BME 595 - Medical Imaging ApplicationsPart 2: INTRODUCTION TO MRI

Lecture 1 Fundamentals of Magnetic Resonance

Feb. 16, 2005

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

Department of RadiologyResearch II building, E002C

jadchris@iupui.edu317-274-3815

ReferencesBooks 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.

ReferencesOnline 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 slideshttp://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html

Douglas Noll’s Primer on MRI and Functional MRIhttp://www.bme.umich.edu/~dnoll/primer2.pdf

Joseph Hornak’s Web Tutorial, The Basics of MRIhttp://www.cis.rit.edu/htbooks/mri/mri-main.htm

Timeline of MR Imaging

1920 1930 1940 1950 1960 1970 1980 1990 2000

1924 - Pauli suggests that nuclear particles

may have angular momentum (spin).

1937 – Rabi measures magnetic moment of

nucleus. Coins “magnetic resonance”.

1946 – Purcell shows that matter absorbs energy at a resonant

frequency.

1946 – Bloch demonstrates that nuclear precession can be

measured in detector coils.

1972 – Damadian patents idea for large

NMR scanner to detect malignant

tissue.

1959 – Singer measures blood flow

using NMR (in mice).

1973 – Lauterbur publishes method for

generating images using NMR gradients.

1973 – Mansfield independently

publishes gradient approach to MR.

1975 – Ernst develops 2D-Fourier transform for MR.

NMR renamed MRI

MRI scanners become clinically

prevalent.

1990 – Ogawa and colleagues create functional images using endogenous, blood-oxygenation

contrast.

1985 – Insurance reimbursements for MRI exams begin.

Nobel Prizes for Magnetic Resonance

• 1944: RabiPhysics (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 TechniquesNuclear 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

Magnet Gradient Coil RF Coil

RF Coil

4T magnet

gradient coil(inside)

B0

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

rfcoil

rfcoil

mainmagnet

mainmagnet

gradientShimming

ControlComputer

Main Magnet Field Bo• Purpose is to align H protons in H2O (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?Reason? It is impossible to arrange these nuclei so that a zero net angularIt is impossible to arrange these nuclei so that a zero net angular momentum is achieved. Thus, these nuclei will display a magneticmomentum is achieved. Thus, these nuclei will display a magnetic moment and angular momentum necessary for NMR.moment and angular momentum necessary for NMR.

Examples:Examples: 11H, H, 1313C, C, 1919F, F, 2323N, and N, and 3131P with gyromagnetic ratio of 42.58, 10.71, P with gyromagnetic ratio of 42.58, 10.71, 40.08, 11.27 and 17.25 MHz/T. 40.08, 11.27 and 17.25 MHz/T.

Since hydrogen protons are the most abundant in human body, we useSince hydrogen protons are the most abundant in human body, we use11H MRI most of the time.H MRI most of the time.

Angular Momentum

JJ = m = m=m=mvvrrmm

vvrr

JJ

magnetic moment magnetic moment = = JJwherewhere is the gyromagnetic ratio, is the gyromagnetic ratio,and it is a constant for a given nucleusand it is a constant for a given nucleus

A Single Proton

++++

++

There is electric charge There is electric charge on the surface of the on the surface of the proton, thus creating a proton, thus creating a small current loop and small current loop and generating magnetic generating magnetic moment moment ..

The proton also The proton also has mass which has mass which generates angenerates anangular angular momentummomentumJJ when it is when it is spinning.spinning.

JJ

Thus proton “magnet” differs from a magnetic bar in that itThus proton “magnet” differs from a magnetic bar in that italso possesses angular momentum caused by spinning.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.Spinning protons in a magnetic field will assume two states.If the temperature is 0If the temperature is 0o K, all spins will occupy the lower energy state. K, all spins will occupy the lower energy state.

Protons align with fieldOutside magnetic field

randomly oriented

• 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

Inside magnetic field Mz Mxy = 0longitudinal

axis

transverseplane

Longitudinalmagnetization

Transversemagnetization

M

Net Magnetization

BoM

TBcM o

Larger B0 produces larger net magnetization M, lined up with B0

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 B0

The Boltzman equation describes the population ratio of the two energy states:

N-/N+ = e –E/kT

Energy Difference Between States

Energy Difference Between States

Eh E = 2 z Bo

/2known as Larmor frequency

/2= 42.57 MHz / Tesla for proton= 42.57 MHz / Tesla for proton

Knowing the energy difference allows us to useelectromagnetic waves with appropriate energy level to irradiate the spin system so that some spins at lower energy level can absorb right amount ofenergy to “flip” to higher energy level.

Spin System Before Irradiation

BoLower Energy

Higher Energy

Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR

The Effect of Irradiation to the Spin System

Lower

Higher

Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR

Spin System After Irradiation

Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR

Precession – Quantum MechanicsPrecession – Quantum Mechanics

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

Precession –Precession – ClassicalClassical

= = ×× B Bo torque = dJ / dt J = /

d/dt = ( × Bo)

(t) = ((t) = (xocos cos BBot + t + yosin sin BBot) t) xx + ( + (yocos cos BBot - t - xosin sin BBot) t) yy + + zozz

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 ExcitationExcite 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

B1

B0

Transversemagnetization

Signal Detection via RF coil

Signal Detection

Signal is damped due to relaxation

Relaxation via magnetic field interactions with the local environment

Spin-Lattice (T1) relaxation via molecular motion

T1 Relaxation efficiency as function of freq is inversely related to the

density of states

Effect of temperature Effect of viscosity

Spin-Lattice (T1) relaxation

Spin-Spin (T2) Relaxation via Dephasing

Relaxation

Relaxation

T2 Relaxation

Efffective T2 relaxation rate:

1/T2’ = 1/T2 + 1/T2*

Total = dynamic + static

Spin-Echo Pulse Sequence

Spin-Echo Pulse Sequence

Multiple Spin-Echo

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.