fMRI
Joe Mandeville
Martinos Center for Biomedical Imaging
Massachusetts General Hospital
What is fMRI
• Many ways to measure “function”
· Diffusion, flow, spectroscopy, BBB, T2, …
• “fMRI” usually refers to
· Task-induced changes in function
· BOLD signal most common
· Relatively rapid ON/OFF paradigms
• Sensory, motor, cognitive
• But also …
· CBF, or CBV in animal models
· Drug stimuli or other slow/non-averaged responses
History of fMRI
(History really starts long before fMRI)
• Brain activity is coupled to metabolism
· Roy & Sherington, 1890
• Invasive “imaging” in animal brain
· Bolus contrast material for CBF,CBV (1954)
· Radiolabeled diffusible tracers for CBF (1960)
· 2-DG for metabolism (1977)
• PET used similar methods
· Radiolabeled diffusible tracer (1969)
· CBV using labeled blood pool agent (1974)
· FDG for metabolism (1980s)
History of fMRI
• First “brain mapping” by fMRI used bolus infusions of
gadolinium for assessing CBV (Belliveau, 1991)
Not quite what we want in terms
of temporal resolution, BUT this
study forecast the use of
steady-state agents
History of fMRI
• BOLD signal
·
·
·
·
·
Deoxygenated hemoglobin is paramagnetic (1936)
Oxygen changes T2 relation (1982)
Optical “intrinsic signals” depend upon blood oxygenation (1986)
Respiration produces “BOLD signal” in large veins in rats
fMRI using BOLD signal (1992)
• CBF
· Demonstration of arterial spin labeling (1992)
· fMRI using ASL (1992)
fMRI characteristics
• Good spatial resolution (1 mm)
· … but only good enough to study systems biology,
not biomolecular or mechanisms
• Good temporal resolution (1 sec)
· … but only good enough to study the blood supply,
not electrical activity
• Strongly affected by contrast agents
· … but only those within the blood stream, as MRI
agents do not cross the BBB
• Good for activation studies
· … but less good for assessing basal physiology
Function of the brain: 1800
Methods based upon comparisons:
• human versus animal
• young versus old
• personality versus post-mortem
Shared by human & animal
Only human
Firmness of purpose
Poetic talent
Pride &
Arrogance
Love of
offspring
Wisdom
Gall, 1810
Tendency to
Murder
Cleverness Instinct of reproduction
Example: temporal response
• Typical BOLD time response
· For analysis, we predict response based upon the
stimulus timing and the hemodynamic response
function (impulse response model)
Example: brain mapping
• Visually-cued reward produces activation
in visual areas (sensory) and frontal
areas (cognitive)
Tri-planar view of 3D
Inflated cortical view (2D)
fMRI: general considerations
• Time & space
· … a trade-off that is regulated by SNR
• Contrast mechanisms
· We have to encode physiology into MR signal
• CNR & SNR
· determine how we approach fMRI in terms of contrast
mechanisms, averaging, …
All
related
time: 3 considerations for fMRI
1. Want sampling time ~ T1
·
·
T1 for gray matter >~ 1 second
Want TR/T1< ~ 2 seconds
2. Want sampling time ~ hemodyamic
response
·
·
arterial response ~ 1-2 seconds
add time for wash-out (BOLD) or wash-in (ASL) of
contrast  ~ 2-3 seconds
3. We need many time point for averaging
of small signal changes
SNR per unit time
• Loss of SNR per unit time is
significant only for TR >> T1
• Example: Averaging every 10
images using 100 ms sampling
produces an SNR only about
4% larger than collecting the
data at 1 second resolution
For TR < T1, SNR ~ sqrt(TR/T1)
space: 2 considerations for fMRI
1. Spatial resolution must produce enough
SNR every 2-3 seconds
·
·
SNR ~ r3 * sqrt(time)
 for a given SNR, time ~ (1/r)6 !!!
2. Want to freeze motion by “snapshot”
imaging (1 image per excitation)
•
Less necessary in certain models (e.g., anesthesia)
Time & Space: acquisition
Review of k-space:
   B
,
  / 2 
k (t)  
(r) 



t
0
 42 .6 MHz/T
G ( t ) d t 
 G is a velocity in k-space
 (k) exp(2  i k  r ) d k

conjugate
relationships:

resolution determines excursion
FOV determines sample spacing
k x 
:
:
k x 
1
x
1
x
FOV & resolution determine gradients & sampling rate;
Images can be obtained following one excitation or many.

