fmri – week 2 – mr signal scott huettel, duke university mr signal generation fmri undergraduate...

FMRI – Week 2 – MR Signal Scott Huettel, Duke University

MR Signal Generation

FMRI Undergraduate Course (PSY 181F) FMRI Graduate Course (NBIO 381, PSY

362)

Dr. Scott Huettel, Course Director


Housekeeping

• Undergraduate students– Syllabus has incorrect course number: 181F =

correct– Go with TAs to Bell Building laboratory after

lecture

• Graduate students– Syllabus refers to old grading system; you are

now graded on standard A,B, etc. system– Please complete self-assessment questions

weekly; email to me (with “SAQ”, “Ch1” etc., in the title)


Outline for Today

• Lecture: MR Signal Generation– Protons and the NMR property– Protons in a magnetic field: Alignment,

Precession– Excitation and resonance– Reception and relaxation

• Laboratory: Introducing MRI / fMRI data– Basic MATLAB use– Properties of MRI data– Basic neuroanatomy


Synopsis of MRI

M: Put subject in strong magnetic fieldR: Transmit radio waves into subject, turn

off transmitter, receive radio waves emitted by subject’s brain (the MR signal).

I: Modulate the strength of the magnetic field slightly over space (next week).


1. Protons and the NMR property


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.


The electric charge on the surface of the

proton creates a small current loop, which generates magnetic

moment μ.

The spinning mass of the proton generates

an angular momentum J.

Both μ and J are vectors that point along the spin axis and whose direction

is given by the right hand rule.


What nuclei can we measure?

• Most common in our bodies:– 12C– 16O– 1H– 14N

• Of these, only Hydrogen has the NMR property.

• But, Hydrogen is the most abundant atom in the body– Mostly in water (H2O)

This means that nearly all forms of MRI are measuring properties of Hydrogen.


2. Protons in a magnetic field


MM


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).


Introduction of a Magnetic Field (B)

Bo

Computer simulation of Earth’s magnetic field (~0.3-0.6 Gauss,

or 0.00006T)

Image from G.A. Glatzmaier

Helmholtz Pair Solenoid

http://apod.nasa.gov/apod/image/0211/field_glatz_big.gif


Some Terminology

Bo

Bo

Longitudinal Axis (z

direction)

Transverse Plane (xy plane)

B is used for magnetic fields.

B0 is the scanner’s main field.


Alignment with a magnetic field


Protons align with a magnetic field…


… but move around the field axis in a motion known as precession.

Precession axis


In a magnetic field, protons can take 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).


Energy states: Temperature effects

Low-energy protons at room temperature in

Earth’s B:

~50.000000001%

High-energy protons at room temperature in

Earth’s B:

~49.999999999%

Protons move back and forth between states because of thermal energy. As temperature decreases to near absolute zero, all protons

move to lower-energy state.


Energy states: Magnetic field effects

When the magnetic field is weak, little energy is required for a proton to change between high and low states (ΔE is

small).

But, when the magnetic field is strong, much more energy

is required (ΔE is large).

Thus, protons in the lower-energy state tend to stay in

that state


T

Bk 0M

The net magnetization (M) increases with increasing field strength (B0), but decreases with increasing temperature (T).


3. Excitation and Resonance


RR


Excitation: Conceptual Overview


Key Concept: To measure magnetization we must perturb it

• Protons must absorb energy to change between states – Parallel (aligned with) to B0 is lowest-energy state– Anti-parallel (aligned against) to B0 is highest-energy

state

• We can apply energy as electromagnetic radiation– Higher frequency radiation more energy

• How can we calculate how much energy (i.e., at what frequency) to apply?


Let’s try adding another magnetic field…

B0

(main

field

of

scan

ner)

M(n

et

mag

neti

zati

on

)

B1

(another very strong field)

M

(net

mag

netiz

atio

n)

θ


So, we could reorient some of the protons (i.e., change the net magnetization) by introducing a second, very strong

magnetic field.

Why is this impractical?


The angular momentum (The angular momentum (JJ) is the product of the ) is the product of the proton’s mass (proton’s mass (mm)),, it’s velocity ( it’s velocity (vv), and the rotation ), and the rotation

radius (radius (rr).).

rmvJ

The magnetic moment (The magnetic moment (μμ) is given by the rotational ) is given by the rotational force experienced by the proton (torque, or force experienced by the proton (torque, or ττmaxmax) )

divided by the strength of the magnetic field. These divided by the strength of the magnetic field. These are proportional to the moving charge of the proton are proportional to the moving charge of the proton

((II) times the area around which it precesses () times the area around which it precesses (AA). ).

AB

Iμ max

Cool Fact #1: Cool Fact #1: The current flow (The current flow (II) and velocity () and velocity (vv) are vectors in the ) are vectors in the same direction (i.e., the charge is precessing just like same direction (i.e., the charge is precessing just like

the mass).the mass).

