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Statistical Methods for fMRI Activation and Effective Connectivity Studies

  • Xingfeng Li
  • Damien Coyle
  • Liam Maguire
  • T. Martin McGinnity

Abstract

Functional magnetic resonance imaging (fMRI) is a technique to indirectly measure activity in the brain through the flow of blood. fMRI has been a powerful tool in helping us gain a better understanding of the human brain since it appeared over 20 years ago. However, fMRI poses many challenges for engineers. In particular, to detect and interpret the blood oxygen level-dependent (BOLD) signals on which fMRI is based is a challenge; For example, fMRI activation may be caused by a local neural population (activation detection) or by a distant brain region (effective connectivity). Although many advanced statistical methods have been developed for fMRI data analysis, many problems are still being addressed to maximize the accuracy in activation detection and effective connectivity analysis. This chapter presents general statistical methods for activation detection and effective connectivity analysis in fMRI scans of the human brain. A linear regression model for activation detection is introduced (Sect. 38.2.1), and a detailed statistical inference method for activation detection (Sect. 38.2.2) when applying an autoregression model to correct residual terms of the linear model is presented in Sect. 38.2.3. We adopt a two-stage mixed model to combine different subjects (Sect. 38.3) for second-level data analysis. To estimate the variance for the mixed model, a modified expectation-maximization algorithm is employed. Finally, due to the false positives in the activation map, a Bonferroni-related threshold correction method is developed to control the false positives (Sect. 38.3.3). An fMRI dataset from retinotopic mapping experiments was employed to test the feasibility of the methods for both first- and second-level analysis.

In Sect. 38.4, we present a nonlinear system identification method (NSIM) for effective connectivity study. The mathematical theory of the method is presented in Sect. 38.4.1. An F statistical test is proposed to quantify the magnitude of the relationship based on two-connection and three-connection visual networks (Sect. 38.4.3). To circumvent the limitation of the model overfitting in NSIM, a model selection algorithm is suggested subsequently. In the model selection, we propose a nongreedy search method, e.g., least angle regression for effective connectivity analysis (Sects. 38.4.7 and 38.4.8). Three datasets obtained from standard block and random block designs are used to verify the method, and we outline some research directions and conclude our study in Sect. 38.5.

Keywords

Granger Causality Activation Detection Lateral Geniculate Nucleus Effective Connectivity Hemodynamic Response Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Abbreviations

AIC

Akaike information criterion

AR

auto regressive

ARMA

autoregression and moving average

Ach

achromatic

BOLD

blood oxygen level-dependent

BY

blue–yellow

CBF

cerebral blood flow

DCM

dynamic causal modeling

EM

expectation-maximization

FDR

false discovery rate

FFT

fast Fourier transformation

FWE

familywise error rate

FWHM

full-width at half-maximum

GC

Granger causality

GCM

Granger causality model

GE-EPI

gradient-echo, planar images

GLM

general linear model

GLMM

general linear mixed model

HRF

hemodynamic response function

LARS

least angle regression

LGN

lateral geniculate nucleus

LM

likelihood multiplier

LOO

leave-one-out

LR

likelihood ratio

MAR

multivariate autoregression

MIMO

multiple-output

MINC

medical imaging NetCDF

MNI

4-methoxy-7-nitroindolinyl

MP-RAGE

magnetization prepared rapid gradient echo

MP

maximum parsimony

MR

magnetic resonance

MRI

magnetic resonance imaging

MSE

mean square error

MT

middle temporal cortex

NARMAX

autoregressive moving-average model with exogenous input

NARX

autoregressive with exogenous inputs

NSIM

nonlinear system identification method

PINV

Moore–Penrose pseudoinverse

PRESS

predicted sum of squares

RAGE

receptor for advanced glycation end products

REML

restricted maximum-likelihood

RG

red–green

ROI

region of interest

RSS

residual sum of squares

SC

Schwartzʼs criterion

SVD

singular value decomposition

TE

Tsallis entropy

TR

repetition time

fMRI

functional magnetic resonance imaging

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Copyright information

© Springer-Verlag 2014

Authors and Affiliations

  1. 1.Department of Computing and EngineeringUniversity of UlsterDerryUK
  2. 2.Intelligent System Research CentreUniversity of UlsterDerryUK
  3. 3.Intelligent Systems Research CentreUniversity of UlsterDerryUK
  4. 4.School of Computing and Intelligent Systems, Computer Science Research InstituteUniversity of UlsterDerryUK

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