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# Mri system block diagram

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### Mri system block diagram

1. 1. MRI System Block Diagram RF amp spectrometer r.f.coil gradient coil X amp Y amp Z amp
2. 2. Principle of Gradient Coil ∂Bz ∂x ∂Bz ∂z
3. 3. Isotope Spin %age γ I abundance MHz/T 1 H 1/2 99.985 42.575 2 H 1 0.015 6.53 13 C 1/2 1.108 10.71 14 N 1 99.63 3.078 15 N 1/2 0.37 4.32 17 O 5/2 0.037 5.77 19 F 1/2 100 40.08 23 Na 3/2 100 11.27 31 P 1/2 100 17.25 Common NMR Active Nuclei
4. 4. Alignment of Spins in a Magnetic Field spin magnetic moment B0 field M M=0
5. 5. Energy in a Magnetic Field (Zeeman Splitting, Spin ½) E+1/2= −γB0/2 E-1/2= +γB0/2 P+1/2= 0. 5000049 P-1/2= 0.4999951 1.5T, T=310K, P(E)∝exp(−E/kT) mI = +½ mI = −½
6. 6. Larmor Frequency E+1/2= −γB0/2 E-1/2= +γB0/2 Allowed transitions ∆E = γB0 = ω0 mI = −½ mI = +½ ω0 = γB0
7. 7. Quantum Mechanical Description (Spin ½ Case) ψ> = a−½−½> + a+½+½> I=½, 2I+1 Zeeman splittings mI = −½ mI = +½ Mz = <ψIzψ> = a+½2 − a−½2 Mxy = <ψIx+ iIyψ>
8. 8. Coupling with a B1 Field B0 B1 Birdcage coil A time
9. 9. Spin Excitation M M M rotating frame laboratory frame
10. 10. Free Induction Decay FT FT frequency frequency time time M
11. 11. Free Induction Decay M M M 90° 90° 90° small positive shim mis-set medium positive shim mis-set large positive shim mis-set
12. 12. Free Induction Decay M M M 90° 90° 90° small negative shim mis-set medium negative shim mis-set large negative shim mis-set
13. 13. Product Operators Mx → Mx My → Mycosθ + Mzsinθ Mz → Mzcosθ − Mysinθ θx θx θx Mx → Mycosθ − Mzsinθ My → My Mz → Mzcosθ + Mxsinθ θy θy θy Mx → Mxcosωt + Mysin ωt ω t My → Mycosωt − Mxsin ωt ω t Mz → Mz ω t r.f. free precession x y z
14. 14. Bloch Equations dMz(t) = − [Mz(t) − M0] dt T1 dMxy(t) = − Mxy(t) dt T2 Mz Mxy Mz Mz Mxy Mxy
15. 15. T1 Relaxation Mz(t) = M0 + {Mz(0) − M0}exp(-t/T1) Mz Mz t t saturation– recovery inversion–recovery dMz(t) = − [Mz(t) − M0] dt T1 M0 M0 Mz(0) = 0 Mz(0) = −M0
16. 16. Spin Echo M M M 180° 180° 180°90° 90° 90° small positive shim mis-set medium positive shim mis-set large positive shim mis-set
17. 17. Spin Echo M M M 180° 180° 180°90° 90° 90° small negative shim mis-set medium negative shim mis-set large negative shim mis-set
18. 18. T2 Relaxation Mxy(t) = Mxy(0) exp(−t/T2) Mxy t dMxy(t) = − Mxy(t) dt T2
19. 19. Slice Selection ω0 ω0 time time frequency frequency FT FT
20. 20. Slice Selection ω0 time frequency G