Magnetic Resonance Imaging in a Nutshell

Transcription

1 Magnetic Resonance Imaging in a Nutshell Oliver Bieri, PhD Department of Radiology, Division of Radiological Physics, University Hospital Basel Department of Biomedical Engineering, University of Basel, Switzerland

2 What do YOU know about MRI?

3 What do YOU know about MRI? Some big machine which is quite expensive $$$ (>1MFr) which makes noise (besides images, of course) which has a (more or less) PERMANENT magnet which has no ionizing radiation but some other safety issues

4 Useful Sources of Information

5 Part I: Nuclear Magnetic Resonance (NMR) Contents Overview History Magnetism Spin & Magnetic Moments Magnetization Motion of Magnetization Scheme of an NMR Experiment Polarization Excitation (Transmit) Relaxation Acquisition (Receive)

6 History of NMR Nobel prize winners related to the history of NMR

7 Today's Imaging Modalities

8 7T magnet bore Today's Imaging Modalities

9 Today's Imaging Modalities MRI PET SPECT CT? 99mTc-tetrofosmin

10 Today's MRI Systems 1.5 Tesla 3.0 Tesla 7.0 Tesla Magnetic earth field: Tesla 1.5T: the earth field which has consequences for patient safety!!

11 Main Magnetic Field superconducting magnet homogeneous always on static Today's MRI Systems

12 MRI: Strong magnetic fields! A static magnetic field B 0 is induced by an electric current. B 0 is between 0.2T and 3T for clinical applications. Superconducting magnets are used for B 0 > 1.0T.

13

14 Strong magnetic fields! Strong PERMANENT Magnet!!! Problem: We do not hear smell feel see the magnetic field!!! THE MAGNET IS ALWAYS ON!!!!

15 Attention: Strong magnetic fields!

16 Attention: Strong magnetic fields!

17 Main Magnetic Field superconducting magnet homogeneous always on static Today's MRI Systems

18 Magnetism rod magnet (ferromagnetic material) magnetic field (current loop) nuclei (magnetic moment)

19 Behavior of magnetic moment in a magnetic field s Compass needle aligns in magnetic field B 0 Nuclear spin s makes precession movement in magnetic field

20 The good news first: for spin ½ nuclei it is not! The famous physicist and Nobel laureate Richard Feynman and coworkers showed (1) that the class of phenomena called two-level quantum dynamics can be understood in the light of classical MR, and that an abstract vector quantity (the Bloch vector) descriptive of the quantum state moves like a magnetic dipole in a magnetic field. (1) Feynman RP et al. Geometrical representation of the Schrödinger equation for solving MASER problems (1957). J Appl Phys 28:49-52.

21 Angular Momentum & Torque gravity µ gravity B 0 dl dt = r F º M M = µ B 0 M = 1 dµ g dt

22 Precession µ Referenced is given here to the local field experienced by the nucleus (B) rather than to the external field (B 0 ). The reason for will become more obvious later Change in time of the orientation of µ is: B 0 z - always perpendicular to both µ and B! - proportional to g and B! - no change in the amplitude of <µ>! Circular motion with angular frequency: w = gb w: Larmor frequency (42.56 MHz/T for protons)

23 Spin & Nuclear Magnetic Moment µ If the number of neutrons and the number of protons are both even, then the nucleus has NO spin. If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin S (i.e. 1/2, 3/2, 5/2). If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin S (i.e. 1, 2, 3). If the nucleus has a spin, then it also has a dipolar magnetic moment (g : gyromagnetic ratio): µ = g S

24 Spin & Nuclear Magnetic Moment in an External Field B 0 Due to quantum-mechanics, the spin (S) and thus of the magnetic moment (µ), if measured, can only have a limited number of orientations (ħ = Planck s quantum constant): µ = ghm, where m= S, S-1,..., -S z

25 Energy Levels for a nuclei with spin S = 1/2 The magnetic moment interacts with the external field B 0 (E: potential Energy): E =- µb µ z = ½għ µ z = -½għ and are thus associated with different energy levels! For S = 1/2 (e.g., 1H, 13C, 19F, 31P), µ = ghm =± 1/2gh z and thus, the magnetic moment µ z is parallel or antiparallel to the field B 0 with different energy levels: 1 E± =- µ B = m ghb 2 D E = g hb 1/2 z 0 0 0

