Tracking the Development of Brain Connectivity in Adolescence through a Fast Bayesian Integrative Method

Aiying Zhang, Bochao Jia, Yu-Ping Wang

Feb 14th, 2018

Adolescence

  • "Impulsive",  "Vulnerable", "Rebellious"
  • Second dramatic brain growth
  • Evolution of modular functional organization
    • sub-network communities
    • the expansion of cognitive and behavioral capabilities

@ Katrina Schwartz, 2015

@ Marisa Silveri, 2016

Graphical Model

Node: Brain region

Edge: Connectivity/ Association

Method: Gaussian Graphical Model

  • Partial correlation: 
    • Measure of direct connectivity
    • The absolute value indicates the strength of the connectivity 

@ istockphoto/mbortolino

 Motivations

  • Clinically:

Track functional brain connectivity development

  • Mathematically:

Jointly estimate multiple  graphical models under distinct but related conditions

 

Material

Data description:

  • Source:

Philadelphia Neurodevelopmental Cohort (PNC)

  • Sample size:

861 individuals, age from 8-22

  • Image type:

Resting- state fMRI

Data acquisition & prepossessing:

  • All data were aquired on the same scanner with the same imaging sequences.

  • Standard preprocessing steps were applied using SPM12

  • Parcellated the rs-fMRI into 264 functionally defined regions using the power atlas

 

Group Stage Age Number of subjects
1 Pre-adolescence 8-11 131
2 Early adolescence 11-14 199
3 Middle adolescence 14-17 244
4 Late adolescence 17-20 236
5 Post-adolescence 20-22 51

Table 1. Group division information

Material

Due to physical and cognitive changes, we divided the subjects into five  distinct stages related to adolescence.

Method

Joint estimation of multiple graphs

  • Based on GGM
  • Take into consideration of time influence 
    • Maximize the similarities
    • Keep distinguished differences
  • Notations:  
    • K = 5 conditions,      = 264 nodes 
    •      ---- the status of the l-th edge under  condition k
    •      ---- the score that indicates       
e_l^k
e_l^k
\psi_l^k
k=1,...,5; l =1,..., p(p-1)/2
p

Fast Bayesian integrative analysis

--- FBIA

Assumption:

  •        ’s are mutually independent
  •  Follow a mixed Gaussian distribution given       :
\psi_l^k
e_l^k
p(\psi_l^k|e_l^k) = \left\{ \begin{array}{lr} N(\mu_{l_0},\sigma_{l_0}^2), & e_l^k =0 \\ N(\mu_{l_1},\sigma_{l_1}^2), & e_l^k =1 \end{array} \right.

Fast Bayesian integrative analysis

--- FBIA

Introduce Bayesian Inference:

posterior \propto prior \times data
\pi(e_l|\psi_l)
\pi(e_l)
\pi(\psi_l|e_l)
e_l = (e_l^1,...,e_l^K), \psi_l = (\psi_l^1,...,\psi_l^K)

Fast Bayesian integrative analysis

--- FBIA

posterior \propto prior \times data
e_l = (e_l^1,...,e_l^K)
\pi(e_l) :
e_l^k \sim Bin(\theta)
\theta \sim Beta(a,b)

In total,         possible configurations of       with posterior probability  

2^K
e_l
\pi_{ld}
d=1,2,...,2^K
\pi(e_l) = \theta^{\sum_{i=1}^{K-1} c_l^i}(1-\theta)^{\sum_{i=1}^K(1-c_l^i)}

Fast Bayesian integrative analysis

--- FBIA

Introduce Stouffer's meta-analysis for integration

\bar{\psi}_{ld}^k = \left\{ \begin{array}{lr} \sum_{\{i:e_{ld}^i=0\}} \omega_{ik}\psi_l^i/\sqrt{\sum_{\{i:e_{ld}^i=0\}}\omega_{ik}^2}, & e_{ld}^k =0 \\ \sum_{\{i:e_{ld}^i=1\}} \omega_{ik}\psi_l^i/\sqrt{\sum_{\{i:e_{ld}^i=1\}}\omega_{ik}^2}, & e_{ld}^k =1 \end{array} \right.

Bayesian integrated 

\psi
\hat{\psi}_l^k = \sum_{d=1}^{2^K} \pi_{ld}\bar{\psi}_{ld}^k

Results

 Figure 1. The visualization of brain connectivity patterns (sagittal views) from pre-adolescence to  post adolescence

Stage 1 Stage 2 Stage 3 Stage 4 Stage 5
Characteristic path length 0.0055 0.0056 0.0059 0.0055 0.0039
Clustering coefficient 0.0835 0.0593 0.0857 0.0735 0.0170
Transitivity 0.1834 0.1592 0.1680 0.1494 0.0583

Table 2. Global network measures for different stages in adolescence

Clustering coefficient & transitivity

  • ​Clustering strength of a network
  • Maximum: middle adolescence (14-17)

Characteristic path length

  • Ability to rapidly combine specialized information from distributed brain regions
  • Remains steady in adolescence and then drops rapidly

 

Results

Figure 2. Brain connectivity development in different functional modules over various adolescence stages. The x-axis stands for each stage and the y-axis is the number of the total connectivity’s in each module.

  • Significant changes:

Default mode

Sensory/somatomotor hand

Fronto-parietal

  • Steady performance:

​Ventral attention

Dorsal attention

Cerebellar

  • Late puberty:

Cingulo-opercular Task Control

Auditory

Fronto-parietal Task Control

Acknowledgement

The work is funded by

  • NIH   R01GM109068, R01MH104680,  R01MH107354
  • NSF   #1539067

 

 

Main References

1. Power, J. D., Fair, D. A., Schlaggar, B. L., & Petersen, S. E. (2010). The development of Human Functional Brain Networks. Neuron, 67(5), 735–748.

2. Satterthwaite TD, Elliott MA, Ruparel K, Loughead J, Prabhakaran K, Calkins ME, Hopson R, Jackson C, Keefe J, Riley M, Mentch FD, Sleiman P, Verma R, Davatzikos C, Hakonarson H, Gur RC,Gur RE (2014a): Neuroimaging of the Philadelphia neurodevelopmental cohort. Neuroimage 86:544–553.

3. Jia, B., Tseng,G., Liang, F. (2017). Fast Bayesian Integrative Analysis for Joint Estimation of Multiple Gaussian Graphical Models.

4. Kim, J., Wozniak, J. R., Mueller, B. A., Shen, X., & Pan, W. (2014). Comparison of Statistical Tests for Group Differences in Brain Functional Networks. NeuroImage, 101, 681–694.

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