gradients in a later lecture

•  Gradient strength is measured in mTesla per metre (mT/m) –  10mT/m = 1G/cm

Correction!!!!

Field Gradients •  What happens

when magnetic field, B, is not uniform over the object? –  if field increases

linearly with position

–  resonant frequency also increases linearly with position

Position

Fiel

d Si

gnal

Frequency

Projection-reconstruction imaging

• A single 90o pulse, followed by a field gradient, can give a 1 dimensional (1D) image, or projection.

Position

Sign

al Brightness

represents signal

intensity

Projection-reconstruction Imaging

• Rotating gradient can build up complete image from projections

Position

Sign

al

Position

Sign

al

Position

Sign

al

Position

Sign

al

Projection-reconstruction Imaging

•  Full 2D image can be formed –  similar to how a CT

scanner works –  early MR scanners

used this approach

Swinburne University of Technology, Medical Imaging HET408,

David Liley (dliley@swin.edu.au)

Projection-reconstruction Imaging

•  It is difficult to measure signal immediately after 90o pulse

•  We can’t control degree of T2 or T2* decay –  More in next lecture

•  It is difficult to

reconstruct artefact free images from projections

•  Collect an echo

•  Use a phase encoding technique –  spin warp imaging

Echo Signals

t = 0 t = TE/2

t = TE/2

All stop, and reverse direction

t = ΤΕ

Spin & Gradient Echo Imaging

•  ‘Spin Echo’ imaging uses an extra (180o) RF pulse to refocus effects of dephasing – basis for many sMRI sequences

•  ‘Gradient Echo’ imaging refocuses spins without a 180o pulse – used for both sMRI and fMRI

ΤΕ/2

ΤΕ/2

180ox

Spin Echo Imaging

•  90o pulse (along x') produces transverse magnetisation along y'

•  magnetisation dephases due to variations (inhomogeneities) in the local field

•  180o pulse (along x') flips spins

•  spins precess in same direction and at same speed as before

•  transverse magnetisation rephases along –y’

Gradient Echo Imaging

•  90o pulse (along x') produces transverse magnetisation along y'

•  magnetisation dephases –  applied gradient

•  plus time-invariant local field inhomogeneities

•  spins precess in opposite direction and at same speed as before –  transverse magnetisation

rephases •  effect of local inhomogeneity

is NOT refocused

ΤΕ/2

ΤΕ/2

Recap •  We can use magnetic field gradients to

encode spatial positions

•  For practical reasons, we often want to collect an echo signal, rather than the FID. We can do this with either: –  Gradient echoes

•  Uses reversal of a magnetic field gradient

–  Spin echoes •  Uses 180o RF pulses

SPIN WARP IMAGING MRI Physics

Spin Warp Imaging •  Remember, creating an image requires:

– Slice selection – Spatial encoding

•  Frequency encoding uses a gradient during data acquisition, affecting frequency of signal received

•  Phase encoding uses a gradient before data acquisition, affecting phase of signal received

– All of these processes depend on the Fourier Transform

Δs

Δs = slice thickness

Frequency encoding

Phase encoding

Fourier Transformation •  We can describe any

signal in two ways: –  frequencies that make it

up, along with their relative proportions

–  amplitude of the total signal at each instant of time

•  eg: Sound –  wave form (pressure wave)

•  time domain –  frequency (musical notes)

•  frequency domain

•  The Fourier Transform (FT) is a mathematical formula that translates one description into the other

•  Any continuous function f(x) has a FT, F(s) –  If x is time, then s is spatial

frequency –  f(x) and F(s) describe same

thing in different ways

Fourier Transformation •  FT of f(x)

•  Inverse transform

–  Note convention to use same letter for each member of a Fourier pair, with one in upper- and one in lower-case

•  FT then inverse FT gets you back where you started

–  there are several different conventions for positioning of the '2π's in these equations

•  pick one and stick with it!

