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Alz forum webinar_4-10-12_raj
1. IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
Network-Diffusion Model For Dementia
Progression in the Brain
Ashish Raj, PhD
Co-Director, Image Data Evaluation and Analysis Laboratory (IDEAL)
Department of Radiology
Weill-Cornell Medical College
New York, NY
Webpage:
www.ideal-cornell.com
2. People Involved
Ashish Raj Amy Kuceyeski
Weill Cornell IDEAL Lab
Mentors: Norman Relkin (Cornell), Mike Weiner, Bruce
Miller (UCSF)
Lots of help from: Yu Zhang, Duygu Tosun (UCSF)
Want to thank Lea Grinberg, Howie Rosen, John
Trojanowski, David Vinters for great conversations
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 2
3. Setting the stage
Network-level understanding is essential for further advances in
neurological disorders
“The connection matrix of the human brain (the human “connectome”) represents an
indispensable foundation for basic and applied neurobiological research.”
- From Sporns, Tononi and Kotter, “The Human Connectome: A Structural Description
of the Human Brain”, PLoS Computational Biology 2005
Currently brain network analysis mainly rehashes the work
done in social network theory
Finds conventional summary network measures:
– path length
– “small world”
– scale-free
– Hubs, communities, centrality,…
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 3
4. STOP!!
•Brain is NOT a social
network!
•No strong justification or
evidence for
hubs, “communities”, high
clustering
Need to find brain-appropriate and disease-
directed graph theory…
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 4
5. How to get brain networks in vivo
Functional Networks Structural Networks
fMRI: measures neuronal activity as Diffusion MRI: measures direction of
function of time water diffusion in brain
Connectivity between 2 regions is Fit a 3D shape to several directional
given by the correlation between their diffusion measurements
temporal signals Max diffusion aalong fiber direction
This provides a measure of functional Draw fibers by “following the nose”
co-activation between regions whole brain tractography
Infer connectivity network
Problem: co-activation ≠ connection Problem: inferred fiber ≠ real fiber
Cant measure anatomic connectivity Can measure anatomic connectivity,
Changes w/ time, even resting state! but with some error
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 5
7. IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
Modeling Neurodegenerative Diseases as
Network Disorders
Simple idea: Lets go back to first principles and apply
them to neurodegeneration
This stuff is MUCH cooler than just applying social
network methods and metrics to the brain
8. Diffusion on Graphs and
Relationship to Dementias
“Signal”: amount of pathological agent in neuronal
population
– Misfolded tau, A-beta, alpha-synuclein, TDP43, etc
We model neurodegeneration as a diffusive process
x2 c12 R1
R2 x1
Laplacian of the connectivity matrix
𝑑𝑥1
= 𝛽𝑐1,2 (𝑥2 − 𝑥1 ) −𝑐 𝑖,𝑗 𝑓𝑜𝑟 𝑐 𝑖,𝑗 ≠ 0
𝑑𝑡
𝐻 𝑖,𝑗 = 𝑐 𝑖,𝑗 ′ 𝑓𝑜𝑟 𝑖 = 𝑗
𝑑𝐱(𝑡)
= −𝛽H𝐱(𝑡) 𝑖,𝑗 ′ : 𝑒 𝑖,𝑗′ ∈ ℰ
𝑑𝑡
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 8
9. Graph Diffusion Theory
Note: this is graph-analogue of heat eqn
Solution of heat equation given by
𝐱(𝑡) = 𝑒 −𝛽𝐻𝑡 𝐱 0
This is easily computed via the eigen-
decomposition of H:
which gives 𝐻 = 𝑈Λ𝑈 †
𝑛
𝐱(𝑡) = 𝑈 𝑒 −Λβ𝑡 𝑈 † 𝐱 0 = (𝑒 −𝛽𝜆 𝑖 𝑡 𝐮† 𝐱 0 ) 𝐮 𝑖
𝑖
𝑖=1
Meaning that the solution of heat eqn is simply
the sum of all eigen-modes ui of H
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
10. From misfolded proteins to
atrophy
We hypothesize that regional atrophy =
accumulation of the proteinopathic agent over time
Modeled as the time integral
On whole brain, atrophy as function of time
This is the model
– Deterministic, not statistical model
– Fully quantitative, hence predictive, testable
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11. Dynamics of protein vs atrophy
After initial attack the protein eigenmode gets dispersed,
dissipating over time until the diffusion process is completely
dispersed into the entire network.
