Cardiff University Brain Research Imaging Centre

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Where Have we Been, Where are we Now
and Where are we Going with Diffusion MRI?
Derek K Jones
Cardiff University Brain Research Imaging
Centre Wales, United Kingdom
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Pulsed Gradient Spin Echo Experiment
?
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Roughly how many H2O molecules in each voxel?
2.5 mm
2.5 mm
2.5 mm
Volume 2.5 x 2.5 x 2.5 mm .016 cc 1 mole of
water 18g 18 cc Molecules (0.016/18) x
Navogadro 5.23 x 1020
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Number of water molecules in each voxel 1020
We can only say something about the
bulk-averaged properties of those molecules
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Random walk 106 molecules
100 steps
400 steps
900 steps
1600 steps
Percentage of water molecules
x
2x
3x
4x
Net displacement from origin (arbitrary units)
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THE MOTIVATION
Nothing defines the function of a neuron better
than its connections M. Mesulam
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THE MOTIVATION
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THE TRENDSETTERS (COMPETITORS)
Dejerine, 1895 Anatomie des Centres Nerveux
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area deWernicke
area de Broca
fibres courtes
fibres longues
fibres de linsula
Faisceau longitudinal supérieur
fibres temporales
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The Complexity
Water (almost) everywhere!
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More Complexity
Courtesy Yaniv Assaf
Axon Diameter Distribution
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Wouldnt This Be Nice?
Courtesy D. Alexander / Kieran Seunarine
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Even More Complexity
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Even More Complexity
Courtesy D. Alexander / Kieran Seunarine
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Even More Complexity
Courtesy D. Alexander / Kieran Seunarine
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Even More Complexity
Courtesy D. Alexander / Kieran Seunarine
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Even More Complexity
Courtesy D. Alexander / Kieran Seunarine
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?
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Standard q-space diffusion propagator formalism
At low q, everything looks Gaussian
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DIFFUSION WEIGHTED IMAGES
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At low q, everything looks like a tensor
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Conventional MR Images
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DIFFUSION TENSOR
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Gray Matter
MRI pixel unit


Isotropic Motion


Anisotropic Motion
MRI pixel unit
Courtesy of Yaniv Assaf
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Measured Diffusion Ellipsoids in Human Brain
T2-weighted image
1992 / 1994
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DIFFUSION TENSOR MRI
Splenium of the corpus callosum
1997
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Fractional Anisotropy
1996
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2000
6 dyslexics (age 31.5 /- 5.3 years) 6 controls
(age 23.1 /- 1.4 years) Voxel-wise comparison
of FA
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2005

• 32 volunteers (14 male, 18 female).
• Age range 8.3-12.9 years (Mean 11.3 /- 1.3
  years)
• Word ID test
• Voxelwise search for correlation between FA and
  Word ID score

