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.

Fig. 1.

Diagram of the linear transform model. The output of the Retinal-V1 Pathway (Neural Response) is a nonlinear function of stimulus–contrast. fMRI signal, mediated byHemodynamics, is a linear transform of neural activity. That is, fMRI signal is proportional to the local average neural activity, averaged over a small region of the brain and averaged over a period of time. Noise might be introduced at each stage of the process, but the effects of these individual noises on the fMRI Response can be summarized by a single noise source.

Fig. 2.

Schematic of visual stimuli used in the experiments. A, One frame of the periodic stimulus consisted of vertical bars of checkerboard patternsalternating with vertical bars of uniform gray(mean). Over time, the checkerboard patterns flickered (contrast reversing with a flicker rate of 8 Hz), and the bars drifted slowly leftward. B, The time course of a single pixel of the periodic stimulus as the bars drifted. C, The time course of pixels for the pulse stimulus. Each stimulus cycle began by displaying a full-field flickering checkerboard pattern (contrast reversing at 8 Hz) for a period of time (the pulse duration). Each stimulus cycle was completed by replacing the checkerboard with uniform gray for 24 sec.

Fig. 3.

Analysis of data for periodic stimuli.A, Sequence of fMR images. B, Time course of response at a single pixel (dashed curve) superimposed with the best-fitting sinusoid. C, Aligned anatomical image with pixels in the calcarine sulcus highlighted. D, Mean and SE of the response amplitudes of the selected pixels.

Fig. 4.

fMRI responses to pulse stimuli. Eachcurve is the mean time course of the fMRI response (pixel intensity) averaged across cycle repetitions and averaged across all pixels in the calcarine sulcus. Each panel shows data for a different pulse duration. Different curves within a panel correspond to different contrasts. The stimulus time course also is depicted in each panel. The fMRI responses increase with stimulus contrast, and the fMRI responses are blurred and delayed with respect to the time course of the stimulus. Error bars represent 1 SE.

Fig. 5.

Time–contrast separability test using pulse stimuli. Data in each panel are scaled copies of data in the corresponding panel of Figure 6. Error bars represent 1 SE of the scaled data. The resulting scaled data align without significant systematic error, consistent with time–contrast separability. The first principal components (solid curves) account for 86.81% of the variance in the data.

Fig. 6.

fMRI response amplitudes for periodic stimuli as a function of stimulus contrast and temporal period for both subjects.Amplitudes are in pixel intensity units, andContrast is plotted on a logarithmic scale. Data points are mean response amplitudes (averaged over the calcarine sulcus). Error bars represent 1 SE of the mean. fMRI response amplitude increases monotonically with stimulus contrast, and it decreases as theTemporal Period shortens.

Fig. 7.

Time–contrast separability test using periodic stimuli for both subjects. Each data set is a scaled copy of the corresponding data from Figure 6, after compensating for the noise (see text). Error bars represent 1 SE of the scaled data. The curves align without significant systematic error, consistent with separability. The first principal components (solid curves) account for 99.64 and 99.01% of the variance in the data for subjects gmb andsae, respectively.

Fig. 8.

fMRI responses from shorter pulses can predict the responses to longer pulses. The four principal component curves (corresponding to pulse durations of 3, 6, 12, and 24 sec) from Figure5 were used to make six predictions. The predictions are generally consistent with the linear transform model. However, the responses to the shortest (3 sec) pulse tend to overestimate slightly the responses to the longer pulses.

Fig. 9.

Noise analysis. A, fMRI response amplitudes for periodic stimuli as a function of stimulusContrast, stimulus Temporal Period, andAnalysis Period. Each panel corresponds to a different analysis period. Different curves correspond to different stimulus temporal periods. Error bars represent 1 SE. Response amplitude increases with Contrast only when the Analysis Period is the same as the stimulus Temporal Period. The other curves are measurements of the noise. The noise curves are flat, demonstrating that the noise is independent of both stimulus contrast and stimulus temporal period. B, Noise amplitudes for all periodic stimulus conditions and for all possible analysis periods. The noise is broad-band; that is, the noise amplitudes are significantly nonzero for each of the analysis periods. The solid curve, drawn for comparison, is the temporal fMRI frequency–response function, that is, the amplitude of the Fourier transform of the temporal fMRI impulse–response function (from Fig. 13).

Fig. 10.

Model fit to the pulse data set for subjectgmb. The model predictions and corresponding data points were shifted vertically so that the predicted responses asymptote at zero. The best-fitting model parameters do not vary greatly between subjects. The model accounts for 76.98% of the variance in the data.

Fig. 11.

Model fit to the pulse data set for subjectsae. The model accounts for 62.49% of the variance in the data.

Fig. 12.

Model fit to the periodic data sets for both subjects. Best-fitting model parameters do not vary greatly between subjects. The model accounts for 99.56 and 98.76% of the variance for subjects gmb and sae, respectively.

Fig. 13.

Estimated impulse response (Time, top)and contrast response (Contrast, bottom) functions for subjects gmb (left) and sae (right). The functions are plotted using the model parameter values fit to the pulsed (thin line) and periodic (thick line) data sets.