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

Methods based upon comparisons:• human versus animal• young versus old• personality versus post-mortem

Function of the brain: 1800

Instinct of reproduction

Love ofoffspring

Cleverness

Pride &Arrogance

Tendency toMurder

Poetic talent

Firmness of purpose

Wisdom

Gall, 1810

Shared by human & animal

Only human

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)

Inflated cortical view (2D)Tri-planar view of 3D

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: acquisitionReview of k-space:

conjugate relationships:

FOV & resolution determine gradients & sampling rate;

Images can be obtained following one excitation or many.€

resolution determines excursion : Δkx =1

δx

FOV determines sample spacing : δkx =1

Δx

€

ω = ′ γ B , ′ γ = γ /2π = 42.6 MHz/T

€

rk (t) = ′ γ

r G ( ′ t ) d ′ t

0

t

∫

€

ρ(r) = ρ (k) exp(2πi k • r) dk∫

G is a velocity in k-space

Time & Space: acquisition

• EPI = echo-planar imaging

Rectilinear EPI Spiral EPI

Most common

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: CBVBolus 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: CBVLet’s be a little bit more quantitative:• Think about relaxation rates, not times: R2 = 1/T2

• Relaxation has components independent & dependent upon agent:

• MRI signal for long TR:

• We can calculate V/V (t):

€

R2Total = R2

Static + R2Agent , R2 =

1

T2

= R2Static + k[A]

€

S(t) = S0 e−TE R2Static

e−TE R2Agent (t)

€

R2Agent(t) = −

1

TE

lnS(t)

SPRE

⎛

⎝ ⎜

⎞

⎠ ⎟

€

R2Agent(t)

R2Agent(0)

=A[ ](t)

A[ ](0)=

V(t)

V(0)= 1+

ΔV(t)

V(0)

1st BOLD experiments @ MGHrespiratory challenge

(rabbit)controlvisual stimulation

Ken Kwong, Ph.D.

time

space

Kwong et al. 1992

Contrast mechanism: BOLDVery similar to CBV, because deoxygenated hemoglobin is a paramagnetic contrast agent

• Relaxation has components independent & dependent upon agent:

• 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]€

R2Total = R2

Static + R2BOLD , R2 =

1

T2

= R2Static + k[dHb]

€

S(t) = S0 e−TE R 2Static

e−TE R 2BOLD (t= 0) e−TE ΔR 2

BOLD (t)

δS(t)

Sbaseline

= −TEΔR2BOLD(t)

ΔR2BOLD(t) = k [dHb](t)

Modeling BOLD signalGoal: relate [Hbr] to CBF (F), CBV (V), and CMRO2 (M)

€

1( ) Hbr[ ] = HbT[ ] − HbO[ ]

= 1− Y( ) HbT[ ]

€

2( )dO2

dt IN

−dO2

dt OUT

=dO2

dt USED

OR

F O2[ ]ART1− Y( ) = M

€

1& 2( ) Hbr[ ] ∝M HbT[ ]

F

Y = venous oxygen saturation

Accounting for mass;no physiology yet

So Hbr (or dHB)Depends upon CBF,Total Hb (CBV), &CMRO2

Modeling BOLD signal (cont.)• So, functional changes in deoxyhemoglobin are:

• Linearize: drop terms of order small2, and HbT V

• Convert to BOLD

• Convert to percent signal change:

• SO FINALLY

€

Hbr(t)

Hbr(0)=

M(t)

M(0)

HbT(t)

HbT(0)

F(t)

F(0)

⎡

⎣ ⎢

⎤

⎦ ⎥

−1

€

Hbr(t)

Hbr(0)=

ΔM(t)

M(0)+

ΔV(t)

V(0)−

ΔF(t)

F(0)

€

R2(t) = k Δ Hbr[ ](t)

€

S

S≈ − TE ΔR2

€

S(t)S(0)BOLD,%

= ΔS(t)S(0)BOLD,Max%

ΔF(t)F(0)−

ΔV(t)V(0)−

ΔM(t)M(0)

⎛ ⎝ ⎜ ⎞

⎠ ⎟

BOLD overview

“Simple” BOLD equation

• 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

€

S(t)S(0)BOLD,%

= ΔS(t)S(0)BOLD,Max%

ΔF(t)F(0)−

ΔV(t)V(0)−

ΔM(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: v f v, f = normalized values

· Functional relationship: v = f, = 2.6 from data ( = 2 for pipe)

• CBF versus CMRO2

· Regional relationship: v f

· Functional relationship: m < f (MRI) OR m<<f (PET investigators)

Model: diffusion limitation on oxygen

Delivery to capillaries follows CBF

Extraction fraction falls due to reduced MTT

Net oxygen increase to brain is small

-50

-25

0

25

50

75

100

0 25 50 75 100

% change

/ (%)F F

Buxton & Frank, JCBFM 1997

• Oxygen is delivered from capillaries to brain by diffusion.• All capillaries are perfused in normal brain.• Oxygen reserve in brain is small.

Implication:CBF & CMRO2 are coupled

fMRI sensitivity3 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):

• 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

€

CNR =δS

N=

δS

N

S

N= percent signal*SNR

BOLD CNR versus TE

CNR is a compromise between:

1) SNR ~ exp(-TE/T2)2) % change ~ TE

Err on the side of low TE toreduce 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

€

CNRT2(t) = S0e−TE R2

OTHER

{ } TER2AGENT(0) e−TE R2

AGENT (0){ }

ΔR2(t)

R2AGENT(0)

⎧ ⎨ ⎩

⎫ ⎬ ⎭

scalefactor

Baselinephysiology activation

3T, versus basal CBV Dose as a model for field

Exogenous agent @ low field (2 T)BOLDBOLD

Cocaine, 0.5 mg/kg IV (n = 5)

Mandeville et al., MRM 2001

CBVCBV

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 labelingASL signal difference (label - nonlabel) is proportional to CBF (F), labeling efficiency (), and exponential decay of label

€

S

S∝ α F e−t / T1

PET-CBF ASL Background << label >> label Decay Time minutes

(>> longer than MTT) seconds

(~ same as MTT) Repeated

measurements minutes seconds

analogies to PET

CBF: baseline & activation

CBF

BOLD

Labeling a single corotid artery, 3 Tesla, 8 minutes

control

control- tag

Wald, MGH

7 Tesla CBF Flow activation @ 7 T

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, faster

periodic, too fast

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??)