Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo

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. Mathematical models in biology involve many parameters that are uncertain and uncertainty quantification techniques are needed to determine the reliability of the model results. However, this is nontrivial given the complexity of the models and geometries involved. In this paper, we design and apply quasi Monte Carlo and multilevel Monte Carlo (MLMC) methods to quantify the uncertainty in a convection‐diffusion model for brain tracer transport. Numerical experimentation shows that MLMC should be preferred for brain transport models.