Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields

Abstract

BackgroundInflux and clearance of substances in the brain parenchyma occur by a combination of diffusion and convection, but the relative importance of thiese mechanisms is unclear. Accurate modeling of tracer distributions in the brain relies on parameters that are partially unknown and with literature values varying up to 7 orders of magnitude. In this work, we rigorously quantified the variability of tracer enhancement in the brain resulting from uncertainty in diffusion and convection model parameters.\n\nMethodsIn a mesh of a human brain, using the convection-diffusion-reaction equation, we simulated tracer enhancement in the brain parenchyma after intrathecal injection. Several models were tested to assess the uncertainty both in type of diffusion and velocity fields and also the importance of their magnitude. Our results were compared with experimental MRI results of tracer enhancement.\n\nResultsIn models of pure diffusion, the expected amount of tracer in the gray matter reached peak value after 15 hours, while the white matter does not reach peak within 24 hours with high likelihood. Models of the glymphatic system behave qualitatively similar as the models of pure diffusion with respect to expected time to peak but display less variability. However, the expected time to peak was reduced to 11 hours when an additional directionality was prescribed for the glymphatic circulation. In a model including drainage directly from the brain parenchyma, time to peak occured after 6-8 hours for the gray matter.\n\nConclusionEven when uncertainties are taken into account, we find that diffusion alone is not sufficient to explain transport of tracer deep into the white matter as seen in experimental data. A glymphatic velocity field may increase transport if a directional structure is included in the glymphatic circulation.