The Physical Basis of Nuclear Magnetic Resonance Part I ESMRMB. Jürgen R. Reichenbach

Transcription

1 The Physical Basis of Nuclear agnetic Resonance Part I Jürgen R. Reichenbach odule 1 October 17, 216

2 Outline of odule Introduction Spin and magnetic moment Spin precession, Larmor frequency agnetic properties of nuclei icroscopic magnetism Spin-lattice relaxation Transverse magnetization and transverse relaxation Return to equilibrium and its parameters T1 and T2

3 Chart of the Electromagnetic Spectrum

4 NR in a nutshell Nuclear magnetic resonance (NR) Nuclei (of the object under investigation) agnetic fields (static fields, gradient fields) (are produced by the spectrometer or scanner) (static fields.2 7. T (9.4 T), for comparison: earth magnetic field 3 µt - 6 µt) Resonance phenomenon (due to interaction of nuclei with radiofrequency magnetic fields) Electron shells Neutron Proton Electron Nuclei have: Nucleus finite radius: finite mass: electrical charge: ~1-14 m ~1-27 kg ~1-19 C

5 NR in a nutshell Furthermore: Nuclei possess spin (angular momentum), which is quantized and an intrinsic property of the particles. Classical angular momentum L Quantization of direction: number of protons even odd even odd I ( I 1 ) I = spin quantum number number of neutrons even odd odd even The component L z of the angular momentum L along the direction of an external magnetic field (z-axis) is also quantized. L z m m = magnetic quantum number m I, I 1, I 2,..., 1,...I 1,I

6 NR in a nutshell 2I + 1 possible orientations of angular momentum L (in an external magnetic field) Example: Proton ( 1 H): I = 1/2 2 possible orientations: m = + 1/2 m = -1/2 L agnetic dipole moment µ: 3 Another example: I =? 2 For I 1/2 the nucleus has an intrinsic magnetic dipole moment µ I = gyromagnetic ratio [] = rad s -1 T -1 measurable nuclei: non-measurable nuclei: 1 H, 2 D, 13 C, 15 N, 19 F, 23 Na, 29 Si, 31 P, 12 C, 16 O, 32 S,

7 NR-Properties of Some Stable Nuclei Nucleus Spin quantumnumber I Gyromagnetic ratio [1 8 rad s -1 T -1 ] Gyromagnetic ratio [Hz/T] Natural abundance in % Sensitivity for B = const in % (rel. zu 1 H) 1 H 1/ P 1/ Na 3/ C 1/ N , O 5/ F 1/ Cl 3/ K 3/ g 5/ Ca 7/ S 3/ * Relative sensitivity (signal strength compared to hydrogen) for the same number of nuclei at constant field strength (expressed in percent relative to 1 H). S ~ *

8 Proton magnetic moment B rotation charge 65 % water 1 g (H 2 O) = molecules m = mechanical moment (spin) m = B I = 1 2 E m µ B E m = B m = 1 2 B

9 echanical Spinning Top Wolfgang Pauli and Niels Bohr demonstrating 'tippe top' toy at the inauguration of the new Institute of Physics at Lund; Sweden, July 19544

10 Nuclei in a agnetic Field p kt B = : B = B : m e mb Z / kt I mb / kt Z e mi N V N V I mi I mi p p m m m m m B z S N Boltzmann statistics high temperature approximation E All orientations of the magnetic moment are energetically equivalent z B Spin density r N V 2 = 2 I ( I 3k T 1) B agnetization in thermal equilibrium 1 T B

11 acroscopic Nuclear agnetization agnetization Population difference between states Quelle: J. Lissner,. Seiderer, Klinische Kernspintomographie, 1987

12 Boltzmann-Population of Two States for Different Spectral Regions NR IR Vis ESR Excited state (E) m I = -1/2 n = 1 S 1 (p*) m S = -1/2 Ground state (G) m I = +1/2 n = S (p) m S = +1/2 E (kj mol -1 ) N E / N G E for T = 3 K n = 9 Hz (NR) v ~ = 2 cm -1 (IR) l = 5 nm (Vis) n = 1 GHz (ESR) N E N G e E kt Boltzmann-constant k = J K -1 Ex. N E / N G = ( 1 H, 9 Hz, T) 1 6 nuclear spins in excited state nuclear spins in ground state

13 Excitation with radiofrequency magnetic fields Applying high frequency magnetic field (rf-field) perpendicular to B : HF( t ) BHF (cos t, sin t, ) B Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of RI, University Toronto, Canada Rotation of magnetization vector (by 9 ) caused by an electromagnetic rf-field with Larmor frequency that is applied for a certain duration and oriented perpendicular to the static field. The resulting transverse magnetization xy induces a voltage in the receive coil, the nuclear magnetic resonance signal S(t). rf pulse with frequency Coil B H F t p

14 Schematics of an NR Experiment Frequency generator Signal processing Transmit amplifier Signal amplifier Switch The object ist placed in a strong homogeneous static magnetic field B. A magnetic rf-field B 1 is applied perpendicular to B with an rf-coil Following excitation the detected nuclear resonance signal of the object in the coil is passed via the detector electronics to the host computer

15 Signal Detection Dynamo Wire loop in an alternating magnetic field Rotating magnetization vector N S x Signal intensity B z y xy y time U ind Φ( t ) ( t ) t t Faraday s induction law B r 3 B ( r ) ( r,t ) d r r Object (r ) coil sensitivity

16 Excitation and Detection of agnetic Resonance B B agnetic field Excitation Transmit coil rf-pulse of frequency Receive coil Detection Receive coil

17 Free Induction Decay Signal = - B B Receive coil xy S(t) FID-Signal (free induction decay) damped oscillation Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of RI, University Toronto Larmor frequency