∫∞

∞−

−= dxexfsF xsi π2)()(

∫∞

∞−

= dsesfxF xsi π2)()(

∫ ∫∞

∞−

∞

∞−

−= dsedxexfxf xsixsi ππ 22 ])]([[)(

Common FT Pairs

Gaussian Gaussian ‘top hat’ sinc triangle sinc2 cosine even

impulse pair

sine odd impulse pair

constant delta function

Rep

rodu

ced

from

: Bra

cew

ell,

The

Four

ier T

rans

form

and

its

App

licat

ions

, McG

raw

Hill

, 196

5

Slice Selection •  Apply a shaped

Radio Frequency (RF) pulse in presence of a slice select gradient –  Only excites (affects)

spins whose resonant frequency falls within range of frequencies in pulse

⇐ FT ⇒ Bandwidth

Position R

eson

ant

Freq

uenc

y

Not excited Not excited

Exci

ted

Resonant frequency within

bandwidth of pulse

Shaped Pulses •  One of the most common

RF pulse shapes is the sinc –  mathematically defined as

–  α is a constant which determines bandwidth

•  Its FT has a 'top hat' shape –  defines amplitude, and

therefore effectiveness, at various frequencies

tty

αα )sin(

= τ

Time →

2/τ = Δω Frequency →

Shaped Pulses •  Another common RF

pulse shapes is a Gaussian –  mathematically defined as

–  α is again a constant which determines the bandwidth

•  FT of a Gaussian is also a Gaussian

•  Unfortunately, effect of any of these pulses at high flip angles is not exactly what would be expected from FT –  Numerically optimised

pulses can be used to produce slice profiles which are closer to optimum

Time →

)exp( 2ty α−=

Slice Selection •  Note that a rephase

gradient lobe is needed, to counteract dephasing during portion of pulse for which magnetisation has a transverse component –  gradient area required

depends on pulse shape –  typically approximately

half that of main slice select gradient

90o

Gslice

Slice Selection •  As well as the

excitation pulse, we also need the spin echo refocusing pulse

•  This must also be slice selective, so we apply a gradient –  Note that this is

symmetrical •  no rephase lobe needed

90o 180o

Frequency Encoding •  Apply a gradient during

data acquisition (often called read or readout gradient) –  Notice dephase lobe before

readout period. •  ensures that halfway

though readout period, when spin echo occurs, spins are all in phase

•  gradient area required is exactly half that of main read gradient

•  can also be placed before 180o pulse, in which case amplitude is positive:

180o

Gread

Gread

Frequency Encoding •  Spins at different

positions experience slightly different local fields and therefore precess at different rates –  Resulting signals

thus have different frequencies

+

... etc.

Position

Local

FT

+

+

+

+

Bottles of water

fieldPosition Fi

eld

Phase Encoding

•  How do we encode final direction?

•  Can’t just apply another gradient at 90o to readout, as this would just give an effective gradient at 45o

–  Instead, manipulate phase of the signal

Phase Encoding

-1

-0.5

0

0.5

1

low freq.high freq.

-1

-0.5

0

0.5

1phase = 0 degphase = 20 deg

Same amplitude and phase, but different frequencies

Same amplitude and frequency, but different phases

Phase Encoding •  Apply a gradient before

data acquisition –  usually called phase

encoding gradient •  As before, spins at

different positions experience slightly different local fields and precess at different rates –  By end of gradient they

have precessed through different angles, giving signals with different phases

–  Can also be placed before 180o pulse:

Gread

180o

Gread

Gphase

Gphase

Phase Encoding •  We can only

measure phases between 0 and 2π –  can not unambiguously

distinguish the spins

•  Repeat acquisition with different phase encode gradient strengths –  way in which phase

changes with gradient strength is unique to spins in a particular position + ... etc.

Position

Local field

++

FT

y =

stay in phase

B0

B0

B0

B0

B0

1 2-1-2 0

y = 1 2-1-2 0

Spins at y = 0

Fiel

d

Spins at y=0 stay in phase

Position

Phase Encoding •  Repetition is often

shown with dotted or dashed gradients –  Sequence must be

repeated ‘matrix size’ times to collect complete information

–  takes 64, 128, 256 … TR periods

Gread

Gphase

Pulse Sequence Diagrams •  Putting it all together…

•  Pulse sequence diagrams, show all gradients & RF pulses used –  Give relative timing and

amplitudes of each pulse –  not usually drawn exactly to

scale. –  shading is often used to indicate

gradient areas which should be equal (or equal and opposite)

