Statistical Connectomics: Developing Methods Towards Understanding Populations of Networks


Jaewon Chung

(he/him) - NeuroData lab
Johns Hopkins University
Department of Biomedical Engineering

icon j1c@jhu.edu
icon @j1c (Github)
icon @j1c (Twitter)

Acknowledgements

Committee

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Joshua Vogelstein

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Carey Priebe

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Mike Powell

Collaborators

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Alex B.

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Eric B.

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Derek P.

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Cencheng S.

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Ronak M.

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Alex

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Ali

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Alice

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Anton

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Ashwin

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Bear

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Ben 1

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Ben 2

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Bijan

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Brandon

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Devin

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Drishti

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Eric

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Hao

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Hayden

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Javier

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Jayanta

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Jesus

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Jong

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Kareef

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Jesse

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Ronak

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Ronan

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Ross

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Sambit

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Suki

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Tingshan

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Tyler

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Tommy

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Vikram

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Vivek

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Yuxin

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Ziyan


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Outline

  • Connectomes of Human Brains
  • Statistical Modeling for Connectomes
  • Heritability of Human Connectomes
  • Open-source Software

Connectomes: maps of neural wiring

  • Brains contain neurons, which carry information via electrical signals
  • Neurons connect to each other via synapses, allowing neurons to "talk" to each other
  • Connectome is a map of the structure of neurons and the connections between them
    • Shaped by evolution, experience, influences neural activity, behavior

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Pedigo et al.

How do we measure connectomes in humans?

  • Diffusion MRI (dMRI): in vivo imaging technique
  • Exploits direction of water diffusion
    • Anisotropic in white matter tracts
    • Isotropic in other tissues

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MRI Scans


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Preprocessing

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Tractography

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Representing brains as networks

Networks (or graphs) are mathematical abstractions to represent relational data
  • Vertices - the set of objects (brain regions)
  • Edges - the set of connections between those objects (brain regions)
    • E.g. region 1 connects to region 2 with 100 neural bundles

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MRI to graphs (m2g)

  • Easy to use end-to-end pipeline
    • Input: MRI data
    • Output: Connectomes, QA measures, derivatives
  • Reproduces biological properties
    • Stronger ipsilateral connections
  • High discriminability
    • Same subjects' connectomes are more similar than different subjects'

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Connectomes: maps of neural wiring

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Images from SciDraw

Linking connectivity to other phenotypes

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Images from SciDraw

Linking connectivity to other phenotypes

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Images from SciDraw

Linking connectivity to other phenotypes

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Images from SciDraw

Outline

  • Connectomes of Human Brains
  • Statistical Modeling for Connectomes
  • Heritability of Human Connectomes
  • Open-source Software

Different data, same statistics (Ascombe's Quartet)

  • These four datasets have same statistics!
    • Mean (): 9
    • Variance (): 11
    • Mean (): 7.5
    • Variance (): 4.12
    • Correlation ():0.816

Different networks, same statistics

  • These four networks have same (network) statistics!

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Show the other figure of the same statistics

  • Consider all non-isomorphic graphs with 10 vertices

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Statistical models for networks

  • Random dot product graphs (RDPGs)
    • Each vertex has a low dimensional latent position.
    • Estimate latent position matrix via adjacency spectral embedding.
    • =

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Two sample graph testing

  • Suppose we have two networks
  • Want to test if they are "same" or not

Hypothesis:

  • Network 1Network 2
  • Network 1Network 2

More precisely:

Drosophila Left vs Right Brain

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Outline

  • Connectomes of Human Brains
  • Statistical Modeling for Connectomes
  • Heritability of Human Connectomes
  • Open-source Software

Heritability?

  • Proportion of phenotypic variance due to genetic variance

    • Predict disease risk
    • Potential for targeted treatments
  • Do genomes cause connectomes?



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Human Connectome Project

  • Brain scans from identical (monozygotic), fraternal (dizygotic), non-twin siblings.
  • Regions defined using Glasser parcellation (180 regions).

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Van Essen, David C., et al., The WU-Minn human connectome project: an overview (2013)

Glasser, Matthew F., et al. "A multi-modal parcellation of human cerebral cortex." Nature (2016).

Heritability as causal problem

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Methods of comparing connectomes

  • Exact : measures all differences in latent positions
    • Differences in the latent positions implying differences in the connectomes themselves
  • Global : considers the latent positions of one connectome are a scaled version of the other
    • E.g. males may have globally fewer connections than females
  • Vertex : similar to the global differences, but it allows for each vertex to be scaled differently
    • E.g regions have preferences in connections
    • regions tend to connect strongly within hemisphere

Distribution of distances between connectomes

  • Stochastic ordering along familial relationships
  • Monozygotic twins have the smallest distances
  • Medians (diamonds) shift towards the right as relatedness decreases
  • Shifts in medians "decrease" in vertex model

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Do genomes affect connectomes?

