Fig. 11

Uncertainty quantification for Model V3. The integrated amount of tracer in the a gray matter \(Q_g\) and b white matter \(Q_w\) over time; \(Q_g\) and \(Q_w\) as defined by (13). The blue curves show the expected value. The light blue vertical bars indicate the variability: 99.73% of the samples fall within the plotted range (with 0.135% of the samples above and 0.135% below). The dashed orange lines in a and b indicate the analogous expected value curve resulting from Model D1 (constant diffusion only), for comparison. Large variations in the white matter is found depending on the inflow velocity. c The probability density functions (PDFs) corresponding to \(Q_g\) at 3, 5, 8 and 24 h after tracer injection. d Histogram of white matter activation time \(F_w\) as defined by (15) (bars), corresponding estimated PDF (orange curve), and corresponding cumulative density function (CDF). We note that the CDF peaks at 0.96 (< 1.0) as some samples never reached the white region activation threshold