Recent developments in the complex networks analysis, based largely on graph theory, have been used to study the brain network organization. The brain is a complex system that can be represented by a graph. A graph is a mathematical representation which can be useful to study the connectivity of the brain. Nodes in the brain can be identified dividing its volume in regions of interest and links can be identified calculating a measure of dependence between pairs of regions whose activation signal, measured by functional magnetic resonance imaging (fMRI) techniques, represents the strength of the connec-tion between regions. A graph can be synthesized by the so-called adjacency matrix, which, in its simplest form, is an undirected, binary, and symmetric matrix, whose en-tries are set to one if a link exists between a pair of brain areas and zero otherwise. The adjacency matrix is particularly useful because allows the calculation of several measures which summarize global and local character-istics of functional brain connectivity, such as centrality, e ciency, density and small worldness property. In this work, we consider the global measures, such as the clustering coe cient, the characteristic path length and the global e ciency, and the local measures, such as centrality measures and local e ciency, in order to represent global and local dynam-ics and changes between networks. This is achieved by studying with resting state (rs) fMRI data of healthy subjects and patients with neurodegenerative diseases. Furthermore we illustrate an original methodology to construct the adjacency matrix. Its entries, containing the information about the ex-istence of links, are identified by testing the correlation between the time series that characterized the dynamic behavior of the nodes. This involves the problem of multiple comparisons in order to control the error rates. The method based on the estimation of positive false discovery rate (pFDR) has been used. A similar measure involving false negatives (type II errors), called the positive false nondiscovery rate (pFNR) is then considered, proposing new point and interval estimators for pFNR and a method for balancing the two types of error. This approach is demonstrated using both simulations and fMRI data, and providing nite sample as well as large sample results for pFDR and pFNR estimators. Besides a ranking of the most central nodes in the networks is proposed using q-values, the pFDR analog of the p-values. The di erences on the inter-regional connectivity between cases and controls are studied. Finally network models are discussed. In order to gain deeper insights into the complex neurobiological interaction, exponential random graph models (ERGMs) are applied to assess several network properties simultaneously and to compare case/control brain networks.

(2013). Statistical analysis of brain network. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2013).

Statistical analysis of brain network

SALA, SARA
2013

Abstract

Recent developments in the complex networks analysis, based largely on graph theory, have been used to study the brain network organization. The brain is a complex system that can be represented by a graph. A graph is a mathematical representation which can be useful to study the connectivity of the brain. Nodes in the brain can be identified dividing its volume in regions of interest and links can be identified calculating a measure of dependence between pairs of regions whose activation signal, measured by functional magnetic resonance imaging (fMRI) techniques, represents the strength of the connec-tion between regions. A graph can be synthesized by the so-called adjacency matrix, which, in its simplest form, is an undirected, binary, and symmetric matrix, whose en-tries are set to one if a link exists between a pair of brain areas and zero otherwise. The adjacency matrix is particularly useful because allows the calculation of several measures which summarize global and local character-istics of functional brain connectivity, such as centrality, e ciency, density and small worldness property. In this work, we consider the global measures, such as the clustering coe cient, the characteristic path length and the global e ciency, and the local measures, such as centrality measures and local e ciency, in order to represent global and local dynam-ics and changes between networks. This is achieved by studying with resting state (rs) fMRI data of healthy subjects and patients with neurodegenerative diseases. Furthermore we illustrate an original methodology to construct the adjacency matrix. Its entries, containing the information about the ex-istence of links, are identified by testing the correlation between the time series that characterized the dynamic behavior of the nodes. This involves the problem of multiple comparisons in order to control the error rates. The method based on the estimation of positive false discovery rate (pFDR) has been used. A similar measure involving false negatives (type II errors), called the positive false nondiscovery rate (pFNR) is then considered, proposing new point and interval estimators for pFNR and a method for balancing the two types of error. This approach is demonstrated using both simulations and fMRI data, and providing nite sample as well as large sample results for pFDR and pFNR estimators. Besides a ranking of the most central nodes in the networks is proposed using q-values, the pFDR analog of the p-values. The di erences on the inter-regional connectivity between cases and controls are studied. Finally network models are discussed. In order to gain deeper insights into the complex neurobiological interaction, exponential random graph models (ERGMs) are applied to assess several network properties simultaneously and to compare case/control brain networks.
QUATTO, PIERO
False Discovery Rate; False Nondiscovery Rate; Brain functional Networks; Resting State Functional Magnetic Resonance Imaging
SECS-S/01 - STATISTICA
English
28-gen-2013
STATISTICA - 11R
25
2011/2012
open
(2013). Statistical analysis of brain network. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2013).
File in questo prodotto:
File Dimensione Formato  
Phd_unimib_734382.pdf

Accesso Aperto

Tipologia di allegato: Doctoral thesis
Dimensione 1.58 MB
Formato Adobe PDF
1.58 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/43723
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
Social impact