Linear systems analysis of the fMRI signal

Department of Psychology, University of Washington, PO Box 351525, Seattle, WA 98195-1525, USA.
NeuroImage (Impact Factor: 6.36). 01/2012; 62(2):975-84. DOI: 10.1016/j.neuroimage.2012.01.082
Source: PubMed


In 1995 when we began our investigations of the human visual system using fMRI, little was known about the temporal properties of the fMRI signal. Before we felt comfortable making quantitative estimates of neuronal responses with this new technique, we decided to first conduct a basic study of how the time-course of the fMRI response varied with stimulus timing and strength. The results ended up showing strong evidence that to a first approximation the hemodynamic transformation was linear in time. This was both important and remarkable: important because nearly all fMRI data analysis techniques assume or require linearity, and remarkable because the physiological basis of the hemodynamic transformation is so complex that we still have a far from complete understanding of it. In this paper, we provide highlights of the results of our original paper supporting the linear transform hypothesis. A reanalysis of the original data provides some interesting new insights into the published results. We also provide a detailed appendix describing of the properties and predictions of a linear system in time in the context of the transformation between neuronal responses and the BOLD signal.

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Available from: Geoffrey Boynton, Sep 29, 2015
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    • "HRF and use this HRF to deconvolve BOLD signals [13]. When estimating a voxel-specific HRF, the BOLD response is often assumed to be a linear time-invariant (LTI) system [14]. Then, one of the main solutions is to represent the HRF with a linear combination of basis functions [15] [16]. "
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    ABSTRACT: Brain state decoding or "mind reading" via multivoxel pattern analysis (MVPA) has become a popular focus of functional magnetic resonance imaging (fMRI) studies. In brain decoding, stimulus presentation rate is increased as fast as possible to collect many training samples and obtain an effective and reliable classifier or computational model. However, for extremely rapid event-related experiments, the blood-oxygen-level-dependent (BOLD) signals evoked by adjacent trials are heavily overlapped in the time domain. Thus, identifying trial-specific BOLD responses is difficult. In addition, voxel-specific hemodynamic response function (HRF), which is useful in MVPA, should be used in estimation to decrease the loss of weak information across voxels and obtain fine-grained spatial information. Regularization methods have been widely used to increase the efficiency of HRF estimates. In this study, we propose a regularization framework called mixed L2 norm regularization. This framework involves Tikhonov regularization and an additional L2 norm regularization term to calculate reliable HRF estimates. This technique improves the accuracy of HRF estimates and significantly increases the classification accuracy of the brain decoding task when applied to a rapid event-related four-category object classification experiment. At last, some essential issues such as the impact of low-frequency fluctuation (LFF) and the influence of smoothing are discussed for rapid event-related experiments.
    Computational and Mathematical Methods in Medicine 05/2013; 2013:643129. DOI:10.1155/2013/643129 · 0.77 Impact Factor
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    ABSTRACT: In Kilner et al. [Kilner, J.M., Kiebel, S.J., Friston, K.J., 2005. Applications of random field theory to electrophysiology. Neurosci. Lett. 374, 174-178.] we described a fairly general analysis of induced responses-in electromagnetic brain signals-using the summary statistic approach and statistical parametric mapping. This involves localising induced responses-in peristimulus time and frequency-by testing for effects in time-frequency images that summarise the response of each subject to each trial type. Conventionally, these time-frequency summaries are estimated using post-hoc averaging of epoched data. However, post-hoc averaging of this sort fails when the induced responses overlap or when there are multiple response components that have variable timing within each trial (for example stimulus and response components associated with different reaction times). In these situations, it is advantageous to estimate response components using a convolution model of the sort that is standard in the analysis of fMRI time series. In this paper, we describe one such approach, based upon ordinary least squares deconvolution of induced responses to input functions encoding the onset of different components within each trial. There are a number of fundamental advantages to this approach: for example; (i) one can disambiguate induced responses to stimulus onsets and variably timed responses; (ii) one can test for the modulation of induced responses-over peristimulus time and frequency-by parametric experimental factors and (iii) one can gracefully handle confounds-such as slow drifts in power-by including them in the model. In what follows, we consider optimal forms for convolution models of induced responses, in terms of impulse response basis function sets and illustrate the utility of deconvolution estimators using simulated and real MEG data.
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    ABSTRACT: An increasing number of functional near-infrared spectroscopy (fNIRS) studies utilize a general linear model (GLM) approach, which serves as a standard statistical method for functional magnetic resonance imaging (fMRI) data analysis. While fMRI solely measures the blood oxygen level dependent (BOLD) signal, fNIRS measures the changes of oxy-hemoglobin (oxy-Hb) and deoxy-hemoglobin (deoxy-Hb) signals at a temporal resolution severalfold higher. This suggests the necessity of adjusting the temporal parameters of a GLM for fNIRS signals. Thus, we devised a GLM-based method utilizing an adaptive hemodynamic response function (HRF). We sought the optimum temporal parameters to best explain the observed time series data during verbal fluency and naming tasks. The peak delay of the HRF was systematically changed to achieve the best-fit model for the observed oxy- and deoxy-Hb time series data. The optimized peak delay showed different values for each Hb signal and task. When the optimized peak delays were adopted, the deoxy-Hb data yielded comparable activations with similar statistical power and spatial patterns to oxy-Hb data. The adaptive HRF method could suitably explain the behaviors of both Hb parameters during tasks with the different cognitive loads during a time course, and thus would serve as an objective method to fully utilize the temporal structures of all fNIRS data.
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