Basic Physical Principlesof MRI

James Voyvodic, Ph.D.Brain Imaging and Analysis Center

Synopsis of MRI

1) Put subject in big magnetic field

2) Transmit radio waves into subject [2~10 ms]

3) Turn off radio wave transmitter

4) Receive radio waves re-transmitted by subject0

5) Convert measured RF data to image

Many factors contribute to MR imaging

• Quantum properties of nuclear spins

• Radio frequency (RF) excitation properties

• Tissue relaxation properties

• Magnetic field strength and gradients

• Timing of gradients, RF pulses, and signal detection

MRI uses a combination of Magnetic and Electromagnetic Fields

• NMR measures magnetization of atomic nuclei in the presence of magnetic fields

• Magnetization can be manipulated by manipulating the magnetic fields (this is how we get images)

• Static magnetic fields don’t change (< 0.1 ppm / hr):

The main field is static and (nearly) homogeneous

• RF (radio frequency) fields are electromagnetic fields that oscillate at radio frequencies (tens of millions of times per second)

• Gradient magnetic fields change gradually over space and can change quickly over time (thousands of times per second)

Radio Frequency Fields

• RF electromagnetic fields are used to manipulate the magnetization of specific types of atoms

• This is because some atomic nuclei are sensitive to magnetic fields and their magnetic properties are tuned to particular RF frequencies

• Externally applied RF waves can be transmitted into a subject to perturb those nuclei

• Perturbed nuclei will generate RF signals at the same frequency – these can be detected coming out of the subject

MRI

X-Ray, CT

Electromagnetic Radiation Energy

What kinds of nuclei can be used for NMR?

• Nucleus needs to have 2 properties:– Spin– charge

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

• Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin – Good MR nuclei are 1H, 13C, 19F, 23Na, 31P

Hydrogen atoms are best for MRI

• Biological tissues are predominantly 12C, 16O, 1H, and 14N

• Hydrogen atom is the only major species that is MR sensitive

• Hydrogen is the most abundant atom in the body

• The majority of hydrogen is in water (H2O)

• Essentially all MRI is hydrogen (proton) imaging

Nuclear Magnetic Resonance Visible Nuclei

Why do protons interact with a magnetic field?

• Moving (spinning) charged particle generates its own little magnetic field

• Spinning particles with mass have angular momentum

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 the magnetic bar in that itThus proton “magnet” differs from the magnetic bar in that italso possesses angular momentum caused by spinning.also possesses angular momentum caused by spinning.

Magnetic Moment

II

BB

FFLL

F = IBLF = IBL

BB

LLWW

= IBLW = = IBLW = IBAIBA

maxmax

sinsinForceForce TorqueTorque

Angular Momentum

JJ = m = m=m=mvvrr

mm

vvrr

JJ

= = JJ

is the gyromagnetic ratiois the gyromagnetic ratio is a constant for a given nucleusis a constant for a given nucleus

The magnetic moment and angular momentum are vectors lying along the spin axis

• Magnetic field B and magnetization M are vectors:– Quantities with direction as well as size– Drawn as arrows ....................................– Another example: velocity is a vector (speed is its size)– Vector operations: dot product AB cos cross product AB sin

• Magnetic field exerts torque to line magnets up in a given direction– direction of alignment is direction of B– torque proportional to size of B [units=Tesla, Gauss=10–4 T]

Vectors and Fields

How do protons interact with a magnetic field?