Cool Fact #2:Cool Fact #2:The rotation radius (The rotation radius (rr) and area () and area (AA) are proportional.) are proportional.

Jμ Magnetic Moment and Angular

Momentum have a constant relation!


Magnetic Moment and Angular Momentum have a constant

relation!

Jμ

The constant γ (gamma) is known as the gyromagnetic

ratio. It is fixed for any given atomic nucleus.

If we assume that the proton is a point charge moving

around in a circle, then the gyromagnetic ratio is given by a very simple equation (see book for derivation).

m

q

2The gyromagnetic ratio (γ)

depends on only two things: charge (q) and mass (m).

That’s it.


The gyromagnetic ratio (γ) is critical for MRI.

It allows us to calculate the energy (expressed in electromagnetic frequency, v)

needed to change an atomic nucleus from the low- to high-energy states in a given magnetic field (B0).

02Bv

This frequency (v) is known as the Larmor Frequency.

It is the same as the precession frequency of the nucleus!


The Canonical Analogytm for resonance: a swing set

• Option #1– A single, strong push to

lift the person off the ground

– Requires an enormous amount of exertion, delivered very rapidly

• Option #2– Many small pushes at

the resonant frequency of the swing set

– Allows distribution of the energy over time!

This is a random illustrative photo. The internet is great.


… moving from happy kids to atomic nuclei

• Option #1– Using a very strong

perpendicular field– Impractical (perhaps

impossible) to do quickly in a real device

• Option #2– Many small pushes at

the resonant frequency of the atomic nucleus of interest

– Allows distribution of the energy over time!

Giving energy for a longer time period increases the flip angle.


“Tipping” in a rotating frame of reference

The RF energy is called B1 because it is, effectively, a second magnetic field.


Resonance Frequencies of Common Nuclei

Remember, the resonant frequency is constant for a given atomic nucleus and proportional to magnetic

field strength.

02Bv


MRI (e.g., 6 x 107Hz)

X-Ray, CT

What are the consequences of electromagnetic energy at this frequency?

MRI uses electromagnetic energy in the radio wave portion of the electromagnetic spectrum. It can cause heating of biological tissue, but does not break molecular bonds.


Radiofrequency Coils for Excitation (and Reception)

• 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 geometryVolume coil (low sensitivity but uniform coverage)Surface coil (High sensitivity but limited coverage)Phased-array coil (High sensitivity, near-uniform coverage)


4. Reception and relaxation


Tipping the net magnetization provides measurable MR signal!

Before 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.


Relaxation: Nothing Lasts Forever

• Once we stop applying energy, M will go back to being aligned with static field B0

• This process is called relaxation

• The part of M perpendicular to B0 shrinks [Mxy]

– This part of M is called transverse magnetization

– It provides the detectable RF signal

• Part of M parallel to B0 grows back [Mz] – This part of M is called longitudinal magnetization

– Mz is not directly detectable, but can be again converted into transverse magnetization by energy (e.g., B1)


T1 T2


Relaxation Times and Rates

• Net magnetization changes in an exponential fashion– Constant rate (R) for a given tissue type in a given magnetic field– R = 1/T, leading to equations like e–Rt

• T1 (recovery): Relaxation of M back to alignment with B0

– Usually 500-1000 ms in the brain (lengthens with bigger B0)

• T2 (decay): Loss of transverse magnetization over a microscopic region ( 5-10 micron size)– Usually 50-100 ms in the brain (shortens with bigger B0)

• T2*: Overall decay of the observable RF signal over a macroscopic region (millimeter size)– Usually about half of T2 in the brain (i.e., faster relaxation)


T1 and T2 parameters

By selecting appropriate pulse sequence parameters (Week 4’s

lecture), images can be made sensitive to tissue differences in

T1, T2, or a combination.


Tissue T1 (s) T2 (ms)

CSF 2 - 6 110 - 2000

White matter 0.76 - 1.08 55 -100

Gray matter 1.09 - 2.15 61 - 109

Meninges 0.5 - 2.2 50 - 165

Muscle 0.95 - 1.82 20 - 67

T1 and T2 values at 1.5T


What about “I”?


II We just have signal, so far. We

need spatial gradients to

generate images. Next week.


MR Signal Generation

• Scanners use very strong static fields (Tesla range) to generate net magnetization (M)

• Protons in magnetic fields precess around the longitudinal axis of a field at the Larmor Frequency

• Electromagnetic energy, when supplied at the Larmor frequency (radio waves) by head coils, is absorbed by the protons

• This tips the net magnetization down into the transverse plane

• As the net magnetization rotates through the transverse plane, it induces a changing current in the head coils.

• This current is the MR signal

fmri – week 2 – mr signal scott huettel, duke university mr signal generation fmri undergraduate...

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