Numerical Simulation of Higher-Order Nonlinearity of Human Brain Functional Connectivity Using Hypergraph p -Laplacian

Jichao Ma, Chunyu Du, Weifeng Liu and Yanjiang Wang
Additional contact information
Jichao Ma: College of Control Science and Engineering, China University of Petroleum, Qingdao 266580, China
Chunyu Du: College of Control Science and Engineering, China University of Petroleum, Qingdao 266580, China
Weifeng Liu: College of Control Science and Engineering, China University of Petroleum, Qingdao 266580, China
Yanjiang Wang: College of Control Science and Engineering, China University of Petroleum, Qingdao 266580, China

Mathematics, 2021, vol. 9, issue 18, 1-11

Abstract: Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p -Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p -Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p -Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian.

Keywords: brain connectivity; structure–function relation; graph Laplacian; hypergraph Laplacian; p -Laplacian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/18/2345/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/18/2345/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:18:p:2345-:d:640003

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().