Nguyên lý tạo ảnh trong MRI (MRI dx rad imaging physics course)

Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Take Aways: Five Things You should be able
to Explain after the MRI Lectures
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Magnetic Resonance Imaging – Chapter 15

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Brent K. Stewart, PhD, DABMP
Professor, Radiology and Medical Education
Director, Diagnostic Physics

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a copy of this lecture may be found at:
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© UW and Brent K. Stewart, PhD, DABMP

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© UW and Brent K. Stewart, PhD, DABMP

Localization of the MR Signal

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2, 9 and 16 June 2005

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Magnetic Field Gradients

Spatial localization requires the imposition of magnetic
nonuniformities
Linear gradients are superimposed on the homogeneous
and much stronger main magnetic field (B0)
The change in Larmor frequency of the precessing nuclei
are used to distinguish position of the NMR signal within
the object
Conventional MRI involves RF excitations (NMR)
combined with magnetic field gradients to localize the
signal from volume elements (voxels) within the patient

© UW and Brent K. Stewart, PhD, DABMP

How the MR signal is localized within the patient (2D)
How the collected FID echoes are collected (‘k(‘k-space’
data acquisition) and how these are reconstructed into

the grayscale image data visualized on PACS (2D)
How 3D volume data is acquired and reconstructed
What factors of the MRI data collection process play into
the resulting quality of reconstructed image slices and
volumes
How consideration of artifacts, safety/bioeffects and
instrumentation play into the decisions you will be
making in the future with regards to image interpretation,
magnet operation and system purchase

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Linear magnetic field gradients
with prescribed directionality
and strength are produced in
paired wire coil configurations
energized with a DC current of
specific polarity and amplitude
Gradient null point; reverse
grad. polarity w/ opp.
opp. current
Linear over a predefined field

of view (FOV)
Three sets: x, y and z; can also
generate oblique w/ superpos.

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 416416-7.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Magnetic Field Gradients
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Magnetic Field Gradients

Larmor freq. changes along gradient: e.g., Gz = ∂B/∂z,
B/∂z, Gx = ∂B/∂x
B/∂x

Location of nuclei along gradient is determined by their frequency
frequency
(∆f = (γ
∂z·∆
∆z) and phase (∆φ
(γ/2π
/2π)·∂B/
·∂B/∂z·
(∆φ = 2π
2π·∆f·∆t)
Peak amplitude of gradient (G) field (‘steepness’): [1,80] mT/m
Slew rate (‘quickness’ of gradient ramping): [5,200] mT/m/msec

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Gradient amplitude and number of samples over the FOV
determines the frequency bandwidth across each pixel
10 mT/m · 42.58 MHz/T · 1T/1,000 mT · 1 m/100 cm = 4258 Hz/cm
Localization of nuclei in 2D requires the application of three distinct
distinct
and orthogonal gradients during the pulse sequence: slice select,
select,
frequency encode and phase encode gradients
From the above
calculation, it’s easy to
see that with gradients
our old friend:

π=
friend: γ/2
γ/2π
426 HzHz-cm-1/mT/mT-m-1,
so then it’s just a
matter of multiplying
the number of mT/m
by this factor to get the
bandwidth (Hz)/cm.

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 417.

© UW and Brent K. Stewart, PhD, DABMP

c.f. Hashemi,
Hashemi, et al.. MRI the
Basics, p. 105.

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 418.

Slice Select Gradient (SSG)
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Applied RF pulse bandwidth (BW)
Gradient strength across the FOV

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 418.

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

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Slice Select Gradient (SSG)

RF pulse antennas can’t spatially direct the RF energy within FOV
FOV
In conjunction with a selective frequency narrowband RF pulse
applied to the entire volume, the SSG determines the imaging slice

slice
Slice thickness (ST) determined by:
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© UW and Brent K. Stewart, PhD, DABMP

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For a given gradient strength,
ST determined by RF BW
For fixed RF BW, the gradient
strength determines ST
Excite a rectangular slab
(slice) of nuclei ‘sinc’
waveform: sinc(t) = sin(t)/t
Need an infinitely long sinc
pulse to get a perfectly
rectangular slice
Truncation in time of sinc pulse
leads to rounded slice profiles

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 419419-20.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Slice Select Gradient (SSG)

Frequency Encode Gradient (FEG)
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Width of sinc pulse determines
the output frequency BW
Both narrow BW w/ weak
gradient and wide BW w/
strong gradient
same ST
SNR ∝ [SQRT(BW)][SQRT(BW)]-1
Narrow BW
SNR

Narrow BW
chemical shift
Gradients cause spin
dephasing: phase important!
ReRe-establish original phase
with opp. polarity gradient with
½ integrated area (∆f ∝ G·∆
G·∆t)

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 421.

© UW and Brent K. Stewart, PhD, DABMP

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 422.

Frequency Encode Gradient (FEG)
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© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

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Phase Encode Gradient (PEG)

Composite signal is amplified,
digitized and decoded by
Fourier Transform (FT)
∆f = (γ
∆f ∝ ∆x

(γ/2π
/2π)·Gx·∆x
Rotation of FEG direction
provides projections through
object as a function of angle
Like CT: filtered backprojection
However, due to sensitivity to
motion artifacts phase
encoding gradients used

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 423.

