Locally Regularized Spatiotemporal Modeling and Model Comparison for Functional MRI

In this work we treat fMRI data analysis as a spatiotemporal system identification problem and address issues of model formulation, estimation, and model comparison. We present a new model that includes a physiologically based hemodynamic response and an empirically derived low-frequency noise model. We introduce an estimation method employing spatial regularization that improves the precision of spatially varying noise estimates. We call the algorithm locally regularized spatiotemporal (LRST) modeling. We develop a new model selection criterion and compare our model to the SPM-GLM method. Our findings suggest that our method offers a better approach to identifying appropriate statistical models for fMRI studies.

[1]  P. Mitra,et al.  Analysis of dynamic brain imaging data. , 1998, Biophysical journal.

[2]  R. Weisskoff,et al.  Effect of temporal autocorrelation due to physiological noise and stimulus paradigm on voxel‐level false‐positive rates in fMRI , 1998, Human brain mapping.

[3]  Emery N. Brown,et al.  A signal estimation approach to functional MRI , 2001, IEEE Transactions on Medical Imaging.

[4]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[5]  R B Buxton,et al.  Probabilistic analysis of functional magnetic resonance imaging data , 1998, Magnetic resonance in medicine.

[6]  V. Solo.  Transfer function order estimation with a H/sub /spl infin// criterion , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[8]  C. W. Groetsch,et al.  Inverse Problems in the Mathematical Sciences , 1993 .

[9]  Michael Unser,et al.  Statistical analysis of functional MRI data in the wavelet domain , 1998, IEEE Transactions on Medical Imaging.

[10]  A. Aldroubi,et al.  Wavelets in Medicine and Biology , 1997 .

[11]  A M Dale,et al.  Estimation and detection of event‐related fMRI signals with temporally correlated noise: A statistically efficient and unbiased approach , 2000, Human brain mapping.

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

[13]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[15]  X Hu,et al.  Retrospective estimation and correction of physiological artifacts in fMRI by direct extraction of physiological activity from MR data , 1996, Magnetic resonance in medicine.

[16]  B. Rosen,et al.  Dynamic functional imaging of relative cerebral blood volume during rat forepaw stimulation , 1998, Magnetic resonance in medicine.

[17]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[18]  Karl J. Friston,et al.  Nonlinear event‐related responses in fMRI , 1998, Magnetic resonance in medicine.

[19]  I. Johnstone,et al.  Wavelet Threshold Estimators for Data with Correlated Noise , 1997 .

[20]  E. Bullmore,et al.  Statistical methods of estimation and inference for functional MR image analysis , 1996, Magnetic resonance in medicine.

[21]  David R. Anderson,et al.  Model Selection and Inference: A Practical Information-Theoretic Approach , 2001 .

[22]  Mark S. Cohen,et al.  Parametric Analysis of fMRI Data Using Linear Systems Methods , 1997, NeuroImage.

[23]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

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

[25]  T A Carpenter,et al.  Colored noise and computational inference in neurophysiological (fMRI) time series analysis: Resampling methods in time and wavelet domains , 2001, Human brain mapping.

[26]  J. R. Baker,et al.  Detection of inferior colliculus activity during auditory stimulation using cardiac gated functional MRI with T1 correction , 1996, NeuroImage.

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

[28]  Karl J. Friston,et al.  Statistical parametric maps in functional imaging: A general linear approach , 1994 .

[29]  V. Solo,et al.  Wavelet signal estimation in coloured noise with extension to transfer function estimation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[30]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[31]  Emery N. Brown,et al.  A signal processing approach to functional MRI for brain mapping , 1997, Proceedings of International Conference on Image Processing.

[32]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[33]  Emery N. Brown,et al.  Regularization for functional MRI models , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[34]  R. S. Hinks,et al.  Time course EPI of human brain function during task activation , 1992, Magnetic resonance in medicine.

[35]  P. J. Jennings,et al.  Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging , 1997, Human brain mapping.

[36]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[37]  Xavier Descombes,et al.  Spatio-temporal fMRI analysis using Markov random fields , 1998, IEEE Transactions on Medical Imaging.

[38]  Christopher R. Genovese.  Statistical Inference in Functional Magnetic Resonance Imaging , 1997 .