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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.
Measuring Water Diffusion
In Biological Systems Using
Nuclear Magnetic Resonance
Image removed due to copyright restrictions.
"Diffusion-weighted axial image"
http://www.medicineau.net.au/clinical/Radiology/Radiolog1768.html
Karl Helmer
HST 583, 2006
Cite as: Karl Helmer, 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.
Why Would We Want to Measure the
Self - Diffusion Coefficient of Water
In Biological Tissue?
Cite as: Karl Helmer, 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.
Why Would We Want to Measure the
Self - Diffusion Coefficient of Water
In Biological Tissue?
We Don’t.
Cite as: Karl Helmer, 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.
Why Would We Want to Measure the
Self - Diffusion Coefficient of Water
In Biological Tissue?
We Don’t.
What we are really interested in is how
what we measure for a diffusion-weighted signal
reflects the structure of the sample.
Cite as: Karl Helmer, 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.
Why Would We Want to Measure the
Self - Diffusion Coefficient of Water?
We Don’t.
What we are really interested in is how
what we measure for a diffusion-weighted signal
reflects the structure of the sample.
So, what are we measuring???
Cite as: Karl Helmer, 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.
How Can the Diffusion Coefficient Reflect
Sample Structure?
Self-diffusion in bulk samples is a wellunderstood random process Displacement (z) has a Gaussian
probability distribution
Courtesy of InductiveLoad.
probability(t)
<z2>1/2 = (2nDt)1/2
D = Self-Diffusion
Coefficient
n = # of dimensions
z
Cite as: Karl Helmer, 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.
How Can We Measure the
Diffusion Coefficient of Water
Using NMR?
Cite as: Karl Helmer, 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.
How Can We Measure the
Diffusion Coefficient of Water
Using NMR?
We Can’t.
Cite as: Karl Helmer, 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.
How Can We Measure the
Diffusion Coefficient of Water
Using NMR?
We Can’t.
Instead we measure the displacement
of the ensemble of spins in our sample
and infer the diffusion coefficient.
Cite as: Karl Helmer, 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.
How can we measures the (mean)
displacement of water molecules using NMR?
g(z) is a
magnetic field
added to B0 that
varies with position.
ω(z) = γ (B0 + g(z)×z)
Cite as: Karl Helmer, 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.
How can we measures the (mean)
displacement of water molecules using NMR?
z=0
z
Tagging the
initial position
using phase
of M
Applying g(z)
for a time δ
results in a
phase shift
that depends
upon location
in z
Cite as: Karl Helmer, 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.
Now, after waiting a time ∆ we apply
an equal gradient, but with the opposite sign
Apply -g(z) for
a time δ
z
if no diffusion:
signal = M0
Cite as: Karl Helmer, 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.
But, in reality, there is always diffusion so
we find that:
Apply -g(z) for
a time δ
z
if diffusion:
2Dt)
(-q
signal = M0e
(t = ∆ - δ/3)
q = q(g)
Cite as: Karl Helmer, 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.
Pulse Sequences
DW Spin Echo
π
π/2
δ
Δ
δ = gradient duration
Δ = separation of gradient leading edges
Cite as: Karl Helmer, 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.
But what do we do with:
2Dt)
(-q
?
signal = M = M0e
One equation, but two unknowns (M0, D)
How do we get another equation?
Cite as: Karl Helmer, 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.
Change the diffusion-sensitizing gradient
to a different value and acquire more data.
q2t
b = q2 t = 0
ln(M)
Slope = D
Intercept = ln(M0)
b = q2 t ≠ 0
Cite as: Karl Helmer, 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.
Unrestricted Diffusion
r'
r
Cite as: Karl Helmer, 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.
Restricted Diffusion
r
r'
Cite as: Karl Helmer, 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.
The effect of barriers to the free diffusion
of water molecules is to modify their
probability distribution.
P(z)
⇒ Diffusion
coefficient
decreases
with increasing
diffusion time
Cite as: Karl Helmer, 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.
Determination of D?