18 Relaxation: Recovery and Decay Thermal equilibrium: agnetization parallel to B Relaxation: Re-establishment of thermal equilibrium after some perturbation is applied Relaxation back to thermal equilibrium T1-Erholung T 1 recovery Zeit T2*-Zerfall T 2 * decay T 1 - and T 2 *- relaxation are simultaneous processes T 2 * < T 1 Dephasing of spin ensembles

19 Combination of the free equation of motion with the relaxation terms leads to the famous Bloch equations: T B dt d T B dt d T B dt d z z z y y y x x x Bloch Equations Felix Bloch

20 () ) (1 ) ( )) sin( () ) cos( () ( ) ( )) sin( () ) () cos( ( ) ( T t z T t z x y T t y y x T t x e e t t t e t t t e t B Solution to these differential equations:,, B B Bloch Equations

21 T 1 - or Spin-Lattice-Relaxation longitudinal relaxation ( B ) Properties Energy exchange between spin and magnetic surroundings (lattice) T 1 depends on tissue type viscosity (if liquid) B temperature T 1 can be shortened by contrast agents z / T 1 (1 - e -t/t1 ) Tissue T1 [ms] T1 [ms] (@ 1.5 T) (@ 3T) Liver ~6 ~81 Skeletal muscle ~16 ~142 WB 78 ~111 GB ~16 ~147 CSF 3 ~4 Time t

22 T 1 -Weighting Stopped Pulse Experiment z / 9 -Pulse 1. 9 rf pulse repetition time: TR Courtesy of. Bock, DKFZ Heidelberg time

23 T 2 -Relaxation transverse relaxation ( B ) xy x z z B y x z Signal Intensity y y x z y y x z time y = y RF 9 - Pulse

24 T 2 -Relaxation transverse relaxation ( B ) Properties Loss of phase coherence between spins T 2 depends on tissue type B T 2 can be shortened by contrast agents /e x,y / T 2 e -t/t 2 Tissue T2 [ms] T2 [ms] (@ 1.5 T) (@ 3T) Liver Skeletal muscle WB 9 ~6 GB 1 ~7 CSF 22 ~2 time t

25 T 2 -Weighting 1. x,y /.5 time t

26 Longitudinal and Transverse Relaxation T 2 -w fat skeletal muscle fat skeletal muscle liver brain (W) brain (G) CSF liver brain (W) brain (G) CSF T 1 -, PD-w time in ms e.g., R myelography Adapted from Schick F, Radiologe 213;53:

27 BPP-Theory of Relaxation in Liquids Bloembergen, Purcell, Pound Phys. Rev. 73, (1948) Interaction between nuclear spins: dipole-dipole-interaction H ( t) 1 2 ( 1 r ) ( 2 r ) r r locally fluctuating small magnetic fields B local at the sites of the nuclear spins due to Brownian motion (i.e. thermal motion) of proximate spins (both intra- and inter-molecular) r

28 BPP Plot T 1 T 2 increasing viscosity

29 Rotating Frame of Reference y y HF x In the rotating frame the x - y - plane rotates in synchrony with the frequency of the rf-field. B 1 - vector is stationary in this system!! B 1 x

30 Rotating Frame of Reference 9 -rf-pulse in the laboratory (fixed) and in the rotating frame 18 -rf-pulse in the laboratory (fixed) and in the rotating frame Quelle: J. Lissner,. Seiderer, Klinische Kernspintomographie, 1987

31 Field Inhomogeneities Problem apparent signal decay faster than T 2 effective relaxation time: T 2 * T 2 * depends on T 2 magnetic surroundings Solution refocusing B B R 1 1 B * 2 * T2 T2 B 1..5 x,y / time t EL Hahn: Spin Echoes. Phys Rev (195)

32 Spinensemble - Dephasing Transverse magnetization NR signal (free induction decay)

33 9 18 TE AQ t Spin-Echo-Experiment Erwin Hahn too fast too slow too fast too slow

34 The first nuclear spin echo observed by E. Hahn in 195 E. Hahn, "Spin echoes", Phys. Rev. 8, 58 (195) Erwin Louis Hahn ( )

35 Spin-Echo a) Pulse scheme b) Time course of longitudinal magnetization z c) Induced measurement signal rephasing signal part dephasing signal part Quelle: W. Schlegel, J. Bille (Hrsg.) edizinische Physik Bd. 2, 22

36 ultiple Spin-Echoes rf exciation T 2 * < T 2 1/T 2 * = 1/T 2 + 1/T 2 irreversible dephasing reversible dephasing due to static constant field inhomogeneities

37 Inversion-Recovery-Sequence Inversion of longitudinal magnetization by 18 -pulse Inversion time TI 9 -pulse (reading pulse) tips actual longitudinal magnetization in x -y -plane Longitudinal magnetization approaches equilibrium magnetization Transverse magnetization decays with T 2 * and induces signal S ~ [1-2 exp (-TI / T1)] TR >> T1

38 Some References RI in Practice Westbrook C, Kaut Roth C with Talbot J, 4 th ed. 211, John Wiley & Sons Clinical R Imaging A practical approach Reimer P, Parizel P, eaney JF, Stichnoth FA (Eds.), 21, Springer Imaging Systems for edical Diagnostics: Fundamentals, Technical Solutions and Applications for Systems Applying Ionizing Radiation, Nuclear agnetic Resonance and Ultrasound Oppelt A (Editor) 2 nd ed. 25, Publicis Publishing agnetic Resonance Imaging: Physical Principles and Sequence Design Brown RW, Cheng YCN, Haacke E, Thompson R, Venkatesan R, Wiley-Blackwell; 2nd edition, 214 The Basics of RI