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Presentation made by Dr Ashish Raj, April 10, 2012, at Alzheimer Research Forum (www.alzforum.org). All rights reserved.

Presentation made by Dr Ashish Raj, April 10, 2012, at Alzheimer Research Forum (www.alzforum.org). All rights reserved.

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Alz forum webinar_4-10-12_raj Alz forum webinar_4-10-12_raj Presentation Transcript

  • IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)Network-Diffusion Model For Dementia Progression in the BrainAshish Raj, PhDCo-Director, Image Data Evaluation and Analysis Laboratory (IDEAL)Department of RadiologyWeill-Cornell Medical CollegeNew York, NYWebpage: www.ideal-cornell.com
  • People InvolvedAshish Raj Amy KuceyeskiWeill Cornell IDEAL LabMentors: Norman Relkin (Cornell), Mike Weiner, BruceMiller (UCSF)Lots of help from: Yu Zhang, Duygu Tosun (UCSF)Want to thank Lea Grinberg, Howie Rosen, JohnTrojanowski, David Vinters for great conversations IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 2
  • Setting the stageNetwork-level understanding is essential for further advances inneurological 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
  • STOP!! •Brain is NOT a social network! •No strong justification or evidence for hubs, “communities”, high clusteringNeed to find brain-appropriate and disease- directed graph theory… IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 4
  • 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 directionalgiven by the correlation between their diffusion measurements temporal signals Max diffusion aalong fiber directionThis provides a measure of functional Draw fibers by “following the nose” co-activation between regions  whole brain tractography  Infer connectivity networkProblem: co-activation ≠ connection Problem: inferred fiber ≠ real fiberCant 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
  • 6IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 6
  • 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
  • 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
  • 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)
  • 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 IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 10
  • 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. IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 11
  • 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 IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 12
  • 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? IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 13
  • Validation with dementia dataThanks: Bruce Miller, Mike Weiner, Yu Zhang, Duygu Tosun (UCSF) IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
  • Eigenmode 2IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 15
  • Eigenmode 3IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 16
  • Surface atrophy maps Measured atrophy using Freesurfer volumetrics IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 17
  • Surface atrophy maps Atrophy measured by SPM volumetric s/w IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 18
  • Statistical correlation analysis IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
  • 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 IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 20
  • Eigen-modes predict prevalence rates IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
  • Eigen-modes as clinical biomarkersIMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL)
  • 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)
  • The first deterministic,predictive, testable,computational modelof spread ofneurodegeneration IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 24
  • 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
  • Clinical/neurological Implication• Do neurological diseases have “innate” tissue targets? – Selective vulnerability – Differential stress – Network disconnection Occam’s razor: choose the simplest explanation
  • Reserve SlidesIMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 27
  • Raj et al Zhou et alUses structural networks Uses functional networksData on only 2 dementias Data on 5 dementiasExplicit, a priori model of Phenomenological model?neurodegenerationModel  observed atrophy Observed atrophy  modelDistributed eigenmodes Anchored epicenters IMAGING DATA EVALUATION AND ANALYTICS LAB (IDEAL) 28
  • Mapping Human Whole-Brain Structural Networks with Diffusion MRIPatric 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 organizationof 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)