Slope = ‘D’×tdif
0
-1
ln(M/M0)
-2
bead pack water
-3
-4
-5
bulk water
-6
Slope = D0×tdif
-7
0.0
0.5
1.0
2
7
1.5
2
q x 10 [1/cm ]
a = 15.8 μm bead pack, tdif = 50 ms, δ = 1.5 ms, g(max) = 72.8 G/cm
See Helmer, et al. NMR in Biomedicine 8 (1995): 297-306.
Cite as: Karl Helmer, 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.
Water Diffusion in an Ordered System – High q
0
-1
ln(M/M0)
-2
2π/a
-3
-4
-5
-6
-7
0
1
2
3
4
5
6
q22 x 1 0 7 [1 /c m 2 ]
k
a = 15.8 μm bead pack, tdif = 100 ms
Cite as: Karl Helmer, 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.
Short diffusion times:
Long diffusion times:
Cite as: Karl Helmer, 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.
‘D’(tdif) gives information on different
length scales
160
T = tortuosity
S/V = surface-to-volume ratio
120
∝1/T
-7
2
‘D’(t)
D(t) x 10 [cm /sec]]
∝S/V
80
40
t1/2 [sec 1/2]
0
0
0.2
0.4
0.6
0.8
1
t
a = 15.8 μm bead pack
Cite as: Karl Helmer, 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.
DW-Weighted Tumor Data
0.0
ln M(q,t)/M(0,t)
-0.5
tdif =
-1.0
-1.5
42 ms
-2.0
92 ms
-2.5
192 ms
292 ms
492 ms
-3.0
-3.5
0
50
100
2
q [x10
-9
150
-2
m ]
D(t) ⇒ Apparent Diffusion Coefficient (ADC)
Cite as: Karl Helmer, 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.
D(t) ×105 [cm2/s]
ADC(t) for water in a RIF-1 Mouse Tumor
Necrosis!!
0.10
0.24
0.60
0.75
0.10
2.55
(t)1/2 [s1/2]
Cite as: Karl Helmer, 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.
ADC for water in a RIF-1 Mouse Tumor
Control
Day 1
Day 2
Day 3
Day 4
cm2/sec
> 255 x10-7
ADC
1 x 10-7
Tumor Volume
0.68 cm3
0.97 cm3
Day 5
Day 6
1.70 cm3
2.04 cm3
1.26 cm3
1.42 cm3
Histology
ADC
Tumor Volume
Cite as: Karl Helmer, 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.
ADC for water in a RIF-1 Mouse Tumor
Treatment, 100mg/kg 5-FU
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
> 255 x10-7
Tumor Volume
cm2/sec
ADC
0.60 cm3
Day 7
0.70 cm3
0.95 cm3
Day 8
Day 9
0.86 cm3
Day 10
0.71 cm3
Day 11
0.76 cm3
1 x 10-7
Histology
cm2/sec
> 255 x10-7
ADC
1 x 10-7
Tumor Volume
1.13 cm3
1.36 cm3
1.60 cm3
1.79 cm3
2.08 cm3
Cite as: Karl Helmer, 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.
ADCav Maps vs Post-Occlusion Time
Rat Brain – 30 min Occlusion
See Fuhai Li, M. D., K. Helmer, et al. "Secondary Decline in Apparent Diffusion Coefficient and Neurological Outcomes after
a Short Period of Focal Brain Ischemia in Rats." Ann Neurol 48, no. 2 (2000): 236.
MCAO
2 hr
3 hr
4 hr
5 hr
6 hr
7 hr
8 hr
9 hr
10 hr
11 hr
12 hr
ADC (x10-5 mm2/s)
ROI Positions
< 30
Cite as: Karl Helmer, 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.
> 60
ADCav Maps vs Post-Occlusion Time
Rat Brain – 30 min Occlusion
Temporal ADC Changes in the Caudoputamen:
30-minute Transient Occlusion (n = 4)
80
75
60
55
ADC (x10
2
65
-5
mm /s)
70
50
45
40
Ipsilateral
35
Contralateral
30
Rep
1
2
3
4
5
6
7
8
9
10
11
12
Time (hours post reperfusion)
See Fuhai Li, M. D., and K. Helmer, et al. "Secondary Decline in Apparent Diffusion Coefficient and Neurological Outcomes after a Short
Period of Focal Brain Ischemia in Rats." Ann Neurol 48, no. 2 (2000): 236.