FEG aka readout gradient
Applied to SSG
∆f = (γ
∆f ∝ ∆x
(γ/2π
/2π)·Gx·∆x
Applied throughout formation
and decay of the FID echo
from slab excited by the SSG
Demodulation of the composite
signal produces a net
frequency variation that is
symmetrically distributed from
+fmax to –fmax at FOV edges
Spatial projection: column sum

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Short duration gradient applied
before FEG and after SSG to
provide 3rd spatial dimension
After SSG all spins in φ coherence
During PEG application
linear
variation in precessional
frequency introducing a persistent
phase shift across the slice slab
(∆φ ∝ By·∆y·t)
After all FID data collected, a FT is
applied to decode the spatial
position along the PE direction
Motion during data collection
produces ghosting in along PE

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 424.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Gradient Sequencing
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Raphex 2001 Diagnostic Questions

For the SE pulse sequence
Timing of the gradients in conjunction with RF excitation pulses and
data acquisition during echo evolution and decay
Sequence repeated periodically (TR) with only slight changes in the
PEG amplitude to provide the 3D identity of protons of the object
object in
the resulting image

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D43. In MRI, the RF frequency is dependent on the:

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A. Diameter of the body part being imaged
B. Magnetic field strength
C. Pulse sequence
D. Relaxation time
E. RF coil

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 425.

© UW and Brent K. Stewart, PhD, DABMP

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© UW and Brent K. Stewart, PhD, DABMP

Raphex 2001 Diagnostic Questions
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D46. Gradient fields in MRI are principally used to:

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A. Eliminate perturbations in the magnetic field due to
site location
B. Maintain a uniform magnetic field in the field of view
C. Measure the spin coupling
D. Provide spatial localization
E. Shorten T1 to reduce scan time

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© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

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Raphex 2000 Diagnostic Questions
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D48.
D48. In MRI images, motion during the scans results in
ghost images which appear in the ______ direction.

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A. Amplitude
B. Frequency encoding
C. Phase encoding
D. Relaxation
E. Slice thickness

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© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

‘K-space’ Data Acq. and Image Reconstruction

TwoTwo-dimensional Data Acquisition

Max. signal in center of kk-space
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MRI data initially stored in a ‘k‘kspace’ matrix (spatial
frequency domain corr. time
domain; x : k, f : t – FT pairs;
Larmor relation through
gradients: ∆f = (γ

(γ/2π
/2π)·Gx·∆x)
k-space divided into 4
quadrants w/ origin at center
FID data encoded in kx by FEG
and in ky by PEG
Spat. Freq. enc.: [[-kmax,kmax]
Complex conjugate symmetry:
only ½ matrix + one line req.

adapted from Bushberg, et al. The Essential
Physics of Medical Imaging, 2nd ed., p. 426.

+k

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+k
-k

© UW and Brent K. Stewart, PhD, DABMP

+k

adapted from. Hashemi,
Hashemi, et
al. MRI the Basics, p. 140.

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 427.

© UW and Brent K. Stewart, PhD, DABMP

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Amendment to Bushberg Figure 1515-15

Pulse Sequences
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Example: 3 cycles/sec in kx
MR data acquired as a complex, composite frequency waveform
With methodical variations of the PEG during each excitation, the
the kkspace matrix is filled (or partially filled) to produce the desired
desired

variations across the FE and PE directions

Tailoring pulse sequences
emphasizes the image contrast
dependent on ρ, T1 and T2
Timing, order, polarity, pulse
shaping, and repetition
frequency of RF pulses and x,
y and z gradient application
Major pulse sequences
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Spin Echo (SE)
Inversion recovery (IR)
Fast Spin Echo (FSE)
Gradient Recalled Echo
(GRE)
Echo Planar Image (EPI)
c.f. />© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 428.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Summary of 2D SE Acquisition Steps
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Summary of 2D SE Acquisition Steps

(1) Narrowband RF pulse applied
simultaneously with SSG (center
t=0); SSG: ∂(∆
∂(∆f)/∂z
)/∂z
(1) Mz converted to Mxy, the extent
determined by the flip θ

(2) PEG applied to SSG for short
time (encoding precessional ∆φ
along PE grad.) and with differing
amplitudes for each repetition to
create ∂(∆φ)/
∂y along PE direction:
∂(∆φ)/∂y
multiple views along ky
(3) Refocusing 180°
180° RF pulse
delivered at t = TE/2: inverting
spins

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 428.

© UW and Brent K. Stewart, PhD, DABMP

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 428.

Summary of 2D SE Acquisition Steps

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© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

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Summary of 2D SE Acquisition Steps

(5) ADC sampling rate determined
by the excitation BW
(6) Data stored in kk-matrix row (k
(kx)
the position (k
(ky) determined by the
PEG magnitude
(6) Inc. changes in PEG mag. fills
matrix one row at a time (may be
nonnon-sequential)

(6) When filled partially then copy
complex conjugate data into
remaining blank rows
(7) 2D FT decodes time (spatial
frequency - k) domain data
piecewise along the rows (k
(kx) and
then columns (k
(ky)

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 428.