Time & Space: acquisition
• EPI = echo-planar imaging
Rectilinear EPI
Most common
Spiral EPI
Advanced acquisition strategies
• Parallel imaging
fMRI Contrast Mechanisms
• Goal: encode physiology into MR signal
• Experimental knobs: T1, T2, T2*
• One potential method: use a contrast agent:
· Think about a vial of water: we can progressively shorten T1 &
T2 by adding more agent.
· The brain is mostly water! And CBV increases during brain
activation, so a blood-borne agent will alter MRI signal!
• Potential strategies using agents or “labels”:
· CBV (cerebral blood volume)
· CBF (cerebral blood flow)
· BOLD signal (blood oxygen level dependent)
Contrast mechanism: CBV
Bolus method: fix physiology & measure temporal response
as contrast agent flows through the tissue:
CTissue(t) = Cblood(t) V
Steady state method: fix blood concentration so that every sample
reflects tissue physiology through CBV(t)
CTissue(t) = Cblood(t) V
Contrast mechanism: CBV
Let’s be a little bit more quantitative:
• Think about relaxation rates, not times: R2 = 1/T2
• Relaxation has components independent & dependent upon agent:
R
Total
2


R
Static
2

Static

R2
• MRI signal for long TR:
R
Agent
2
,
R
• We can calculate V/V(t):
Agent
R2
Agent
S0 e

(t)
(t)
(0)
Agent
Static

Agent
2
R2

T2
k[A]
S(t)

R2 
1

 TE R 2
1
TE

A (t)
A (0)
e
 TE R 2
(t)
 S(t) 
ln 

 SPRE 

V(t)
V(0)

1
 V(t)
V(0)
st
1
BOLD experiments @ MGH
respiratory challenge
(rabbit)
visual stimulation
control
Ken Kwong, Ph.D.
time
space
Kwong et al. 1992
Contrast mechanism: BOLD
Very similar to CBV, because deoxygenated
hemoglobin is a paramagnetic contrast agent
• Relaxation has components independent & dependent upon agent:
R
Total
2


R
Static
2

Static

R2
R
BOLD
2
,
R2 
1
T2
k[dHb]
• A difference versus injected agent: we can’t easily separate the BOLD
component from the static component, but we can measure changes in
signal related to changes in [dHb]


S(t)
 S(t)
S baseline
R 2
BOLD
Static
S0 e
TE R 2
  TE  R 2
BOLD
BOLD
e
TE R 2
(t)
(t) = k [dHb](t)
(t 0)
BOLD
e
 TE R 2
(t)
Modeling BOLD signal
Goal: relate [Hbr] to CBF (F), CBV (V), and CMRO2 (M)
1 Hbr 
 2

dO 2
dt

HbT 

1  Y  HbT 

IN
dO 2
dt

HbO 
USED
OR
1 & 2 Hbr 


Y = venous oxygen
saturation
dO 2
dt
OUT
F O 2 ART 1  Y


Accounting for mass;
no physiology yet
M
M HbT
F
 So Hbr (or dHB)
Depends upon CBF,
Total Hb (CBV), &
CMRO2
Modeling BOLD signal (cont.)
• So, functional changes in deoxyhemoglobin are:
Hbr(t)

Hbr(0)
M(t)
HbT(t)
M(0)
HbT(0)
1
 F(t) 


F(0) 
• Linearize: drop terms of order small2, and HbT  V
Hbr(t)

Hbr(0)

 M(t)

M(0)
 F(t)

V(0)
• Convert to BOLD
• Convert to percent signal change:

 V(t)
F(0)
R 2 (t)  k  Hbr (t)
S

 TE  R 2
S

• SO FINALLY
 S(t)
S(0)

BOLD, %
 S(t) 
S(0) BOLD,
 F(t)

F(0)
Max% 

 V(t)
V(0)

 M(t) 

M(0) 

BOLD overview
“Simple” BOLD equation
 S(t)
S(0)

BOLD, %
 S(t)
S(0)
BOLD,
 F(t)

F(0)
Max% 

 V(t)

V(0)
• Factors that increase BOLD signal: CBF
• Factors that decrease BOLD signal: CBV & CMRO2
• How is BOLD different from CBV
as an fMRI technique:
1) endogenous
2) blood magnetization changes in
addition to CBV
3) baseline is difficult to assess
 M(t) 

