A comparative study of one‐level and two‐level semiparametric estimation of hemodynamic response function for fMRI data

Functional magnetic resonance imaging (fMRI) is emerging as a powerful tool for studying the process underlying the working of the many regions of the human brain. The standard tool for analyzing fMRI data is some variant of the linear model, which is restrictive in modeling assumptions. In this paper, we develop a semiparametric approach, based on the cubic smoothing splines, to obtain statistically more efficient estimates of the underlying hemodynamic response function (HRF) associated with fMRI experiments. The hypothesis testing of HRF is conducted to identify the brain regions which are activated when a subject performs a particular task. Furthermore, we compare one-level and two-level semiparametric estimates of HRF in significance tests for detecting the activated brain regions. Our simulation studies demonstrate that the one-level estimates combined with a bias-correction procedure perform best in detecting the activated brain regions. We illustrate this method using a real fMRI data set and compare it with popular methods offered by AFNI and FSL.

[1]  Alan C. Evans,et al.  A General Statistical Analysis for fMRI Data , 2000, NeuroImage.

[2]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited—Again , 1995, NeuroImage.

[3]  R W Cox,et al.  AFNI: software for analysis and visualization of functional magnetic resonance neuroimages. , 1996, Computers and biomedical research, an international journal.

[4]  B. Silverman,et al.  Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[5]  C. Genovese,et al.  Statistical Issues in fMRI for Brain Imaging , 2001 .

[6]  N Lange.  Statistical approaches to human brain mapping by functional magnetic resonance imaging. , 1996, Statistics in medicine.

[7]  Robert J. Boik,et al.  Spectral models for covariance matrices , 2002 .

[8]  Emery N. Brown,et al.  Locally Regularized Spatiotemporal Modeling and Model Comparison for Functional MRI , 2001, NeuroImage.

[9]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[10]  P J Diggle,et al.  Nonparametric estimation of covariance structure in longitudinal data. , 1998, Biometrics.

[11]  B. Douglas Ward,et al.  Deconvolution Analysis of FMRI Time Series Data , 2006 .

[12]  Jianqing Fan,et al.  Generalized likelihood ratio statistics and Wilks phenomenon , 2001 .

[13]  Karl J. Friston,et al.  A unified statistical approach for determining significant signals in images of cerebral activation , 1996, Human brain mapping.

[14]  Stephen M. Smith,et al.  Temporal Autocorrelation in Univariate Linear Modeling of FMRI Data , 2001, NeuroImage.

[15]  G. Glover.  Deconvolution of Impulse Response in Event-Related BOLD fMRI1 , 1999, NeuroImage.

[16]  Chunming Zhang.  Calibrating the Degrees of Freedom for Automatic Data Smoothing and Effective Curve Checking , 2003 .

[17]  Mark W. Woolrich,et al.  Advances in functional and structural MR image analysis and implementation as FSL , 2004, NeuroImage.

[18]  T. W. Anderson.  Asymptotically Efficient Estimation of Covariance Matrices with Linear Structure , 1973 .

[19]  R. Adler,et al.  The Geometry of Random Fields , 1982 .