(4) ReRe-establishment of phase
coherence at t = TE (FID echo)
(4) During echo formation and
subsequent delay, FEG
(∂(∆
∂(∆f)/∂x)
)/∂x) applied to both
SSG and PEG, encoding
precessional frequency along
the readout gradient
(5) Simultaneous to application
of FEG and echo formation,
the computer acquires the
timetime-domain signal (FID echo)
using ADC

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(8) Object spatial and contrast
characteristics manifested in
the resulting image
(8) Final image a spatial
representation of the ρ, T1, T2
and flow characteristics of the
tissues in each voxel using a
graygray-scale range
Voxel thickness determined by
SSG and RF freq. bandwidth
Pixel dimension determined by
varying PEG magnitudes and
readout digitization rate

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 428.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Summary of 2D SE Acquisition Steps
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TwoTwo-dimensional MultiMulti-planar Acquisition

Bulk of information representing lower spatial frequencies near
center of kk-space – provides large area contrast in the image
Higher spatial frequency nearer the periphery – provides resolution
and detail in the image

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Max. signal in center of kk-space

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+k

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Axial (SSG: z, PEG: y, FEG: x)
Coronal (SSG: y, PEG: x, FEG: z)
Sagittal (SSG: x, PEG: y, FEG: z)
Oblique (SSG: a1x + a2y + a3z, etc.)
Data acquisition into the kk-space matrix same for all

··
·
y

z

z

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+k

x
-k

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 429.

© UW and Brent K. Stewart, PhD, DABMP

adapted from Hashemi,
Hashemi, et
al. MRI the Basics, p. 140.

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 430.

Acq. Time, 2DFT SE and Multislice Acq.
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© UW and Brent K. Stewart, PhD, DABMP

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Data Synthesis

Acq. time = TR · no. PE steps ·
NEX (number of excitations)
Example (256x192 matrix,
TR=600, NEX=2)
230 sec
PE along lesser matrix
dimension to speed acquisition
Multiple slice acquisition also
speeds image collection
Max number slices =
TR/(TE+C)
C dependent on MRI system
capabilities
Longer TR
more slices

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 431.

x

+k

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Take advantage of symmetry
and redundant characteristics
of kk-space domain signals
In PE direction ‘½ Fourier’, ‘½
NEX’ or ‘phase conjugate
symmetry’ techniques reduce
data collection to ½ ky matrix
dimension + 1 line
In FE direction ‘fractional echo’
and ‘read conjugate symmetry’
shorten FID echo sampling
time
Both SNR and artifacts

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 432.

With quadrature detection, have real
and “imaginary” (90° out of phase)
components of induced voltage from
FID (t):
V(t) = V1·cos(2πft) + i·V2·sin(2πft).
Two data values per digitized FID
sample. Complex conjugate =

V1·cos(2πft) – i·V2·sin(2πft)

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Inversion Recovery (IR) Acquisition
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180180-(TI)(TI)-9090-(TE/2)(TE/2)-180180-(TR)
SSG, PEG and FEG as SE
TR long
many slices per TR
STIR
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Fast Spin Echo (FSE) Acquisition
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Short Tau IR
Eliminate Fat
TI = 180 msec

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FLAIR
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FLuid
FLuid Attenuated IR
Eliminate CSF
TI = 2,400 msec

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 434.

© UW and Brent K. Stewart, PhD, DABMP

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 433.

Gradient Recalled Echo (GRE) Acquisition
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© UW and Brent K. Stewart, PhD, DABMP

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© UW and Brent K. Stewart, PhD, DABMP

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Echo Planar Image (EPI) Acquisition

Similar to SE but with readout
gradient reversal for 180°
180° pulse
Repetition of acq. for each PE
With small flip angles and gradient
reversals
large reduction in TR
and TE
fast acq.
PEG rewinder pulse (opp. polarity)
to maintain φ relationship between
pulses (due to short TR)
Acq. time=TR
time=TR·· no. PE steps · NEX
Example (256x192 matrix,
TR=30): 15.5 sec
SNR and artifacts; one slice
GRASS, FISP, FLASH, etc.

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 434.

FSE uses multiple PE steps w/
multiple 180°
180° pulses per TR
First echos placed near ky=0

Best SNR
least T2 decay
Immunity from B0 inhomogen.
with up to 16x faster collection
Lower SNR for highhigh-freq ky
Fewer slices collected per TR
SE: 8.5 min (TR=2000, 256
PE)
FSE: 2.1 min (TR=2000, 256
PE steps and 4 echos per TR)
aka: ‘turbo SE’
SE’ & RARE (R
(Rapid
Acq. w/ Refocused Echoes)

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Extremely fast imaging
Single (1 TR) and multimulti-shot
90°
90° flip, PEG/FEG, 180°
180° flip
Oscillating PEG/FEG ‘blips’
stimulate echo formation
Rapid ‘zig‘zig-zag’ kk-space filling
Acq. occurs in a period < T2*:
2525-50 msec
High demands on sampling
rate, gradient coils and RF
deposition limitations
Poor SNR, low res. (642) and
many artifacts
‘Real‘Real-time’ snapshot

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 435.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Spiral KK-space Acquisition
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Gradient Moment Nulling

Simultaneous oscillation of
PEG/FEG to sample data
during echo formation in a
spiral starting at kk-space origin
Regridding to 2D kk-space
array for 2D FT
Efficient method placing
maximum samples in the lowlowfrequency are of kk-space
Like EPI sensitive to T2*: field
inhomogeneities and
susceptibility agents

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In SE and GRE SSG/FEG
balanced so that the uniform
dephasing caused by the initial
gradient application is
rephased by an opposite
polarity gradient of equal area
Moving spins
phase
dispersal not compensated
Constant flow: spins can be
rephased with a gradient triplet
HigherHigher-order corrections
Applied to both SSG/FEG to
correct motion ghosting and
pulsatile flow
A = -1, B = 3 and C = -3

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 436.

