Analysis of fMRI Single Subject Data in the Fourier Domain Acquired Using a Multiple Input Stimulus Experimental Design

Daniel Rio, Robert Rawlings, Lawrence Woltz, Jodi Gilman, Daniel Hommer

Laboratory of Neuroimaging and Genetics, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, USA.
NIAAA, Columbia, USA; 3Synergy Research Inc., Monrovia, USA.
Section of Brain Electrophysiology and Imaging, LCTS, NIAAA, National Institutes of Health, Bethesda, USA.
Synergy Research Inc., Monrovia, USA.

DOI: 10.4236/jsip.2012.34060                

Abstract

Analysis of functional MRI (fMRI) blood oxygenation level dependent (BOLD) data is typically carried out in the time domain where the data has a high temporal correlation. These analyses usually employ parametric models of the hemodynamic response function (HRF) where either pre-whitening of the data is attempted or autoregressive (AR) models are employed to model the noise. Statistical analysis then proceeds via regression of the convolution of the HRF with the input stimuli. This approach has limitations when considering that the time series collected are embedded in a brain image in which the AR model order may vary and pre-whitening techniques may be insufficient for handling faster sampling times. However fMRI data can be analyzed in the Fourier domain where the assumptions made as to the structure of the noise can be less restrictive and hypothesis tests are straightforward for single subject analysis, especially useful in a clinical setting. This allows for experiments that can have both fast temporal sampling and event-related designs where stimuli can be closely spaced in time. Equally important, statistical analysis in the Fourier domain focuses on hypothesis tests based on nonparametric estimates of the hemodynamic transfer function (HRF in the frequency domain). This is especially important for experimental designs involving multiple states (drug or stimulus induced) that may alter the form of the response function. In this context a univariate general linear model in the Fourier domain has been applied to analyze BOLD data sampled at a rate of 400 ms from an experiment that used a two-way ANOVA design for the deterministic stimulus inputs with inter-stimulus time intervals chosen from Poisson distributions of equal intensity.

Keywords

fMRI (BOLD); Time Series Analysis; Single Subject Analysis; Fourier Domain; Statistical Analysis; Complex General Linear Model; Alcoholism Research

