E. Wong, BE278, UCSD Winter 2013!
Bioengineering 278 "Magnetic Resonance Imaging"
"Winter 2013 "
Lecture 1!
Topics:!• Hardware Overview!• Nuclear magnetization!• Spin excitation!• The NMR signal!• The Fourier Transform!
E. Wong, BE278, UCSD Winter 2013!
Hardware Overview!
Three fields:!• Main Field (B0)!
• Gradient Fields (G[XYZ])!
• RF Fields (B1)!
E. Wong, BE278, UCSD Winter 2013!
Main Field (B0)!
• Mass!• Spin!• Charge!
Angular Momentum!Magnetic Moment!
Hydrogen Nucleus = Proton!
ΔΕ = γhΒ0%
Ε = �µzΒ0%
Ε = µzΒ0% down_ spinsup_ spins
= e−ΔE kT
= 0.99998@3T
Boltzmann!Distribution!
E. Wong, BE278, UCSD Winter 2013!
Main Field (B0)!
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∴
How do we decide on B0?!
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ΔE = γhB0M0 ∝ΔE
Bigger is better! … except …!
3T Human @UCSD. 7T Rodent @UCSD 7T Human @U.Minn. 9.4T Human @UIC!
Slide Credit: T.T. Liu!
Boltzmann!
E. Wong, BE278, UCSD Winter 2013!
Main Field (B0)!
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E =12µ0
B2∫ dV
For B=3T over 1m3:!
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E =1
2(1.25 ×10−6)9 = 3.6MJ
Heat of Vaporization of He = 2.5KJ/l!
A quench can boil off 3.6MJ/2.5KJ/l=1400l of Helium !in 3.6MJ/1MW ~3.6s !!!!
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∴
Energy in a Magnetic Field:!
During a quench, R goes from 0 to ~100Ω,%I~100A, so P=I2R~1MW!
= dropping a 1000Kg! car from 360m high!
E. Wong, BE278, UCSD Winter 2013!
Equation of Motion for Magnetization Vector M!
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dMdt
= M × γB −Mx
ˆ i + Myˆ j
T2
−Mz −M0( ) ˆ k
T1
Precession! Transverse!Relaxation!
Longitudinal!Relaxation!
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Mz(t) = M0 + (Mz(0) −M0)e− t /T1
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MXY (t) = M(0)e− jω 0te−t /T2
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ω0 = γB
Bloch Equation:!
Solution:!
MZ!
MX!MY!
M0!
Gyromagnetic!Ratio (4257Mhz/T)!
Magnetic!Field!
Precession!Frequency!
B!
Angular!Momentum!
Aligning!Force (Gravity)!
Precession!
E. Wong, BE278, UCSD Winter 2013!
Gradient Fields!
How big do gradient fields need to be?!• Shortest soft tissue T2* ~ 1ms!• For 0.2mm resolution in 1ms:!
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GX ≡∂BZ
∂X
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GZ ≡∂BZ
∂Z
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GY ≡∂BZ
∂Y
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G =Kmax
γT=
(0.5 /0.2mm)(4257Hz /G)(1ms)
≈ 5G /cm
• To fill 1m3 with 5G/cm gradients in 0.2ms requires:!
• Modern gradient systems are also up against dB/dt limits for peripheral nerve stimulation (~50T/s)!
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P =ET
=1 2µ0 B2dV∫
T≈1/2µ0(BRMS (5G /cm))
2(1m3)0.2ms
≈ 500KW About 3 simultaneous!Rolling Stones concerts!
E. Wong, BE278, UCSD Winter 2013!
RF Fields!
dMdt
=M×γB
MXY (t) =M (0)e− jωt
Bloch Equation (without relaxation):!
Solution:!
B0!
ω=γB0!
Laboratory Frame!ωr=γB0!
Rotating Frame!
?!M!M!
E. Wong, BE278, UCSD Winter 2013!
The NMR Experiment!
B0!
M!
B0!
ω=γB0!
M!
α%M0!
MX=M0sin(α)!MZ=M0cos(α)! α=γB1
+TRF!
x!
y!
MX=M0sin(α)cos(ωt)!MY=M0sin(α)sin(ωt)!MZ=M0cos(α)!
RF (B1+)!
A/D! computer!V!
V (t)∝ MXY (r)B1−(r)e jωt dr∫
B1- is the vector
reception field of the RF coil!
E. Wong, BE278, UCSD Winter 2013!
The Discrete Fourier Transform!
Xk = xnej2πkn/N
n=−N /2
N /2−1
∑
k=-N/2:N/2-1!
• Basis functions orthogonal over FOV!
• What does that mean?!• X and x are time and
frequency?!• X and x are space and
spatial frequency?!
