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1 Magnet Resonance Imaging A practical use of nuclear magnetic resonance all pictures are property of Siemens

2 Outline The NMR signal Relaxation and Spin Echos From the Signal to the Image Chemical Shift and MR Spectroscopy 2

3 Which Nuclei do have a Spin? Nuclei with an odd number of nucleons have a halfintegral spin: 1 H, 13 C, 19 F,... Nuclei with an odd number of protons and an odd number of neutrons have an integer spin Nuclei with an even number of protons and an even number of neutrons have no spin: 16 O, 12 C,... these nuclei are useless for NMR MR Tomographs focus on hydrogen nuclei (spin ½ ) How the NMR signal is created 3

4 Nuclei in an external magnetic Field How the NMR signal is created 4

5 Nuclei in an external magnetic Field Spins are aligned with (parallel) or against (anti-parallel) the magnetic field (Paramagnetism) There is a small surplus of parallel spins, due to lower energy (groundstate) ΔE = µ B How the NMR signal is created 5

6 Nuclei in an external magnetic Field Spins are aligned with (parallel) or against (anti-parallel) the magnetic field (Paramagnetism) There is a small surplus of parallel spins, due to lower energy (groundstate) ΔE = µ B At 1 Tesla and 36 C there is an surplus of 6 ppm one Voxel of 1mm³ contains e.g hydrogen protons surplus of protons How the NMR signal is created 6

7 Nuclei in an external magnetic Field Spins precess with the Larmor frequency around the field lines How the NMR signal is created 7

8 Nuclei in an external magnetic Field Spins precess with the Larmor frequency around the field lines Larmor frequency: ω=γb γ is the gyromagnetic moment The Larmor frequency of hydrogen at 1 T is 42 MHz How the NMR signal is created 8

9 Nuclei in an external magnetic Field Reference system: z-axis along the field lines x-y-plane perpendicular to the field lines How the NMR signal is created 9

10 Nuclei in an external magnetic Field Spins precess with the Larmor frequency around the field lines Larmor frequency: ω=γb γ is the gyromagnetic moment The Larmor frequency of hydrogen at 1 T is 42 MHz Surplus of parallel spin orientation creates a magnetisation along the z-axis Spins precess out of phase, there is no effective crossmagnetisation in the x-y-plane How the NMR signal is created 10

11 Nuclear Magnetic Resonance The nature of (N)MR is to deflect the magnetisation from the ground state, by disturbing the balance of the spins A HF-pulse in resonance with the precessing spins (Larmor-frequency) tilts the spins The tilt angle depends on the energy of the pulse How the NMR signal is created 11

12 Nuclear Magnetic Resonance 180 tilt angle spins now in the energetic higher and non-stable state phase of the precessing spins now in the opposite direction How the NMR signal is created 12

13 Nuclear Magnetic Resonance 90 tilt angle cross-magnetisation in the x-y-plane spins precess along the effect axis of the HF-pulse How the NMR signal is created 13

14 Nuclear Magnetic Resonance 90 tilt angle (after the pulse) cross-magnetisation in the x-y-plane spins precess in phase along the axis of the magnetic field no longitudinalmagnetisation anymore magnitude of crossmagnetisation as large as original longitudinalmagnetisation How the NMR signal is created 14

15 (N)MR Signal The time devolution of the cross-magnetisation is called the MR signal or FID (free induction decay) free rotation after the pulse induction of a signal decay of the signal in time How the NMR signal is created 15

16 Relaxation After each HF-pulse disturbance the spins return to the groundstate Two independent processes Relaxation and Spin Echos 16

17 Longitudinal Relaxation (T 1 ) At T 1 63% of the longitudinal magnetisation is restored M Z =M 0 (1-c exp(-t/t1)) Relaxation and Spin Echos 17

18 Longitudinal Relaxation (T 1 ) At T 1 63% of the longitudinal magnetisation is restored T 1 constant depends on the tissue Relaxation and Spin Echos 18

19 Longitudinal Relaxation (T 1 ) At T 1 63% of the longitudinal magnetisation is restored T 1 constant depends on the tissue and on the magnetic field intensity Relaxation and Spin Echos 19

20 Longitudinal Relaxation (T 1 ) At T 1 63% of the longitudinal magnetisation is restored T 1 constant depends on the tissue and on the magnetic field intensity Spin-Lattice-Relaxation: fluctuating magnetic fields in the vicinity of the hydrogen nuclei due to molecular movements (magnetic noise) the closer fluctuations are to the Larmor frequency the larger the influence on the nuclei is protons in a macro-molecule (proteine) or bigger molecules (lipide, adipic) are more influenced than protons in liquids (liquor) Relaxation and Spin Echos 20

21 Longitudinal Relaxation (T 1 ) Relaxation and Spin Echos 21

22 Cross Relaxation (T 2 ) Directly after the pulse the spins precess in phase but after a short time the spins start to dephase M XY =M 0 exp(-t/t2) Relaxation and Spin Echos 22

23 Cross Relaxation (T 2 ) Directly after the pulse the spins precess in phase but after a short time the spins start to dephase T 2 depends only on the tissue Relaxation and Spin Echos 23

24 Cross Relaxation (T 2 ) Directly after the pulse the spins precess in phase but after a short time the spins start to dephase T 2 depends only on the tissue Relaxation and Spin Echos 24

