Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1

Abstract

The linear transform model of functional magnetic resonance imaging (fMRI) hypothesizes that fMRI responses are proportional to local average neural activity averaged over a period of time. This work reports results from three empirical tests that support this hypothesis. First, fMRI responses in human primary visual cortex (V1) depend separably on stimulus timing and stimulus contrast. Second, responses to long-duration stimuli can be predicted from responses to shorter duration stimuli. Third, the noise in the fMRI data is independent of stimulus contrast and temporal period. Although these tests can not prove the correctness of the linear transform model, they might have been used to reject the model. Because the linear transform model is consistent with our data, we proceeded to estimate the temporal fMRI impulse-response function and the underlying (presumably neural) contrast-response function of human V1. Functional magnetic resonance imaging (fMRI) measures changes in blood oxygenation and blood volume that result from neural activity (Ogawa et al., 1990;Belliveau et al., 1992) (for review, see Moseley and Glover, 1995). Deoxygenated hemoglobin acts as an endogenous paramagnetic agent, so a reduction in the concentration of deoxygenated hemoglobin increases the T2*-weighted magnetic resonance signal.A typical fMRI experiment measures the correlation between the fMRI response and a stimulus. From this, scientists hope to infer something about neural activity. Often it is assumed that there is a simple and direct relationship between neural activity and fMRI response, but the nature of this relationship remains unclear.The goal of the research reported in this article is to understand how the fMRI response relates to neural activity. The vascular source of the fMRI signal places important limits on the technique. Because the hemodynamic response is sluggish, perhaps the fMRI response is proportional to the local average neural activity, averaged over a small region of the brain and averaged over a period of time. We will refer to this as the "linear transform model" of fMRI response. The linear transform model, specialized for a visual area of the brain, is depicted in Figure 1. According to this model, neural activity is a nonlinear function of the contrast of a visual stimulus, but fMRI response is a linear transform (averaged over time) of the neural activity in V1. Noise might be introduced at each stage of the process, but the effects of these individual noises can be summarized by a single noise source that is added to the output.To date, this linear transform model of fMRI response has not been tested, despite the fact that some studies rely explicitly on the linear model for their data analysis (Friston et al., 1994;Lange and Zeger, 1996). The sequence of events from neural response to fMRI response is complicated and only partially understood. It is unlikely that the complex interactions among neurons, hemodynamics, and the MR scanner would result in a precisely linear transform. However, the line...

Modeling the hemodynamic response to brain activation

“…In a subsequent study, they showed that the Volterra kernel characterization of experimentally observed nonlinearities could be accounted for with the balloon model plus a linear transformation up to the CBF response, again supporting the idea that the primary nonlinearity is in the transformation from the CBF to the BOLD response (Friston et al, 2000). In the current model, we also explicitly included an additional nonlinearity of the neural response itself, allowing for an initial sharp response followed by adaptation (a picture originally proposed by Boynton et al, 1996). The two sources of nonlinearity can be distinguished experimentally by whether the nonlinearity is present in just the BOLD response or in both the BOLD and CBF responses.…”

“…Then if the resting stimulus level is N 0 = 0, there is no dip following the end of the stimulus. This is the adaptation pattern originally proposed by Boynton et al to describe the observed nonlinearities of the BOLD response in the visual cortex (Boynton et al, 1996). On the other hand, if N 0 N 0, there will be a post-stimulus undershoot of the neural response.…”

“…5. The BOLD response typically exhibits a temporal nonlinearity such that an appropriately shifted and added response to a brief stimulus over-predicts the true response to an extended stimulus (Birn et al, 2001;Boynton et al, 1996;Friston et al, 1998;Glover, 1999;Miller et al, 2001;Robson et al, 1998;Vasquez and Noll, 1998). This temporal nonlinearity is most pronounced when the brief stimulus is less than about 4 s and the extended stimulus is longer than 6 s. Comparing short and long duration stimuli that are both longer than about 4 s, the temporal nonlinearity is reduced.…”

“…6. Nonlinearity has also been reported as a brefractory periodQ, such that two identical stimuli presented close together in time produce a net response with less than twice the integrated response of a single stimulus alone (Boynton et al, 1996;Buckner, 1998;Huettel and McCarthy, 2001). 7.…”

Activity in human reward-sensitive brain areas is strongly context dependent

“…A final regressor accounted for the fixation period before each choice display and feedback display. The hemodynamic response to each event was modeled by convolving each regressor with a standard gamma function (Boynton et al, 1996). For each voxel and each event type, a parameter estimate (beta coefficient) was computed that indicated the strength of covariance between the data and the modeled response function; these estimates were corrected for temporal autocorrelation using a first-order autoregressive model.…”