  • Our hypothesis:
    C, GCG
    C, GCG

  • Known as independence testing

  • Test statistic: distance correlation (Dcorr)

  • p-value: "If genomes don't affect connectomes, what is the probability there is associational correlation?"



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Genomes affect connectomes

  • Our hypothesis:
    C, GCG
    C, GCG

  • p-value: "If genomes don't affect connectomes, what is the probability there is associational correlation?"

  • All p-values


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Do genomes affect connectomes given covariates?

  • Want to test:
    C, G|CoC|CoG|Co
    C, G|CoC|CoG|Co
  • Known as conditional independence test
  • Test statistic: Conditional distance correlation (CDcorr)
  • p-value: "If genomes don't affect connectomes, what is the probability there is causal correlation?"

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Genomes affect connectomes given covariates

  • Want to test:
    C, G|CoC|CoG|Co
    C, G|CoC|CoG|Co
  • p-value: "If genomes don't affect connectomes, what is the probability there is causal correlation?"
  • p-values for only exact and global models


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What if we remove "heritable" vertices?

  • Test per vertex :
    , G|Co|CoG|Co
    , G|Co|CoG|Co

  • Then test "non-heritable" subgraphs ():
    , G|Co|CoG|Co
    , G|Co|CoG|Co

  • p-value: "If genomes don't affect connectome subgraphs, what is the probability there is causal correlation?"

  • p-values for 3 hypotheses



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To sum up...

Are human connectomes heritable?

Depends on the context.

  • Connectomes are heritable, up to some common structures.

Outline

  • Connectomes of Human Brains
  • Statistical Modeling for Connectomes
  • Heritability of Human Connectomes
  • Open-source Software

How to use these tools?

Questions?




Jaewon Chung

icon j1c@jhu.edu
icon @j1c (Github)
icon j1c.org

Appendix

How do we compare genomes?

  • Neuroimaging twin studies do not sequence genomes.
  • Coefficient of kinship ()
    • Probabilities of finding a particular gene at a particular location.
  • d(Genome, Genome) = 1 - 2.

Relationship
Monozygotic
Dizygotic
Non-twin siblings
Unrelated

Neuroanatomy (mediator), Age (confounder)

  • Literature show:
    • neuroanatomy (e.g. brain volume) is highly heritable.
    • age affects genomes and potentially connectomes
  • d(Covariates, Covariates) = ||Covariates - Covariates||

How do we compare connectomes?

  • Random dot product graph (RDPG)

    • Each vertex (region of interest) has a low dimensional latent vector (position).
    • Estimate latent position matrix via adjacency spectral embedding.
  • d(Connectome, Connectome) =

Distance correlation

  • Measures dependence between two multivariate quantities.
    • For example: connectomes, genomes.
  • Can detect nonlinear associations.
  • Measures correlation between pairwise distances.

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Conditional distance correlation

  • Augment distance correlation procedure with third distance matrix.

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Associational Test for Connectomic Heritability

  • Connectome, GenomeConnectomeGenome
    Connectome, GenomeConnectomeGenome

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Sex All Females Males
p-value

Associational Test for Neuroanatomy

  • Neuroanatomy, GenomeNeuroanatomyGenome
    Neuroanatomy, GenomeNeuroanatomyGenome

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Sex All Females Males
p-value

Causal Test for Connectomic Heritability

  • Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
    Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates

Sex All Females Males
p-value

before i get into the bulk of the talk, i want to steal a page from previous lab members, and start my defense with the acknowledgements. That way if you glaze over or fall asleep later in the talk, I hope you'll remember the important part, which is my graditute to the people which I should probably express more often.

First, to my advisor, my committee, and close collaborators. I will be forever humbled that you all trusted me to work on data and problems that you all have spent so much time and energy on. I'm grateful for that opportunity and for all I've learned from you over the years, and I'm confident that we'll keep working together for a long while...

I want to thank many current and past members of the neurodata lab and hopkins. It has been a great honor to get to learn from you all on a daily basis, and not just about machine learning or neuroscience or statistics, but also frisbee

Loftus

Saad-Eldin

Wang

...

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Falk

...

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Crowley

Bridgeford

Helm

How

Dey

Arroyo

Shin

Ullah

Patsolic

Mehta

Perry

Lawrence

Panda

Panda

Bai

To my parents and my brother - I obviously owe them everything that got me to this point. Their unwavering support, encouragement, and love have been the foundation of my journey.

To my partner Lina. Im so grateful for the support and that we've made it through this chapter and with so many great memories from traveling many parts of the world. i cant wait to see what the future holds for us in the future.

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Brain diseases disrupt communication between brain regions. This is why studying connectivity can help us develop targeted therapies for diseases like Alzheimer's and Parkinson's.

<footer> Athreya et al. "RDPG..." _JMLR_ (2021) </footer>

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