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![Page 1: Measuring Water Diffusion In Biological Systems Using Nuclear Magnetic Resonance Karl Helmer HST 583, 2006](https://reader035.fdocuments.net/reader035/viewer/2022062401/5a4d1b457f8b9ab0599a2f47/html5/thumbnails/1.jpg)
Measuring Water Diffusion In Biological Systems Using
Nuclear Magnetic Resonance
Karl HelmerHST 583, 2006
http://www.medicineau.net.au/clinical/Radiology/Radiolog1768.html
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Why Would We Want to Measure the Self - Diffusion Coefficient of Water
In Biological Tissue?
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We Don’t.
Why Would We Want to Measure the Self - Diffusion Coefficient of Water
In Biological Tissue?
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We Don’t.
What we are really interested in is howwhat we measure for a diffusion-weighted signal
reflects the structure of the sample.
Why Would We Want to Measure the Self - Diffusion Coefficient of Water
In Biological Tissue?
![Page 5: Measuring Water Diffusion In Biological Systems Using Nuclear Magnetic Resonance Karl Helmer HST 583, 2006](https://reader035.fdocuments.net/reader035/viewer/2022062401/5a4d1b457f8b9ab0599a2f47/html5/thumbnails/5.jpg)
We Don’t.
What we are really interested in is howwhat we measure for a diffusion-weighted signal
reflects the structure of the sample.
So, what are we measuring???
Why Would We Want to Measure the Self - Diffusion Coefficient of Water?
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How Can the Diffusion Coefficient Reflect Sample Structure?
Self-diffusion in bulk samples is a well-understood random process -
Displacement (z) has a Gaussian probability distribution
<z2>1/2 = (2nDt)1/2
D = Self-Diffusion Coefficientn = # of dimensions
z
H.C. Berg, 1993
proba-bility(t)
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How Can We Measure the Diffusion Coefficient of Water
Using NMR?
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We Can’t.
How Can We Measure the Diffusion Coefficient of Water
Using NMR?
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Instead we measure the displacementof the ensemble of spins in our sample
and infer the diffusion coefficient.
We Can’t.
How Can We Measure the Diffusion Coefficient of Water
Using NMR?
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How can we measures the (mean) displacement of water molecules using NMR?
g(z) is amagnetic field added to B0 that varies with position.
(z) = (B0 + g(z)z)
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How can we measures the (mean) displacement of water molecules using NMR?
Applying g(z) for a time results in a phase shift
that depends upon location
in z
z
z = 0
Tagging the initial positionusing phase
of M
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Now, after waiting a time ∆ we apply an equal gradient, but with the opposite sign
Apply -g(z) for a time
if no diffusion:signal = M0
z
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But, in reality, there is always diffusion sowe find that:
Apply -g(z) for a time
if diffusion:signal = M0e(-q2Dt)
(t = ∆ - /3)q = q(g)
z
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Pulse Sequences
DW Spin Echo/2
= gradient duration = separation of gradient leading edges
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But what do we do with:signal = M = M0e(-q2Dt)?
One equation, but two unknowns (M0, D)
How do we get another equation?
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q2t
ln(M)
Slope = DIntercept = ln(M0)
Change the diffusion-sensitizing gradient to a different value and acquire more data.
b = q2 t = 0
b = q2 t ≠ 0
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Unrestricted Diffusion
r
r'
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r
r'
Restricted Diffusion
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The effect of barriers to the free diffusion of water molecules is to modify their
probability distribution.
P(z)
Diffusioncoefficient decreaseswith increasingdiffusion time
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Determination of D?
-7
-6
-5
-4
-3
-2
-1
0
0.0 0.5 1.0 1.5
q2 x 107 [1/cm2]
ln(M
/M0)
Slope = D0tdif
Slope = ‘D’tdif
bead pack water
a = 15.8 m bead pack, tdif = 50 ms, = 1.5 ms, g(max) = 72.8 G/cm
bulk water
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-7
-6
-5
-4
-3
-2
-1
0
0 1 2 3 4 5 6
k2 x 107 [1/cm2]
ln(M
/M 0)
Water Diffusion in an Ordered System – High q
a = 15.8 m bead pack, tdif = 100 ms
2/a
q2
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Short diffusion times:
Long diffusion times:
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0
40
80
120
160
0 0.2 0.4 0.6 0.8 1
D(t
) x
10-7 [
cm2 /sec
] S/V
t
1/T
t1/2 [sec 1/2]
‘D’(tdif) gives information on different length scales
]
a = 15.8 m bead pack
T = tortuosityS/V = surface-to-volume ratio
‘D’(t
)
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-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0ln
M(q
,t)/M
(0,t)
150100500
q2 [x10
-9 m
-2]
42 ms
92 ms
192 ms292 ms492 ms
DW-Weighted Tumor Data
D(t) Apparent Diffusion Coefficient (ADC)
tdif =
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ADC(t) for water in a RIF-1 Mouse Tumor
D(t)
10
5 [c
m2 /s
]
(t)1/2 [s1/2]
0.10
0.240.60 0.75
0.10
2.55
Necrosis!!
