### Abstract

Estimating brain wiring patterns is critical to better understand the brain organization and function. Anatomical brain connectivity models axonal pathways, while the functional brain connectivity characterizes the statistical dependencies and correlation between the activities of various brain regions. The synchronization of brain activity can be inferred through the variation of blood-oxygen-level dependent (BOLD) signal from functional MRI (fMRI) and the neural connections can be estimated using tractography from diffusion MRI (dMRI). Functional connections between brain regions are supported by anatomical connections, and the synchronization of brain activities arises through sharing of information in the form of electro-chemical signals on axon pathways. Jointly modeling fMRI and dMRI data may improve the accuracy in constructing anatomical connectivity as well as functional connectivity. Such an approach may lead to novel multimodal biomarkers potentially able to better capture functional and anatomical connectivity variations. We present a novel brain network model which jointly models the dMRI and fMRI data to improve the anatomical connectivity estimation and extract the anatomical subnetworks associated with specific functional modes by constraining the anatomical connections as structural supports to the functional connections. The key idea is similar to a multi-commodity flow optimization problem that minimizes the cost or maximizes the efficiency for flow configuration and simultaneously fulfills the supply-demand constraint for each commodity. In the proposed network, the nodes represent the grey matter (GM) regions providing brain functionality, and the links represent white matter (WM) fiber bundles connecting those regions and delivering information. The commodities can be thought of as the information corresponding to brain activity patterns as obtained for instance by independent component analysis (ICA) of fMRI data. The concept of information flow is introduced and used to model the propagation of information between GM areas through WM fiber bundles. The link capacity, i.e., ability to transfer information, is characterized by the relative strength of fiber bundles, e.g., fiber count gathered from the tractography of dMRI data. The node information demand is considered to be proportional to the correlation between neural activity at various cortical areas involved in a particular functional mode (e.g. visual, motor, etc.). These two properties lead to the link capacity and node demand constraints in the proposed model. Moreover, the information flow of a link cannot exceed the demand from either end node. This is captured by the feasibility constraints. Two different cost functions are considered in the optimization formulation in this paper. The first cost function, the reciprocal of fiber strength represents the unit cost for information passing through the link. In the second cost function, a min-max (minimizing the maximal link load) approach is used to balance the usage of each link. Optimizing the first cost function selects the pathway with strongest fiber strength for information propagation. In the second case, the optimization procedure finds all the possible propagation pathways and allocates the flow proportionally to their strength. Additionally, a penalty term is incorporated with both the cost functions to capture the possible missing and weak anatomical connections. With this set of constraints and the proposed cost functions, solving the network optimization problem recovers missing and weak anatomical connections supported by the functional information and provides the functional-associated anatomical subnetworks. Feasibility is demonstrated using realistic diffusion and functional MRI phantom data. It is shown that the proposed model recovers the maximum number of true connections, with fewest number of false connections when compared with the connectivity derived from a joint probabilistic model using the expectation-maximization (EM) algorithm presented in a prior work. We also apply the proposed method to data provided by the Human Connectome Project (HCP).

Original language | English (US) |
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Title of host publication | Medical Imaging 2015 |

Subtitle of host publication | Image Processing |

Editors | Martin A. Styner, Sebastien Ourselin |

Publisher | SPIE |

ISBN (Electronic) | 9781628415032 |

DOIs | |

State | Published - Jan 1 2015 |

Event | Medical Imaging 2015: Image Processing - Orlando, United States Duration: Feb 24 2015 → Feb 26 2015 |

### Publication series

Name | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |
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Volume | 9413 |

ISSN (Print) | 1605-7422 |

### Other

Other | Medical Imaging 2015: Image Processing |
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Country | United States |

City | Orlando |

Period | 2/24/15 → 2/26/15 |

### Fingerprint

### Keywords

- Brain connectivity
- diusion MRI
- functional MRI
- information flow
- network
- tractography

### Cite this

*Medical Imaging 2015: Image Processing*[941321] (Progress in Biomedical Optics and Imaging - Proceedings of SPIE; Vol. 9413). SPIE. https://doi.org/10.1117/12.2082346

**Joint brain connectivity estimation from diffusion and functional MRI data.** / Chu, Shu Hsien; Lenglet, Christophe; Parhi, Keshab K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Medical Imaging 2015: Image Processing.*, 941321, Progress in Biomedical Optics and Imaging - Proceedings of SPIE, vol. 9413, SPIE, Medical Imaging 2015: Image Processing, Orlando, United States, 2/24/15. https://doi.org/10.1117/12.2082346

