Transcript MR Diffusion Imaging - University at Albany, SUNY

MaxEnt 2007 Saratoga Springs, NY
Computing the Probability
Of Brain Connectivity with
Diffusion Tensor MRI
JS Shimony
AA Epstein
GL Bretthorst
Neuroradiology Section
NIL and BMRL
Part 1: Diffusion Tensor (DT) MRI
(Brain Connectivity later)
• Diffusion MR images can measure water
proton displacements at the cellular level
• Probing motion at microscopic scale (mm),
orders of magnitude smaller than
macroscopic MR resolution (mm)
• This has found numerous research and
clinical applications
Diffusion: Left MCA stroke
Standard Spin Echo
Mz
Mxy
Mxy
RF/RO
Gz
90
180
echo
Diffusion Spin Echo
M=Mxyexp(-bD)
Mz
Mxy
RF/RO
90
180
Gz
D
echo
Diffusion: Pulse Sequence
90
180
Echo Train
RF
Gss
EPI Readout
Gro
Gpe
Anisotropic Diffusion in WM Fibers
Diffusion: Single Direction
Diffusion Tensor Imaging Model
λ1
λ2
λ3
Basser et al., JMR, 1994 (103) 247
Uses 8 parameters (D ≠ data)


S q  S 0exp  qDq D  C
 1 0

D  R  ,  ,  0 2
0 0

T
0
 T
0 R  ,  , 
3 
Signal Amplitude
How Diffusion is Measured by MRI
Diffusion Sensitization (q)
Image courtesy: C. Kroenke
Signal Amplitude
Diffusion Anisotropy
Diffusion Sensitization (q)
Image courtesy: C. Kroenke
Mean Diffusivitiy
λ1
λ2
λ3
• Mean Diffusivity is the
average of the diffusion in
the different directions
 1 0

DT   0 2
0 0

0

0

3 
1
MD  1  2  3 
3
Diffusion Anisotropy
• Anisotropy is normalized
standard deviation of
diffusion measurements in
different directions
• FA and RA most common
• Range from 0 to 1
RA 
RA=0
1  MD 2  2  MD 2  3  MD 2 RA<1
6 MD
Baseline image / Anisotropy
Color Diffusion
Part 2: Brain Connectivity
• DT data provides a directional tensor field in
the brain, used to map neuronal fibers
• Detailed WM anatomy used in:
–Pre-surgical planning
–Neuroscience interest in functional networks
• Previously could only be done using
cadavers or invasive studies in primates
• Termed DT Tractography (DTT)
3D Diffusion Tensor Field
Example of Streamline Tracking
Streamline DTT
• Advantages:
– Conceptually and computationally simple
– Was the first to be developed
• Disadvantages:
– Limited to high anisotropy, high signal areas
– Can only produce one track
– Can’t handle track splitting
– Has the greatest difficulty with crossing fibers
Applications: Anatomy
Jellison
AJNR 25:356
DTT and Crossing Fibers
• Major limitation of current
methods of DTT
• Difficult to resolve with
current methods and SNR
• Volume averaging effects
• Known areas in the brain
• Decrease sensitivity and
specificity, distorts
connection probabilities
Crossing Fibers Locations
Probabilistic DTT
• Behrens et al. MRM 2003 50:1077-1088
• Advantages:
– Better accounts for experimental errors
– More robust tracking results
– Better deals with crossing fibers, low SNR
• Disadvantages:
– Computationally intense
– Probabilities will be modified by crossing fibers
Probabilistic Tractography
• Express DT parameters for pixel i
i  1i , 2i , 3i ,i ,i , i , Si 0, Ci 
• Since each pixel is independent in this model
the probability for the DT parameters given
the data D can be factored:
P DI    PDi i I Pi I 
N
i 1
Utilize Angular Error Estimations
Cone of angular
uncertainty
Low Anisotropy
High Anisotropy
Angular
pdf
Probabilistic Tracking
End
zone
Start
zone
Example Probabilistic DTT
Part 3: Methods and Results
• Use prior information!!!
• Assumption of pixel independence is
non_biological
• Nerve fiber bundles can travel over long
distances in the brain and cross many pixels
• Incorporate this into the model via a:
“Nearest Neighbor Connectivity Parameter”
Adding the Connectivity Parameter
• Add nearest neighbor connectivity parameter
i  1i , 2i , 3i ,i ,i , i , Si 0, Ci , ij 
• No independence between the pixels
• Each pixel depends on its neighbors via the
prior of its connectivity
P DI    PDi i I Pi I 
N
i 1
Connectivity Parameter Prior
Adding Connectivity Parameter
• The preference for connectivity is indicated
by the prior for ij
• Express this as the probability that a water
molecule will diffuse from pixel i to j


  wD 

  wD 

P ij I   exp
exp


T
T 
r
D
r
r
D
r




ij
i
ij
ij
j
ij




Parallel Processing Details
• Connection between
neighboring pixels
complicates the calculations
• When processing on a
parallel computer, the values
of the neighbors cannot
change
• Example in 1D and 2D
Method: 3x3x3 Simulation
Results: Connectivity Parameter
Coronal Section in Crossing Fiber area
Anatomy Comparison
Results: Connectivity Parameter
Summary
• DT imaging provides accurate estimation of the
tensor field of the WM in the brain
• Accurate estimation of the connectivity between
different brain regions is of great clinical and
research interest
• Prior work has assumed independent pixels
• Prior information on local connectivity may provide
a more accurate representation of the underlying
tissue structure
• Acknowledgements: NIH K23 HD053212, NMSS
PP1262, and Chris Kroenke