–  arrows indicating exact timing of events

Data acquisition

G

G G

RF

TE TR

90 180

Acq or,

slice read

phase

Echo Time & Repetition Time

•  TE and TR determine appearance of a spin echo image – different combinations will produce different

degrees of contrast (intensity difference) between tissues

•  changing TR will change contrast between tissues with different T1 relaxation times

•  changing TE will change contrast between tissues with different T2s

– more in next lecture

2D & 3D IMAGING

Multi Slice Imaging •  TR is often much longer than

TE (to give required image contrast) –  long delay between end of data

acquisition and next 90o pulse –  provided we don't interfere with

recovery of longitudinal magnetisation from slice we have excited we can use this delay to measure something else

•  Ideally, a slice selective pulse only affects magnetisation within the slice which it is selecting –  by adjusting frequency of RF

pulse we can excite a second slice without affecting first

–  can then phase and frequency encode as for first slice

Readout

Phase Encoding

Slice Selection

The magnetisation from this slice has been tilted in the xy plane and has formed the echo.

The magnetisation from anywhere outside the excited slice is still aligned along B0

and has NOT contributed to the spin echo.

Readout

Phase Encoding

Slice Selection

The magnetisation from this slice has been tilted in the xy plane and has formed the echo.

The magnetisation from anywhere outside the excited slice is still aligned along B0

and has NOT contributed to the spin echo.

Multi Slice Imaging

•  If TR is long enough we can fit several slices into a single TR:

Slice 1 Slice 2 Slice 3

TR TR

Phase encode 1 Phase encode 2

Multi Slice Imaging •  Pulse sequence diagrams

usually don’t show repetition of gradients needed for multiple slices

•  (Also don’t typically show repetitions for averaging, multple cardiac phases, etc,)

Data acquisition

G

G G

RF

TE TR

90 180

Acq or,

slice read

phase

3D (‘Volumetric’) Imaging •  Acquires data from full 3D volume

rather than single slice –  typically still uses slice selective pulses, but

selects a thick (10 or 20 cm) slab •  phase encode signal from this whole volume along

both y and z •  phase encode gradient steps through a number of

amplitudes equal to the matrix size in that dimension, just as in 2D case

– use readout gradient to encode final dimension, as in 2D case

3D (‘Volumetric’) Imaging •  Imaging time is equal to:

TR * (number of phase encoding steps in dimension 1) * (number of steps in dimension 2)

•  Imaging time will be very long unless TR is short, e.g.:

2 * 256 * 192 = 98304 s = 1638.4 minutes = 27.3 hours!

•  Use gradient echo sequence, with a very short TR and a low flip angle to minimize T1 weighting –  more in next lecture

Recap

•  To create an image we need to spatially encode the signal in 3 dimensions – For 2D imaging we use:

•  Slice selection, frequency encoding in one direction & phase encoding in the other

•  Can often fit multiple slices with in a TR, allowing multi-slice imaging

– For 3D imaging we use: •  (Optional) slice/slab selection, frequency encoding

in one direction & phase encoding in the other two directions

K-SPACE Image Reconstruction

k-space •  Remember:

–  MR data points are collected as a function of: •  phase encode step number (n) •  time from start of readout window, (t)

•  Can visualise this as a 2D plot –  Turns out to be convenient to think of the axes as how

much x (or y, or both) gradient has been “seen” when data are collected

–  A value ‘k’ (with components kx, ky, kz) defines where we are in ‘k-space’ ''

0))(()( dttt

t

∫= Gk γ

Spatial Frequencies •  Spatial frequencies (positions in

k-space) have a useful, physical, interpretation –  High spatial frequencies describe things

that change rapidly from pixel to pixel •  convey detail of image

–  Low spatial frequencies describe things that change slowly

•  convey overall form of image

–  Zero spatial frequency describes overall intensity of image

•  contrast of image is largely determined by spatial frequencies close to zero

•  The Fourier Transform (FT) can convert k-space data into an image

‘Rule of Thumb’

•  Something large in one domain corresponds to something small in other, eg:

largest values of k smallest object resolvable

total area of k-space covered

pixel size

total area of image covered (ie field of view)

spacing between k-space points

Spin Echo •  What does the k-

space sampling scheme for a simple spin echo sequence look like?