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Ogawa, T. M. Lee, A. S. Nayak and P. Glynn, “Oxygenation-Sensitive Contrast in Magnetic Resonance Image of Rodent Brain at High Magnetic Fields,” Magnetic Resonance in Medicine, Vol. 14, No. 1, 1990, pp. 68-78. Hdoi:10.1002/mrm.1910140108
[2]	S. Ogawa, D. W. Tank. R. Menon, J. M. Ellermann, S. G. Kim, H. Merkle and K. Ugurbil, “Intrinsic Signal Changes Accompanying Sensory Stimulation: Functional Brain Mapping with Magnetic Resonance Imaging,” Proceedings of the National Academy of Sciences, Vol. 89, No. 13, 1992, pp. 5951-5955. Hdoi:10.1073/pnas.89.13.5951
[3]	K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen and R. Turner, “Dynamic Magnetic Resonance Imaging of Human Brain Activity during Primary Sensory Stimulation,” Proceedings of the National Academy of Sciences, Vol. 89, No. 12, 1992, pp. 5675-5679. Hdoi:10.1073/pnas.89.12.5675
[4]	K. Murphy, J. Bodurka and P. A. Bandettini, “How Long to Scan? The Relationship between fMRI Temporal Signal to Noise Ratio and Necessary Scan Duration,” NeuroImage, Vol. 34, No. 2, 2007, pp. 565-574. Hdoi:10.1016/j.neuroimage.2006.09.032
[5]	M. W. Woolrich, B. D. Ripley, J. M. Brady and S. M. Smith, “Temporal Autocorrelation in Univariate Linear Modeling of FMRI Data,” NeuroImage, Vol. 14, No. 6, 2001, pp. 1370-1386. Hdoi:10.1006/nimg.2001.0931
[6]	K. J. Worsley and K. J. Friston, “Analysis of Time-Series Revisited—Again,” NeuroImage, Vol. 2, No. 3, 1995, pp. 173-181. Hdoi:10.1006/nimg.1995.1023
[7]	K. J. Friston, A. P. Holmes, K. J. Worsley, J. P. Poline, C. D. Frith and R. S. J. Frackowiak, “Statistical Parametric Maps in Functional Imaging: A General Linear Approach,” Human Brain Mapping, Vol. 2, No. 4, 1995, pp. 189-210. Hdoi:10.1002/hbm.460020402
[8]	R. W. Cox, “AFNI: Software for Analysis and Visualization of Functional Magnetic Resonance Neuroimages,” Computers and Biomedical Research, Vol. 29, No. 3, 1996, pp. 162-173. Hdoi:10.1006/cbmr.1996.0014
[9]	K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton and J. Ashburner, “Classical and Bayesian Inference in Neuroimaging: Theory,” NeuroImage, Vol. 16, No. 2, 2002, pp. 465-483. Hdoi:10.1006/nimg.2002.1090
[10]	K. J. Worsley, C. H. Liao, J. Aston, V. Petre, G. H. Duncan, F. Morales and A. C. Evans, “A General Statistical Analysis for fMRI Data,” NeuroImage, Vol. 15, No. 1, 2002, pp. 11-15. Hdoi:10.1006/nimg.2001.0933
[11]	C. F. Beckmann, M. Jenkinson and S. M. Smith, “General Multilevel Linear Modeling for Group Analysis in fMRI,” NeuroImage, Vol. 20, No. 2, 2003, pp. 1052-1063. Hdoi:10.1016/S1053-8119(03)00435-X
[12]	S. M. Smith, M. Jenkinson, M. W. Woolrich, C. F. Beckmann, T. E. J. Behrens, H. Johansen-Berg, P. R. Bannister, M. De Luca, I. Drobnjak, D. E. Flitney, R. K. Niazy, J. Saunders, J. Vickers, Y. Zhang, N. De Stefano, J. M. Brady and P. M. Matthews, “Advances in Functional and Structural MR Image Analysis and Implementation as FSL,” NeuroImage, Vol. 23, 2004, pp. 208-219. Hdoi:10.1016/j.neuroimage.2004.07.051
[13]	H. Zhang, W. L. Luo and T. E. Nichols, “Diagnosis of Single-Subject and Group fMRI Data with SPMd,” Human Brain Mapping, Vol. 27, No. 5, 2006, pp. 442-451. Hdoi:10.1002/hbm.20253
[14]	T. E. Lund, K. H. Madsen, K. Sidaros, W. Luo and T. E. Nichols, “Non-White Noise in fMRI: Does Modelling Have an Impact?” NeuroImage, Vol. 18, No. 7, 2006, pp. 54-66. Hdoi:10.1016/j.neuroimage.2005.07.005
[15]	J. L. Marchini and S. M. Smith, “On Bias in the Estimation of Autocorrelations for fMRI Voxel Time-Series Analysis,” NeuroImage, Vol. 18, No. 1, 2003, pp. 83-90. Hdoi:10.1006/nimg.2002.1321
[16]	B. Lenoski, L. C. Baxter, L. J. Karam, J. Maisog and J. Debbins, “On the Performance of Autocorrelation Estimation Algorithms for fMRI Analysis,” IEEE Journal of Selected Topics in Signal Processing, Vol. 2, No. 6, 2008, pp. 828-838. Hdoi:10.1109/JSTSP.2008.2007819
[17]	K. J. Friston, K. E. Stephan, T. E. Lund, A. Morcom and S. Kiebela, “Mixed-Effects and fMRI Studies,” NeuroImage, Vol. 24, No. 1, 2005, pp. 244-252. Hdoi:10.1016/j.neuroimage.2004.08.055
[18]	M. A. Lindquist and T. D. Wager, “Validity and Power in Hemodynamic Response Modeling: A Comparison Study and a New Approach,” Human Brain Mapping, Vol. 28, No. 8, 2007, pp. 764-784. Hdoi:10.1002/hbm.20310
[19]	M. A. Lindquist, J. M. Loh, L.Y. Atlas and T. D. Wager, “Modeling the Hemodynamic Response Function in fMRI: Efficiency, Bias and Mis-Modeling,” NeuroImage, Vol. 45, 2009, pp. 187-198. Hdoi:10.1016/j.neuroimage.2008.10.065
