James D. Christensen, Ph.D. IU School of Medicine

1. BME 595 - Medical Imaging ApplicationsPart 2: INTRODUCTION TO MRILecture 1 Fundamentals of Magnetic ResonanceFeb. 16, 2005 James D. Christensen, Ph.D. IU School of Medicine Department of RadiologyResearch II building, E002C jadchris@iupui.edu317-274-3815

2. References Books covering basics of MR physics: • E. Mark Haacke, et al 1999 Magnetic Resonance Imaging: Physical Principles and Sequence Design. • C.P. Slichter 1978 (1992) Principles of Magnetic Resonance. • A. Abragam 1961 (1994) Principles of Nuclear Magnetism.

3. References Online resources for introductory review of MR physics: • Robert Cox’s book chapters online • http://afni.nimh.nih.gov/afni/edu/ • See “Background Information on MRI” section • Mark Cohen’s intro Basic MR Physics slides • http://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html • Douglas Noll’s Primer on MRI and Functional MRI • http://www.bme.umich.edu/~dnoll/primer2.pdf • Joseph Hornak’s Web Tutorial, The Basics of MRI • http://www.cis.rit.edu/htbooks/mri/mri-main.htm

4. 1920 1930 1940 1950 1960 1970 1980 1990 2000 Timeline of MR Imaging 1972 – Damadian patents idea for large NMR scanner to detect malignant tissue. 1985 – Insurance reimbursements for MRI exams begin. 1973 – Lauterbur publishesmethod for generating images using NMR gradients. MRI scanners become clinically prevalent. 1937 – Rabi measures magnetic moment of nucleus. Coins “magnetic resonance”. 1924 - Pauli suggests that nuclear particles may have angular momentum (spin). NMR renamed MRI 1990 – Ogawa and colleagues create functional images using endogenous, blood-oxygenation contrast. 1946 – Purcell shows that matter absorbs energy at a resonant frequency. 1973 – Mansfield independently publishes gradient approach to MR. 1959 – Singer measures blood flow using NMR (in mice). 1946 – Bloch demonstrates that nuclear precession can be measured in detector coils. 1975 – Ernst develops 2D-Fourier transform for MR.

5. Nobel Prizes for Magnetic Resonance • 1944: Rabi Physics (Measured magnetic moment of nucleus) • 1952: Felix Bloch and Edward Mills Purcell Physics (Basic science of NMR phenomenon) • 1991: Richard Ernst Chemistry (High-resolution pulsed FT-NMR) • 2002: Kurt Wüthrich Chemistry (3D molecular structure in solution by NMR) • 2003: Paul Lauterbur & Peter Mansfield Physiology or Medicine (MRI technology)

6. Magnetic Resonance Techniques Nuclear Spin Phenomenon: • NMR (Nuclear Magnetic Resonance) • MRI (Magnetic Resonance Imaging) • EPI (Echo-Planar Imaging) • fMRI (Functional MRI) • MRS (Magnetic Resonance Spectroscopy) • MRSI (MR Spectroscopic Imaging) Electron Spin Phenomenon (not covered in this course): • ESR (Electron Spin Resonance) or EPR (Electron Paramagnetic Resonance) • ELDOR (Electron-electron double resonance) • ENDOR (Electron-nuclear double resonance)

7. Equipment 4T magnet RF Coil B0 gradient coil (inside) Magnet Gradient Coil RF Coil

8. Main Components of a Scanner • Static Magnetic Field Coils • Gradient Magnetic Field Coils • Magnetic shim coils • Radiofrequency Coil • Subsystem control computer • Data transfer and storage computers • Physiological monitoring, stimulus display, and behavioral recording hardware

9. Shimming gradient rf coil rf coil main magnet main magnet Transmit Receive Control Computer

10. [Main magnet and some of its lines of force] [Little magnets lining up with external lines of force] Main Magnet Field Bo • Purpose is to align H protons in H2O (little magnets)

11. Common nuclei with NMR properties • Criteria: • Must have ODD number of protons or ODD number of neutrons. • Reason? • It is impossible to arrange these nuclei so that a zero net angular • momentum is achieved. Thus, these nuclei will display a magnetic • moment and angular momentum necessary for NMR. • Examples: • 1H, 13C, 19F, 23N, and 31P with gyromagnetic ratio of 42.58, 10.71, • 40.08, 11.27 and 17.25 MHz/T. • Since hydrogen protons are the most abundant in human body, we use • 1H MRI most of the time.