Data acquisition

Gy

Gx

Gz

RF

TE

TR

k Space Sampling Schemes a) apply a 90o pulse

•  No gradients applied yet, so we must be at centre of k-space

k

kx

y

a

k Space Sampling Schemes a) apply a 90o pulse b) apply a large, negative, phase encode gradient along y

•  The integral i.e. ky, is getting more negative with time

•  We’re “moving” along -ky

•  We’re not moving in kx

k

kx

y

a

b

∫t

y dttyG0

'' )(γ

k Space Sampling Schemes a) apply a 90o pulse b) apply a large, negative, phase encode gradient along y c) apply a positive 'dephase' gradient along x

•  We’re now “moving” along kx

k

kx

y

a

b

c

k Space Sampling Schemes a) apply a 90o pulse b) apply a large, negative, phase encode gradient along y c) apply a positive 'dephase' gradient along x d) at time TE/2 after 90o pulse apply 180o pulse

•  “Flips” us to the other side of k-space

k

kx

y

a

b

c d

k Space Sampling Schemes a) apply a 90o pulse b) apply a large, negative, phase encode gradient along y c) apply a positive 'dephase' gradient along x d) at time TE/2 after 90o pulse apply 180o pulse e) apply readout gradient and start measuring echo signal

k

kx

y

a

b

c d

e

k Space Sampling Schemes a) apply a 90o pulse b) apply a large, negative, phase encode gradient along y c) apply a positive 'dephase' gradient along x d) at time TE/2 after 90o pulse apply 180o pulse e) apply readout gradient and start measuring echo signal

peaks at TE/2 after 180o, then dies away again

k

kx

y

a

b

c d

e

k Space Sampling Schemes •  Next phase encode

step samples different line of k space

•  … process continues until all of k space is sampled

k

kx

y

k

kx

y

1234

k Space Sampling Schemes •  order in which k-

space points are acquired is irrelevant, –  We can come up

with complex ways of covering k-space

–  may have practical or theoretical advantages

•  More in later lectures

k

kx

y 12

34

Some Real Data… •  Can plot out S(t,n) and

see echoes and pseudo-echoes in the frequency and phase directions:

•  Can also display the intensity of raw k-space data S(kx,ky) as an image in its own right –  (i.e. without Fourier

Transforming):

Fourier Transforming the Data

FT ? R

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duce

d fr

om: B

race

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l, Th

e Fo

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rm

and

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ill, 1

965

Time

Phas

e en

code

step

Real data, as collect on the scanner:

1 25

6

Fourier Transforming the Data

FT ?

Recap •  K-space is where the raw data from the

scanner “lives” –  The axes of k-space are how much magnetic field

gradient has been “seen” by the object (in each direction)

–  K-space “trajectories” allow us to see how the pulse sequence ensures data is sampled over the whole of k-space

•  Low spatial frequencies (near the centre of k-space) encode the contrast and overall shape of an image

•  High spatial frequencies (at the edges of k-space) encode all the detail

•  The Fourier Transform can convert k-space data into an image

Final Recap •  Creating a 2D or 3D image requires:

– Slice selection – Spatial encoding

•  Frequency encoding uses a gradient during data acquisition, affecting frequency of signal received

•  Phase encoding in 1 or 2 dimensions, uses gradients before data acquisition, affecting phase of signal received

– All of these processes depend on the Fourier Transform and the data collection process can best be described in k-space

Δs

Δs = slice thickness

Frequency encoding

Phase encoding

Bibliography / Suggested Reading

For a good overview: •  MRI from Picture to Proton

–  DW McRobbie, EA Moore, MJ Graves, MR Prince; Cambridge University Press; ISBN-10: 052168384X, 2007.

•  Aimed at radiographers, but useful for everyone.

•  Chapter 7 is particularly relevant

(Very) technical aspects: •  Handbook of MRI Pulse

Sequences –  M.A. Bernstein, K.F. King, X.J.

Zhou, Academic Press; 1 edition, ISBN-10: 0120928612, 2004

–  Also available, from KCL computers, at http://www.sciencedirect.com/science/book/9780120928613

Bibliography / Suggested Reading

•  Online Resources –  http://www.mri-physics.com/bin/mri-physics-uk.pdf

•  Freely available book on MR physics. –  http://www.mritutor.org/mritutor/

•  On-line resource about MR imaging.