The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
Diffusion weighted MRI
Brian Hansen, PhD
brianh@phys.au.dk
Lecture outline
• Background: The physics of diffusion
 Fickian diffusion
 Brownian motion
 Self diffusion
• Diffusion measurements
 PGSE pulse sequence and spin dynamics
 Interpreting the diffusion weighted signal
 Diffusion in biological tissues
• Diffusion MRI in neuroimaging / neuroscience
 Diffusion weighted MRI and the ADC map
 Other applications: Fibre tracking
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
2
Background and motivation
•
Diffusion processes are everywhere in Nature
 Gases
 Solids (semi-conductors, alloys)
 Liquids (chemical reactions, biology, physiology)
•
Diffusion Weighted (DW) MRI is a non-invasive method for measuring
diffusion:
 Diffusion coefficient (physical or apparent)
 Direction of diffusion (preferred direction)
•
From these parameters the state of e.g. tissue can be estimated.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
3
Clinical Application
•
•
Ischemic infarction is not visible on conventional MRI (T1,T2, PD)
DW MRI introduces new sensitivity:
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
4
Physical Principles
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
5
Fickian diffusion
Fick’s two laws describe diffusion
driven by a difference in
concentration.
C(x,t)
Fick’s 1st:
Fick’s 2nd:
x
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Self-diffusion
• All water molecules
perform a thermally driven
random walk.
• We can only describe this
motion statistically:
For Brownian motion z = 2
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
H2O
Brownian Motion
•
•
•
Named after scottish botanist Robert Brown (1773-1858).
Explained by Einstein in 1905.
The thermal motion of the molecules cause them to collide. Random
motion follows.
Described by the Stokes-Einstein relation:
D is diffusion coefficient, kB is the Boltzmann constant, T is absolute temperature,
m is liquid viscosity and r is particle radius.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Diffusion in biological tissue
Diffusion in tissue is resticted by
cell membranes, organelles etc:
These random trajectories will in
time fill the plane and reveal the
structure.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
Measuring Diffusion
•
The Pulsed Gradient Spin Echo (PGSE) sequence
180
90

g
D
time
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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No diffusion:
Stationary spins are unaffected
by diffusion gradient.
time
Spin 1
Spin 2
Spin 3
B
x
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
11
With diffusion:
time
Spin 1
Spin 2
Spin 3
B
x
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
12
Vector sum
+
+
=
No loss of signal in areas with no diffusion.
Diffusion introduces a signal loss.
+
+
=
High diffusion gives strong signal attenuation.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
13
DW MRI parameters
180
90

g
Parameters g, , D are combined in the b-factor:
D
Here g is the proton gyromagnetic ratio.
The b-factor can be varied by varying one of g,  and D.
For the PGSE sequence the case b = 0 corresponds to the simpel SE
sequence.
A large b-factor gives a large signal loss in areas with high diffusion. This is
called strong diffusion weighting.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
14
Signal and b-factor I
The DWMR signal from simple free diffusion is described by:
By ”simple free
diffusion” we
mean that
applies for all
times.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Signal and b-factor II
On a log-plot this yields a straight line:
log(S(b)/S(b=0)) = -bD
The slope of the curve gives us the physical diffusion coefficient.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
16
Measuring D
Remember:
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Diffusion in tissue
Diffusion in biological tissue is not free:
Simple signal behaviour
breaks down due to complex
tissue structure:
Cell membranes, organelles etc. restrict
the diffusion of the water molecules.
This means that
no longer applies
for all times.
Grey matter, ECS in red.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
18
The Apparent Diffusion Coefficient
•
•
•
The value we measure is no longer the physical diffusion coefficient:
 Instead we get an average over many restricted random walks
We introduce the term Apparent Diffusion Coefficient (ADC)
Two measurements at b = 0 and b = 1000 s/mm2 are made:
The slope gives the ADC – not
the physical diffusion
coefficient.
Typical ADC values in brain
(mm2/s):
Normal gray matter: 0.8-1.010-3
Normal white matter: 0.2-1.0  10-3
Free water (CSF):
2.9  10-3
Review and references in Journal of Computer
Assisted Tomography 25(4):515-519.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
19
Increasing b-values
b = 2000
b = 4000
b = 7000
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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DWI and ADC maps
DW MRI provides two new image types:
The Diffusion Weighted Image (DWI)
The ADC map (a calculated image)
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
21
Stroke DWI
Acute
DWI
tPA + 2h
DWI
tPA + 24h
DWI
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Possible cause of the bright areas in the DWI:
Cells in normal tissue
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
Cells in infarct
(stroke)
Summary: Strength of DWI
T2 MRI:
DWI:
• Infarct is not visible – brain appears
normal
• Infarct clearly visible
• Scan time: 30 sec, EPI
• No IV contrast agent needed
• Infarct detectable after few minutes
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
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Summary: Image types
Two image types: DWI and ADC map:
DWI:
ADC map:
• Signal is diffusion weighted.
• Calculated image
• High diffusion: signal loss
• Contrast opposite to DWI
• Low diffusion: no signal loss
• Low intensity: low ADC value (low
• Infarcts are bright
diffusion)
• High intensity: high ADC (high diffusion)
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
25
DWI
ADC
MTT
Osvd
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
26
Diffusion Tensor Imaging
Diffusion is often directional – e.g. along fibers:
Instead of measuring many b-values we measure
along many different directions.
Instead of the ADC we obtain the Diffusion Tensor
which describes the diffusion coefficient in space.
This is the basis of fibre tracking.
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
27
Images courtesy of Jesper Frandsen, CFIN
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital
Image courtesy of Jesper Frandsen, CFIN
The Danish National Research Foundation’s
Center of Functionally Integrative Neuroscience
Aarhus University / Aarhus University Hospital