Magnetic Resonance Imaging. Presented by: Mahyar Nirouei. Synopsis of MRI. 1) Put subject in big magnetic field 2) Transmit radio waves into subject [2~10 ms] 3) Turn off radio wave transmitter 4) Receive radio waves re-transmitted by subject 0 5) Convert measured RF data to image.
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Magnetic Resonance Imaging
Presented by: Mahyar Nirouei
1) Put subject in big magnetic field
2) Transmit radio waves into subject [2~10 ms]
3) Turn off radio wave transmitter
4) Receive radio waves re-transmitted by subject0
5) Convert measured RF data to image
B0 = 3 T = 30,000 gauss
Earth’s magnetic field = 0.5 gauss
m
There is electric charge
on the surface of the proton, thus creating a small current loop and generating magnetic moment m.
The proton also has mass which generates an
angular momentum
J when it is spinning.
J
+
+
+
Thus proton “magnet” differs from the magnetic bar in that it
also possesses angular momentum caused by spinning.
Magnetic Moment
B
B
I
L
m= tmax / B
= IA
W
L
F
t = mB
= m B sinq
F = IBL
t = IBLW = IBA
Force
Torque
J
m
r
v
Angular Momentum
J = mw=mvr
The magnetic moment and angular momentum are vectors lying along the spin axis
m = gJ
g is the gyromagnetic ratio
g is a constant for a given nucleus
Ref: www.simplyphysics.com
The energy difference between
the two alignment states depends on the nucleus
D E = hn
known as Larmor frequency
g/2p = 42.57 MHz / Tesla for proton
Note: Resonance at 1.5T = Larmor frequency X 1.5
X-Ray, CT
MRI
The main field is static and (nearly) homogeneous
Radio Frequency Fields
Basic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin System
Lower
Higher
Basic Quantum Mechanics Theory of MR
Spin System After Irradiation
Net magnetization is the macroscopic measure of many spins
Bo
M
One can consider the quantum mechanical properties of individual nuclei, but to consider the bulk properties of a whole object it is more useful to use classical physics to consider net magnetization effects.
wL
Slope = gyromagnetic ratio
B0
B0
Derivation of precession frequency
J = m/g
dm/dt = g (m× Bo)
m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz
This says that the precession frequency is the
SAME as the larmor frequency
w = g Bo
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Z
Y
X
In a typical
superconducting
magnet having a
a horizontal bore,
the Z axis is down
the center of the
bore, the X axis is
horizontal and the
Y axis is vertical.
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Spatial Localization
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Spatial Localization
What are the frequencies at Inferior 20cm and Superior 20cm?
At I 20cm, Btot = 1.499 T:
At S 20cm, Btot = 1.501 T:
Difference in
frequencies:
.086 MHz
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B inferior = 63.869 MHz/(42.58 MHz/T)
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So, change of field from center to the inferior extent of excitation = (15000 – 14999.765) Gauss
= -0.235 Gauss
The gradient imposes a field change of
0.5 Gauss/cm, so a change of –0.235 Gauss occurs at the following distance from the center:
- .47 cm
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63.871 MHz = (42.58 MHz / Tesla)(B superior)
.235 Gauss
.5 Gauss / cm
.47 cm
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{
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At a specific RF bandwidth (D w), a high magnetic
field gradient (line A) results in slice thickness (D zA).
By reducing the magnetic field gradient (line B), the
selected slice thickness increases in width (D zB).
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Q: Once spins in a slice are excited, how does the scanner “observe” the data?
A: The receive coil in the scanner detects the TOTAL transverse magnetization signal in a particular direction, resulting from the SUM of ALL excited spins.
Example #1: one spin case
Receiver Coil
Spin
Transverse received signal over time
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Receiver Coil
Example #2: two spin case, with different frequencies
Spin #1
+
Spin #2
=
Summed signal can be complicated…but, this is useful.
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Raw data
Processed data
Fourier transform
In 1-D, we can create a wave with a complicated shape by adding periodic waves of different frequency together.
A
A+B
B
C
A+B+C+D
In this example, we could keep going to create a square wave, if we wanted.
D
A+B+C+D+E+F
E
F
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This process works in reverse as well: we can decompose a complicated wave into a combination of simple component waves.
The mathematical process for doing this is known as a “Fourier Decomposition”.
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For each different frequency component, we need to know the amplitude…
…and the phase, to construct a unique wave.
f
f
f
Amplitude change
Phase change
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So, if spins in an excited slice were prepared such that they precess with a different frequency and phase at each position, the resulting signal could only be constructed with a unique set of magnetization amplitudes from each position.
Thus, we could apply a Fourier transform to our total signal to determine the transverse magnetization at every position.
So, let’s see how we do this…
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During signal reception, a gradient is applied in one direction:
B= B0 + Gxx
m(x)
x
The resonant frequency depends on location, so a Fourier transform of the signal tells us where the nuclei are in one dimension
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Phase and Frequency Encoding(continued)
Phase-encode gradient
Phase-encoding of these rows occurs by turning a gradient on for a short period of time…
Total magnetic field
Frequency-encode gradient
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Phase and Frequency Encoding(continued)
Phase-encode gradient
…then, frequency-encoding of the columns occurs by turning a gradient on for a different axis and leaving it on during the readout.
Total magnetic field
Frequency-encode gradient
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The Fourier transformation acts on the observed “raw data” to form an image. A conventional MRI image consists of a matrix of 256 rows and 256 columns of voxels (an “image matrix”).
The “raw data” before the transformation ALSO consists of values in a 256 x 256 matrix.
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This “raw data” matrix is affectionately known as “k-space”. Two-dimensional Fourier Transformation (2DFT) of the “k-space” produces an image.
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For an MRI image having a matrix of 256 rows and 256 columns of voxels, acquisition of the data requires that the spin population be excited 256 times, using a different magnitude for the phase encoding gradient for each excitation.
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1D FT
by row
FT
by column
Plot A-t
1D FT
by row
FT
by column
Plot A-t