Principles of MRI. Vinyl Record. Last time: Today: Homework Due tonight! EE225E / BIO265. Transforms a temporal signal to a spatial signal

Transcription

1 What is this? ` Principles of MRI Lecture 05 EE225E / BIO265 Instructor: Miki Lustig UC Berkeley, EECS The first NMR spectrum of ethanol Today Last time: Linear systems, Fourier Transforms, Sampling Today: Ch 3. Overview Classical description of MRI Basic Imaging Spatial Frequency Vinyl Record Transforms a temporal signal to a spatial signal Homework Due tonight! 3 4

2 What is the frequency? What is the Temporal Frequency? (-1,1) cos(2 (f x x + f y y)) (-1,1) Vinyl rotates at 1 Hz (-1,-1) a) fx=1, fy=2 b) fx=2, fy=1 c) fx = 4, fy=2 d) fx=2, fy=4 (1,-1) (-1,-1) a) cos(2π8t) b) cos(2π8t 2 ) c) cos(2π4t) d) cos(2π4t 2 ) (1,-1) 5 6 What is the Temporal Frequency? (-1,1) Vinyl rotates at 1 Hz Aliasing! (-1,-1) a) cos(2π100t) b) cos(2π100t 2 ) (1,-1) c) cos(2π40t) d) none of the answers 7 8

3 Classical Description of MR Atoms with odd # of protons/neutrons have nuclear spin angular momentum Intrinsic QM property (ch. 4) Also intrinsic magnetic moment Like Spinning magnetic dipoles In biological tissue: Mostly 1 H in H2O Sometimes 31 P, 13 C, 23 Na - Exotic Classical Description of MR Interaction of magnetization with 3 fields B0 - Main field Polarization and resonance B1 - RF field Signal production + reception G - Gradient fields Spatial encoding 9 10 B0 - Main Field Typical B0 Produces polarization of sample M0 Resonance at Larmor frequency For Protons: Others: 23 Na 13 C 15 N! = B 0 Gyromagnetic Ratio =4.257 KHz/G 2 = Krad/G =1.127 KHz/G 2 =1.071 KHz/G 2 2 = 0.43 KHz/G B 0 ~M 0 ẑ T 4.2MHz Very Low! 0.5T 21MHz 1.5T 63MHz 3T 127MHz Low (permanent/ resistive) High Diagnostic (superconducting) High Diagnostic (superconducting) 4T 170MHz Rare 7/9.4T 300/400 MHz Very High - research only 12

4 B0 Field For Spatial/Spectral Localization we require homogeneity This is: 1.5T Pretty remarkable! B 0 1ppm over 40cm 3 FOV Why Resonance For a bar magnet Torque, but no resonance Missing angular momentum Resonance is like a spinning-top B1 - RF Field Can t Directly Detect M0 M induced = µ 1 0 V B Resonance is the key! B0 is DC while spins resonate Detection! Sample resonates at ω0=-γb0 Excite magnetization off the z direction Apply RF field at ω0=-γb0 in the x-verse plane Has to be resonant to do something Q: Why? A: Huge field! RF Excitation In the lab frame B 1 (t) =Aŷ 15 16

5 RF excitation In the lab frame B 1 (t) =Ae i! 0t RF excitation In the rotating B 1 (t) =Aŷ rot RF Excitation Relaxation In the rotating frame: Precession about B1 lab rotating T1 : Longitudal relaxation ~ ms T2 : Transverse relaxation ~ ms Main source of contrast (Later!) T2 < T1 Always! Typical B1 s: G ± (10%/20%) Duration 1-3ms which is a long time at 64MHz! Transverse M xy e -t/t2 Time Peak power 20KW!! 0 = B 1 = = 0.68 KHz 0.367ms 90 ) rotations Longitudinal M z 1-e -t/t1 Time 19 20

6 RF Reception Precession enduces EMF in coil: Faraday s law Free induction decay Gradient Fields B1 has poor localization λ@64mhz ~ 0.5m in tissue Instead encode position in frequency V (t) FID ~G After demodulation t t 21 Small concomitant fields Bx, By are also created. These do not contribute much to precession - fields are NOT oscillating at Larmor freq. -5! 0!(x) =! 0 + G x x 5 22 Gradient Fields Typical # G = 1-10 G/cm = mt/m = KHz/cm Waveforms in audio frequency Slew-Rate = G/cm/ms Safety concern is in db/dt Peripheral nerve stimulation can happen Big Amplifiers: 1200 Volts, 200 Amps 23