### Abstract

The human brain is a network system in which brain regions, as network nodes, constantly interact with each other. The directional effect exerted by one brain component on another is referred to as directional connectivity. Since the brain is also a continuous time dynamic system, it is natural to use ordinary differential equations (ODEs) to model directional connections among brain regions. The authors propose a high-dimensional ODE model to explore directional connectivity among many small brain regions recorded by intracranial EEG (iEEG). The new ODE model, motivated by the physical mechanism of the damped harmonic oscillator, is effective for approximating neural oscillation, a rhythmic or repetitive neural activity involved in many important brain functions. To produce scientifically meaningful network results, a cluster structure is assumed for the ODE model parameters that quantify directional connectivity among regions. The cluster structure is in line with the functional specialization of the human brain; the brain areas specialized in the same function tend to be in the same cluster. Two Bayesian methods are developed to estimate the model parameters of the proposed ODE model and to identify clusters of strongly connected brain regions. The proposed ODE model and Bayesian method are applied to iEEG data collected from a patient with medically intractable epilepsy and used to examine the patient's brain networks before the seizure onset.

Original language | English (US) |
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Article number | 106847 |

Journal | Computational Statistics and Data Analysis |

Volume | 144 |

DOIs | |

Publication status | Published - Apr 2020 |

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### Keywords

- Bayesian methods
- Brain networks
- Dynamic system
- Ordinary differential equation
- Time series

### ASJC Scopus subject areas

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*144*, [106847]. https://doi.org/10.1016/j.csda.2019.106847