Atrophy dynamics resulting from (a) are shown in (b). The
smallest eigen-modes will be slowest to dissipate, cause the most
atrophy, be most wide-spread and persist the longest.
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12. What is an “eigenmode”?
A sub-network that acts like an
attractor for the pathological agent
Imagine a terrain with several distinct
valleys
Entire eigenmode evolves over time
together, in unison
Notes:
spatially distinct but distributed
No hubs
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13. Smallest (Most Persistent)
Eigenmodes dementias?
The smallest eigenmode = steady state distribution
– This is simply prop to node size
– “normal aging”?
The other small eigenmodes correspond to modes
of diffusion that persist the longest
Hypothesis:
– Small eigenmodes might act as channels for
neurodegeneration?
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14. Validation with dementia data
Thanks: Bruce Miller, Mike Weiner, Yu Zhang, Duygu Tosun (UCSF)
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
20. Lets pause – isnt this cool?
Our model is based entirely on healthy brain networks
– Does NOT use any patient or atrophy info!
Network-diffusion: reasonable model for proteopathic trans.
– Model does not “know” it is modeling dementias…
No “fitting” to patient data, on searching for most atrophied
anchors
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23. Clinical Implications
Eigenmodes can be used as feature vectors for
automatic disease classification
Especially useful in mixed/ clinically ambiguous
dementias
Excellent tool for clinical trials
Model is fully predictive
– Can use baseline MRI to predict future atrophy
– Just “play out” the diffusion kernel
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
24. The first deterministic,
predictive, testable,
computational model
of spread of
neurodegeneration
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25. Scientific Implications
Eigenmodes modulate neurodegeneration
Model works reasonably even without any
knowledge of differences in neuropathological
mechanisms in various dementias
Is it possible that all dementias follow a spatial
pattern given by the persistent eigenmodes of
graph diffusion?
point of origin may be unimportant for
eventual spread
– E.g. AD originates in hippocampus, etc
A unique point of origin may not even be needed
IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 25
26. Clinical/neurological Implication
• Do neurological diseases have “innate” tissue
targets?
– Selective vulnerability
– Differential stress
– Network disconnection
Occam’s razor: choose the simplest explanation
28. Raj et al Zhou et al
Uses structural networks Uses functional networks
Data on only 2 dementias Data on 5 dementias
Explicit, a priori model of Phenomenological model?
neurodegeneration
Model observed atrophy Observed atrophy model
Distributed eigenmodes Anchored epicenters
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29. Mapping Human Whole-Brain Structural Networks with Diffusion MRI
Patric Hagmann, Maciej Kurant, Xavier Gigandet, Patrick Thiran, Van J. Wedeen, Reto Meuli, Jean-
Philippe Thiran, PLoS ONE 2(7)
30. Thresholding can change degree distribution statistics
• Without thresholding normal distribution
fits distribution of ROIs connectivity
weights the best
ROIs have comparable connectivity
•With thresholding power law fits
distribution of ROIs connectivity weights
better
31. Lesson: Gaussian degree distribution
all nodes basically have same degree
no priviledged nodes
no hubs
•31
32. Clustering by normalized cuts reveals hierarchical organization
of brain fibers
• 2 parts • 4 parts • 8 parts
• The clustering quality metrics indicated that division into 2
parts is the best for all clusters up to 3rd level ( 8 parts)
• No major hubs detected at this resolution. Brain divides to:
• Left and right hemisphere (2 parts)
• Frontal and parts of parietal lobe; temporal, parietal, occipital lobe (4 parts)