Elsevier

NeuroImage

Volume 37, Issue 1, 1 August 2007, Pages 189-201
NeuroImage

An ARX model-based approach to trial by trial identification of fMRI-BOLD responses

https://doi.org/10.1016/j.neuroimage.2007.02.045Get rights and content

Abstract

Being able to estimate the fMRI-BOLD response following a single task or stimulus is certainly of value, since it allows to characterize its relationship to different aspects either of the stimulus, or of the subject's performance. In order to detect and characterize BOLD responses in single trials, we developed and validated a procedure based on an AutoRegressive model with eXogenous Input (ARX). The use of an individual exogenous input for each voxel makes the modeling sensitive enough to reveal differences across regions, avoiding any a priori assumption about the reference signal. The detection of variability across trials is ensured by a suitable choice, for each voxel, of the order of the moving average, which in our implementation determines the relative delay between the recorded and the reference signal. This is a quality useful in finding different time profiles of activation from high temporal resolution fMRI data. The results obtained from simulated fMRI data resulting from synthetic activations in actual noise indicate that such approach allows to evaluate important features of the response, such as the time to onset, and time to peak. Moreover, the results obtained from real high temporal resolution fMRI data acquired at l.5 T during a motor task are consistent with previous knowledge about the responses of different cortical areas in motor programming and execution. The proposed procedure should also prove useful as a pre-processing step in different approaches to the analysis of fMRI data.

Introduction

Event-related or trial-based protocols are of great relevance for BOLD fMRI studies, since they allow for more flexible designs and can assess specific features of brain activity evoked by different kinds of brief stimuli or tasks (Josephs et al., 1997, Zarahn et al., 1997a, Rosen et al., 1998). Indeed, several studies have underlined the importance of fully characterizing the hemodynamic response (HR) to brief events by determining its onset, time to peak, peak amplitude and width, in order to obtain more comprehensive and quantitative measures of task-related brain activity (e.g., Menon et al., 1998, Bellgowan et al., 2003). Given the low contrast-to-noise ratio, in event-related paradigms one usually needs to take into account information deriving from several repetitions of the event to improve the sensitivity. Typical procedures consist in averaging the responses obtained from replications of the same task or in applying a General Linear Model approach to the identification of the HRs. This, however, implies loss of the unique information associated with each execution of the task, which is particularly crucial in cognitive tasks (Menon and Kim, 1999).

Being able to estimate the hemodynamic response following each single event allows to characterize its relationship to different aspects either of the stimulus or of the subject's performance. In this “time-resolved” approach HR variability across regions and subjects can also be factored out and distinguished from the temporal behaviour of neural activity (Richter et al., 1997a, Richter et al., 1997b, Ugurbil et al., 1999, Menon and Kim, 1999). A trial by trial estimation of the response allows also to control its reliability in different cerebral areas and to detect the presence of artifactual trials. Indeed, several fMRI studies have reported that the task-related HR temporal profile and the noise, notably the “physiological noise” component, may vary across trials (Duann et al., 2002), besides their being also site-, stimulus-, subject-, and procedure-dependent (e.g., Kim et al., 1997, Aguirre et al., 1998, Glover, 1999, Miezin et al., 2000, Handwerker et al., 2004).

The major obstacle to the estimation of the HR following a brief event is the low BOLD signal variation which can be less than 1% (e.g., Josephs et al., 1997).

Moreover, fMRI data are characterized by temporal instability over repeated acquisitions. Different sources of such fluctuations have been disclosed, the most relevant being associated with subject's head motion, scanner-related noise, cardiac and respiration cycles, and hemodynamic/metabolic factors. The spectrum of such “noise” has been reported having a 1/f form (e.g., Zarahn et al., 1997b), with additional peaks corresponding to periodic motions and to their possible aliased components (Weisskoff et al., 1993), and varying across brain areas (Friston et al., 2000).