© UW and Brent K. Stewart, PhD, DABMP

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c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 437.

Raphex 2001 Diagnostic Questions
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D50.
D50. Which of the following does NOT generally affect
the total exam time of an MRI study?

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A. # of acquisitions
B. # of frequency encoding steps
C. # of phase encoding steps
D. # of pulse sequences in the study
E. TR

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© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

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3D Fourier Transform Image Acquisition
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© UW and Brent K. Stewart, PhD, DABMP

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Uses a broadband, nonnonselective RF pulse to excite a
large spin volume
Acq. time = TR · no. PE steps
(z) · no. PE steps (y) · NEX
SE: TR=600, 1283
164 min.
GRE: TR=50, 1283
14 min.
Isotropic or anisotropic (High SNR
thin slice recon.
prob. for motion artifacts

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 438.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Image Characteristics and Quality
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Spatial Resolution

Spatial Resolution and Contrast Sensitivity
SignalSignal-toto-Noise Ratio (SNR)
Basis for evaluating MR image characteristics
Voxel Volume
Signal Averages (NEX)
RF Bandwidth

RF Coil Quality Factor
Magnetic Field Strength
Cross Excitation
Image Acquisition and Reconstruction Algorithms
© UW and Brent K. Stewart, PhD, DABMP

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artifact

© UW and Brent K. Stewart, PhD, DABMP

SNR = I ⋅Volvoxel ⋅
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In plane: 0.50.5-1.0 mm (0.1(0.1-0.2 mm surface coil)
Slice thickness: 55-10 mm
Higher B0
larger SNR
thinner slices
However, RF heating, T1, T1 contrast and

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SignalSignal-toto-Noise Ratio (SNR)

Major attribute of MR = f (ρ
(ρ, T1, T2, flow, pulse param.)
MR contrast agents, usually susceptibility agents disrupt
local B field to enhance T2 decay or provide additional
relaxation mechanisms for T1 decay
important
enhancement agents for differentiation of normal and
diseased tissues
Absolute contrast sensitivity of an MR image is ultimately
limited by the SNR and presence of image artifacts

© UW and Brent K. Stewart, PhD, DABMP

FOV: pixel size
Gradient strength: FOV
Receiver coil characteristics
Sampling bandwidth
Image matrix: 1282 through 1024 x 512

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Contrast Sensitivity
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Dependent on

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NEX
⋅ f (QF ) ⋅ f 2 ( B) ⋅ f 3 (slice gap) ⋅ f 4 (recon.)
BW 1

I = intrinsic signal intensity based on pulse sequence
Volvoxel = voxel volume = f (FOV, matrix, slice thickness)
NEX = number of excitations
BW = freq. BW of RF transmitter/receiver
f1 (QF) = func. of coil quality factor param. (tuning coil)
f2 (B) = function of magnetic field strength
f3 (slice gap) = function of interslice gap effects
f4 (recon.) = function of reconstruction algorithm

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Voxel Volume
Volvoxel =
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Signal Averages (NEX)

FOVy
FOVx
⋅
⋅ Slice thickness ( z )
No. pixels, x No. pixels, y

SNR ∝ voxel volume
matrix size or slice thickness

SNR ∝ NEX
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SNR

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Doubling SNR requires NEX = 4
NEX < 1: ½ or ¾ NEX
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© UW and Brent K. Stewart, PhD, DABMP

Missing data synthesized from the kk-space matrix
SNR

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© UW and Brent K. Stewart, PhD, DABMP

RF Bandwidth
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Range of freq. to which the RF
detector is tuned
Narrow BW
SNR ∝
(SQRT[BW])-1
BW = 1/∆
1/∆T (dwell time – time
between FID sampling)
Narrow BW
∆T
noise
(SNR ∝ SQRT[∆
SQRT[∆T])
BW
gradient strength
chem. shift artifacts)
Also requires longer sampling
time and affects TEmin which in
turn may affect num. slices/TR

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 441.