Cite as: Karl Helmer, 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.
Issues with Interpreting DW Data
In biological tissue, there are always
restrictions. How then can we interpret
the diffusion attenuation curve?
Cite as: Karl Helmer, 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.
Biology-based Model:
Intracellular and extracellular compartments
⇒ Biexponential Model with a
distribution of cell sizes and shapes.
D′ = f1 D1 + (1 − f1 ) D2
S = S 0 ( f1e
−bD1
+ (1 − f1 )e
Fast Exchange
−bD2
) Slow Exchange
But real systems are rarely either/or.
Cite as: Karl Helmer, 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.
DW-Weighted Tumor Data
0.0
ln M(q,t)/M(0,t)
-0.5
tdif =
-1.0
-1.5
42 ms
-2.0
92 ms
-2.5
192 ms
292 ms
492 ms
-3.0
-3.5
0
50
100
2
q [x10
-9
150
-2
m ]
What does non-monexponentiality tell us?
Cite as: Karl Helmer, 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.
‘Fast’ and ‘Slow’ Diffusion?
Slope = ‘Dfast’×tdif
0
-1
ln(M/M0)
-2
-3
-4
-5
Slope = Dslow×tdif
bulk water
-6
-7
0.0
0.5
1.0
2
7
1.5
2
q x 10 [1/cm ]
See Helmer, et al. NMR in Biomedicine 8 (1995): 297-306.
Cite as: Karl Helmer, 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.
Does ‘Fast’ and ‘Slow’ Mean
‘Extracellular’ and ‘Intracellular’?
No, because:
1)The same shape of curve can be found
in the diffusion attenuation curve of
single compartment systems (e.g., beads).
2) It gives almost exactly the opposite values
for extra- and intracellular volume fractions
(20/80 instead of 80/20 for IC/EC).
Exchange?
Cite as: Karl Helmer, 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.
What does ‘fast’ and ‘slow’ measure?
Answer: It depends on…
•range of b-values
•TE
•tdif
•sample structure
•sample tortuosity
Fig 1 in Clark, C. A., et al. "In Vivo Mapping of the Fast and
Slow Diffusion Tensors in Human Brain." Magn Reson Med 47, no. 4
(April 2002): 623-8. doi:10.1002/mrm.10118. Copyright (c) 2002
Wiley-Liss Inc. Reprinted with permission of John Wiley & Sons., Inc.
Cite as: Karl Helmer, 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.
Dave(fast)
FA(fast)
Fig 1 in Clark, C. A., et al. "In Vivo Mapping of the Fast and
Slow Diffusion Tensors in Human Brain." Magn Reson Med 47, no. 4
(April 2002): 623-8. doi:10.1002/mrm.10118. Copyright (c) 2002
Wiley-Liss Inc. Reprinted with permission of John Wiley & Sons., Inc.
Dave(slow)
FA(slow)
∴‘slow’ ⇒ ‘restricted’…
Cite as: Karl Helmer, 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.
Do We Get More Information by Using
the Entire Diffusion Attenuation Curve?
0.0
ln M(q,t)/M(0,t)
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
0
50
100
2
q [x10
-9
150
-2
m ]
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How do I choose my lowest b-value?
1)Diffusion gradients act like primer-crusher
pairs. Therefore, slice profile of g = 0
image will be different from g ≠ 0 image.
2) Diffusion gradients also suppress flowing
spins.
Therefore, the use of a g = 0 image is discouraged.
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How do I choose my highest b-value?
1. Greatest SNR in calculated ADC:
I i = I 0e
− bi D
Si = I i + ε
σ= ε
2 1/ 2
I = true signal
S = measured signal
ε = noise
Cite as: Karl Helmer, 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.
