What is this? ` Principles of MRI Lecture 05 EE225E / BIO265 Instructor: Miki Lustig UC Berkeley, EECS The first NMR spectrum of ethanol 1951. 1 2 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 http://offtosognefjord.tumblr.com Homework Due tonight! 3 4
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
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 =2 4.257 Krad/G =1.127 KHz/G 2 =1.071 KHz/G 2 2 = 0.43 KHz/G B 0 ~M 0 ẑ 11 0.1T 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
B0 Field For Spatial/Spectral Localization we require homogeneity This is: 64Hz @ 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 13 14 B1 - RF Field Can t Directly Detect M0 M induced = µ 1 0 V B 4 10 9 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
RF excitation In the lab frame B 1 (t) =Ae i! 0t RF excitation In the rotating frame @ω0 B 1 (t) =Aŷ rot 17 18 RF Excitation Relaxation In the rotating frame: Precession about B1 lab rotating T1 : Longitudal relaxation ~ 10-2000ms T2 : Transverse relaxation ~ 10-300ms Main source of contrast (Later!) T2 < T1 Always! Typical B1 s: 0.14-0.35G ± (10%/20%) accuracy @(1.5T/3T) Duration 1-3ms which is a long time at 64MHz! Transverse M xy e -t/t2 Time Peak power 20KW!! 0 = B 1 =4.257 0.16 = 0.68 KHz 0.367ms 90 ) 23000 rotations Longitudinal M z 1-e -t/t1 Time 19 20
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 = apple @Bz @x, @B z @y, @B z @z 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 = 10-100 mt/m = 4.2-42 KHz/cm Waveforms in audio frequency Slew-Rate = 15-20 G/cm/ms Safety concern is in db/dt Peripheral nerve stimulation can happen Big Amplifiers: 1200 Volts, 200 Amps 23