In event-related protocols, temporal autocorrelation and random noise may be included in statistical analysis frameworks and/or noise reduction may be applied as a preprocessing step to further improve sensitivity, given the several constraints that exist on the number of trial repetitions. However, a complete modeling of the “no task-related” signal components is still lacking. This is one of the reasons of the many noise reduction strategies developed so far, including among others retrospective correction, pre-whitening, spectral subtraction, band-pass, Wiener and wavelets filters, ICA-based denoising (e.g., Jezzard, 2000, Glover et al., 2000, LaConte et al., 2000, Woolrich et al., 2001, Thomas et al., 2002, Pfeuffer et al., 2002, Bullmore et al., 2004, Kadah, 2004).

Currently, a few studies have monitored the time course of the BOLD response trial by trial. The majority used high magnetic fields (Richter et al., 1997a, Richter et al., 1997b, Kim et al., 1997, Duann et al., 2002) which improve signal sensitivity but also physiological noise sensitivity, therefore mitigating the expected contrast-to-noise ratio improvement (Krüger and Glover, 2001); to our knowledge, only two studies used a 1.5 T scanner (Formisano et al., 2002, Burke et al., 2004). One study (Windischberger et al., 2002) evaluated each single trial on whole-cortex data acquired at 3 T, for a different aim, i.e. to assess the consistency of t-value maps across trials. Only a few of the above-mentioned studies acquired data at an high sampling rate, which is needed to disclose the shape of the HR per trial and per region of interest (Richter et al., 1997a, Richter et al., 1997b, Duann et al., 2002). Duann and colleagues used Infomax ICA to detect variations in single-trial HRs. To characterize the responses, fitting or cross-correlation procedures have been used (Richter et al., 1997b, Kim et al., 1997, Formisano et al., 2002).

The aim of the present work has been to develop a filtering procedure capable to detect HRs and to allow their characterization on a trial by trial basis, even on fMRI data acquired at low magnetic field. The method is based on an AutoRegressive model with eXogenous Input (ARX), that has proved successful for the identification of cerebral-evoked potentials (Liberati et al., 1992) and has also been recently applied to fMRI data (Maieron et al., 2002, Riera et al., 2004, Burke et al., 2004). A new strategy is presented here, focusing on the two aspects which are relevant when using the ARX model on fMRI data, that is the choice of the reference signal (the exogenous input) and its delay relative to the noisy recorded signal. The procedure has been validated using synthetic single trials and a simulated event-related experimental session, and tested on real fMRI data acquired at 1.5 T, while subjects were performing a finger-tapping motor task in an event-related design. This sort of task was chosen because it has been deeply investigated and therefore it is suitable for validation of new data analysis approaches.

Section snippets

The fMRI signal model

For each single trial and each voxel, the fMRI measured signal is considered as the output y(k) of a dynamic system like the one shown in Fig. 1, where it is represented as the additive superimposition of two terms: s(k), the BOLD response and n(k), a pseudo-stochastic signal denoted as “background noise”. An AutoRegressive with eXogenous input model (ARX) is chosen to describe signal–noise interactions: the “background noise” is described as an autoregressive process H(z) driven by a white

Validation tests

First of all, the hypothesis of modeling the “background noise” as an autoregressive process driven by white noise was validated. Then, two sets of synthetic data, both resulting from synthetic activations in actual noise, were generated to test the range of validity of the ARX modeling technique. The first set, simulating a collection of single trials varying in amplitude and shape of the BOLD response, was mainly aimed at testing the sensitivity in response identification; the second set,

Discussion

We developed and tested a procedure based on an AutoRegressive model with eXogenous Input (ARX), aimed at identifying BOLD responses on a trial by trial basis.

The results obtained from modeling synthetic and real fMRI single trials indicate that the developed approach is an effective general filtering procedure, which allows to evaluate important features of the responses, such as time to onset, time to peak, and amplitude. This parametric approach is more powerful than simple linear filtering

Acknowledgments

Supported by grants of Ministry of Research (Italy) to P.B. (PRIN 2005) and to C.A.P. (FIRB 2001, RBNE018ET9).

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