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Positive Correlation Between FA and Word ID Score
L
R
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Correlation in Voxel with Highest Correlation
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CHILDRENS READING PERFORMANCE IS CORRELATED WITH
WHITEMATTER STRUCTURE MEASURED BY DIFFUSION
TENSOR IMAGINGDeutsch et al. Cortex 41, 354
(2005)
Child study (7 poor readers, 7 controls) 7 13
year old age range
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Agreement Between Studies
Deutsch
Beaulieu
R
L
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DEC- Encoded Ellipsoids
Alex Leemans
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DETERMINISTIC TRACKING AS SEEN BY THE TRACT
PROPAGATOR
Alexander Leemans
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Deterministic Tractography For Bird Brains
Starling brain
Alexander Leemans
Alexander Leemans (LeemansA_at_cf.ac.uk)
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Deterministic Tractography For Bird Brains
Fiber Tractography
1999 / 2002
Alexander Leemans (LeemansA_at_cf.ac.uk)
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Superior Longitudinal Fasciculus
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Superior Longitudinal Fasciculus
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PARIETAL FIBRES
FRONTAL FIBRES
EXTERNAL CAPSULE (anterior floor)
Inferior Fronto Occipital Fasciculus
OCCIPITAL FIBRES
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Fornix
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Whats the cause of the lesion here?
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Powder Averaging
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Ubiquity of Planar Diffusion in the Brain
Linear Anisotropy
Planar Anisotropy
1997
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Not a direct measure of myelination
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Frank, 2001
2001
Courtesy of Larry Frank
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Low Bvalue Signal Tensor Estimation Regime
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At low q, everything looks like a tensor
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Frank, 2001
Courtesy of Larry Frank
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Frank, 2001
Courtesy of Larry Frank
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Spherical Harmonic Fitting
Frank, 2001
Single Fibre
Courtesy of Larry Frank
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Spherical Harmonic Fitting
Frank, 2001
2001
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The Spherical Harmonic Series
2002/ 2004
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SPHERICAL HARMONIC DECONVOLUTION
Modelling To Recover Peaks in Fibre Orientation
Density
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Standard q-space diffusion propagator formalism
E(q) is Fourier Transform of P
Take sufficiently large number of measurements up
to sufficiently large values of q ? estimate P
directly!
At low q, everything looks Gaussian
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Diffusion Spectrum Imaging (b ?17, 000)
Brainstem Coronal
2005
Courtesy of Van Wedeen
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Diffusion Spectrum Imaging
DTI
DSI
crossing of corpus callosum, corona radiata, and
slf
Courtesy David Tuch, MGH
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A Big Challenge
KNOTS ON COTTON
SIGNAL TO NOISE RATIO A CHALLENGE
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A Big Challenge
b 20,000 s/mm2
b 1,000 s/mm2
DTI
Not-DTI
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b 20 s/mm2
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DTI
b 1,000 s/mm2
1.000 0.000 0.000
0.167 -0.199 0.966
0.726 0.688 0.000
-0.239 -0.710 0.662
-0.759 0.223 0.612
0.544 0.480 0.688
0.079 0.997 -0.005
0.773 -0.183 0.608
0.485 0.782 0.392
0.081 0.788 -0.611
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N-DTI
b 5,000 s/mm2
1.000 0.000 0.000
0.167 -0.199 0.966
0.726 0.688 0.000
-0.239 -0.710 0.662
-0.759 0.223 0.612
0.544 0.480 0.688
0.079 0.997 -0.005
0.773 -0.183 0.608
0.485 0.782 0.392
0.081 0.788 -0.611
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1.000 0.000 0.000
0.167 -0.199 0.966
0.726 0.688 0.000
-0.239 -0.710 0.662
-0.759 0.223 0.612
0.544 0.480 0.688
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A-N-DTI
b 20,000 s/mm2
1.000 0.000 0.000
0.167 -0.199 0.966
0.726 0.688 0.000
-0.239 -0.710 0.662
-0.759 0.223 0.612
0.544 0.480 0.688
0.079 0.997 -0.005
0.773 -0.183 0.608
0.485 0.782 0.392
0.081 0.788 -0.611
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1.000 0.000 0.000
0.167 -0.199 0.966
0.726 0.688 0.000
-0.239 -0.710 0.662
-0.759 0.223 0.612
0.544 0.480 0.688
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Another Challenge
UNCERTAINTY IN FIBRE ORIENTATION
UNCERTAINTY IN FIBER ORIENTATION
?1
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Optic radiation
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(Architectural milieu will be discussed later)
Seedpoint
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Probabilistic Tracking
Threshold gt 10
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UNCERTAINTY IN FIBER ORIENTATION
?
?1
Heuristic Models
Analytical Error Propagation
Matrix Perturbation Analyses
How Big Is The Uncertainty?
Monte Carlo Techniques
Bayesian Approaches
Bootstrap Methods
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Motor Cortex
2001
0.05 0.1 0.2 0.4 1
Courtesy of Martin Koch
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Major fibre bundles in visual system (PICo)
high
OR temporal loop
low
LGN
Optic tract
OR dorsal loop
Superior colliculus
2003
Geoff Parker, ISBE, University of Manchester.
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But
At gt 1 Visitation anatomically inaccurate
At gt 50 Visitation more accurate but
incomplete
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(Important)
ACCURACY / PRECISION