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RF Coil Quality Factor

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Indication of RF coil sensitivity to induced currents in
response to signal emanating from the patient
Patient loading: electrical impedance characteristics of
the body
variation of B field, different for each patient
Tuning the receiver coil to ω0 mandatory
Also dependent on volume of subject : coil volume
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43

Body coil positioned in magnet bore: moderate QF
Surface coil: high QF

TradeTrade-off with FOV uniformity
¬

BW = (γ

(γ/2π
/2π)·Gx·FOVx
remember:
π=
remember: γ/2
γ/2π
426 HzHz-cm-1/mT/mT-m-1

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

½ NEX: half Fourier imaging
½ PEPE-matrix dimension + 1
¾ NEX: ¾ PEPE-matrix dimension

Body coil: relatively uniform over FOV
Surface coil: signal falls off abruptly (1/r3-5)
© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Magnetic Field Strength

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¬

Cross Excitation

1.0-1.5
Influences SNR ∝ B1.0Other considerations mitigate SNR improvement
¬
¬

¬
¬

Longer T1
Greater RF absorption (and heating)

© UW and Brent K. Stewart, PhD, DABMP

¬
¬

45

© UW and Brent K. Stewart, PhD, DABMP

Image Acquisition and Reconstruction Algorithms
¬
¬

Profound effect on SNR

Acquisition methods in order of increasing SNR:
¬
¬
¬
¬

¬
¬
¬

Point
Line
2DFT
3DFT

© UW and Brent K. Stewart, PhD, DABMP

¬

D54.
D54. In MRI the signalsignal-toto-noise ratio can be increased by
all of the following except:

¬

A. Decreasing the slice thickness
B. Increasing the number of acquisitions
C. Increasing the static magnetic field strength
D. Increasing TR
E. Switching from a volume to a surface coil

¬

2, 9 and 16 June 2005

¬
¬

47

46

Raphex 2003 Diagnostic Questions

¬

Volume of tissue the major contributing factor in SNR
HighSNR
High-pass filtration methods
LowSNR, but spat. resol.
Low-pass filtration methods

Due to nonnon-rectangular RF slice selection profiles
Overlap of adjacent slices in multislice sequence
Saturates spins
contrast
Use interslice gaps or multislice interleaving

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Instrumentation
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¬

Magnet

Magnet
Resistive Magnet
Superconductive Magnet
Permanent Magnet
Ancillary Equipment
Magnet Siting and Shielding
Quality Control

¬

Performance criteria:
¬
¬
¬

¬

Air core magnets
¬
¬

¬

¬

¬
¬

49

¬

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¬
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¬

¬

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

50

Superconductive Magnet

Ferromagnetic properties of
Fe, Ni, Co and alloys
Bulky and heavy, though new
lighter alloys
Finding a niche in clinical MRI
B0: 0.10.1-0.35 T
Lowest operating costs
Field uniformity typically less
than superconductive with
similar FOV
Inability to turn off field in an
emergency

© UW and Brent K. Stewart, PhD, DABMP

Permanent magnets
Wire wrapped iron core
B0 between poles (usu. vert.)

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 458.

Permanent Magnet

¬

Wire wrapped cylinders
B0 produced through wire
current flow
B0 parallel to core (usu. horiz.)

Solid core magnets
¬

© UW and Brent K. Stewart, PhD, DABMP

Field strength
Temporal stability
Field homogeneity

¬
¬
¬
¬

¬

¬
¬

51

Air core: 1m diam., 22-3m depth
Wrapped with supercon. wire

Liquid helium cooling
B0: 0.30.3-3.0 T clinical (4(4-7 T
research)
High field uniformity: <1 ppm
over 40 cm DSV
Most widely used
Disadvantages: high initial
capital and siting costs,
cryogen costs, difficulty turning
B off in emergency and
extensive fringe fields

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 459.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Resistive Magnet
¬
¬
¬

¬
¬

¬
¬
¬

Ancillary Equipment

Either air core or solid core
Continuous electrical power ($)
Produce a significant amount
of heat (cooling system)
B0: 0.10.1-0.7 T
Able to turn off magnet in an
emergency
Open design
Fringe field well contained
Relatively poor
uniformity/homogeneity

© UW and Brent K. Stewart, PhD, DABMP

¬

¬

¬

¬

¬

¬

53

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 460.

Ancillary Equipment
¬
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¬
¬
¬
¬
¬
¬

¬

¬

¬

¬

¬

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

54

Magnet Siting and Shielding

Pulse programmer
Control interfaces
RF transmitter
RF detector (coils)
RF amplifiers
Gradient power supplies
ADC electronics
Computer system
Image display

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 461.

Shim coils – active or passive,
adjust B0 to homogeneity
Gradient coils – noise caused
by torque on coil and flexing
RF coils – transmitter and body

receiver within bore covers
RF coils need to be ‘tuned’
prior to each acquisition
Kinds: birdbird-cage, singlesingle-turn
solenoid, saddle, surface and
phasedphased-array
Quadrature detection SNR
by √2

55

Superconductive magnets:
extensive fringe fields
Patients w/ pacemakers or
ferromagnetic aneurysm clips:
avoid fringe fields >0.5 mT (5g)
Magnetically sensitive
equipment: video monitors, γ
cameras and fluoroscopic II
Areas above 1.0 mT (10 g)
require controlled and
restricted access w/ signs
Stray RF signal protection:
Faraday cage (copper
sheeting/mesh)

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 463.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Quality Control
¬

Periodical checking of:
¬
¬
¬
¬
¬
¬
¬

¬
¬

Raphex 2001 Diagnostic Questions

Magnetic field strength
Magnetic field homogeneity
System field shimming

Gradient linearity
System RF tuning
Receiver coil optimization
Display monitors

© UW and Brent K. Stewart, PhD, DABMP

D45. Superconducting magnets, compared to resistive
magnets:

¬

A. Are less expensive
B. Are more easily turned off
C. Do not require liquid helium
D. Have higher field strength

¬
¬
¬

ACR MRI accreditation prog.
Uses phantoms composed of
materials that simulate patient
relaxation times

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 464.

