Measuring Water Diffusion

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Measuring Water Diffusion In Biological Systems
Using Nuclear Magnetic Resonance Karl
Helmer HST 583, 2006
http//www.medicineau.net.au/clinical/Radiology/Ra
diolog1768.html
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Why Would We Want to Measure the Self -
Diffusion Coefficient of Water In Biological
Tissue?
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Why Would We Want to Measure the Self -
Diffusion Coefficient of Water In Biological
Tissue?
We Dont.
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Why Would We Want to Measure the Self -
Diffusion Coefficient of Water In Biological
Tissue?
We Dont.
What we are really interested in is how what we
measure for a diffusion-weighted signal reflects
the structure of the sample.
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Why Would We Want to Measure the Self -
Diffusion Coefficient of Water?
We Dont.
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???
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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
ltz2gt1/2 (2nDt)1/2 D Self-Diffusion
Coefficient n of dimensions
proba- bility(t)
z
H.C. Berg, 1993
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How Can We Measure the Diffusion Coefficient of
Water Using NMR?
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How Can We Measure the Diffusion Coefficient of
Water Using NMR?
We Cant.
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How Can We Measure the Diffusion Coefficient of
Water Using NMR?
We Cant.
Instead we measure the displacement of the
ensemble of spins in our sample and infer the
diffusion coefficient.
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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.
?(z) ? (B0 g(z)?z)
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How can we measures the (mean) displacement of
water molecules using NMR?
z 0
z
Applying g(z) for a time ? results in a phase
shift that depends upon location in z
Tagging the initial position using 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 ?
z
if no diffusion signal M0
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But, in reality, there is always diffusion so we
find that
Apply -g(z) for a time ?
z
if diffusion signal M0e(-q2Dt) (t ? - ?/3) q
q(g)
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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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Change the diffusion-sensitizing gradient to a
different value and acquire more data.
q2t
b q2 t 0
Slope D Intercept ln(M0)
ln(M)
b q2 t ? 0
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Unrestricted Diffusion
r'
r
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Restricted Diffusion
r
r'
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The effect of barriers to the free diffusion of
water molecules is to modify their probability
distribution.

• Diffusion
• coefficient
• decreases
• with increasing
• diffusion time

P(z)
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Determination of D?
Slope D?tdif
bead pack water
bulk water
Slope D0?tdif
a 15.8 ?m bead pack, tdif 50 ms, ? 1.5 ms,
g(max) 72.8 G/cm
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Water Diffusion in an Ordered System High q
2?/a
q2
a 15.8 ?m bead pack, tdif 100 ms
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Short diffusion times
Long diffusion times
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D(tdif) gives information on different
length scales
T tortuosity S/V surface-to-volume ratio

D(t)
t1/2 sec 1/2
a 15.8 ?m bead pack
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DW-Weighted Tumor Data
0.0
-0.5
tdif
-1.0
-1.5
ln M(q,t)/M(0,t)
-2.0
-2.5
-3.0
-3.5
D(t) ? Apparent Diffusion Coefficient (ADC)
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ADC(t) for water in a RIF-1 Mouse Tumor
Necrosis!!
0.10
0.24
D(t) ?105 cm2/s
0.60
0.75
0.10
(t)1/2 s1/2
2.55
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ADC for water in a RIF-1 Mouse Tumor
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ADC for water in a RIF-1 Mouse Tumor
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ADCav Maps vs Post-Occlusion Time Rat Brain 30
min Occlusion
ADC (x10-5 mm2/s)
ROI Positions
lt 30
gt 60
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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
always restrictions. 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.
Fast Exchange
Slow Exchange
But real systems are rarely either/or.
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DW-Weighted Tumor Data
0.0
-0.5
tdif
-1.0
-1.5
ln M(q,t)/M(0,t)
-2.0
-2.5
-3.0
-3.5
What does non-monexponentiality tell us?
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Fast and Slow Diffusion?
Slope Dfast?tdif
Slope Dslow?tdif
bulk water
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Does Fast and Slow Mean Extracellular and
Intracellular?

• No, because
• 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. MRM 47, 623, 2002.
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Dave(fast)
Dave(slow)
FA(slow)
FA(fast)
Clark et al. MRM 47, 623, 2002.
?slow ? restricted
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Do We Get More Information by Using the Entire
Diffusion Attenuation Curve?
0.0
-0.5
-1.0
-1.5
ln M(q,t)/M(0,t)
-2.0
-2.5
-3.0
-3.5
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Practical Issues in DWI
How do I choose my lowest b-value?

• 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.

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Practical Issues in DWI
How do I choose my highest b-value? 1. Greatest
SNR in calculated ADC
I true signal S measured signal ? noise
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Practical Issues in DWI
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Practical Issues in DWI
How do I choose my highest b-value? 2. Greatest
sensitivity to ?ADC
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Practical Issues in DWI
How to distribute the b-values?
q2t
This or ?
ln(M)
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Practical Issues in DWI
How to distribute the b-values?
q2t
This or?
ln(M)
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Practical Issues in DWI
How to distribute the b-values?
q2t
This?
ln(M)
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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 different numbers for the
optimum values, but ?bopt 1()/D and
Nhigh-b Nlow-b ? 4
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Diffusion Tensor Imaging
What effect does the direction of the
diffusion-sensitizing gradient have upon what we
measure?
In the 1- dimensional case (we measure Dx or
Dy) Dy ? D0, the bulk value Dx lt(lt) D0 D /
ADC is a scalar
y
x
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What effect does the direction of the
diffusion-sensitizing gradient have upon what we
measure?
In the 3- dimensional case (we measure Dx, Dy and
Dz) Dy ? D0, the bulk value Dx Dz lt(lt)
D0 D (Dx, Dy, Dz)
z
y
x
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Diffusion Tensor Imaging
Why not stick with vectors? Because is not
z
x
y
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The ADC is greatest along White Matter fiber
tracts.
Taylor et al., Biol Physhiatry, 55, 201 (2004)
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1. There is nothing special about using
tensors to characterize anisotropic diffusion.
Rotate to principal frame 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.edu8000/pages/papers/ma
ier/radiology2001.pdf
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Distribution of Gradient Sampling Directions
Need at least 6 different sampling directions
LeBihan et al., JMRI, 13, 534 (2001)
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Diffusion Tractography
Follow Voxels With Largest Eigenvalues Being
Continuous Between Two Regions of Interest
http//splweb.bwh.harvard.edu8000/pages/papers/ma
rtha/DTI_Tech354.pdf