• Moving (spinning) charged particle generates its own little magnetic field– Such particles will tend to line up with external

magnetic field lines (think of iron filings around a magnet)

• Spinning particles with mass have angular momentum– Angular momentum resists attempts to change

the spin orientation (think of a gyroscope)

[Little magnets lining up with external lines of force]

[Main magnet and some of its lines of force]

Ref: www.simplyphysics.com

Net Magnetization

BoM

T

BcM o

Net magnetization

• Small B0 produces small net magnetization M

• 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 of anti-parallel versus parallel protons is roughly 100,000 to 100,006 per Tesla of B0

The Energy Difference Between the Two Alignment States

E = 2 z Bo

Eh

/2known as larmor frequency

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

Resonance frequencies of common nuclei

To measure magnetization we must perturb it

• Need to apply energy to tip protons out of alignment– aligned with magnetic field is lowest energy– aligned opposite magnetic field is next lowest

energy state

• Amount of energy needed depends on nucleus and applied field strength (Larmor frequency)

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

If M is not parallel to B, then it precesses clockwise aroundthe direction of B. “Normal” (fully relaxed) situation has M parallel to B, and therefore does not precess

Precession

This is like a gyroscope

Derivation of precession frequencyDerivation of precession frequency

This says that the precession frequency is the This says that the precession frequency is the SAME as the larmor frequencySAME as the larmor frequency

= = ×× B Bo

= dJ / dtJ = /

d/dt = ( × Bo)

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

RF Coil: Transmitting B1 Field• To tip spins in the static B0 field we apply (transmit)

a magnetic field B1 that fluctuates at the precession frequency and points perpendicular to B0 (how do we achieve this? – by making a coil)

The effect of the tiny B1 is to cause M to spiral away from the direction of the static B0 field B110–4 Tesla If B1 frequency is not close to resonance, B1 has no effect

A Mechanical Analogy: A Swingset• Person sitting on swing at rest is “aligned” with

externally imposed force field (gravity)• To get the person up high, you could simply

supply enough force to overcome gravity and lift him (and the swing) up– Analogous to forcing M over by turning on a huge

static B1

• The other way is to push back and forth with a tiny force, synchronously with the natural oscillations of the swing– Analogous to using the tiny RF B1 to slowly flip M

over

gg

NMR signal decays in time• T1 relaxation – Flipped nuclei realign with the magnetic

field

• T2 relaxation – Flipped nuclei start off all spinning together, but quickly become incoherent (out of phase)

• T2* relaxation – Disturbances in magnetic field (magnetic susceptibility) increase rate of spin coherence T2 relaxation

• NMR signal is a combination of the total number of nuclei (proton density), minus the T1 relaxation and T2 relaxation components

Different tissues have different relaxation times

Relaxation times are important for generating image contrast

• T1 - Gray/White matter• T2 - Tissue CSF• T2* - Susceptibility (functional MRI)

MRI Scanner

Things needed for a typical MRI scanner

Strong magnetic field, usually from superconducting magnets.

RadioFrequency coils and sub-system.

Gradient coils and sub-system.

Shimming coils and sub-system.

Computer(s) that coordinate all sub-systems.

MRI scanner components

Using NMR signals for imaging

• Need to prolong and amplify the decaying signal

• Need to know the spatial location of the tissue generating the signal

The decaying NMR signal can be recovered by realigning spins

Spin EchoImaging

Gradient EchoImaging

Spatial location is identified by using spatially varying magnetic fields

Proton resonance withuniform magnetic field

Proton resonance withaxial field gradient

It is actually spatial frequency, not physical location, that is scanned

• Gradients cause spins to spread out and realign at different times• Bands of tissue with uniform spacing will realign together• MRI scanning systematically samples the strength of the signal at different spatial frequencies

Horizontal sampling (Kx) Vertical sampling (Ky)

MRI scanner collects spatial frequency data (in k-space)

Horizontal spatial frequency density

Verticalspatial

frequencydensity

A 2-dimensional Fourier transform mathematically converts from spatial

frequency to reconstructed MR images

The versatility of MRI arises from the different types of tissue contrast that can be generated by manipulating parameters

• TR – adjusting the time between acquisitions affects T1 relaxation

• TE – adjusting the time between refocusing pulses affects T2 and T2* relaxations

• Timing of gradients affects sampling in k-space

• Additional gradient pulses before the RF pulse can enhance specific tissue properties

• Chemical agents can further enhance image contrast