25 Cross Relaxation (T 2 ) Directly after the pulse the spins precess in phase but after a short time the spins start to dephase T 2 depends only on the tissue Spin-spin relaxation increase of longitudinal-magnetisation leads to decrease of crossmagnetisation in addition: flipping spins (T 1 relaxation) loose their phase coherence, dephasing of the cross-magnetisation plus: change of a spin state changes the local magnetic field, which leads to a change of the Larmor frequency in the vicinity of flipping spins Relaxation and Spin Echos 25

26 Cross Relaxation (T 2 ) Relaxation and Spin Echos 26

27 Effective cross Relaxation (T * 2 ) In reality the cross-magnetisation decays faster than with T 2 due to inhomogenities in the static magnetic field and field variations in the human body much faster dephasing of the spins Relaxation and Spin Echos 27

28 Spin Echo Decay of FID is too fast for a precise measurement A 180 pulse after a time τ rephases the spins and builds up the MR signal again At TE (echo time) the signal reaches its maximum Relaxation and Spin Echos 28

29 Spin Echo Repeating the 180 -pulses leads to more echos The amplitudes are smaller than the FID T 2 limits the number of iterations The echo signal decays with T * 2 the amplitude with T 2 Relaxation and Spin Echos 29

30 Gradientecho A magnetic gradient field switched on right after the pulse dephases the spins more, the FID decays faster The inverted field rephases the spins and builds up the signal Due to the accelerated decay of the signal the build up must be very fast, therefore shorter test time Relaxation and Spin Echos 30

31 Spatial Allocation of the Signal Tomography means images of layers From the Signal to the Image 31

32 Spatial Allocation of the Signal Tomography means images of layers Spatial allocation of the layer due to a magnetic gradient field along the probe (patient) From the Signal to the Image 32

33 Layer Selection To select a layer one switches on a gradient field just in time with the HF-pulse From the Signal to the Image 33

34 Layer Selection To select a layer one switches on a gradient field just in time with the HF-pulse Now only at position Z 0 the field has the original strength Only there the probe is sensitive to the HF-pulse and the spins can be excited From the Signal to the Image 34

35 Layer Selection - Thickness This layer is too thin, the resulting signal too weak Whobbling of the Larmor frequency defines the thickness of the layer From the Signal to the Image 35

36 Layer Selection - Thickness This layer is too thin, the resulting signal too weak Whobbling of the Larmor frequency defines the thickness of the layer Alternative: the slope of the gradient field defines the thickness From the Signal to the Image 36

37 Layer Selection 3D Due to different gradient fields layers in all planes can be defined From the Signal to the Image 37

38 From Pixels and Voxels The MR image of one layer contains pixels, ordered in the image matrix Each pixel represents one voxel of the selected layer How to address all the pixels? From the Signal to the Image 38

39 Frequency Coding During the measurement of the signal a second field gradient is switched on The spin ensembles precess with increasing frequency along one direction (here x-axis) A Fourier transformation deconvolves the single frequencies out of the measured signal From the Signal to the Image 39

40 Phase Coding Gradient coding for the second dimension is useless due to ambiguities For each strip in x direction a third field gradient is switched on to bring the spins in a defined phase From the Signal to the Image 40

41 Phase Coding Gradient coding for the second dimension is useless due to ambiguities For each strip in x direction a third field gradient is switched on to bring the spins in a defined phase This phase coding (with different well known phases) has to be repeated for all strips in the second dimension From the Signal to the Image 41

42 Phase Coding Gradient coding for the second dimension is useless due to ambiguities For each strip in x direction a third field gradient is switched on to bring the spins in a defined phase This phase coding (with different well known phases) has to be repeated for all strips in the second dimension Again a Fourier Transformation can deconvolve the single frequencies out of the measured signal From the Signal to the Image 42

43 The k-space The overlap of all single frequencies in the measured signal leads to a complex image in the k-space A 2-dimensional Fourier transformation filters out the information for each pixel From the Signal to the Image 43

44 The k-space The overlap of all single frequencies in the measured signal leads to a complex image in the k- space A 2-dimensional Fourier transformation filters out the information for each pixel Each pixel in the raw matrix contains information of all pixels From the Signal to the Image 44

45 The final Pulse Sequence From the Signal to the Image 45

46 The final Pulse Sequence Layer Selection From the Signal to the Image 46

47 The final Pulse Sequence Phase Coding From the Signal to the Image 47

48 The final Pulse Sequence Frequency Coding From the Signal to the Image 48

49 Chemical Shift and MR Spectroscopy Protons are bound at different places in the molecules Different places means different magnetic fields and different Larmor frequencies The splitting of the Larmor frequency is called Chemical shift The unit of this shift is again ppm (in relation to the unbiased frequency) Chemical Shift and MR Spectroscopy 49

50 Chemical Shift and MR Spectroscopy Protons are bound at different places in the molecules Different places means different magnetic fields and different Larmor frequencies The splitting of the Larmor frequency is called Chemical shift The unit of this shift is again ppm (in relation to the unbiased frequency) The chemical shift allows MR spectroscopy of probes and of the tissue Chemical Shift and MR Spectroscopy 50

51 All pictures in this presentation are property of the Siemens AG, Siemens Medical Solutions MAGNETOM_World/MR_Basics/Magnete_Spins_und_Resonanzen.pdf 51