Fig. 9

Uncertainty quantification for Model V1. The average tracer concentration in a subregion of a gray matter \(q_g\) and b white matter \(q_w\) as defined by (14). 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. Expected values for \(q_g\) are nearly identical as for Model D1 and D2, but variation is much lower. Expected values for \(q_w\) are lower than for Model D1 and variation is much lower (c). The probability density functions (PDFs) corresponding to \(q_g\) at 3, 5, 8 and 24 h after tracer injection. The PDFs show very low variation. Variation increases slightly over time. d Histogram of white subregion activation time \(f_w\) as defined by (16) (bars), corresponding estimated PDF (orange curve), and corresponding cumulative density function (CDF)