Basic fMRI Physics

In BOLD fMRI, we are measuring: the inhomogeneities introduced into the magnetic field of the scanner… as a result of the changing ratio of oxygenated:deoxygenated blood… via their effect on the rates of dephasing of hydrogen nuclei.

Ehhh???

History of MRI

NMR = nuclear magnetic resonancenuclear: properties of nuclei of atomsmagnetic: magnetic field requiredresonance: magnetic field x radio frequency

1946: Block and Purcellatomic nuclei absorb and re-emit radio frequency energy

1992: Ogawa and colleaguesfirst functional images using BOLD signal

Bloch Purcell

NMR MRI: Why the name change?

most likely explanation: nuclear has bad connotations

Ogawa less likely explanation: NMR means Nouveau Mouvement Religieux

Necessary Equipment

Magnet Gradient Coil RF Coil

Source: Joe Gati, photos

RF Coil

3T magnet

gradient coil(inside)

Recipe for MRI

1) Put subject in big magnetic field (leave him there)

2) Transmit radio waves into subject [about 3 ms]

3) Turn off radio wave transmitter

4) Receive radio waves re-transmitted by subject– Manipulate re-transmission with magnetic fields during this readout interval [10-100 ms]

5) Store measured radio wave data vs. time– Now go back to 2) to get some more data

6) Process raw data to reconstruct images

7) Allow subject to leave scanner (this is optional)

Source: Robert Cox’s web slides

x 60,000 =

The Big Magnet

Source: www.spacedaily.com

Main field = B0

• Continuously on

• Very strong : Earth’s magnetic field = 0.5 Gauss / 1 Tesla (T) = 10,000 Gauss

3 Tesla = 3 x 10,000 0.5 = 60,000 x Earth’s magnetic field

B0

Robarts Research Institute 3T

SafetyThe strength of the magnet makes safety essential : things fly – even big things!

Source: www.howstuffworks.com Source: http://www.simplyphysics.com/flying_objects.html

Anyone entering the magnet must be metal free

This subject was wearing a hair band with a ~2 mm copper clamp. Left: with hair band. Right: without.

Source: Jorge Jovicich

Develop screening strategies :do the metal macarena!

1H aligns with B0

longitudinalaxis

Outside magnetic field • randomly oriented

M = 0

transverseplane

Inside magnetic field • 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

Source: Mark Cohen’s web slidesMSource: Robert Cox’s web slides

Longitudinalmagnetization

Protons are abundant: high concentration in human body have high sensitivity: yields large signals

Larmor Frequency

Larmor equation : resonance frequency f = B0/2π for 1H = 42.58 MHz/T

Field Strength (Tesla)

127.7

63.8

1.5 3.0

Fre

quen

cy (

MH

z)

Turn your dial to 3T fMRI …… broadcasting at a frequency of 127.7 Mhz

Radio-Frequency Excitation

• transmission coil: apply magnetic field along B1

(perpendicular to B0 for ~3 ms)

• oscillating field at Larmor frequency• frequencies in range of radio transmissions• B1 is small: ~1/10,000 T

• tips M to transverse plane – spirals down• analogies: guitar string (Noll), swing (Cox)• final angle between B0 and B1 is the flip angle

Transversemagnetization

longitudinalaxis

Source: Robert Cox’s web slides

Relaxation and Receiving

Receive Radio Frequency Field• receiving coil: measure net magnetization (M)• readout interval (~10-100 ms)• relaxation: after RF field turned on and off, magnetization returns to normal

longitudinal magnetization T1 signal recovers (realignment)transverse magnetization T2 signal decays (dephasing)

Source: Robert Cox’s web slides

Why the dephasing ?

Source: Mark Cohen’s web slides

• protons precess at slightly different frequencies because of (1) random fluctuations in the local field at the molecular level that affect both T2 and T2*; (2) larger scale variations in the magnetic field that affect T2* only.