12. J m r v Angular Momentum J = mw=mvr magnetic moment m = gJ whereg is the gyromagnetic ratio, and it is a constant for a given nucleus

13. A Single Proton m There is electric charge on the surface of the proton, thus creating a small current loop and generating magnetic moment m. The proton also has mass which generates an angular momentum J when it is spinning. J + + + Thus proton “magnet” differs from a magnetic bar in that it also possesses angular momentum caused by spinning.

14. Protons in a Magnetic Field Bo Parallel (low energy) Anti-Parallel (high energy) Spinning protons in a magnetic field will assume two states. If the temperature is 0o K, all spins will occupy the lower energy state.

15. Protons align with field Outside magnetic field • spins tend to align parallel or anti-parallel to B0 • net magnetization (M) along B0 • spins precess with random phase • no net magnetization in transverse plane • only 0.0003% of protons/T align with field randomly oriented Inside magnetic field longitudinal axis Mz Mxy = 0 M transverse plane Transverse magnetization Longitudinal magnetization

16. Net Magnetization Bo M

17. The Boltzman equation describes the population ratio of the two energy states: N-/N+ = e –E/kT • Larger B0 produces larger net magnetization M, lined up with B0 • Thermal motionstry to randomize alignment of proton magnets • At room temperature, the population ratio is roughly 100,000 to 100,006 per Tesla of B0

18. Energy Difference Between States

19. Energy Difference Between States D E = hn • D E = 2 mz Bo • n = g/2p Bo known as Larmor frequency g/2p = 42.57 MHz / Tesla for proton Knowing the energy difference allows us to use electromagnetic waves with appropriate energy level to irradiate the spin system so that some spins at lower energy level can absorb right amount of energy to “flip” to higher energy level.

20. Basic Quantum Mechanics Theory of MR Spin System Before Irradiation Bo Lower Energy Higher Energy

21. Basic Quantum Mechanics Theory of MR The Effect of Irradiation to the Spin System Lower Higher

22. Basic Quantum Mechanics Theory of MR Spin System After Irradiation

23. Precession – Quantum Mechanics Precession of the quantum expectation value of the magnetic moment operator in the presence of a constant external field applied along the Z axis. The uncertainty principle says that both energy and time (phase) or momentum (angular) and position (orientation) cannot be known with precision simultaneously.

24. Precession –Classical • = m× Bo torque • = dJ / dt J = m/g dm/dt = g (m× Bo) m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz

25. A Mechanical Analogy of Precession • A gyroscope in the Earth’s gravitational field is like magnetization in an externally applied magnetic field

26. Equation of Motion: Block equation T1 and T2 are time constants describing relaxation processes caused by interaction with the local environment

27. RF Excitation: On-resonance Off-resonance

28. B0 B1 RF Excitation • Excite Radio Frequency (RF) field • transmission coil: apply magnetic field along B1 (perpendicular to B0) • oscillating field at Larmor frequency • frequencies in RF range • B1 is small: ~1/10,000 T • tips M to transverse plane – spirals down • analogy: childrens swingset • final angle between B0 and B1 is the flip angle Transverse magnetization

29. Signal Detection via RF coil

30. Signal Detection Signal is damped due to relaxation

31. Relaxation via magnetic field interactions with the local environment

32. Spin-Lattice (T1) relaxation via molecular motion Effect of temperature Effect of viscosity T1 Relaxation efficiency as function of freq is inversely related to the density of states

33. Spin-Lattice (T1) relaxation

34. Spin-Spin (T2) Relaxation via Dephasing

36. Relaxation

37. Relaxation

38. T2 Relaxation Efffective T2 relaxation rate: 1/T2’ = 1/T2 + 1/T2* Total = dynamic + static

39. Spin-Echo Pulse Sequence

40. Spin-Echo Pulse Sequence

41. Multiple Spin-Echo

42. HOMEWORK Assignment #1 1) Why does 14N have a magnetic moment, even though its nucleus contains an even number of particles? 2) At 37 deg C in a 3.0 Tesla static magnetic field, what percentage of proton spins are aligned with the field? 3) Derive the spin-lattice (T1) time constant for the magnetization plotted below having boundary conditions: Mz=M0 at t=0 following a 180 degree pulse; M=0 at t=2.0 sec.