26 Resonance 1 E+ =- µ B =- ghb 2 1/2 z 0 0 D E = g hb 0 1 E- =- µ B = ghb 2 1/2 z 0 0 D E = g hb 0

27 Statistics! Interaction with external field: DE ( 1 1.5T) ~ 4E-26 J Tends to align magnetic moment parallel (low energy state) to external field B 0. Thermal energy (k B : Boltzmann constant, T S : Temperature): k b T s ~ 4E-21 J Tends to randomize orientation of magnetic moment. In thermal equilibrium, the occupation of the energy levels is given by the Boltzmann statistics. The difference in occupation Dn for n nuclei is: D n= n - 1/2-1/2 ng hb kt 2 B S 0 Boltzmann-Statistics: only 1 in protons is net aligned (@1.5T)! Boltzmann-Statistics: only 6 in protons is net aligned (@9.4T)!

28 Gyromagnetic Ratio g = g q 2 m q: charge of nucleus, m: mass of nucleus, g: G-factor of nucleus (calculation of this factor requires deep knowledge of quantum electrodynamics and quantum chromodynamics) a Magnetization is proportinal to S(S-1) and proportional to g 2 and the induced signal in the coil is proportional to g. Therefore the induced signal in the MR is proportional to g 3.

29 Today's MRI Systems Main Magnetic Field Atoms that give an NMR signal... X X 17 O 13 C

30 Today's MRI Systems Main Magnetic Field Relative NMR signal strength...? Abundance in the body?

31 1mm mm 3 Today's MRI Systems

32 Magnetization Visible (measurable) magnetization: = å = M µ 0 iz 0 i 1x1x1mm 3 = 1µL» 1 mg» 6.7E19 1 H (H 2 O = 18g/Mol)

33 Magnetization Visible (measurable) magnetization: = å = M µ 0 iz? i 2 2 ng B0 ng 0 =D µ z = h h µ z = 0 2kT B S 4kT B S M n B 1x1x1mm 3 = 1µL» 1 mg» 6.7E19 1 H (H 2 O = 18g/Mol)

34 Polarization If placed in an external field, the magnetization appears not instantanouesly: Small Proton Box (1x1x1mm 3 ) M M M M 0 t=0 time M 0 is called equilibrium magnetization This characteristic polarization time is called T 1 (longitudinal relaxation)

35 Magnetization Visible (measurable) magnetization: M 0 = å = M µ 0 iz? i 2 2 ng B0 ng 0 =D µ z = h h µ z = 0 2kT B S 4kT B S M n B Magnetization M 0 1x1x1mm 3 = 1µL» 1 mg» 6.7E19 1 H (H 2 O = 18g/Mol) increases with increasing B 0 (systems with higher field strength ) increases with decreasing T S (hyperpolarization ) is proportional to the number of nuclei (e.g., proton density PD)

36 Motion of Magnetization Magnetization: Precession For all practical purposes we can treat M 0 as one classical magnetic moment d µ dt = g µ B dm = g M B dt M 0 precesses around B 0 with the Larmor frequency w = gb 0 0 By convention, the direction of the external field is along the z-direction é 0 ù émxù émxù é 0 ù B ê M ú y xy z, where ê xy M ú y, ê z 0 ú 0 = ê 0 ú ê ú, M= ê ú º M + M M = ê ú M = ê ú êëb ú 0 û êëm ú ê zû ë 0 úû êëm ú zû

37 Motion of Magnetization Magnetization: Rotating Frame For all practical purposes we can treat M 0 as one classical magnetic moment d µ dt = g µ B dm = g M B dt M 0 precesses around B 0 with the Larmor frequency w = gb 0 0 Since all nuclei precess (in the laboratory, i.e., for the observer) with the Larmor frequency, it is convenient to transform into a rotating frame of reference (i.e., to a stationary frame for the protons): édmù édmù ê = + g ë dt ú û ê ë dt ú M B û lab rot note that in the rotating frame of reference there is no B 0!!!! 0

38 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

39 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

40 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

41 Today's MRI Systems Main Magnetic Field Radio-frequency (RF) Coils Can be switchen on and off Transmit (excitation) Receive (acquisition)

42 Motion of Magnetization Magnetization: Excitation By convention, the direction of the external field is along the z-direction B 0 é 0 ù = ê 0 ú ê ú êëb ú 0 û M 0 é 0 ù é 0 ù = ê 0 ú ê 0 ú ê ú µ ê ú êm ú êpdú ë 0 û ë û Direction of M 0 can be influenced by magnetic fields! lab frame rotating frame

43 Motion of Magnetization Magnetization: Excitation Application of a second temporary B field, called B 1, perpendicular to B 0 B 1 éb1( t)cos( w0t) ù é0ù é0ù = ê 0 ú M( t = 0) = M0 = M ê 0 0 ú µ PD ê 0 ú ê ú, ê ú ê ú êë 0 úû êë1úû êë1úû é 0 ù t dm = g M B M( t) = M ê 1 0 sin( w1t) ú, w1 g B1( t) dt dt ê ú = ò 0 êëcos( w1t ) úû Laboratory frame!

44 Motion of Magnetization Magnetization: Excitation B = B()cos( t w t) This is a linearly polarized field, and not circularly polarized So, in the rotating frame of reference we have actually 2 RF fields: B B B()cos(2 t w t) 2 1 = B1() t 1 = 1 0 (very far from resonance, no effect)

45 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

46 Relaxation of Magnetization Components Upon excitation, the magnetization M returns back to the thermal equilibrium state. This is what we call relaxation (the excited system relaxes back to equilibrium) T1 relaxation: determines how the longitudinal magnetization is recovered (polarization). This is sometimes also called spin-lattice relaxation. T2 relaxation: relates to the loss of coherence in the transverse magnetization from irreversible (stochastic) dephasing processes. T2 determines how fast the signal decays. This is sometimes also called spin-spin relaxation. T2* relaxation: Like T2, but taking into account reversible and irreversible dephasing processes from off-resonance or susceptibilities. As a result: T2* < T2

47 Recovery of longitudinal Magnetization Model: random flip of magnetic moments (spin) Different probabilities for and flip! D n= n - 1/2-1/2 ng hb kt 2 B S 0 What happens after an inversion of the equilibrium magnetization?

48 Recovery of longitudinal Magnetization Model: random flip of magnetic moments (spin) M () t = ( M - M ) e + M -tt / z,0 0 0 Result: exponential relaxation to equilibrium 1 z longitudinal magnetization time

49 T1 Relaxation The time which is needed for the magnetization to built up, we called T1 Return to equilibrium from M z = M 0 is called inversion recovery z,0 ( / ) 1 M () t = M 1-2 e -tt z Return to equilibrium from M z = 0 is called saturation recovery z,0 ( / ) 1 M () t = M 1-e -tt z

50 Molecular Origin of T1 Relaxation rotations diffusion Rotation and diffusion with frequencies around the Larmor frequency are sources of time varying magnetic fields which cause spin-flips and thus T1 relaxation (little RF fields). T1 relaxation thus depends on: Viscosity Temperature State (solid, liquid, gas) Ionic content B 0 Diffusion etc.

51 T2 and T2* Relaxation The magnetization to built up from many nuclear magnetic moments: M = å µ 0 iz i 1x1x1mm 3 = 1µL» 1 mg» 6.7E19 1 H (H 2 O = 18g/Mol) The magnetic moment of every nucleus follows the equation of motion: d µ dt i = g µ B i 0, i µ µ i 0, i () t = xy i,0 xy i () t t e - g B Changes in local B 0 fields (B 0,i ) due to microscopic or macroscopic effects will induce a dephasing of the transverse magnetization components: M t = å µ t = å µ e g 0, i () () xy i xy i,0 i i xy - i B () t t

52 T2 and T2* Relaxation: T2 loss of phase coherence due to random field fluctuations B 0 transverse magnetization 1,0 0,8 0,6 0,4 0,2 Exponential decay of transverse magnetization M M x y = = M e xi M e yi -tt / 2 -tt / 2 0, time

53 Molecular Origin of T2 Relaxation å å M t µ t µ e g - i B () t t 0, i xy () = i () = xy i,0 xy i i Rigid structures cause very efficient dipolar interactions of magnetic moments (interactions with long correlation times) T2 ~ 10 µs (bone or macromlecular protons are difficult to image)

54 Molecular Origin of T2 Relaxation rotations diffusion Rotation and diffusion average out these different magnetic fields leading to higher T2 relaxation times in fluids (motional narrowing) In tissues: T2 ~ ms In fluids: T2 ~ several seconds

55 Typical T1 and T2 times of tissues

56 T2 and T2* Relaxation: T2 loss of phase coherence due to static field inhomogeneities This actually generates a sinc (~sin[x]/x) like decay of the transverse magnetization

57 T2 and T2* Relaxation: T2* T2 relaxation takes place at microscopic scale, whereas T2* relaxation is dephasing caused by microscopic and macroscopic field inhomogeneities macroscopic field inhomogeneities = + = + gdb T T T T * microscopic field inhomogeneities (for Lorentzian frequency distributions only)

58 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

59 Longitudinal and Transverse Magnetization Components transverse magnetization longitudinal magnetization Only the transverse magnetization component generates a time-variable magnetic flux in a receive coil and thus a detectable NMR signal!

60 Excitation and Reception of the Free Induction Decay (FID) transmission (90 pulse ) Receive (signal from precession of transverse magnetization) ~T2* on-resonance off-resonance spectrum

61 The General Scheme for an NMR Experiment 1. Bring object in a magnetic field (B 0 ) 2. Excitation of M 0 3. Relaxation processes (T1, T2 and T2*) 4. Measure NMR signal 5. Wait (Delay) 6. Go to 2

62 The Bloch Equation The differential form of the Bloch Equation (1946) Relaxation Polarization (only for a field pointing along the z-axis) dm 1 1 = M B - M + ( M -M )ˆ z 0 z dt T T ^ 2 1 Equation of Motion

63 Summary: Part I Nuclei have a magnetic moment (if they have a spin ¹ 0). In an external field, magnetic moments precess with the larmor frequency. In an external (main) magnetic field (B 0 ) and in thermal equilibrium, a net magnetization (M 0 ) is formed (M 0 B 0 ). A second external field B 1 (perpendicular to the main magnetic field) can be used to perturb M 0 from thermal equilibrium. The excited magnetization precesses with the larmor frequency and generates a time-variable magnetic field that can be recorded. The excited magnetization relaxes back to thermal equilibrium. Transverse components with T2. Longitudinal ones with T1. The motion of the magnetization is captured by the Bloch equation.

64 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What is nuclear spin? Rotation of a nucleus. Intrinsic angular momentum. Both of the above.

65 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 Where do MRI signals come from? Hydrogen atoms (H). Water molecules (H 2 O). The hydrogen nucleus ( 1 H).

66 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What happens to spins placed in a magnetic field, before a net magnetisation forms? They precess around the field direction. They align parallel and antiparallel with the field. Both of the above. Nothing.

67 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What is T2*? A time constant describing the exponential decay of signal, due to spin-spin interactions. A time constant describing the loss of signal, due to spinlattice interactions. A time constant describing the exponential decay of signal, due to spin-spin interactions, magnetic field inhomogeneities, and susceptibility effects.

68 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What is a free induction decay (FID)? Destruction of the net magnetisation vector without loss of energy to the environment ("free"). The oscillating decaying MRI signal in the transverse plane. The process by which spins are excited by an RF pulse.

69 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 Why do we measure the MRI signal perpendicular to the external magnetic field (in the transverse plane)? There is no MRI signal when the net magnetisation vector is aligned with the main (external) magnetic field. The net magnetisation vector is too small to measure when it is aligned with the main magnetic field because the main field is so large. When net magnetisation is at an angle to the main magnetic field, it precesses, and this generates a measureable signal perpendicular to the field. All of the above.

70 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What are the time constants T1 and T2? T1 is the spin-lattice or longitudinal relaxation time, and T2 is the spin-spin or transverse relaxation time. T1 and T2 are magnetic timing parameters which differ from one tissue to the next. They can be used as a source of contrast in MRI images. The T1 and T2 time constants dictate the shape of the exponential recovery and decay curves of the longitudinal and transverse magnetisation, respectively.

71 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What is an RF pulse? A magnetic field oscillating at radio frequency. A magnetic field gradient. A burst of radio waves.

72 Exercises: Part I Topics: nuclear magnetization, precession, free induction decay, B1, T1, T2 What is a flip angle? The degree of rotation of a net magnetisation vector towards the xy-plane. The initial angle of precession of a net magnetisation vector with B0. The result of an RF pulse.