Fig. 8

Uncertainty quantification for Model D2. 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. c The probability density functions (PDFs) corresponding to \(q_g\) at 3, 5, 8 and 24 h after tracer injection. 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). Uncertainty in the heterogeneity of the diffusion coefficient leads to a wide range of likely average tracer concentrations in the white matter throughout the time span