MULTISCALE ADAPTIVE SMOOTHING MODELS FOR THE HEMODYNAMIC RESPONSE FUNCTION IN FMRI.

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and temporal information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-art methods, such as the smooth finite impulse response (sFIR) model.

[1]  L. Shah,et al.  Functional magnetic resonance imaging. , 2010, Seminars in roentgenology.

[2]  D. Donoho.  CART AND BEST-ORTHO-BASIS: A CONNECTION' , 1997 .

[3]  Ravi S. Menon,et al.  Motor Area Activity During Mental Rotation Studied by Time-Resolved Single-Trial fMRI , 2000, Journal of Cognitive Neuroscience.

[4]  Thomas E. Nichols,et al.  Nonparametric permutation tests for functional neuroimaging: A primer with examples , 2002, Human brain mapping.

[5]  D. Brillinger.  Time Series: Data Analysis and Theory. , 1981 .

[6]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[7]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

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

[9]  Tao Yu,et al.  MULTIPLE TESTING VIA FDRL FOR LARGE SCALE IMAGING DATA , 2011 .

[10]  Karsten Tabelow,et al.  Diffusion tensor imaging: Structural adaptive smoothing , 2008, NeuroImage.

[11]  M. Lindquist,et al.  RESIDUAL ANALYSIS FOR DETECTING MIS-MODELING IN fMRI , 2008 .

[12]  B. Ripley,et al.  A new statistical approach to detecting significant activation in functional MRI , 2000, NeuroImage.

[13]  Ron Borowsky,et al.  Inferring neural activity from BOLD signals through nonlinear optimization , 2007, NeuroImage.

[14]  D. Heeger,et al.  Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1 , 1996, The Journal of Neuroscience.

[15]  Kevin Murphy,et al.  The impact of global signal regression on resting state correlations: Are anti-correlated networks introduced? , 2009, NeuroImage.

[16]  C. Mountford.  Non-linear Fourier time series analysis for human brain mapping by functional magnetic resonance imaging - Discussion , 1997 .

[17]  M. Lindquist,et al.  Validity and power in hemodynamic response modeling: A comparison study and a new approach , 2007, Human brain mapping.

[18]  David R. Brillinger,et al.  Cross-Spectral Analysis of Processes with Stationary Increments Including the Stationary $G/G/\infty$ Queue , 1974 .

[19]  Karl J. Friston,et al.  Statistical Parametric Mapping: The Analysis of Functional Brain Images , 2007 .

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

[21]  Martin A. Lindquist,et al.  Adaptive spatial smoothing of fMRI images , 2010 .

[22]  P. Bandettini,et al.  Understanding neural system dynamics through task modulation and measurement of functional MRI amplitude, latency, and width , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Christopher R. Genovese,et al.  A Bayesian Time-Course Model for Functional Magnetic Resonance Imaging Data , 2000 .

[24]  R. Turner,et al.  Detecting Latency Differences in Event-Related BOLD Responses: Application to Words versus Nonwords and Initial versus Repeated Face Presentations , 2002, NeuroImage.

[25]  조재현.  Goodness of fit tests for parametric regression models , 2004 .

[26]  K. Worsley,et al.  Unified univariate and multivariate random field theory , 2004, NeuroImage.

[27]  Karsten Tabelow,et al.  Analyzing fMRI experiments with structural adaptive smoothing procedures , 2006, NeuroImage.

[28]  L. Fahrmeir,et al.  Bayesian Modeling of the Hemodynamic Response Function in BOLD fMRI , 2001, NeuroImage.

[29]  E. Mammen,et al.  Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors , 1997 .

[30]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[31]  Martin A. Lindquist,et al.  Modeling the hemodynamic response function in fMRI: Efficiency, bias and mis-modeling , 2009, NeuroImage.

[32]  Mark W. Woolrich,et al.  Constrained linear basis sets for HRF modelling using Variational Bayes , 2004, NeuroImage.

[33]  Ravi S. Menon,et al.  Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Dinggang Shen,et al.  Multiscale adaptive regression models for neuroimaging data , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[35]  Hans Knutsson,et al.  Adaptive analysis of fMRI data , 2003, NeuroImage.

[36]  Jianqing Fan,et al.  Goodness-of-Fit Tests for Parametric Regression Models , 2001 .

[37]  R. Goebel,et al.  Tracking cognitive processes with functional MRI mental chronometry , 2003, Current Opinion in Neurobiology.

[38]  C M Zhang,et al.  A comparative study of one‐level and two‐level semiparametric estimation of hemodynamic response function for fMRI data , 2007, Statistics in medicine.

[39]  H. Bohman,et al.  Approximate fourier analysis of distribution functions , 1961 .

[40]  Yul-Wan Sung,et al.  Functional magnetic resonance imaging , 2004, Scholarpedia.

[41]  Eric R. Ziegel,et al.  Time Series: Theory and Methods (2nd ed,) , 2012 .

[42]  Paul J. Laurienti,et al.  The impact of temporal regularization on estimates of the BOLD hemodynamic response function: A comparative analysis , 2008, NeuroImage.

[43]  Z. Q. John Lu,et al.  Nonlinear Time Series: Nonparametric and Parametric Methods , 2004, Technometrics.

[44]  N. Wermuth,et al.  Nonlinear Time Series: Nonparametric and Parametric Methods , 2005 .

[45]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[46]  S. Petersen,et al.  Characterizing the Hemodynamic Response: Effects of Presentation Rate, Sampling Procedure, and the Possibility of Ordering Brain Activity Based on Relative Timing , 2000, NeuroImage.

[47]  M. Corbetta,et al.  Separating Processes within a Trial in Event-Related Functional MRI II. Analysis , 2001, NeuroImage.

[48]  J. Polzehl,et al.  Adaptive weights smoothing with applications to image restoration , 1998 .

[49]  M. D’Esposito,et al.  The variability of human BOLD hemodynamic responses , 1998, NeuroImage.

[50]  Scott L. Zeger,et al.  Non‐linear Fourier Time Series Analysis for Human Brain Mapping by Functional Magnetic Resonance Imaging , 1997 .

[51]  Hal S. Stern,et al.  A Bayesian Mixture Approach to Modeling Spatial Activation Patterns in Multisite fMRI Data , 2010, IEEE Transactions on Medical Imaging.

[52]  竹安 数博,et al.  Time series analysis and its applications , 2007 .

[53]  J. Polzehl,et al.  Propagation-Separation Approach for Local Likelihood Estimation , 2006 .

[54]  F. Bowman,et al.  Spatiotemporal Models for Region of Interest Analyses of Functional Neuroimaging Data , 2007 .

[55]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .