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HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis
Fall 2006
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HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006
Harvard-MIT Division of Health Sciences and Technology
Course Director: Dr. Randy Gollub.
Quantitative fMRI Lecture: BOLD, CBV, & ASL
Questions: BOLD
1. We know that R2 = 1/T2. If we want to measure the BOLD relaxation rate, why not approach this
problem by using different values of TE and then fitting for T2, rather than using the hypercapnia
calibration method?
2. Roughly, how much of the total relaxation rate at 1.5 Tesla is due to the BOLD effect (e.g., express
BOLD effect as a percentage of the total effect)?
3. What does the BOLD resting state relaxation rate (equivalently, maximum possible BOLD signal)
depend upon in terms of basal physiology? Give multiple answers in terms of physiological
variables, with and without coupling assumptions.
4. Draw a plot of BOLD CNR versus echo time. Where is the maximum? Suppose you have
problems with image artifacts, and you find that the images are much better using an echo time that
is only half as large as the echo time you were told (by some dumb physicist) should be used
maximize CNR. How much CNR do you lose with the smaller value of TE?
5. Suppose that you perform a task with and without pretreatment by a drug. With drug pretreatment,
the BOLD response is smaller. Give 2 possible interpretations.
6. Suppose you are attempting to image the acute effects to a drug that is known to depress
respiration, leading to an increase in PaCO2. Thus, one should expect the response to contain
nonspecific vascular effects in addition to potential hemodynamic responses modulated by changes
in neural activity. Will the nonspecific effects be more problematic (larger relative to neuronally
modulated signals) using BOLD signal or CBF, and why?
7. When might “typical” coupling relationships between CBF and CBV not hold? How about CBF
versus CMRO2?
Questions: CBV
1. What is the baseline BOLD relaxation rate at 1.5 Tesla? Based upon the BOLD relaxation rate at
this field strength, and assuming we use an echo time of 40 ms, how much larger could we make
the “amplification factor” using contrast agent? How could we further increase the detection
power (CNR) of the CBV method by manipulating the echo time and agent dose?
2. During a functional challenge using a contrast agent, BOLD effects occur in addition to swelling of
vessels. How can we estimate this “BOLD contamination” in CBV-weighted fMRI?
3. Could we measure CBV by T1? If so, would this method be more or less sensitive to functional
changes than a T2 or T2* method?
4. The use of exogenous contrast agent makes fMRI using T2 or T2* methods much more sensitive
than BOLD fMRI at clinical field strengths. Can you explain why the relative sensitivity of these
two methods (BOLD versus CBV) depends upon B0? Dose of contrast agent? Basal CBV? TE?
Stimulus presentation rate?
Questions: ASL
1. Could we detect CBF through T2, rather than T1? What are the major conceptual problems with
this suggestion? One-word hints: 1) time scale, 2) coherence
2. What problem might one encounter when applying ASL to stroke?
1
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Measuring CBV and Hbr through transverse relaxation
• Relaxation has components independent & dependent upon agent
• Agent-dependent relaxation occurs at rates roughly ~ [A]
R Total
= R Static
+ R Agent
2
2
2
, R2 =
1
T2
= R Static
+ k[A]
2
MRI signal:
!
S(t) = S0 e
"T E R Static
2
e
"T E R Agent
(t)
2
1) Suppose we inject exogenous contrast agent.
Then we know the pre-injection signal,
!
R Agent
(t) = "
2
SPRE = S0 e
"T E R Static
2
1 # S(t) &
ln%
(
TE $ SPRE '
!
!
Agent
2
Agent
2
R
R
(t)
(0)
=
[A](t)
[A](0)
=
V(t)
"V(t)
= 1+
V(0)
V(0)
∴ We can measure ΔV/V versus time using injected agent
2)
! How about BOLD signal?
Problem: We can’t easily separate R2Agent from R2Static.
→ See BOLD model & “hypercapnia calibration”
2
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
BOLD model
Goal:
relate [Hbr] to CBF (F), CBV (V), and CMRO2 (M)
(1) [Hbr]
=
=
!
(2)
dO 2
dt
"
IN
[HbT] " [HbO]
(1" Y) [HbT]
dO 2
dt
=
OUT
dO 2
dt
USED
OR
F [O 2 ] ART (1" Y) = M
!
(1& 2) [Hbr ]
"
M[HbT]
F
So, functional changes in deoxyhemoglobin are …
!
Hbr(t)
M(t)
=
Hbr(0)
M(0)
(1
HbT(t) " F(t) %
$
'
HbT(0) #F(0) &
Linearize: drop terms of order small2, and HbT → V
! "Hbr(t)
"M(t)
"V(t)
"F(t)
=
+
#
Hbr(0)
M(0)
V(0)
F(0)
"R 2 (t) = k " [Hbr ](t)
"S
ii) Convert to percent signal change: S # $ TE "R 2
i) Convert to BOLD:
!
$ "F(t)
!
"S(t)
"S(t)
"V(t)
=
#
&
S(0) BOLD,%
S(0) BOLD, Max% % F(0)
V(0)
#
"M(t) '
)
M(0) (
!
!
3
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
“Hypercapnia calibration” for BOLD
Goal:
BOLD
determine BOLD basal relaxation rate,
R 2
• Equivalent to basal [Hbr]
• Equivalent to maximum obtainable BOLD signal
!
Start with BOLD equation:
$ "F(t)
"S(t)
"S(t)
"V(t)
=
#
&
S(0) BOLD,%
S(0) BOLD, Max% % F(0)
V(0)
#
"M(t) '
)
M(0) (
Assumptions
1)
! 2)
3)
CMRO2 does not change during hypercapnia.
All measurements are performed between steady states to avoid transients (undershoot, etc.)
CBF and CBV are coupled (human fMRI cannot easily measure CBV)
2-step procedure in humans:
1)
2)
Measure BOLD signal and ΔF/F for hypercapnia → R BOLD
or maximum BOLD signal, above
2
Repeat BOLD and ΔF/F for a task → ΔM/M (once the calibration factor is determined in step 1)
!
Coupling relationships (normal physiology)
Question:Are the contributors to BOLD (F,V,M) independent?
Regional relationships, basal physiology:
• V(r) = kvf F(r)
• M(r) = kmf F(r)
everything is linear!
Functional relationships:
K1
V(t) " F(t) %
=$
'
V(0) #F(0) &
, or
(V(t)
(F(t)
) K1
V(0)
F(0)
(M(t)
(F(t)
) K2
M(0)
F(0)
K1 ~ 0.35, K2 ∈ (0.3,0.5), so assume K2 ~ 0.35 for simplicity
Inserting into BOLD equation (above):
BOLD
! Hypercapnia = BOLD 0 (.65 "F F) , "M M = 0
BOLDTask
= BOLD0 (.30 "F F)
#BOLDHypercapnia $ 2 BOLDTask
(for matched "F/F)
4
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Sensitivity of T2 (or T2*) fMRI
Goal:
Understand basic relationships for BOLD, CBV fMRI CNR = contrast to noise ratio
It is useful to break this into SNR and the relative signal change:
CNR = SNR
"S
S
• SNR depends upon quantities of interest as a decaying exponential
• Percentages signal changes depend linearly upon quantities of interest
CNR " x e#x
, x = TE , dose, rCBV
!
∴ Maximizing CNR is a balance between SNR and relative signal change
MRI signal:
!
Relative change:
Agent
Static
e"TE R 2
S(t) = S0 e"TE R 2
(t)
exp(#TER Agent
(t))
"S
S(t) # S(0)
2
=
=
#1
S
S(0)
exp(#TER Agent
(0)
)
2
!
Agent
= e#TE "R 2
(t)
#1
$ # TE"R Agent
(t)
2
• BOLD CNR is maximized @ TE=T2
SNR
!S/S
CNR
relative units
!
• CNR is rather flat versus TE, so choose
a somewhat smaller value to minimize
signal loss in short T2* regions
probablity
Below
T2* distribution at 9.4T
0
1
2
TE / T2
3
0
5
10
20
30
40
T2* (ms)
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Sensitivity (continued)
CNR = SNR
"S
S
Use expressions on previous page, and rearrange terms:
Static
CNR = !"S0e"TE R 2
Agent
TER Agent
(0) e"TE R 2
2
↑
SCALE
#R 2 (t)
R Agent
(0)
2
(0)
↑
AMPLIFICATION
↑
ACTIVATION
!
For global CBV, plot versus dose or field
For fixed dose or field, plot versus rCBV
large
vessels
Tissue
amplification factor
amplification factor
0.4
~ BOLD, 1.5 T
0
1
0.3
0.2
0.1
0
0
2
TE R2Agent
IRON fMRI
BOLD fMRI
1
2
3
relative CBV
6
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Arterial spin labeling (ASL)
• Analogies: similar to microspheres or diffusible tracers
• Examples: PET-CBF using [15O]-water, autoradiography using iodoantipyrene
delivery = F C A (t)
Principle:
total tracer
Q(" ) = F
"
#C
o
A
(t) dt
For ASL, the label is magnetic via inversion
!
Differences between PET-CBF and ASL
Background
Decay Time
PET-CBF
<< label
minutes
(>> longer than MTT)
ASL
>> label
seconds
(~ same as MTT)
Repeated
measurements
minutes
seconds
7
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
R1Apparent
= R1Static + F " , " # 1
R1Static =
1
T1
F ~ 60
~ 1 sec$1
ml
100g $ min
~ .01 sec$1
∴ F << R1
ASL techniques must address these issues:
!
1. Accurate
subtraction of “background”
a. Static tissue
b. Magnetization transfer
(tagging induces off-resonance saturation of image volume
2. Minimizing errors induced by variable blood transit times ~ T1
3. Label must be applied in time, not in space
Measuring CBF
Difference signal:
"S = SControl # SLabel
$ 2 % S0
, % & labeling efficiency
!
From Buxton, JMRI 2005; 22:723-726
"S(t) = F 2#S 0 $
e%t/T1
8
Cite as: Joe Mandeville, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.