¬

57

© UW and Brent K. Stewart, PhD, DABMP

Raphex 2003 Diagnostic Questions
¬

Safety and Bioeffects

D57D57-D59. Match the following MRI terms. (Answers may be used
more than once.)

¬

Important safety considerations
¬
¬

¬
¬
¬
¬
¬

¬
¬
¬

A. Gradient fields

B. RF
C. Shim coils
D. T1
E. T2

¬
¬
¬
¬
¬

¬

D57.
D57. Used to adjust magnetic field uniformity
D58.
D58. Used to localize MR signal
D59.
D59. Used to tip the net magnetization of spins
© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

58

¬

59

Strong magnetic fields

RF energy
TimeTime-varying magnetic gradient fields
Confined imaging space (claustrophobia)
Noisy operation
Implants – ferromagnetic (torque) and nonnon-ferromagnetic (heat)
Ferromagnetic implements (IV pole, gas cylinders, etc.)

LongLong-term biological effects of high magnetic fields not
well known
Most common bioeffect: tissue heating (RF/gradients)
© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Safety and Bioeffects

Safety and Bioeffects
¬

Static Magnetic Fields
¬

¬

¬

Varying Magnetic Field Effects
¬
¬

¬

¬
¬
¬
¬

© UW and Brent K. Stewart, PhD, DABMP

61

¬
¬
¬
¬

D49.
D49. Patients who have MRI scans should be screened
to eliminate those who have:

¬
¬

A. Internal steel fragments
B. Metallic prostheses
C. Pacemakers
D. Surgical clips
E. All of the above

¬
¬
¬
¬
¬
¬
¬

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

62

Artifacts

¬
¬

RF exposure causes tissue heating
Power deposition limits: (< 1° C head, < 2° C trunk, < 3° C extremities)
extremities)
4 W/kg averaged over the whole body for any 1515-minute period
3 W/kg averaged over the head for any 1010-minute period; or

8 W/kg in any gram of tissue in the extremities for any period of
of 5 min
© UW and Brent K. Stewart, PhD, DABMP

Raphex 2000 Diagnostic Questions
¬

Gradient switching can cause current flow
At very high levels: visual phosphenes

Magnetic Field, RF Exposure and Noise Limits
¬

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 466.

> 20 T: membrane permeability, enzyme kinetic changes and altered
altered
biopotentials
< 10 T: these effects have not been demonstrated

63

Machine Dependent Artifacts
Susceptibility Artifacts
Gradient Field Artifacts
Radiofrequency Coil Artifacts
Radiofrequency Artifacts
K-space Errors
Chemical Shift Artifacts

Ringing Artifacts
Wraparound Artifacts
Partial Volume Artifacts
© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Machine Dependent Artifacts
¬

¬

¬

Susceptibility Artifacts
¬

Magnetic field inhomogeneities
distortion or
misplacement of anatomy
Proper site planning, selfself-shielded magnets, automatic
shimming and PM procedures
> homogeneity

Focal field inhomogeneities
ferromagnetic objects:
field distortions, signal void

¬
¬
¬
¬

Magnetic susceptibility: ratio of
induced internal magnetization in
a tissue to external magnetic field
(B0)
Drastic changes in mag. suscept.
distort B0
TissueTissue-air interfaces: lungs and
sinuses
rapid T2*
Metal: ferrous or not
Paramagnetic agents (Gd)
¬
¬

¬

Paramagnetic effects shorten T2
Hydration layer interactions
shorten T1

Mag. suscept. of blood

degradation products
¬

Diagnose the age of a
hemorrhage
EPI diffusion study suffers from severe susceptibility
artifact due to retained metal after surgery. Courtesy,
GE Medical Systems.

© UW and Brent K. Stewart, PhD, DABMP

65

© UW and Brent K. Stewart, PhD, DABMP

Gradient Field Artifacts
¬

¬

¬

¬

Radiofrequency Coil Artifacts

Reconstruction algorithm
assume linear gradients
Tendency for gradient field
strength at periphery of FOV to

deviate from linear assumption
Reduce FOV or lower gradient
strength
Need balanced gradient
strength for PEG and FEG
¬

¬

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

Stray RF signals
¬

¬

¬

¬
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¬

67

TV, radio, electric motors,
fluorescent lights & computers
Narrowband: zipper artifact

perpendicular to FEG direction
Broadband: herringbone artifact
across larger area

RF shielding : Faraday cage
RF quadrature coils: imbalanced
amplifiers
DC offset
¬

Otherwise nonnon-square pixels

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 449.

