Alz forum webinar_4-10-12_raj

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

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

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,…


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…


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


6


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

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


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


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


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.


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


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?


Validation with dementia data
Thanks: Bruce Miller, Mike Weiner, Yu Zhang, Duygu Tosun (UCSF)


Eigenmode 2


Eigenmode 3


Surface atrophy maps
 Measured atrophy using Freesurfer volumetrics


Surface atrophy maps
 Atrophy measured by SPM volumetric s/w


Statistical correlation analysis


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


Eigen-modes predict prevalence rates


Eigen-modes as clinical
biomarkers


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


The first deterministic,
predictive, testable,
computational model
of spread of
neurodegeneration


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


Clinical/neurological Implication
• Do neurological diseases have “innate” tissue
targets?
– Selective vulnerability
– Differential stress
– Network disconnection

Occam’s razor: choose the simplest explanation

Reserve Slides


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


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)

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

Lesson: Gaussian degree distribution
 all nodes basically have same degree
 no priviledged nodes
 no hubs

•31

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)

Alz forum webinar_4-10-12_raj

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