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What Do Most Connectivity Maps Show?
Measurements of connectivity are often nothing
more than measures of precision
VERY EASY TO FALL INTO THE TRAP OF VIEWING THE
MOST PRECISE PATH AS THE MOST RELIABLE
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MOST probabilistic maps are maps of
reproducibility of the reconstruction through the
data
Therefore they are just as prone to
inaccuracies as deterministic methods
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MOST PROBABILISTIC ALGORITHMS ARE BASED
ON PERFORMING DETERMINISTIC STREAMLINING MANY
TIMES
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Start
Start
FA 0.6
FA 0.8
FA 0.6
FA 0.8
Finish
Finish
Courtesy of Sean Deoni
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95 Cone of Uncertainty Represented with
Hyperstreamlines
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Cone of uncertainty hyperstreamlines and
bootstrapped tracts in superior longitudinal
fasciculus
Challenge How much uncertainty due to
modelling and how much due to noise?
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WILD BOOTSTRAP OF Q-BALL DATA
Courtesy of Geoff Parker
2007
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WILD BOOTSTRAP OF Q-BALL DATA
Courtesy of Geoff Parker
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WILD BOOTSTRAP OF Q-BALL DATA
Courtesy of Geoff Parker
2007
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Where are we goingwith Probabilistic
Tractography?


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2001
0.05 0.1 0.2 0.4 1
Courtesy of Martin Koch
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WHERE ARE WE GOING WITH PROBABILISTIC
TRACTOGRAPHY?
FOR DISCUSSION AT 5 pm!
Yield of Probabilistic Tracking The most
probable pathway between two points The most
likely path between two points The set of all
possible paths between the two points The
connectivity between two points
Definitely a challenge!
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Other Challenges.
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Ambiguous Topology
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What will solve the problem?
HARDI?
HARDLY!
Twisting, bending, splaying non-specific.
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Ambiguous Topology
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Effect of Architectural Milieu
Most Definitely a Challenge!
False Negatives
False Positives
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Fiber Tracking Simulations
50 tracks from a single point obtained for 50
different noise realizations at S/N10 and for
l1l2l3 211
Solutions proposed based on Poisson Statistics
not very successful
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B
Which region does X have the highest connectivity
to?
FA 0.9
A
FA 0.9

Challenging!
FA 0.9
Shortest, straightest, simplest
FA 0.9
FA 0.9
FA 0.9
E
C
D
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Hows your connectivity today?


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DEC Fiber Orientation Maps
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Confidence Maps - Genu
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Important to identify (and reduce / remove)
physiological noise
Challenging but important!
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PROBABILITY MAPS ARE MAPS OF PRECISION NOT
ACCURACY
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• CONNECTIVITY
• Information can only pass between 2 regions if
  they are connected
• Function is dependent on information transfer
• White matter connects different cortical regions
• Aim of grading white matter connectivity is to
  assess effects of changes in connectivity on
  function.
• Therefore, impairment of whatever we call
  connectivity, should imply impairment of
  information transfer and therefore of function.

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Motor Cortex
0.05 0.1 0.2 0.4 1
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THE SAD TRUTH Probabilistic tracking tells us
nothing quantitatively useful about connectivity
in the human brain
Lets talk about that at 5 pm
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Where are we Going?
Listen to the rest of the tutorial!
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Image Resolution
RESOLUTION
25 106
Å
- Single Shot EPI
Axon Size
2 10 ?m
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Roland Bammer, Stanford 2007/ 2008
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Skare et al. 2008
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Boosting SNR
HARDWARE
Higher Field Strengths
Stronger Gradients?
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2006
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Number of water molecules in each voxel 1020
We can only say something about the
bulk-averaged properties of those molecules
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Improved Modelling / Analyses
A large part of what you are about to hear!
Perhaps undue focus to date on orientational
information?
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More Compartment-Specific Information
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The Complexity
Water (almost) everywhere!
How is each part behaving?
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Whole Brain T1 and T2 Maps (isotropic 1 mm
resolution)
T1 Map
T2 Map
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Myelin Water Mapping
T2
Tshort
9 minutes
Myelin Water Fraction
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Superior Longitudinal Fasciculus
Myelination Along Specific Tracts
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The Complexity
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Combined Hindered And Restricted ModEl of
Diffusion
CHARMED Assaf et al. Magn Reson Med. 52965-78,
2004 .
?
?
?
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Thats where weve been since 1992
So.
Heres where we are now
Challenges, challenges, challenges
Where we are we going?
Ill come back at 5 p.m. and well see whether
we agree!
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• OVERVIEW
• Introduction to white matter
• Introduction to diffusion tensor MRI
• Tract-specific measurements - obstacles
• New ways of extracting orientational PDFs
• Application to probabilistic tracking
• The future for probabilistic tracking
• Diffusion based segmentation (new methods)