Heritability of Human Structural Connectomes

Jaewon Chung

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

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What is heritability?

  • Variations in phenotype caused by variations in genotype.
  • Potentially discover relationships between diseases and genetics.




Are the patterns of brain connectivity heritable?

Brain connectivity as connectomes

(aka networks or graphs)

  • Vertex: region of the brain
  • Edges: connectivity measure between a pair of vertices
  • Structural connectomes: estimated # of neuronal fibers
  • Undirected: neurons have no direction

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Image from Gu, Zijin, et al. "Heritability and interindividual variability of regional structure-function coupling." (2021)

How do we get structural connectomes?


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Quick detour to causal land

Directed acyclic graphs

  • Representation of causal relationships of variables
    • From domain knowledge
Li, Ruoran, Rhian Daniel, and Bernard Rachet. "How much do tumor stage and treatment explain socioeconomic inequalities in breast cancer survival? Applying causal mediation analysis to population-based data." European journal of epidemiology 31.6 (2016): 603-611.

Confounding

  • Common cause for both exposure and outcome
    • Exposure: alcohol consumption
    • Outcome: lung cancer
  • Causes sprious association!
  • Solution: "condition" confounding

Toy example

  • Smoking =
  • Alcohol = Smoking +
  • Lung Cancer = Smoking +
  • n = 100
Indep. Test Conditional Indep. Test
Null Hypothesis AlcoholLung cancer AlcoholLung cancerSmoking
Alternate Hypothesis AlcoholLung cancer AlcoholLung cancerSmoking
Correlation ()
p-value

Backdoor paths

  • Non-causal path from exposure (X) to outcome (Y)
  • Flow backwards out of exposure (arrow pointing towards exposure)
  • Confounders create backdoor paths
  • Path is blocked if a variable in the path is conditioned on.

Examples

  • Four possible paths
  • Sufficient condition sets:

Backdoor criterion

Causal effect exists between exposure () and outcome () if:

  1. No backdoor paths from to exist
    • Typically plausible in randomized trials
  2. Measured covariates block all backdoor paths from and

Mediation

  • Lies on the causal path between exposure and outcome
    • Exposure: grades
    • Outcome: happiness
    • Mediator: self-esteem
  • Total effect: effect from both exposure and mediators
  • Direct effect: effect only from exposure

Toy example

  • Grades =
  • Self-esteem = Grades +
  • Happiness = Grades + Self-esteem +
  • n = 100
Indep. Test Conditional Indep. Test
Null Hypothesis GradesHappiness GradesHappinessSelf-esteem
Alternate Hypothesis GradesHappiness GradesHappinessSelf-esteem
Correlation ()
p-value

Collider

  • A variable causally influenced by two or more variables
  • Conditioning on collider does not block path
  • Solution: also condition on a parent

Toy example

  • X =
  • Y =
  • C = X + Y +
Indep. Test Conditional Indep. Test
Null Hypothesis XY XYC
Alternate Hypothesis XY XYC
Correlation ()
p-value

Heritability as causal problem

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Do genomes affect connectomes?

  • Our hypothesis:
    Connectome|GenomeConnectome
    Connectome|GenomeConnectome

  • Alternatively:
    Connectome, GenomeConnectomeGenome
    Connectome, GenomeConnectomeGenome

  • Known as independence testing

  • Test statistic: distance correlation (dcorr)

  • Implication if false: there exists an associational heritability.

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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Do genomes affect connectomes given covariates?

  • Want to test:
    Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
    Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
  • Known as conditional independence test
  • Test statistic: Conditional distance correlation (cdcorr)
  • Implication if false: there exists causal dependence of connectomes on genomes.

Conditional distance correlation

  • Augment distance correlation procedure with third distance matrix.

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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

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.

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  • d(Connectome, Connectome) =

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||

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).

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

Summary

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  • Present a causal model for heritability of connectomes.
  • Leveraged recent advances:
    1. Statistical models for networks, allowing meaningful comparison of connectomes.
    2. Distance and conditional distance correlation as test statistic for causal analysis.
  • Connectomes are dependent on genome, suggesting heritability.

Bridgeford, Eric W., et al. "Batch Effects are Causal Effects: Applications in Human Connectomics." (2021).

Test: Alcohol$\perp\!\!\!\!\perp$Smoking

- $P[i\rightarrow j]$ = $\langle x_i, x_j\rangle$