[20]	M. Luchtmann, K. Jachau, C. Tempelmann and J. Bernarding, “Alcohol Induced Region-Dependent Alterations of Hemodynamic Response: Implications for the Statistical Interpretation of Pharmacological fMRI Studies,” Experimental Brain Research, Vol. 204, No. 1, 2010, pp. 1-10. Hdoi:10.1007/s00221-010-2277-4
[21]	J. Tanabe, D. Miller, J. Tregellas, R. Freedman and F. G. Meyer, “Comparison of Detrending Methods for Optimal fMRI Preprocessing,” NeuroImage, Vol. 15, No. 4, 2002, pp. 902-907. Hdoi:10.1006/nimg.2002.1053
[22]	T. Johnstone, K. S. O. Walsh, L. L. Greischar, A. L. Alexander, A. S. Fox, R. J. Davidson and T. R. Oakes, “Motion Correction and the Use of Motion Covariates in Multiple-Subject fMRI Analysis,” Human Brain Mapping, Vol. 27, No. 10, 2006, pp. 779-788. Hdoi:10.1002/hbm.20219
[23]	G. H. Glover, T. Li and D. Ress, “Image-Based Method for Retrospective Correction of Physiological Motion Effects in fMRI: Retroicor,” Magnetic Resonance in Medicine, Vol. 44, No. 1, 2000, pp. 162-167. Hdoi:10.1002/1522-2594(200007)44:1<162::AID-MRM23>3.3.CO;2-5
[24]	R. Sladky, K. J. Friston, J. Trostl, R. Cunnington, E. Moser and C. Windischberger, “Slice-Timing Effects and Their Correction in Functional MRI,” NeuroImage, Vol. 58, No. 2, 2011, pp. 588-594. Hdoi:10.1016/j.neuroimage.2011.06.078
[25]	N. Lange and S. L. Zeger, “Non-Linear Fourier Time Series Analysis for Human Brain Mapping by Functional Magnetic Resonance Imaging,” Applied Probability & Statistics, Vol. 46, No. 1, 1997, pp. 1-29. Hdoi:10.1111/1467-9876.00046
[26]	J. L. Marchini and B. D. Ripley, “A New Statistical Approach to Detecting Significant Activation in Functional MRI,” NeuroImage, Vol. 12, No. 4, 2000, pp. 366-380. Hdoi:10.1006/nimg.2000.0628
[27]	D. R. Brillinger, “TIME SERIES Data Analysis and Theory,” Holden-Day, San Francisco, 1981. Hdoi:10.2307/2530198
[28]	D. R. Brillinger, “The General Linear Model in the Design and Analysis of Evoked Response Experiments,” Journal of Theoretical Neurobiology, Vol. 1, 1981, pp. 105-119.
[29]	D. E. Rio, R. R. Rawlings and D. W. Hommer, “Application of a Linear Time Invariant Model in the Fourier Domain to Perform Statistical Analysis of Functional Magnetic Resonance Images,” Proceedings SPIE, Vol. 3978, 2000, pp. 265-275. Hdoi:10.1117/12.383406
[30]	P. Bai, Y. Truong and X. Huang, “Nonparametric Estimation of Hemodynamic Response Function: A Frequency Domain Approach,” IMS Lecture Notes—Monograph Series. Optimality: The Third Erich L. Lehmann Symposium, Vol. 57, 2009, pp. 190-215. Hdoi:10.1214/09-LNMS5712
[31]	D. E. Rio, R. R. Rawlings, L. A. Woltz, J. B. Salloum and D. W. Hommer, “Single Subject Image Analysis Using the Complex General Linear Model—An Application to Functional Magnetic Resonance Imaging with Multiple Inputs,” Computer Methods and Programs in Biomedicine, Vol. 82, No. 1, 2006, pp. 10-19. Hdoi:10.1016/j.cmpb.2005.12.003
[32]	D. Rio, R. Rawlings, L. Woltz, J. Gilman and D. Hommer, “An Application of the Complex General Linear Model to Analysis of fMRI Single Subjects Multiple Stimuli Input Data,” Proceedings in Medical Imaging, Biomedical Applications in Molecular, Structural, and Functional Imaging, Vol. 7262, 2009. Hdoi:10.1117/12.811811
[33]	J. M. Gilman and D. W. Hommer, “Modulation of Brain Response to Emotional Images by Alcohol Cues in Alcohol-Dependent Patients,” Addiction Biology, Vol. 13 No. 3-4, 2008, pp. 423-434. Hdoi:10.1111/j.1369-1600.2008.00111.x
[34]	R. H. Shumway and D. S. Stoffer, “Time Series Analysis and Its Applications: With R Examples,” Springer, New York, 2006.
[35]	H. Akaike, “On the Statistical Estimation of the Frequency Response Function of a System Having Multiple Input,” Annals of the Institute of Statistical Mathematics, Vol. 17, No. 1, 1965, pp. 185-210. Hdoi:10.1007/BF02868166
[36]	P. J. Lang, M. M. Bradley and B. N. Cuthbert, “International Affective Picture System (IAPS): Technical Manual and Affective Ratings,” The Center for Research in Psychophysiology, University of Florida, Gainsville, 1995.
[37]	A. M. Dale, “Optimal Experimental Design for Event-Related fMRI,” Human Brain Mapping, Vol. 8, No. 2-3, 1999, pp. 109-114. Hdoi:10.1002/(SICI)1097-0193(1999)8:2/3<109::AID-HBM7>3.0.CO;2-W
[38]	J. E. Desmond and G. H. Glover, “Estimating Sample Size in Functional MRI (fMRI) Neuroimaging Studies: Statistical Power Analyses,” Journal of Neuroscience Methods, Vol. 118, No. 2, 2002 pp. 115-128. Hdoi:10.1016/S0165-0270(02)00121-8