MRI Physics: Just the Basics

An Introduction to MRI Physics and Analysis

Michael Jay Schillaci, PhDMonday, February 4th, 2008

Overview Background

Forces Causes and Effects of MagnetismQuantum Theory - Larmor FrequencyBrain Physiology

Magnetic Fields in an MR SystemMain and Gradient CoilsRF Coils and Spatial EncodingGradient and Spin Echo Sequences

Background

Fields in General: Gravity

ssftGgrM //322

*Actual cause is force of attraction of the mass of ball to the mass of Earth through the “field of gravity”…

gmFg

Fields are covariates of motionWhen a ball falls… We refer to “gravity”…

Fields in General: Electricity

dV

r

QkE 2

*Actual cause is force of attraction of the charge of particle to the charge of Capacitor through the “field of electricity”…

EqFE

EdV

When a particle rises… We refer to “electricity”…

The Causes of Magnetism

Macroscopic ViewCurrent in wireField is “around” wire

Depends on current Depends on distance

Microscopic ViewMoment of atomField is “about” nucleus

Depends on material

r

IB

2

0

cosAB

Properties of Atomic Nuclei

Nuclei have two properties: Spin (conceptual, not literal) Charge (property of protons)

Nuclei are made of protons and neutrons Both have spin values of ½ Protons have charge

Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin

A nucleus has the NMR Property if it has both angular momentum and a magnetic moment. Such nuclei have an odd number of protons or an odd

number of neutrons.

Kinds of Magnetism Ferromagnetic materials (e.g., Iron)

Both attract and repel other magnets Create own field

Paramagnetic materials (e.g., Gadolinium) Attracted toward magnets Align with other fields

Diamagnetic materials (e.g., Water) Repelled by magnets Anti-align with other fields

Protons align with a magnetic field…

The Effects of Magnetism

Two ways to assess effects of magnetic fields:Determine Magnetic Force

Forces move objects Field is a covariate of force

Determine Magnetic Energy Density Energy heats objects Field is correlated with energy

BvqFM

2

02

1BM

Radiation is absorbedEnergy increases

Radiation is emittedEnergy decreases

Lower

Higher

Basic Quantum Theory

Static Field “splits” states Zeeman splits high/low

energy states

RF Field “rotates” moments Precession Frequency

Magnetic Precession

00 B m

qg

42

B0

B0

B0 J

dJ / dt = × × BBo

d/dt = ( × Bo)* For comparison: In the Earth’s magnetic field ( 0.00005 T ), hydrogen precesses at ~2100 Hz.

NMR Parameters B0=1T*

~ 1 ppm excess in spin-up state creates the net Magnetization…

M = net (bulk) magnetizationM

Energy Difference

FrequencyEquate differences

Larmor Frequency

E = Eup – Edown

= z Bo - (-z Bo )z Bo

E = hv0 = z Bo

h B0

002 Bv

Larmor Equation

Quantum Mechanics governs state transitions Energy of transition

Planck’s constant

Energy valuesMRI

X-Ray, CT

Electromagnetic Energy

hE

seVh 15101357.4

eVOE RayX 100102

eVOEMRI 10001910

Excites Electrons

Excites Protons

Brain Physiology - Chemistry

Energy of Fields Heats Brain Tissue

Drives Chemistry Energy covaries with the

wavelength

Higher energy breaks bonds Medium energy vibrates molecules Lower energy rotates molecules

0

2

2B

Volume

Energy

WavelengthEnergy

Material Dependence Magnetization varies with field,

temperature and material

Magnetic susceptibility alters the local field

T

B

kVT

BcM

B

z 02

0 1

0

20

0

11 B

TVkMB

B

zmmLocal

Conductivity

Susceptibility

Brain Physiology – Empirical Brain Conductivity

Measure conductivity of 20 human brainsLess than 10 hours after death

ResultsConductivity depends on frequency:

1.39 S/m (0.14 S/m) at 900 MHz 1.84 S/m (0.16 S/m) at 1,800 MHz

Brain Physiology – Measures

Energy Density

Conductivity

Relationship

2ESAR

2

02

1BM

202 cSAR

M

Magnetic Fields in an MR System

USC Trio – Siemens 3T MRI

Protons in no magnetic field

In the absence of a strong magnetic field, the spins are oriented

randomly.

Thus, there is no net magnetization (M).

Transverse Magnetization

Bo

Bo

Longitudinal Axis (z

direction)

Transverse Plane (xy plane)

B is used for magnetic fields.

B0 is the scanner’s main field.

In a magnetic field, protons can take either high- or low-energy states

The difference between the numbers of protons in the high-energy and low-energy states results in a net magnetization (M) and gives rise to the

Larmor Equation.

