Introduction to NMR

Physical principles Skejby Sept. 2003 Sune N. Jespersen MRI of the human brain Basic steps

1) 2) Object Data/Signal Image

1) By means of magnetic fields and RF pulses

2) Data processing (Fourier transformation) Outline z Nuclear spins z Spin dynamics in magnetic fields z Spin interactions z Spin excitation z Spin RF radiation and detection Spin and magnetic fields

Proton A charged proton that spins will create a circulating current which in turn induces a +e magnetic field. The dipole vector µ describes the strength and direction of magnetic Permanent field. C.g. permanent Magnet (dipole) magnet. Spin is a fundamental quantum mechanical property. All nuclei (and other particles) have spin:

S=0,1/2,1,3/2….. h/2π (Planck’sconstant). For S=I there are 2I+1 states, corresponding to the possible orientations of the spin.

Proton

µ Spin and magnetic field T=Tesla.T=Tesla. 11 Gauss=10000Gauss=10000 The fundamental relationship is Tesla.Tesla. EarthsEarths magneticmagnetic fieldfieldµ = isisγ Sroughlyroughly .5.5 Gauss.Gauss. γ (gamma) is the gyromagneticAA clinicalclinical scannerscanner ratio. hashas It 1.51.5 depends on the nucleus.Tesla,Tesla, i.e.Fori.e. 30000 30000the proton timestimes it is 2,675*108 rad/s/T.thethe earthsearths magneticmagnetic field.field. Only nuclei with non-zero spin have magnetic moments, and are thus NMR active. Spins in external fields MMM (magnetization)((magnetizationmagnetization)) A magnetic dipole tendsisisis thetothethe align magneticmagneticmagnetic along an external field (e.g. a compass indipole the earths moment magnetic per field). Thermal motion opposesdipoledipole this. momentmoment perper unitunitunit volume.volume.volume

B = 0.1 tesla B = 0 tesla B = 0.1 tesla B = 0.5 tesla T=0K M T = 300 K T = 300 K T=300K M M

Spins aligned Spins aligned Spins aligned Spins aligned 100% 0% 1 ppm 5 ppm Magnetization

B0 z B0 z

Mz Mz(=M) M x x

Transverse Mxy=0 Transverse plane (xy) y plane (xy) y Mxy Longitudinal axis (z) Longitudinal axis (z) M is the sum of the individual spin magnetic moments. Spin dynamics

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P m Larmor frequency

ω is the Larmor frequency: B0

ω0=γB0 Direction For protons in a clinical of nuclear scanner, B =1.5T so magnetic 0 moment ω0=63.87Mhz. Compare [email protected]. Direction of applied magnetic field Magnetization

Magnetization M is:

B 0 Mz = M 0

Mxy = 0 Transverse magne- tization is zero because of random phases. Radio-frequency pulses

B 0 Radio waves at Larmors frequency force pro- tons to pre- cess in phase antiparallel or parallel to B0 RF pulses and magnetization

z Initial B 0 magnetization M0 z'

y y' Magnetization M after 90o pulse B 1 B 1 Rotating coordinate x x' system Spin interactions

Instead of precessing Mz forever in the M0 transverse plane, the T1 Longitudinal relaxation magnetization relaxes 63% back to the equilibrium Time value. 0 Mxy M T1 and T2 are 0 characteristic relaxation T2 Transverse relaxation constants. 37% Time 0 T2 and T2*

T2 dephasing The dephasing in T2 relaxation results from differing local interactions, leading to locally varying z Larmor frequencies. T2* is the same phenomenon, but is a result from Mxy magnetic field inhomogeneities. Biological T1-T2 values

TISSUE T1 at 1.5 T T1 at 0.5 T T2 (ms) (ms) (ms) Skeletal muscle 870 600 47 Liver 490 323 43 Kidney 650 449 58 Spleen 780 554 62 Fat 260 215 84 Grey matter 920 656 101 White matter 790 539 92 Cerebrospinal fluid >4000 >4000 >2000 Lung 830 600 79

Spin RF radiation and detection

Larmor Signal detection Free Induction Decay precession Bo

Signal amplitude Y Time M(t) X RF coil Z Law of induction: changing magnetic field induces electromotoric force. From Mxy Detected by RF coil and measured as a time varying current. Decays according to T2*. What about T2? Spin echo Spin echo

- Or spin refocussing

Relative signal amplitude T2* decay T2 decay Dephasing 90° pulse

Time 180° 2nd echo pulse 1st echo Spin echo FID

Rephasing

[90]-TE/2-[180]-TE/2-ECHO Pulse sequences and contrast

By using different pulse sequences, one can create contrast on the basis of e.g. T1, T2, T2* or spin density.

Spin echo:

S = ρ ⋅(1− e−TR /T1 )⋅e−TE /T2 Overview

Generation of a NMR-spectrum

Radio wave Radio wave

FT FID

Time