Voxel + venules = multipronged sensor of fine-grained pattern information?
A simple toy simulation of hemodynamic sampling suggests that the filter producing an fMRI voxel's signal is not Gaussian and not space-time separable and that it is unique at each location because its spatiotemporal structure depends on the unique vascular architecture supplying each voxel with its signal and on the dynamics of blood flow. (a) Hemodynamic delay map for a cross-section of the human cortical ribbon (pial surface at the top). This map has been computed by a two-dimensional toy simulation based on a modification of a drawing of cortical vasculature (Fig. 248 in Duvernoy et al. 1999). At each location, the color encodes the time in seconds required for the blood drained from that location to reach the pial surface (top. Because the drawing contained only venules and no capillaries, we simulated capillary drainage assuming that the blood drains in a straight line toward the closest venule end point at a speed of 0.5mm/s. For the venules, we assume a drainage speed of 5mm/s. (Keener and Sneyd (1998) report values of 0.3mm/s for the capillary bed and 5mm/s for venules, so our toy simulation should be slightly conservative, yielding coarser-than-actual spatial filters.) The simulation suggests spherical iso-delay surfaces and Voronoi-type drainage domains. The white square indicates the position of a 1ï‚´1 mm2 voxel. (b) Based on the hemodynamic delay map (a) and assuming that the fMRI acquisition averages across 100 ms (typical EPI slice acquisition time) and is repeated at 100-ms intervals, we computed the spatiotemporal filter of the voxel. Each panel shows the spatial domain, whose BOLD signal (reflecting neural activity at time 0) would be reflected in the voxel (white square in a and b) in each of 9 consecutive acquisitions. Note that the voxel essentially samples its contents in the first acquisition. In the ninth acquisition, by contrast, it samples a discontiguous set of domains distributed around it, whose spatial extent depends on the EPI-slice acquisition time and capillary blood velocity, not on the size of the voxel.