Imaging neuroscience: Principles or maps?
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Figure 1Volterra kernels h0, h1, and h2 based on parameter estimates from a voxel in the left superior temporal gyrus at −56, −28, and 12 mm. These kernels can be thought of as a characterization of the second-order hemodynamic response function. The first-order kernel (Upper) represents the (first-order) component usually presented in linear analyses and reflects the contribution of the input as a function of time. The second-order kernel (Lower) is presented in image format and reflects the contribution of the product of the input at two distinct times in the recent past. The color scale is arbitrary; white is positive and black is negative.
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Figure 2(Left) SPM(F) testing for the significance of the first- and second-order kernel coefficients (h1 and h2) in a word-presentation rate, single-subject fMRI experiment. This is a maximum-intensity projection of a statistical process of the F statistic, after a multiple-regression analysis at each voxel. The format is standard and provides three orthogonal projections in the standard space conforming to that described in Talairach and Tournoux (14). The grey scale is arbitrary, and the SPM(F) has been thresholded (F = 32). (Right) The design matrix used in the analysis. The design matrix comprises the explanatory variables in the general linear model. It has one row for each of the 1,200 scans and one column for each explanatory variable or effect modeled. The left-hand columns contain the explanatory variables of interest, x i(t) and x i(t),x j(t), where x i(t) is word presentation rate convolved with the ith basis function used in the expansion of the kernels. The remaining columns contain covariates or effects of no interest designated as confounds. These include (left to right) a constant term (h0), periodic (discrete cosine set) functions of time to remove low-frequency artifacts and drifts, global or whole brain activity G(t), and interactions between global effects and those of interest, G(t).x i(t) and G(t).x i(t),x j(t). The latter confounds remove effects that have no regional specificity.
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Figure 3(Upper) The simulated responses to a pair of words (bars) (1 sec apart) presented together (solid line) and in isolation (broken lines) based on the second-order hemodynamic response function in Fig. 1. (Lower) The response to the second word when preceded by the first (broken line), obtained by subtracting the response to the first word from the response to both, and when presented alone (broken). The difference reflects the impact of the first word on the response to the second.
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Figure 4(Upper) Hemodynamic response to a single word (bar at 0 sec) modeled by using the Volterra kernel estimates of Fig. 1. (Lower) The empirical event-related response in the same region based on an independent, event-related, single-subject fMRI experiment. The solid line is the fitted response using only first-order kernel estimates, and the dots represent the adjusted responses.
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Figure 5Effective connections associated with visual attention to motion. Direct effects (of one region on another) are shown in gray, and modulatory effects are shown in black. Direct effects pertain to terms that include only the activity of the source region. Modulatory effects were assessed by using the contribution of second-order terms that involve the source and another (modulated) input. Note that direct effects are almost always reciprocal and conform to predictions based on anatomical connectivity. Modulatory effects are limited to interactions between posterior parietal cortex (PPC) and V5 and between V3a and V1/V2. V1/V2 and V5 also intrinsically modulate their responses to afferent input. All the connections shown are significant at P < 0.05 (corrected for the number of connections tested). These effects were tested using the F statistic after a multiple regression for serially corrected data based on a Volterra series model of interregional influences. The modulatory interaction between PPC and V5 was extremely significant (F = 3.49, df = 25,691, P < 0.001, corrected).
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Figure 6(Upper) SPM thresholded at P = 0.001 (height uncorrected) and P = 0.05 (volume corrected) superimposed on a structural T1-weighted image. This SPM tests for a significant psychophysiological interaction between activity in V1/V2 and attention to visual motion. The most significant effects are seen in the vicinity of V5 (white region, lower right). The time series of the most significant (Z = 4.46) voxel in this region is shown in the Upper panel (line, fitted data; dots, adjusted data). (Lower) Regression of V5 activity (at 42, −78, and −9 mm) on V1/V2 activity when the subject was asked to attend to changes in the speed of radially moving dots and when the subject was not asked to. The lines correspond to the regression. The dots correspond to the observed data adjusted for confounds other than the main effects of V1/V2 activity (dark grey dots, attention; light grey dots, no attention). Attention can be seen to augment the influence of V1/V2 on V5.
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Figure 7The data above were acquired from a single subject using echo planar imaging (EPI) fMRI at a rate of one volume image every 1.7 sec. The subject listened to words in epochs of 34 sec at a variety of different frequencies. The fitted periauditory responses (lines) and adjusted data (dots) are shown for two rates (30 and 60 words per minute) on the left. The solid bar denotes the presentation of words. By removing confounds and specifying the appropriate design matrix, one can show that fMRI is exquisitely sensitive to single events. The data shown on the right were acquired from the same subject while simply listening to single words presented every 34 sec. Event-related responses were modeled by using a small set of temporal basis γ functions of the peristimulus time. The SPM(F) shown, reflecting the significance of these event-related responses, has been thresholded at P = 0.001 (uncorrected) and displayed on a T1-weighted structural MRI.
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Figure 8(Left) SPM(F) testing for the significance of a second-order polynomial regression of activity on the duration of visually presented words as measured in five normal subjects by using PET. Bilateral extrastriate regions are shown as white regions surviving a threshold of P = 0.05 (uncorrected) on a structural T1-weighted MRI. (Right) An example of this regression for the voxel under the cross-hairs on the left. It can be seen that the observed response function deviates from the linear relationship that would be expected if the amount of neural activity evoked was proportional to the duration over which it was elicited.
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Figure 9Adjusted activity from a voxel in the posterior superior temporal region is shown as a function of word-production rate under the two conditions of extrinsic and intrinsic word generation. The change in the slope of these response functions under the two contexts is obvious. The voxel from which these data are derived is shown on the SPM(t) (Upper). These data come from a PET study of six normal subjects.
Footnotes
- Copyright © 1998, The National Academy of Sciences