M(0) 
BOLD coupling
• So far we have taken an account’s point of view by
adding up the oxygen; but CBF, CBV, and CMRO2
presumably don’t change in arbitrary ways
• CBF versus CBV
· Regional relationship:
· Functional relationship:
• CBF versus CMRO2
· Regional relationship:
· Functional relationship:
vf
v = f,
v, f = normalized values
 = 2.6 from data ( = 2 for pipe)
vf
m < f (MRI) OR m<<f (PET investigators)
Model: diffusion limitation on oxygen
• Oxygen is delivered from capillaries to brain by diffusion.
• All capillaries are perfused in normal brain.
• Oxygen reserve in brain is small.
Delivery to capillaries follows CBF
100
% change
75
Implication:
CBF & CMRO2 are coupled
50
25
Net oxygen increase to brain is small
0
-25
-50
0
25
50
 F/F (%)
75
100
Buxton & Frank, JCBFM 1997
Extraction fraction falls due to
reduced MTT
fMRI sensitivity
3 very general considerations
1. T1 contrast agents effect brain signal
weakly due to the BBB
2. T2* agents/methods effect brain signal
strongly through gradients extending
from the vessels into the tissue
3. T2 methods (spin echoes) refocus a
large portion of available signal, and so
are weak compared to T2*
fMRI sensitivity
• “sensitivity” means CNR per unit time
• The sensitivity dependence upon SNR is only indirect
(always think CNR):
CNR 
S
N

S S
 percent signal
* SNR
N N
• BOLD signal: maximize CNR at the expense of SNR by
using TE = T2*

• IRON signal: maximize CNR at the expense of SNR by
injecting agent (losing SNR) to get bigger signal changes
BOLD CNR versus TE
CNR is a compromise between:
1) SNR ~ exp(-TE/T2)
2) % change ~ TE
Err on the side of low TE to
reduce susceptibility artifacts
IRON CNR
• More complicated/flexible than BOLD, because
· BOLD has only one “knob”: TE
· IRON has two “knobs”: TE & dose
· IRON dose has analogies with BOLD magnetic field
strength, in that both modulate blood magnetization
• Cut along TE axis:
· Looks like BOLD curve
• Cut along dose axis:
· Same basic curve
IRON as a model for BOLD
• Increasing blood magnetization using IRON signal (dose) or BOLD
signal (mgnetic field) both increase CNR and tissue selectivity
relative to vessels
CNR
(t)
T2


OTHER
S0 e
 TE R 2
scale
factor

3T, versus basal CBV

AGENT
TE R 2
AGENT
(0) e
T E R 2
Baseline
physiology
(0)

 R (t) 
2
 AGENT

R
(0)
 2

activation
Dose as a model for field
Exogenous agent @ low field
BOLD
(2 T)
CBV
Cocaine, 0.5 mg/kg IV (n = 5)
Mandeville et al., MRM 2001
Arterial spin labeling
• By magnetically labeling water proximal to the imaging slice,
changes in signal can be related to changes in CBF
• similar to microspheres or diffusible tracers
• Label is magnetic, not radioactive
Arterial spin labeling
ASL signal difference (label - nonlabel) is proportional to CBF (F),
labeling efficiency (), and exponential decay of label
S
  Fe
 t / T1
S
analogies to PET

Bac kg ro und
Deca y T im e
Repeated
m easure m ents
P E T -CBF
<< label
m inutes
(>> lon g er tha n M TT )
ASL
>> label
seconds
(~ sa m e as M TT )
m inutes
seconds
CBF: baseline & activation
Labeling a single corotid artery, 3 Tesla, 8 minutes
Wald, MGH
control
control
- tag
7 Tesla CBF
Flow activation @ 7 T
CBF
BOLD
fMRI designs
• Block designs
· Long stimuli with periodic sampling of the baseline
· Best CNR per unit time
• Event-related designs
· Short stimulus units, multiple interleaved event types,
randomized stimulus presentation
periodic
periodic, too fast
periodic, faster
randomized, same ISI
Current roles for fMRI mechanisms
• BOLD signal
· fMRI work horse for human imaging
• ASL
· Targeted studies of baseline physiology or CMRO2
reactivity
• IRON fMRI
· Method of choice for animal fMRI; not yet available
for human studies (future clinical role??)