Functional and effective connectivity of visuomotor control systems demonstrated using generalized partial least squares and structural equation modeling

Abstract

Tasks employing parametric variation in movement rate are associated with predictable modulations in neural activity and provide a convenient context for developing new techniques for system identification. Using a multistage approach, we explored the functional and effective connectivity of a visuomotor control system by combining generalized partial least squares (gPLS) with subsequent structural equation modeling (SEM) to reveal the relationships between neural activity and finger movement rate in an experiment involving visually paced left or right thumb flexion. The gPLS in the first analysis stage automatically identified spatially distributed sets of BOLD-contrast signal changes using linear combinations of sigmoidal basis functions parameterized by kinematic variables. The gPLS provided superior sensitivity in detecting task-related functional activity patterns via a step-wise comparison with both classical linear modeling and behavior correlation analysis. These activity patterns were used in the second analysis stage, which employed SEM to characterize the areal regional interactions. The hybrid gPLS/SEM procedure allowed modeling of complex regional interactions in a network including primary motor cortex, premotor areas, cerebellum, thalamus, and basal ganglia, with differential activity modulations with respect to rate observed in the corticocerebellar and corticostriate subsystems. This effective connectivity analysis of visuomotor control circuits showed that both the left and right corticocerebellar and corticostriate circuits exhibited movement rate-related modulation. The identification of the functional connectivity among regions participating particular classes of behavior using gPLS, followed by the estimation of the effective connectivity using SEM is an efficient means to characterize the neural interactions underlying variations in sensorimotor behavior.

Figure 1

Schematic diagram of the gPLS analysis, including choice of basis functions, cross validation procedure, and PLS decomposition of the effect space created from the crosscovariance between the neuroimaging data and a model. The dark blue text in parentheses indicates the corresponding formula used in the Methods and Appendix sections. The gPLS analysis procedure includes choice of basis functions, identification of spatiotemporal model parameters, and cross validation components. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 2

(A) Sigmoidal basis functions with the different shifts (κ) and slopes (η) employed in the gPLS analysis. Different colors in the figure indicate different shifts (κ). Different line styles in the figure indicate different slopes (η). Each analysis utilizes one sigmoidal basis function in addition to a constant and a linear basis function. (B) The cross validation error metrics ε calculated for different slopes (/η) and shifts (κ) during the gPLS analysis of left and right hand movement. The minimum error metric is marked with blue boundary box and blue text. The background color represents the linearly normalized value of the error metric ε. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 3

F‐statistic maps from a GLM analysis using constant, linear, and sigmoidal functions as regressors. In addition, to compare the detection sensitivity of this basis set to manual regressor identification methods, we also used a reference vector derived from an ROI surrounding the contralateral MI. The color scale represents the calculated F‐statistic. The critical threshold is P < 0.045, uncorrected. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 4

Relationship between movement rate and the temporal scores, which were calculated using [Eq. 9] after identifying the optimal model. Gray bars depict the standard deviation of recorded paced movement rates. In the group of right handed participants, signal modulation elicited by left hand movement demonstrates a more nonlinear rate dependence on movement frequency, while the right hand shows more linear rate dependence. Note that these curves represent the behavior across the entire LV. The dashed line represents an interval of one standard deviation estimated from 36 iterative cross validation analyses. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 5

Active brain areas from the first brain LV resulting from the gPLS analysis for left (A) and right (B) hand movements using a Z‐score critical threshold of 45 (see text for details). The BOLD‐contrast responses in these areas show differential sensitivity to movement rate in the two hands, as shown in Figure 4. The units in these figures are the Z‐scores calculated from 100 iterative leave‐one‐out cross validations. The maps of Z‐scores transformed from correlation coefficients between movement rate and BOLD‐contrast signal are shown for left (C) and right (D) hand movements, using a critical threshold of Z > 2.0 (P < 0.023, uncorrected). The blue traces in (C) and (D) denote the borders of the active regions in the basal ganglia detected by the gPLS. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 6

Region‐of‐interest (ROI) measurements of BOLD‐contrast movement minus fixation signals revealed by the gPLS technique for left and right hand movements at 0.3, 1.0, and 3.0 Hz. ROIs were identified by thresholding the first dominant brain LV in the gPLS analysis with Z‐scores higher than 45. For this analysis, the brain areas were separated into lateralized corticocerebellar and corticostriate systems containing ipsilateral cerebellum and contralateral MI, putamen, globus pallidus, SMA, and thalamus. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 7

The path coefficients for visually paced variable‐rate movements of the left (left column) and right (right column) hands. Top: 0.3 Hz; Middle: 1.0 Hz; Bottom: 3.0 Hz. The widths of the arrows correspond to the magnitude of the estimated path coefficients, which are also noted directly above the arrows. Red arrows represent positive path coefficients, and blue arrows represent negative path coefficients. Arrows with absolute Z‐scores > 0.6745 (two‐tail uncorrected p < 0.5) are plotted in gray. The brain is shown from the front with the left hemisphere on the right of the figure. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 8

The t‐statistics from the regression analysis using temporal scores shown in Figure 4 to regress path coefficients during left and right hand movement. Note that the lateralized corticocerebellar network switched with respect to hand. Both lateralized corticostriatal networks show statistically significant symmetric movement rate dependence. Statistically significant paths are shown in red (critical threshold at t = 7.0, p < 0.0001, uncorrected). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]