002 Bv

Main Field Field Characteristics Generated by Helmholtz Coils

— Currents are parallel (same direction)

Field along MRI axis

a

a

22

222

2

20 11

2 azaz

aINB

aa

MMM

Coil 1

Coil 2

B M

Gradient Field Field Characteristics Created by Maxwell Pair

— currents are anti-parallel (opposite direction)

Field along MRI axis

b

b

22

222

2

20 11

2 bzbz

bINB

bb

GGG

Coil 1

Coil 2

BG

Total (Static) Field Total Field

Sum of Main and Gradient Fields In practice a “shim” field is also used to “flatten” the field.

B0=BM+BG

Gradient field decreases total

Gradient field increases total

ΔB0 ~ 1mT

Spatial Encoding - Gradient Field varies (almost) linearly Change in field = B0

Frequency depends on position (z) Field depends on material

zz

BBz 0

00 2)(

Image Resolution Strong Gradient → High Resolution Weak Gradient → Low Resolution

B0= 0.018 T

z = 0.16 m

Galois Coils Transverse RF Field

— Radio Frequency Transmitter, 0

Rotating frame— Total field given by

— Receiver currents are anti-parallel — Induced field is perpendicular

RF Fields - Generation

tII C sin2

tII C cos1

zBBB C ˆ00

BC-z

r

+x

tt

oo

= 1/ t= 1/ t

FTFT

BC

oo

Transmitter

Receiver

Radiofrequency Coils

Defined by their function:

Transmit / receive coil (most common)

Transmit only coil (can only excite the system)

Receive only coil (can only receive MR signal)

Defined by geometry

Volume coil (low sensitivity but uniform coverage)

Surface coil (High sensitivity but limited coverage)

Phased-array coil (High sensitivity, near-uniform coverage)

Origin of the MR SignalBefore Excitation

After Excitation

Excitation tips the net magnetization (M) down into the transverse plane, where it

can generate current in detector coils (i.e., via induction).

During Excitation (to)

During Excitation (t1)

The amount of current oscillates at the (Larmor) frequency of the net

magnetization.

1. Assume perfect “spoiling” -transverse magnetization is zero before each excitation:

2. Spin-Lattice (T1) Relaxation occurs between excitations:

3. Assume steady state is reached during repeat time:

4. Spoiled gradient rephases the FID signal at echo time:

Gradient Echo Imaging

coszAzB MM

11 10

TTR

TTR

zBzC eMeMM*2

1

1

cos1

1sin0

TTE

TTR

TTR

Spoil ee

eMS

*2sin T

TE

zASpoil eMS

zAzC MM

1cos TTR

E e

Maximize signal: Ernst Angle

Pulse Sequence Parameters

• GE imaging– complex effects

– maximum SNR typically between 30 and 60 degrees

– long TR sequences (2D)• increase SNR with increased flip angle

– short TR sequences (TOF & 3D)• decreased SNR with increased flip angle

Basic Spin Echo Sequences (SE) The refocusing pulse allows us to recover true T2. Image from

http://www.e-mri.org/cours/ Includes interactive adjustment of T1/T2

T2

T2*

The Spin Echo Sequence

Spin echo sequence applies a 180º refocusing pulse half way between 90º pulse and measurement.

This pulse eliminates phase differences due to artifacts, allowing measurement of pure T2.

Dramatically more signal with Spin Echo.

Sig

na

lTime

0

1

T2

T2*

0.5 TE 0.5 TE

Actual Signal

Image Formation Integrate magnetization to get MRI signal

Select a z “slice” and form image of XY plane variations

Contrast from difference in magnetization— Image at several times— Scanner acquires K-Space weights— Construct image and average slices

dxdyetyxMtSArea

dtyGxGi

XY

t

YX

0,,)(

Horizontal density

Ver

tica

l de

nsit

y

T1 & T2 Weighting

T1 Contrast Echo (TE) at T2 min Repeat (TR) at T1 max

T2 Contrast Echo (TE) at T2 max Repeat (TR) at T1 min

Magnetization is given by

T1 Contrast Weighting

T2 Contrast Weighting

TE

TR TE

TR

Min T2 Contrast Max T1 Contrast

Max T2 Contrast Min T1 Contrast

decay

T

TE

eryre

T

TR

XY eeMM

2

cov

10 1

Static Contrast Images

T2 Weighted Image (T2WI)(Gray Matter – CSF Contrast)

T1 Weighted Image (T1WI)(Gray Matter – White Matter)

Examples from the Siemens 3T T1 and T2 Weighted Images

RF pulse determines “flip angle” Rotation determines amount

of magnetization measured

Field strength determines resolution Increased magnetization

leads to increased signal

Pulse and Field Effects

cosMM Z

Images adapted from: http://www.mri.tju.edu/phys-web/1-T1_05_files/frame.htm

sinMM XY

Muscle

Tissue

Difference

B0= 0.2 T

B0 = 1.5 T