Mapping Heritability of Large-Scale Brain Networks

Multimodal Twin Brain Imaging Study via Persistent Homology


This is a project lead by professor Moo K. Chung (PI), It's a team effort with other professors Paul Rathouz of University of Wisconsin-Madison, David Zald of Vanderbilt University and Benjamin Lahey of University of Chicago on Tenseness twin imaging data. It also involves twin imaging data collected at the University of Wisconsin-Madison in collaboration with professors Richard Davidson and Hill Goldsmith.

Project Description

Figure 1
Figure 1. The schematic of hyper-network construction on twin image vectors. The second pair of images y is modeled as a linear combination of the first pair of images x. The estimated weights of the linear combination gives the hyper-edge weights. See [3] for detail.

The twin study design offers a very effective way of determining the heritability of the human brain. The difference in variability between monozygotic and same-sex dizygotic twins can be used to determine the heritability of an imaging-based phenotype at each voxel. Except for few well known neural circuits, the extent to which heritability influences the brain network is not well established. Compared to many existing studies on univariate phenotypes in brain imaging, there are not many studies on the heritability of brain networks. Measures of network topology and features may be worth investigating as intermediate phenotypes or endophenotypes. However, the existing brain network analysis has not yet been adapted for this purpose. Determining the extent of heritability of brain networks with large number of nodes is the first necessary prerequisite for identifying network-based endophenotypes. This requires constructing the large-scale brain networks by taking every voxel in the brain as network nodes with at least a billion connections, which is a serious computational bottleneck. We propose to map the heritability of large-scale brain networks by taking every voxel in images as network nodes using persistent homology and sparse network models (Figure 1,2). By exploiting the topological structure of data, we can show that it is possible to bypass the bottleneck and learn networks with billion connections without much computational resource such as cluster computing.

Figure 2. Estimated hyper-networks at three different sparse parameters 0.5, 0.7 and 0.9 for MZ- and DZ-twins. As the sparse parameter increases, we have more sparse hyper-connections. HGI measures heritability index at the nodes and along the hyper-edges. See [3] for detail.


[1] Chung, M.K., Vilalta, V.G., Rathouz, P.J., Lahey, B.B., Zald, D.H. 2016 Mapping heritability of large-scale brain networks with a billion connections via persistent homology. arXiv:1509.04771

[2] Chung, M.K., Vilalta, V.G., Rathouz, P.J., Lahey, B.B., Zald, D.H. 2016 Heritability of large-scale functional brain networks. Organization for Human Brain Mapping (OHBM). Lecture slides, Poster

[3] Chung, M.K., Vilalta, V.G., Rathouz, P.J., Lahey, B.B., Zald, D.H. 2017 Hyper network analysis on paired images. International Society of Magnetic Resonance in Medicine (ISMRM) lecture slides

Chung, M.K., Vilalta, V.G., Lee, H., Rathouz, P.J., Lahey, B.B., Zald, D.H. 2017 Exact topological inference for paired brain networks via persistent homology. Information Processing in Medical Imaging (IPMI). lecture slides

Matlab Codes

The MATLAB codes for running two simulation studies in Chung et al. 2017 IPMI are available. Click the link above. It contains codes for computing probability given in Theorem 2 and 3 as well as codes for computing KS-like test statistic and GH-distance.

Postdoctoral Position

Postdoctoral positions are available for multimodal twin brain network study involving DTI, MRI and fMRI at the University of Wisconsin-Madison for years 2017-2020. The postdoctoral fellow will work with Professors Moo K. Chung, Paul J. Rathouz and David H. Zald at Vanderbilt University and Benjamin B. Lahey at the University of Chicago. The position is funded by NIH Brain Initiative. Candidates should have received or expected to receive PhD degree or equivalent in psychology, neuroscience, CS, statistics, mathematics, EE, medical physics, biomedical imaging or related areas. Previous neuroimaging research experience is a plus. Topics include multimodal image integration, persistent homology, sparse learning and brain network analysis. Additional detail of the project can be found in Please email your CV and a representative paper to Dr. Moo K. Chung (


The project is funded by NIH grant EB022856 (PI: Moo K. Chung) as a part of Brain Initiative: Theories, Models and Methods for Analysis of Complex Data from the Brain.