• over time, the frequency differences lead to different phases between the molecules (clock analogy)

• as the protons get out of phase, the transverse magnetization decays

• this decay occurs at different rates in different tissues

T1 and TR

Source: Mark Cohen’s web slides

T1 = recovery of longitudinal magnetization (B0)

due to realignment of spinsTR (time to repetition) = time to wait after excitation before sampling T1

= time before next RF excitation

≈ M0(1-exp(-t/T1))

T2 and TE

Source: Mark Cohen’s web slides

T2 = decay of transverse (B1) magnetization

due to dephasing of spinsTE (time to echo) = time to wait before sampling T2

(after refocusing of signal)

≈ exp(-t/T2))

Source: Mark Cohen’s web slides

TISSUE T1(s) T2(s)

grey matter 1.0 0.10

white matter 0.7 0.08

CSF 2.0 0.25

blood 1.2 0.25

water 4.7 3.50

T1 and T2 contrasts

T2* relaxation

Source: Jorge Jovicich

time

Mxy

Mo sinT2

T2*

• dephasing of transverse magnetization due to both:

- microscopic molecular interactions (as for T2)

- spatial variations of the external main field B (tissue/air, tissue/bone interfaces)

• exponential decay (T2* 30 - 100 ms, shorter for higher Bo)

Spatial Coding: Gradients

How can we encode spatial position?• Add a gradient to the main magnetic field• Excite only frequencies corresponding to slice plane• Use other tricks to get other two dimensions

left-right: frequency encode top-bottom: phase encode

Field Strength ~ z position

Fre

qu

en

cy

Gradient switching – that’s what makes all the beeping & buzzing noises during imaging => EAR PLUGS !

Echos

Source: Mark Cohen’s web slides

Echos = refocusing of signal

Spin echo (not shown) – measure T2

Gradient echo (shown) - measure T2*flip the gradient at t=TE/2measure after refocusing at t=TE

pulse sequence: series of excitations, gradient triggers and readouts

t = TE/2

A gradient reversal at this point will lead to a recovery of transverse magnetization

TE = time to wait to measure refocused spins

(left-right)

(top-bottom)

A walk through the K-space

(inverse Fourier transform)

Source: Traveler’s Guide to K-space (C.A. Mistretta)

Susceptibility

Source: Robert Cox’s web slides

Adding a nonuniform object (like a person) to B0 will make the total magnetic field nonuniformThis is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an

external field

Susceptibility Artifact- occurs near junctions between air and tissue sinuses, ear canals- spins become dephased so quickly (quick T2*), no signal can be measured

sinuses

earcanals

Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue

Hemoglobin

Source: http://wsrv.clas.virginia.edu/~rjh9u/hemoglob.html, Jorge Jovicich

A molecule to breathe with:

- four globin chains - each globin chain contains a heme group - at center of each heme group is an iron atom (Fe)

- each iron ion Fe2+ can attach an oxygen molecule (O2)

- oxy-Hemoglobin (four O2) is diamagnetic no B effects

- deoxy-Hemoglobin is paramagnetic if [deoxy-Hgb] local B

BOLD signal

Source: Brief Introduction to fMRI by Irene Tracey

neural activity blood flow oxyhemoglobin T2* MR signal

Blood Oxygen Level Dependent signal

time

Mxy

SignalMo sin

T2* taskT2* control

TEoptimum

Stask

ScontrolS

Source: Jorge Jovicich

BOLD signal

Source: Doug Noll’s primer

To take away

Tissue protons align with magnetic field(equilibrium state)

RF pulses

Protons absorbRF energy

(excited state)

Relaxation processes

Protons emit RF energy(return to equilibrium state)

Spatial encodingusing magneticfield gradients

Relaxation processes

NMR signaldetection

Repeat

RAW DATA MATRIX

Fourier transform

IMAGE

Magnetic field

Source: Jorge Jovicich

Kwong et al., 1992