}

TY - GEN

T1 - Joint brain connectivity estimation from diffusion and functional MRI data

AU - Chu, Shu Hsien

AU - Lenglet, Christophe

AU - Parhi, Keshab K.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Estimating brain wiring patterns is critical to better understand the brain organization and function. Anatomical brain connectivity models axonal pathways, while the functional brain connectivity characterizes the statistical dependencies and correlation between the activities of various brain regions. The synchronization of brain activity can be inferred through the variation of blood-oxygen-level dependent (BOLD) signal from functional MRI (fMRI) and the neural connections can be estimated using tractography from diffusion MRI (dMRI). Functional connections between brain regions are supported by anatomical connections, and the synchronization of brain activities arises through sharing of information in the form of electro-chemical signals on axon pathways. Jointly modeling fMRI and dMRI data may improve the accuracy in constructing anatomical connectivity as well as functional connectivity. Such an approach may lead to novel multimodal biomarkers potentially able to better capture functional and anatomical connectivity variations. We present a novel brain network model which jointly models the dMRI and fMRI data to improve the anatomical connectivity estimation and extract the anatomical subnetworks associated with specific functional modes by constraining the anatomical connections as structural supports to the functional connections. The key idea is similar to a multi-commodity flow optimization problem that minimizes the cost or maximizes the efficiency for flow configuration and simultaneously fulfills the supply-demand constraint for each commodity. In the proposed network, the nodes represent the grey matter (GM) regions providing brain functionality, and the links represent white matter (WM) fiber bundles connecting those regions and delivering information. The commodities can be thought of as the information corresponding to brain activity patterns as obtained for instance by independent component analysis (ICA) of fMRI data. The concept of information flow is introduced and used to model the propagation of information between GM areas through WM fiber bundles. The link capacity, i.e., ability to transfer information, is characterized by the relative strength of fiber bundles, e.g., fiber count gathered from the tractography of dMRI data. The node information demand is considered to be proportional to the correlation between neural activity at various cortical areas involved in a particular functional mode (e.g. visual, motor, etc.). These two properties lead to the link capacity and node demand constraints in the proposed model. Moreover, the information flow of a link cannot exceed the demand from either end node. This is captured by the feasibility constraints. Two different cost functions are considered in the optimization formulation in this paper. The first cost function, the reciprocal of fiber strength represents the unit cost for information passing through the link. In the second cost function, a min-max (minimizing the maximal link load) approach is used to balance the usage of each link. Optimizing the first cost function selects the pathway with strongest fiber strength for information propagation. In the second case, the optimization procedure finds all the possible propagation pathways and allocates the flow proportionally to their strength. Additionally, a penalty term is incorporated with both the cost functions to capture the possible missing and weak anatomical connections. With this set of constraints and the proposed cost functions, solving the network optimization problem recovers missing and weak anatomical connections supported by the functional information and provides the functional-associated anatomical subnetworks. Feasibility is demonstrated using realistic diffusion and functional MRI phantom data. It is shown that the proposed model recovers the maximum number of true connections, with fewest number of false connections when compared with the connectivity derived from a joint probabilistic model using the expectation-maximization (EM) algorithm presented in a prior work. We also apply the proposed method to data provided by the Human Connectome Project (HCP).

AB - Estimating brain wiring patterns is critical to better understand the brain organization and function. Anatomical brain connectivity models axonal pathways, while the functional brain connectivity characterizes the statistical dependencies and correlation between the activities of various brain regions. The synchronization of brain activity can be inferred through the variation of blood-oxygen-level dependent (BOLD) signal from functional MRI (fMRI) and the neural connections can be estimated using tractography from diffusion MRI (dMRI). Functional connections between brain regions are supported by anatomical connections, and the synchronization of brain activities arises through sharing of information in the form of electro-chemical signals on axon pathways. Jointly modeling fMRI and dMRI data may improve the accuracy in constructing anatomical connectivity as well as functional connectivity. Such an approach may lead to novel multimodal biomarkers potentially able to better capture functional and anatomical connectivity variations. We present a novel brain network model which jointly models the dMRI and fMRI data to improve the anatomical connectivity estimation and extract the anatomical subnetworks associated with specific functional modes by constraining the anatomical connections as structural supports to the functional connections. The key idea is similar to a multi-commodity flow optimization problem that minimizes the cost or maximizes the efficiency for flow configuration and simultaneously fulfills the supply-demand constraint for each commodity. In the proposed network, the nodes represent the grey matter (GM) regions providing brain functionality, and the links represent white matter (WM) fiber bundles connecting those regions and delivering information. The commodities can be thought of as the information corresponding to brain activity patterns as obtained for instance by independent component analysis (ICA) of fMRI data. The concept of information flow is introduced and used to model the propagation of information between GM areas through WM fiber bundles. The link capacity, i.e., ability to transfer information, is characterized by the relative strength of fiber bundles, e.g., fiber count gathered from the tractography of dMRI data. The node information demand is considered to be proportional to the correlation between neural activity at various cortical areas involved in a particular functional mode (e.g. visual, motor, etc.). These two properties lead to the link capacity and node demand constraints in the proposed model. Moreover, the information flow of a link cannot exceed the demand from either end node. This is captured by the feasibility constraints. Two different cost functions are considered in the optimization formulation in this paper. The first cost function, the reciprocal of fiber strength represents the unit cost for information passing through the link. In the second cost function, a min-max (minimizing the maximal link load) approach is used to balance the usage of each link. Optimizing the first cost function selects the pathway with strongest fiber strength for information propagation. In the second case, the optimization procedure finds all the possible propagation pathways and allocates the flow proportionally to their strength. Additionally, a penalty term is incorporated with both the cost functions to capture the possible missing and weak anatomical connections. With this set of constraints and the proposed cost functions, solving the network optimization problem recovers missing and weak anatomical connections supported by the functional information and provides the functional-associated anatomical subnetworks. Feasibility is demonstrated using realistic diffusion and functional MRI phantom data. It is shown that the proposed model recovers the maximum number of true connections, with fewest number of false connections when compared with the connectivity derived from a joint probabilistic model using the expectation-maximization (EM) algorithm presented in a prior work. We also apply the proposed method to data provided by the Human Connectome Project (HCP).

KW - Brain connectivity

KW - diusion MRI

KW - functional MRI

KW - information flow

KW - network

KW - tractography

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U2 - 10.1117/12.2082346

DO - 10.1117/12.2082346

M3 - Conference contribution

AN - SCOPUS:84943374257

T3 - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

BT - Medical Imaging 2015

A2 - Styner, Martin A.

A2 - Ourselin, Sebastien

PB - SPIE

ER -