Practical Issues in DWI
ln S1 − ln S 0
2
D=
,b = q t
b
2
σ
1
2
2
2 bD
2
D
σ D ≈ 2 (σ 0 + σ 1 ) = 2 2 (1 + e )
b
b I0
I0
bD
SNRD =
=
≡ F (bD) ⋅ SNRI 0
2 bD 1 / 2
σ D (1 + e ) σ
D
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How do I choose my highest b-value?
2. Greatest sensitivity to %ΔADC:
∂I
|max ⇒ bD = 1.0
∂D
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How to distribute the b-values?
q2t
This or ?
ln(M)
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How to distribute the b-values?
q2t
This or…?
ln(M)
Cite as: Karl Helmer, 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.
Practical Issues in DWI
How to distribute the b-values?
q2t
This?
ln(M)
Cite as: Karl Helmer, 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.
Multiple measurements of 2 b-values are
better than multiple different b-values.
If the number of measurements can be large,
then Nhigh-b = Nlow-b × 3.6
Note that depending on N and how you
estimate the error, you can get different
numbers for the optimum values, but
Δbopt ~ 1(+)/D
and
Nhigh-b ~ Nlow-b × 4
Cite as: Karl Helmer, 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.
Diffusion Tensor Imaging
What effect does the direction of the diffusionsensitizing gradient have upon what we measure?
In the 1- dimensional case
(we measure Dx or Dy):
y
x
Dy ≅ D0, the bulk value
Dx <(<) D0
D / ADC is a scalar
Cite as: Karl Helmer, 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.
What effect does the direction of
the diffusion-sensitizing gradient
have upon what we measure?
y
z
x
In the 3- dimensional case
(we measure Dx, Dy and Dz):
Dy ≅ D0, the bulk value
Dx = Dz <(<) D0
D = (Dx, Dy, Dz)
Cite as: Karl Helmer, 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.
Diffusion Tensor Imaging
Why not stick with vectors?
Because
is not
z
x
y
Cite as: Karl Helmer, 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.
The ADC is
greatest along
White Matter
fiber tracts.
Taylor et al.,
Biol Psychiatry, 55, 201 (2004)
Courtesy Elsevier, Inc., http://www.sciencedirect.com.
Used with permission.
Cite as: Karl Helmer, 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.
1. There is nothing special about using
tensors to characterize anisotropic diffusion.
Rotate to principal
frame to get eigenvalues.
Cite as: Karl Helmer, 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.
Rotational Invariants for 3D Tensors.
Table from: P.B. Kingsley, "Introduction to Diffusion Tensor Imaging Mathematics: Part I. Tensors, Rotations,
and Eigenvectors." Concepts Magn Reson 28A no. 2 (2006): 101-122. Copyright (c) 2006 Wiley-Liss Inc.
Reprinted with permission of John Wiley & Sons., Inc.
Eigenvalues = D1, D2, D3 or λ1, λ2, λ3
Dav = (Dxx + Dyy + Dzz)/3
Cite as: Karl Helmer, 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.
Trace Imaging and b-value Strength
Set of three images with caption removed due to copyright restrictions.
Figure 1 in Maier, S. E., et al. "Normal Brain and Brain Tumor: Multicomponent
Apparent Diffusion Coefficient Line Scan Imaging." Radiology 219 (2001): 842-849.
Cite as: Karl Helmer, 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.
Distribution of Gradient Sampling
Directions
Need at least
6 different sampling
directions
Fig 2 image + caption, from: Le Bihan, D., et al. "Diffusion Tensor Imaging: Concepts and
Applications." JMRI 13, no 4 (2001): 534-546. Copyright (c) 2001 Wiley-Liss, Inc., a subsidiary
of John Wiley & Sons, Inc. Reprinted with permission of John Wiley & Sons., Inc.
Cite as: Karl Helmer, 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.
Diffusion Tractography
Follow Voxels
With Largest
Eigenvalues
Being
‘Continuous’
Between Two
Regions of
Interest
Courtesy of Dr. Martha Shenton. Used with permission.
Source: Shenton, M. E., M. Kubicki, and R. W.
McCarley. "Diffusion Tensor Imaging: Image
Acquisition and Processing Tools." SPL Technical
Report 354, 2002.
Cite as: Karl Helmer, 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.