BME 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, E002C

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 See “Background Information on MRI” section Mark Cohen’s intro Basic MR Physics slides Douglas Noll’s Primer on MRI and Functional MRI Joseph Hornak’s Web Tutorial, The Basics of MRI

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

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)

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)

Equipment MagnetGradient CoilRF Coil 4T magnet gradient coil (inside) B0B0

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

Transmit Receive rf coil rf coil main magnet main magnet gradientShimming Control Computer

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

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

Angular Momentum J = m  =mvr m v rJ magnetic moment  =  J where  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 . 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.

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 K, all spins will occupy the lower energy state. 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 % of protons/T align with field Inside magnetic field MzMz M xy = 0 longitudinal axis transverse plane Longitudinal magnetization Transverse magnetization M

Net Magnetization Bo M

 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 The Boltzman equation describes the population ratio of the two energy states: N - /N + = e –E/kT

Energy Difference Between States

 E  h  E = 2  z B o  /2   known as Larmor frequency = MHz / Tesla for proton  /2  = 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.

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 Basic Quantum Mechanics Theory of MR

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  =  × B  =  × B o torque  = dJ / dt J =  /  d  /dt =  (  × B o )  (t) = (  cos  Bt +  sin  Bt) x + (  cos  Bt -  sin  Bt) y +  z  (t) = (  xo cos  B o t +  yo sin  B o t) x + (  yo cos  B o t -  xo sin  B o t) y +  zo z

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 T1 and T2 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 B1 (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 B1B1 B0B0 Transverse magnetization

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 T 1 Relaxation efficiency as function of freq is inversely related to the density of states Effect of temperatureEffect of viscosity

Spin-Lattice (T1) 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=M0 at t=0 following a 180 degree pulse; M=0 at t=2.0 sec.