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Control
1 x 10-7
> 255 x10-7
cm2 /s
ec
ADC
ADC
Tumor Volume
Day 1 Day 2 Day 3 Day 4
1.42 cm31.26 cm30.97 cm30.68 cm3
Tumor Volume
Day 5 Day 6 Histology
1.70 cm3 2.04 cm3
ADC for water in a RIF-1 Mouse Tumor
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ADC for water in a RIF-1 Mouse Tumor
Treatment, 100mg/kg 5-FU
1 x 10-7
> 255 x10-7
cm2 /s
ecADC
Tumor Volume 0.76 cm30.71 cm30.86 cm30.95 cm30.70 cm30.60 cm3
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6
ADC1 x 10-7
> 255 x10-7
cm2 /s
ec
Day 7 Day 8 Day 9 Day 10 Day 11 Histology
Tumor Volume 1.13 cm3 1.36 cm3 1.60 cm3 1.79 cm3 2.08 cm3
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ROI Positions < 30 > 60
ADC (x10-5 mm2/s)
MCAO 2 hr 3 hr 4 hr 5 hr 6 hr
7 hr 8 hr 9 hr 10 hr 11 hr 12 hr
ADCav Maps vs Post-Occlusion Time Rat Brain – 30 min Occlusion
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Temporal ADC Changes in the Caudoputamen: 30-minute Transient Occlusion (n = 4)
30
35
40
45
50
55
60
65
70
75
80
Rep 1 2 3 4 5 6 7 8 9 10 11 12
Time (hours post reperfusion)
ADC
(x10
-5 m
m2 /s
)
Ipsilateral
Contralateral
ADCav Maps vs Post-Occlusion Time Rat Brain – 30 min Occlusion
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Issues with Interpreting DW Data
In biological tissue, there are alwaysrestrictions. How then can we interpret the diffusion attenuation curve?
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Biology-based Model:Intracellular and extracellular compartments
Biexponential Model with a distribution of cell sizes and shapes.
))1((
)1(
21110
2111
bDbD efefSS
DfDfD
Fast Exchange
Slow Exchange
But real systems are rarely either/or.
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-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0ln
M(q
,t)/M
(0,t)
150100500
q2 [x10
-9 m
-2]
42 ms
92 ms
192 ms292 ms492 ms
DW-Weighted Tumor Data
What does non-monexponentiality tell us?
tdif =
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‘Fast’ and ‘Slow’ Diffusion?
-7
-6
-5
-4
-3
-2
-1
0
0.0 0.5 1.0 1.5
q2 x 107 [1/cm2]
ln(M
/M0)
Slope = Dslowtdif
Slope = ‘Dfast’tdif
bulk water
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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?
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What does ‘fast’ and ‘slow’ measure?
Answer: It depends on…•range of b-values•TE•tdif
•sample structure•sample tortuosity
Clark et al. MRM47, 623, 2002.
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Dave(fast) Dave(slow)
FA(fast) FA(slow)
Clark et al. MRM47, 623, 2002. ‘slow’ ‘restricted’…
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Do We Get More Information by Usingthe Entire Diffusion Attenuation Curve?
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
ln M
(q,t)
/M(0
,t)
150100500
q2 [x10
-9 m
-2]
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Practical Issues in DWI
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.
How do I choose my lowest b-value?
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Practical Issues in DWI
How do I choose my highest b-value?
1. Greatest SNR in calculated ADC:
2/12
0
ii
Dbi
ISeII i I = true signal
S = measured signal
= noise
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tqbb
SSD 201 ,lnln
)1()(1 220
2
221
202
2 bDDD e
Ibb
Practical Issues in DWI
0)(
)1(0
2/12 IbDD
D SNRbDFIebDDSNR
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Practical Issues in DWI
How do I choose my highest b-value?
2. Greatest sensitivity to %ADC:
0.1|max bDDI
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Practical Issues in DWI
How to distribute the b-values?q2t
ln(M)
This or ?
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Practical Issues in DWI
q2t
ln(M)
This or…?
How to distribute the b-values?
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Practical Issues in DWI
q2t
ln(M)
This?
How to distribute the b-values?
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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 differentnumbers for the optimum values, but
Δbopt ~ 1(+)/D and Nhigh-b ~ Nlow-b 4
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What effect does the direction of the diffusion-sensitizing gradient have upon what we measure?
x
yIn the 1- dimensional case(we measure Dx or Dy):
Dy D0, the bulk value
Dx <(<) D0
D / ADC is a scalar
Diffusion Tensor Imaging
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What effect does the direction ofthe diffusion-sensitizing gradienthave upon what we measure?
x
y
In the 3- dimensional case(we measure Dx, Dy and Dz):
Dy D0, the bulk value
Dx = Dz <(<) D0
D = (Dx, Dy, Dz)
z
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Why not stick with vectors?
Because is not
x
y
z
Diffusion Tensor Imaging
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Taylor et al.,Biol Physhiatry, 55, 201 (2004)
The ADC is greatest along White Matterfiber tracts.
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1. There is nothing special about using tensors to characterize anisotropic diffusion.
Rotate to principalframe to get eigen-values.
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Rotational Invariants for 3D Tensors.
Eigenvalues = D1, D2, D3 or 1, 2, 3
Dav = (Dxx + Dyy + Dzz)/3
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Trace Imaging and b-value Strength
http://splweb.bwh.harvard.edu:8000/pages/papers/maier/radiology2001.pdf
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LeBihan et al.,JMRI, 13, 534 (2001)
Distribution of Gradient Sampling Directions
Need at least6 different samplingdirections
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Diffusion Tractography
Follow Voxels With Largest EigenvaluesBeing ‘Continuous’Between Two Regions of Interest
http://splweb.bwh.harvard.edu:8000/pages/papers/martha/DTI_Tech354.pdf