  Efficient uncertainty quantification algorithms are key to understand the
propagation of uncertainty -- from uncertain input parameters to uncertain
output quantities -- in high resolution mathematical models of brain
physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and
multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon
standard Monte Carlo (MC) methods, but their applicability and performance in
biomedical applications is underexplored. In this paper, we design and apply
QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of
tracer transport within the brain. We show that QMC outperforms standard MC
simulations when the number of random inputs is small. MLMC considerably
outperforms both QMC and standard MC methods and should therefore be preferred
for brain transport models.