66

Causes ghosting of objects
diagonally in image

Surface coils
variations in
uniformity across the image
caused by RF attenuation, RF
mismatching and sensitivity falloff
with distance

The scanner room door was left open during the
acquisition causing the zipper artifacts shown. c.f.,
www.spectroscopynow.com/Spy/pdfs/mritutor.pdf

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Radiofrequency Artifacts
¬

K-space Errors

NonNon-rectangular RF pulses:
sliceslice-toto-slice interference
¬
¬

¬

¬

¬
¬

T2SNR

T2-weighted
T1image
T1-weighted
contrast
Interslice gaps and pseudopseudorectangular RF pulses
Slice interleaving

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 450.

© UW and Brent K. Stewart, PhD, DABMP

69

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 451.

Motion Artifacts

¬

Mostly occur along the PEG
direction
ghost images
Compensation methods:
¬
¬
¬
¬
¬

¬

¬
¬
¬

Cardiac/respiratory gating
Respiratory ordering
Signal averaging
Short TE SE sequences
Gradient moment nulling
Presaturation pulses applied
outside the imaging region

¬
¬
¬

¬

¬
¬
¬
c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 451451-2.

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

70

Chemical Shift Artifacts
¬

¬

Artifactual superimposition of wave patterns across the FOV
Even one bad pixel can produce a significant artifact, especially
especially
when at or near kk-space DC data point (center)

71

f0 variations resulting from
intrinsic magnetic shielding
f = (1 - σ) · (γ/2π
/2π) · B0
Distinct peaks in MR spectrum
Fat: 3.5 ppm lower than H20
B
chemical shift
G
chemical shift
Cannot distinguish freq. shift
by FEG or chemical shift
Misregistration of H20 and fat
moieties

anatomical shift
Cure: G, but SNR
Cure: offoff-reson. presat. pulse
Cure: STIR bounce point

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 454.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Ringing Artifacts
¬
¬

¬

¬

¬

¬

Wraparound Artifacts

AKA Gibbs phenomenon
Occurs near sharp boundaries
and highhigh-contrast transitions
Multiple, regularly spaced
parallel bands of alternating
bright/dark signal fading with
distance
Lack of highhigh-frequency signals
causes ‘ringing’ at sharp
transitions
Most likely for small matrix
dimensions
Skull/brain interface

¬

¬
¬

Result of mismapping anatomy
that lies outside the FOV, but
within the slice volume
Opposite side of image
Caused by:
¬
¬

¬

¬
¬

NonNon-linear gradients
Undersampling of frequencies
within the signal envelope
(Nyquist sampling limit)

FT cannot distinguish freq. >
Nyquist limit
lower freq.
Cure: lowlow-pass filter (Cure: number of PE steps
BW = (γ
(γ/2π
/2π)·Gx·FOVx = 1/∆
1/∆T

c.f.,
c.f. www.spectroscopynow.com/Spy/pdfs/mritutor.pdf
c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 456.

© UW and Brent K. Stewart, PhD, DABMP

73

c.f. Bushberg, et al. The Essential Physics

of Medical Imaging, 2nd ed., p. 441 & 457.

Partial Volume Artifacts
¬
¬
¬

¬

D57.
D57. All of the following are MRI artifacts except:

¬

A. Chemical shift
B. Ring
C. Susceptibility
D. WrapWrap-around
E. Zipper

¬
¬
¬
¬

2, 9 and 16 June 2005

74

Raphex 2002 Diagnostic Questions

Due to finite voxel dimensions
Cure: pixel size/slice thickness
Problem: SNR for similar imaging time

© UW and Brent K. Stewart, PhD, DABMP

© UW and Brent K. Stewart, PhD, DABMP

75

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Some Advanced Topics
¬
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¬
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Signal from Flow

TimeTime-ofof-Flight (TOF) MR Angiography (MRA)
Phase Contrast MRA
Magnetization Transfer Contrast (MTC)
Perfusion and Diffusion Contrast
fMRI and BOLD Imaging

¬

¬

¬

¬

© UW and Brent K. Stewart, PhD, DABMP

77

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 443.

TimeTime-ofof-Flight (TOF) MR Angiography (MRA)
¬

¬

¬

¬

¬

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

78

TimeTime-ofof-Flight (TOF) MR Angiography (MRA)

SingleSingle-slice GRE (α
(α=45=45-60°
60°, TR=50 msec, TE=few
msec)
Differentiates moving blood (unsaturated) from stationary
tissues (saturated)
Penetration of unsaturated blood depends on: velocity
(magnitude and direction)
2D stack of slices usually acquired
Blood moving in unwanted direction (e.g., arterial and
venous) is eliminated with a presaturation pulse in an
adjacent slice

© UW and Brent K. Stewart, PhD, DABMP

Signal from blood dependent
on relative saturation of tissues
and the incoming blood flow
Unsaturated spins entering the
imaged slice(s)

large FIDs
slice(s)
In some cases blood signal
eliminated through prepresaturation pulses outside of
imaged slice(s)
slice(s)
“Black blood”
blood” (flow void) also
caused by rapidly flowing and
turbulent blood (no full 180°
180°
pulse)

79

¬

¬

¬

GRE technique provides
poor anatomic contrast,
but a highhigh-contrast
“bright blood” signal
Maximum intensity
projection (MIP) along
specific viewing angles
used to generate a
series of images for

display
TOF MRA often
produces variation in
vessel intensity
dependent on orientation
wrt viewing plane

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 444.

© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Phase Contrast MR Angiography (MRA)
¬

¬

¬

¬
¬

Phase Contrast MR Angiography (MRA)

Relies on phase change (∆φ
(∆φ))
for moving protons (blood);
∆φ = ½ · γ/2π
/2π · Gx · vx · t2
Application of + and then –
polarity gradients in rapid
succession (∆
(∆T)
Second acquisition during
same phase encode cancels
(∆φ)
∆φ) for stationary spins
Moving spins accumulate (∆φ
(∆φ))
Amount of (∆φ
(∆φ)) ∝ (∆T) and v

¬

¬

¬

¬

¬

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 446.

© UW and Brent K. Stewart, PhD, DABMP

81

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 446.

Magnetization Transfer Contrast
¬

¬

¬

¬

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

© UW and Brent K. Stewart, PhD, DABMP

82

Magnetization Transfer Contrast

Result of selective observation
of the interaction between the
p+ in free H2O molecules and
p+ in macromolecular proteins
due to coupling or chemical
exchange
Can be excited separately
using narrownarrow-band RF
Magnetization transferred from
macromolecular p+ to free H2O
p+
Reduced signal from adjacent
free H2O p+

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 412.

Intensity variations depend on
the amount of (∆φ
(∆φ))
Brightest pixels – highest +v,
midmid-gray 0v, lowest –v
Unlike TOF MRA, the phase
contrast image is inherently
quantitative
When calibrated provides an
estimate of the mean blood
flow v (magnitude and
direction)
2D and 3D possible

¬

¬

¬

83

This process affects only those
p+ having chemical exchange
with the macromolecules and
improves image contrast
Anatomic imaging of heart,
eye, MS, knee cartilage and
general MR angiography
Tissue characterization
possible as the magnetization
transfer ratio (MTC
(MTCon/MTCoff) is
caused in part by tissuetissuespecific surface chemistry

c.f. Yao L, Thomasson D. Magnetization
transfer contrast in rapid threethree-dimensional
MR imaging using segmented
radiofrequency prepulses.
prepulses. AJR 2002; 179:
863863-5 .

MR arthrograms of shoulder in 32-year-old man with suspected glenohumeral instability. Axial 3D gradient-echo MR image obtained using

parametric magnetization transfer pulses no discernible magnetization
transfer contrast in injected fluid or in fatty marrow spaces, whereas
degree of magnetization transfer contrast varies in skeletal muscle,
cartilage, and capsular supporting structures (color scale = 0-100%).
© UW and Brent K. Stewart, PhD, DABMP

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

Perfusion and Diffusion Contrast
¬
¬

Perfusion and Diffusion Contrast

Perfusion of cells via capillary bed
Exogenous tracer methods

¬

¬ 2H, 3He, 17O
¬

¬

and 19F experimental procedures
Intravascular bloodblood-pool agents: GdGd-DTPA

¬

Endogenous tracer methods
¬
¬

Labeling of inflowing spins (‘black blood’): tagging
Tagged spins perfuse into tissues
MR signal intensity

¬

¬

85

© UW and Brent K. Stewart, PhD, DABMP

© UW and Brent K. Stewart, PhD, DABMP

Perfusion and Diffusion Contrast
¬

¬

¬

¬

¬

¬
¬

¬
¬

¬

Spine and spinal cord
pathophysiology
Ischemic injury

SpinSpin-echo and echoplanar pulse
sequences with diffusion gradients
Obstacles

86

fMRI and BOLD Imaging

In vivo structural integrity of
tissues measured
apparent
diffusion coefficient maps
Sensitive indicator for early

detection of
¬

Diffusion depends on the random motion of H2O
molecules in tissues
Interactions of the local cellular structure with the
diffusing H2O molecules produces anisotropic,
directionally dependent diffusion
DiffusionDiffusion-weighted sequences use a strong gradient
signal differences based on mobility/directionality
Tissues with H2O mobility have greater signal loss

BOLD (B
(Blood Oxygen Levelevel-Dependent)
Differential contrast generated by blood metabolism in
brain
Oxyhemoglobin
deoxyhemoglobin (paramagnetic)
increases magnetic susceptibility and induced signal loss
(increased T2*)

DiffusionDiffusion-weighted image (DWI) with gray
scalescale-encoded diffusion coefficients.

Sensitivity to head/brain motion
Eddy currents

c.f. Bushberg, et al. The Essential Physics
of Medical Imaging, 2nd ed., p. 410.

T1
© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

ρ

T2

FLAIR

87

© UW and Brent K. Stewart, PhD, DABMP

88

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Magnetic Resonance Imaging – Bushberg Chapter 15

Diagnostic Radiology Imaging Physics Course

fMRI and BOLD Imaging
¬

¬

¬

Areas of metabolic activity
correlated signal (functional
MR)
Subtract postpost-stimulus image
from prepre-stimulus image
ColorColor-coded overlay to a
grayscale anatomic image
demonstrate activity(t)
activity(t)
correlating with stimulus(t)
stimulus(t)

© UW and Brent K. Stewart, PhD, DABMP

2, 9 and 16 June 2005

Images courtesy of
Stanford University

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