TY - JOUR
T1 - The impact of temporal regularization on estimates of the BOLD hemodynamic response function
T2 - A comparative analysis
AU - Casanova, Ramon
AU - Ryali, Srikanth
AU - Serences, John
AU - Yang, Lucie
AU - Kraft, Robert
AU - Laurienti, Paul J.
AU - Maldjian, Joseph A
N1 - Funding Information:
This work was supported by the Human Brain Project and NIBIB through grant number EB004673, and by NS042568, and EB003880 as well as the Center for Biomolecular Imaging at Wake Forest University. The authors would like to thank Kathy Pearson for her programming support during this project. We also thank the anonymous reviewers for their helpful comments that significantly strengthened this work.
PY - 2008/5/1
Y1 - 2008/5/1
N2 - In fMRI data analysis it has been shown that for a wide range of situations the hemodynamic response function (HRF) can be reasonably characterized as the impulse response function of a linear and time invariant system. An accurate and robust extraction of the HRF is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions. When no assumptions are made about the HRF shape, it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either Fourier or delta basis functions. Recently, regularization methods have been employed to increase the estimation efficiency of the HRF; typically these methods produce more accurate HRF estimates than the least squares approach [Goutte, C., Nielsen, F.A., Hansen, L.K., 2000. Modeling the Haemodynamic Response in fMRI Using Smooth FIR Filters. IEEE Trans. Med. Imag. 19(12), 1188-1201.]. Here, we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the HRF such as time to peak (TTP), height (HR) and width (W) of the response. We implemented a Bayesian approach proposed by Marrelec et al. [Marrelec, G., Benali, H., Ciuciu, P., Pelegrini-Issac, M., Poline, J.-B., 2003. Robust Estimation of the Hemodynamic Response Function in Event-Related BOLD fMRI Using Basic Physiological Information. Hum. Brain Mapp. 19, 1-17., Marrelec, G., Benali, H., Ciuciu, P., Poline, J.B. Bayesian estimation of the hemodynamic of the hemodynamic response function in functional MRI. In: R. F, editor; 2001; Melville. p 229-247.] and its deterministic counterpart based on a combination of Tikhonov regularization [Tikhonov, A.N., Arsenin, V.Y., 1977. Solution of ill-posed problems. Washington DC: W.H. Winston.] and generalized cross-validation (GCV) [Wahba, G., 1990. Spline Models for Observational Data. Philadelphia: SIAM.] for selecting the regularization parameter. The performance of both methods is compared with least square estimates as a function of temporal resolution, color and strength of the noise, and the type of stimulus sequences used. In almost all situations, under the considered assumptions (e.g. linearity, time invariance and smooth HRF), the regularization-based techniques more accurately characterize the HRF compared to the least-squares method. Our results clarify the effects of temporal resolution, noise color, and experimental design on the accuracy of HRF estimation.
AB - In fMRI data analysis it has been shown that for a wide range of situations the hemodynamic response function (HRF) can be reasonably characterized as the impulse response function of a linear and time invariant system. An accurate and robust extraction of the HRF is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions. When no assumptions are made about the HRF shape, it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either Fourier or delta basis functions. Recently, regularization methods have been employed to increase the estimation efficiency of the HRF; typically these methods produce more accurate HRF estimates than the least squares approach [Goutte, C., Nielsen, F.A., Hansen, L.K., 2000. Modeling the Haemodynamic Response in fMRI Using Smooth FIR Filters. IEEE Trans. Med. Imag. 19(12), 1188-1201.]. Here, we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the HRF such as time to peak (TTP), height (HR) and width (W) of the response. We implemented a Bayesian approach proposed by Marrelec et al. [Marrelec, G., Benali, H., Ciuciu, P., Pelegrini-Issac, M., Poline, J.-B., 2003. Robust Estimation of the Hemodynamic Response Function in Event-Related BOLD fMRI Using Basic Physiological Information. Hum. Brain Mapp. 19, 1-17., Marrelec, G., Benali, H., Ciuciu, P., Poline, J.B. Bayesian estimation of the hemodynamic of the hemodynamic response function in functional MRI. In: R. F, editor; 2001; Melville. p 229-247.] and its deterministic counterpart based on a combination of Tikhonov regularization [Tikhonov, A.N., Arsenin, V.Y., 1977. Solution of ill-posed problems. Washington DC: W.H. Winston.] and generalized cross-validation (GCV) [Wahba, G., 1990. Spline Models for Observational Data. Philadelphia: SIAM.] for selecting the regularization parameter. The performance of both methods is compared with least square estimates as a function of temporal resolution, color and strength of the noise, and the type of stimulus sequences used. In almost all situations, under the considered assumptions (e.g. linearity, time invariance and smooth HRF), the regularization-based techniques more accurately characterize the HRF compared to the least-squares method. Our results clarify the effects of temporal resolution, noise color, and experimental design on the accuracy of HRF estimation.
KW - Event-related fMRI
KW - GCV
KW - HRF estimation
KW - Tikhonov regularization
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U2 - 10.1016/j.neuroimage.2008.01.011
DO - 10.1016/j.neuroimage.2008.01.011
M3 - Article
C2 - 18329292
AN - SCOPUS:41649111469
SN - 1053-8119
VL - 40
SP - 1606
EP - 1618
JO - NeuroImage
JF - NeuroImage
IS - 4
ER -