### 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 | |

State | Published - Apr 2020 |

### Fingerprint

### 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

**Bayesian inference of a directional brain network model for intracranial EEG data.** / Zhang, Tingting; Sun, Yinge; Li, Huazhang; Yan, Guofen; Tanabe, Seiji; Miao, Ruizhong; Wang, Yaotian; Caffo, Brian S.; Quigg, Mark S.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 144, 106847. https://doi.org/10.1016/j.csda.2019.106847

}

TY - JOUR

T1 - Bayesian inference of a directional brain network model for intracranial EEG data

AU - Zhang, Tingting

AU - Sun, Yinge

AU - Li, Huazhang

AU - Yan, Guofen

AU - Tanabe, Seiji

AU - Miao, Ruizhong

AU - Wang, Yaotian

AU - Caffo, Brian S.

AU - Quigg, Mark S.

PY - 2020/4

Y1 - 2020/4

N2 - 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.

AB - 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.

KW - Bayesian methods

KW - Brain networks

KW - Dynamic system

KW - Ordinary differential equation

KW - Time series

UR - http://www.scopus.com/inward/record.url?scp=85075799734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075799734&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2019.106847

DO - 10.1016/j.csda.2019.106847

M3 - Article

AN - SCOPUS:85075799734

VL - 144

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

M1 - 106847

ER -