Post on 13-Jan-2016
description
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
Diffusion weighted MRI
Brian Hansen, PhDbrianh@phys.au.dk
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
2
• 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
Lecture outline
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
3
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 NeuroscienceAarhus University / Aarhus University Hospital
4
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 NeuroscienceAarhus University / Aarhus University Hospital
5
Physical Principles
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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Fickian diffusion
Fick’s two laws describe diffusion driven by a difference in concentration.
Fick’s 1st:
Fick’s 2nd:
C(x,t)
x
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
Self-diffusion
• All water molecules perform a thermally driven random walk.
• We can only describe this motion statistically:
H2O
For Brownian motion z = 2
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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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, is liquid viscosity and r is particle radius.
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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 NeuroscienceAarhus University / Aarhus University Hospital
10
Measuring Diffusion
• The Pulsed Gradient Spin Echo (PGSE) sequence
90
180
time
g
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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No diffusion:
x
Spin 1 Spin 2 Spin 3
B
Stationary spins are unaffected by diffusion gradient.
time
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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With diffusion:
x
Spin 1 Spin 2 Spin 3
B
time
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
13
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 NeuroscienceAarhus University / Aarhus University Hospital
14
DW MRI parameters
Parameters g, , are combined in the b-factor:
Here is the proton gyromagnetic ratio.
The b-factor can be varied by varying one of g, and .
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.
90
180
g
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
15
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 NeuroscienceAarhus University / Aarhus University Hospital
16
Signal and b-factor IIOn a log-plot this yields a straight line:
log(S(b)/S(b=0)) = -bD
The slope of the curve gives us the physical diffusion coefficient.
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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Measuring D
Remember:
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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Diffusion in tissue
Diffusion in biological tissue is not free:
Cell membranes, organelles etc. restrict the diffusion of the water molecules.
Simple signal behaviour
breaks down due to complex tissue structure:
Grey matter, ECS in red.
This means that
no longer applies for all times.
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
19
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: 0.8-1.010-3
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 NeuroscienceAarhus University / Aarhus University Hospital
20
Increasing b-values
b = 2000 b = 4000 b = 7000
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus 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 NeuroscienceAarhus University / Aarhus University Hospital
22
Stroke DWI
Acute
DWI
tPA + 2h tPA + 24h
DWIDWI
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
Possible cause of the bright areas in the DWI:
Cells in normal tissue
Cells in infarct (stroke)
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
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Summary: Strength of DWI
T2 MRI:
• Infarct is not visible – brain appears normal
DWI:
• 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 NeuroscienceAarhus University / Aarhus University Hospital
25
Summary: Image types
Two image types: DWI and ADC map:
DWI:
• Signal is diffusion weighted.
• High diffusion: signal loss
• Low diffusion: no signal loss
• Infarcts are bright
ADC map:
• Calculated image
• Contrast opposite to DWI
• Low intensity: low ADC value (low diffusion)
• High intensity: high ADC (high diffusion)
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
26
DWI
ADC
MTT
Osvd
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
27
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 NeuroscienceAarhus University / Aarhus University Hospital
Images courtesy of Jesper Frandsen, CFIN
The Danish National Research Foundation’s
Center of Functionally Integrative NeuroscienceAarhus University / Aarhus University Hospital
Image courtesy of Jesper Frandsen, CFIN