Mapping Heritability of Large-Scale Brain Networks

Twin Brain Imaging Study via Persistent Homology

Project Description

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.

Matlab Codes

The exact topological inference procedure is packaged into a zipped file: The package will run two simulation studies given in Chung et al. (2017, IPMI). It contains codes for computing probability given in Theorem 2 and 3 as well as codes for computing Kolmogorove-Smirnov (KS) and Gromov-Housdorff (GH) distance for networks. The exact topological inference is limited to integer-valued monotone features without any gap between consecutive integer values.

The sparse hyper-network construction is done via soft-thresholding as explained in Chung et al. (2017). Soft-thresholding based sparse network construction is first explained in Chung et al. (2015, IEEE TMI). The procedure is packaged into a single zipped file:, where a toy example is used as an illustration for how the method works.

The heritability index of the constructed sparse hyper-network at the network level is also given: Start heritability-network.m in the zipped file to construct the dense network with more than 5000o nodes. You need large computer RAM memory to even construct and visualize dense connections.

The exact combinatorial inference generalizes the exact topological inference to any arbitrary monotone features. They don't have to be
consecutive integer values. The method is published in Chung et al. (2018, MICCAI) and MATLAB codes are packaged into a zipped file:

The performance of KS-distance against GH-distance and other matrix norm based distances are given in The package will run multiple simulation studies given in Chung et al. (2017).

Exact topological inference can be done to Betti-1 number (the number of cycles
). The number of cycles can be computed from Betti-0 number. The detail is given in Chung et al. (2018). The MATLAB codes for computing Betti-1 plots and simulations done in the paper is given in

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.


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.

Publication from the Project

[1] 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) (invited talk) Lecture slides, Poster

[2] 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) (accepted for oral)

[3] 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) (accepted for oral) MATLAB arXiv:1509.04771

[4]  Chung, M.K., Lee, H., Solo, V., Davidson, R.J., Pollak, S.D. 2017  Topological distances between brain networks, International Workshop on Connectomics in NeuroImaging, Lecture Notes in Computer Science, in press. (plenary talk) Extended version arXiv:1701.04171 MATLAB

[5] Chung, M.K. 2018 Statistical challenges of big brain network data, Statistics & Probability Letters 136:78-82  (invited paper) arXiv:1709:09645

Chung, M.K., Luo, Z., Adluru, A., Alexander, A.L., Richard, D.J., Goldsmith, H.H. 2018 Heritability of hierarchical structural brain network. IEEE Engineering in Medicine and Biology Society (EMBC), in press

[7] Chung, M.K., Luo, Z., Adluru, A., Alexander, A.L., Richard, D.J., Goldsmith, H.H. 2018 Exact Combinatorial Inference for Brain Images, Medical Image Computing and Computer Assisted Intervention (MICCAI), in press



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.


This is a project lead by professor Moo K. Chung (PI). The project involves twin imaging data collected at the University of Wisconsin-Madison in collaboration with professors Richard Davidson and Hill Goldsmith. The project also involves Tenseness twin imaging data in collaboration with 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.

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 2018-2020. The postdoctoral fellow will work under the supervision of Professor Moo K. Chung. 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 but not necessary. Topics include machine learning, multimodal image integration, persistent homology, sparse learning and graph and network analysis. Additional detail of the project can be found in Please email your CV and a representative paper to Dr. Moo K. Chung (