Hardware OverviewE. Wong, BE278, UCSD Winter 2013! Bioengineering 278" Magnetic Resonance Imaging" "...
Transcript of Hardware OverviewE. Wong, BE278, UCSD Winter 2013! Bioengineering 278" Magnetic Resonance Imaging" "...
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?!