BME 595 Medical Imaging Applications Part 2 INTRODUCTION

BME 595 - Medical Imaging Applications Part 2: INTRODUCTION TO MRI Lecture 1 Fundamentals of Magnetic Resonance Feb. 16, 2005 James D. Christensen, Ph. D. IU School of Medicine Department of Radiology Research II building, E 002 C jadchris@iupui. edu 317 -274 -3815

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.

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/Shared. Code/Misc. Shared. html Douglas Noll’s Primer on MRI and Functional MRI http: //www. bme. umich. edu/~dnoll/primer 2. pdf Joseph Hornak’s Web Tutorial, The Basics of MRI http: //www. cis. rit. edu/htbooks/mri-main. htm

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

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 (3 D molecular structure in solution by NMR) • 2003: Paul Lauterbur & Peter Mansfield Physiology or Medicine (MRI technology)

Magnetic Resonance Techniques Nuclear Spin Phenomenon: • NMR (Nuclear Magnetic Resonance) • MRI (Magnetic Resonance Imaging) • EPI (Echo-Planar Imaging) • f. MRI (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)

Equipment 4 T magnet RF Coil B 0 gradient coil (inside) Magnet Gradient Coil RF Coil

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

Shimmingrf rf gradient coil main magnet Transmit Receive Control Computer

Main Magnet Field Bo • Purpose is to align H protons in H 2 O (little magnets) [Main magnet and some of its lines of force] [Little magnets lining up with external lines of force]

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: 1 H, 13 C, 19 F, 23 N, and 31 P 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 1 H MRI most of the time.

Angular Momentum J = mw=mvr J m r v magnetic moment m = g J where g is the gyromagnetic ratio, and it is a constant for a given nucleus

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

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 0 o K, all spins will occupy the lower energy state.

Protons align with field Outside magnetic field randomly oriented • spins tend to align parallel or anti-parallel to B 0 • net magnetization (M) along B 0 • spins precess with random phase • no net magnetization in transverse plane • only 0. 0003% of protons/T align with field longitudinal axis Inside magnetic field Mz M Mxy = 0 transverse plane Longitudinal magnetization Transverse magnetization

Net Magnetization Bo M

The Boltzman equation describes the population ratio of the two energy states: N-/N+ = e –E/k. T ¨ Larger B 0 produces larger net magnetization M, lined up with B 0 ¨ Thermal motions try to randomize alignment of proton magnets ¨ At room temperature, the population ratio is roughly 100, 000 to 100, 006 per Tesla of B 0

Energy Difference Between States

Energy Difference Between States DE = hn D E = 2 mz B o n = g/2 p Bo known as Larmor frequency g/2 p = 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.

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

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

Basic Quantum Mechanics Theory of MR Spin System After Irradiation

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.

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

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

Equation of Motion: Block equation T 1 and T 2 are time constants describing relaxation processes caused by interaction with the local environment

RF Excitation: On-resonance Off-resonance

RF Excitation Excite Radio Frequency (RF) field • transmission coil: apply magnetic field along B 1 (perpendicular to B 0) • oscillating field at Larmor frequency • frequencies in RF range • B 1 is small: ~1/10, 000 T • tips M to transverse plane – spirals down • analogy: childrens swingset • final angle between B 0 and B 1 is the flip angle Transverse magnetization B 0 B 1

Signal Detection via RF coil

Signal Detection Signal is damped due to relaxation

Relaxation via magnetic field interactions with the local environment

Spin-Lattice (T 1) relaxation via molecular motion Effect of temperature Effect of viscosity T 1 Relaxation efficiency as function of freq is inversely related to the density of states

Spin-Lattice (T 1) relaxation

Spin-Spin (T 2) Relaxation via Dephasing

Relaxation

T 2 Relaxation Efffective T 2 relaxation rate: 1/T 2’ = 1/T 2 + 1/T 2* Total = dynamic + static

Spin-Echo Pulse Sequence

Multiple Spin-Echo

HOMEWORK Assignment #1 1) Why does 14 N 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 (T 1) time constant for the magnetization plotted below having boundary conditions: Mz=M 0 at t=0 following a 180 degree pulse; M=0 at t=2. 0 sec.