Hemodynamic traveling waves in human visual cortex

Abstract

Functional MRI (fMRI) experiments rely on precise characterization of the blood oxygen level dependent (BOLD) signal. As the spatial resolution of fMRI reaches the sub-millimeter range, the need for quantitative modelling of spatiotemporal properties of this hemodynamic signal has become pressing. Here, we find that a detailed physiologically-based model of spatiotemporal BOLD responses predicts traveling waves with velocities and spatial ranges in empirically observable ranges. Two measurable parameters, related to physiology, characterize these waves: wave velocity and damping rate. To test these predictions, high-resolution fMRI data are acquired from subjects viewing discrete visual stimuli. Predictions and experiment show strong agreement, in particular confirming BOLD waves propagating for at least 5-10 mm across the cortical surface at speeds of 2-12 mm s-1. These observations enable fundamentally new approaches to fMRI analysis, crucial for fMRI data acquired at high spatial resolution.

Figure 1. The spatiotemporal hemodynamic model.

A: The hemodynamic response is driven by a localized spatiotemporal input, which represents neural activity and causes a change in arterial inflow of blood, which sets up a pressure gradient ∇P. B: This mass inflow deforms surrounding tissue and thus exerts pressure on nearby vessels. C: The rise in pressure causes further volume changes in adjacent vessels, which propagate outwards via interactions with successive regions of tissue. Damping of the response through blood viscosity and losses via outflow. D: The increase of local inflow increases oxygenated hemoglobin (oHb), reducing the amount of local deoxygenated hemoglobin (dHb). As oxygen is simultaneously passively extracted from blood, oHb is converted to dHb, causing a delayed rise of dHb during vessel relaxation.

Figure 2. Predicted responses vs. x and t for a range of physiologically plausible values of of ν_β and Γ.

Each column represents a particular ν_β – as labeled at the top, while each row corresponds to a different Γ – as labeled at the left.

Figure 3. Experimental paradigm and evoked responses.

A: The visual stimulus used in the experiment, where it is superposed on a gray background. The solid black circles and cross are always present, to aid fixation. The three dashed isoeccentric rings reverse 4 times per second, where the two patterns are shown at the bottom of this frame. B: Retinotopic mapping the allowed the locations of the 3 concentric rings to be independently identified, where the colors represent the measured eccentricity, colored from red at the fovea to blue at 6°, as shown in the circular inset, with magenta and gray at larger eccentricities . C: Spatiotemporal snapshots showing the response to first ring at various times after stimulus onset. The colors represent percentage signal change, as labeled on the colorbar.

Figure 4. Traveling waves on the flattened cortical surface.

A: Normalized Fourier power at the peak response frequency 0.1 Hz, calculated for voxels on the flattened surface, with the red rectangle outlining the response at 0.6° eccentricity (the line of high activation just below is at 1.6°). This power level reveals which voxels respond strongly to the experimental manipulation. B: Voxels that are coherent (Methods) with the stimulus (>0.4) provide an estimate of the approximately straight isoeccentricity curve on the cortex (the solid curve at x = 0). A polynomial curve is fitted to estimate the centerline, and perpendiculars are taken from this to find x. C: Averages of signals at all points with equal x, plotted vs. x and t, showing evidence of damped traveling waves in the form of sloping contours at left and right. The average percentage signal change ranges from −0.4 to 0.4 as indicated by the colorbar. D: Estimate of the 0.1 Hz signal delay from the stimulus onset vs. distance. E: Spatial cross-sections of the spatiotemporal response, relative to baseline, at t = 7.5 s (red), showing a clear rise in amplitude, and at t = 12.5 s (black), the central response has decreased and the surrounding signal remains above baseline.

Figure 5. Quantifying the spatiotemporal response.

A Calculation of the instantaneous phase reveal phase fronts of the response. These fronts are nearly stationary at the center and propagate with roughly constant velocity away from the center at |x|>1 mm. They are well described with straight line fits, as seen in panel B: toward the fovea (F) (red) and toward the periphery (P) (black). Along these slopes the BOLD signal decays exponentially in time C: with decay constants Γ_P = −0.56±0.04 s⁻¹, Γ_F = −0.86±0.08 s⁻¹, and D: as a function of perpendicular distance, with decay constants K_P = 0.32±0.02 mm⁻¹, K_F = 0.38±0.02 mm⁻¹. The error bars are 1 s.e.m, and errors of the parameter estimates are 1 s.d. E: Propagation velocity and damping rate for each of the subjects and their hemispheres. Red data points are the foveal values (F), while values toward the periphery (P) are shown in black. These points show a wide scatter, corresponding to individual differences, but there is a significant positive correlation. A straight line fit to this log-log plot yields an overall trendline that corresponds to a power law with exponent 0.24±0.09 (s.d).