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

Abstract

Background Influx and clearance of substances in the brain parenchyma occur by a combination of diffusion and convection, but the relative importance of these mechanisms is unclear. Accurate modeling of tracer distributions in the brain relies on parameters that are partially unknown and with literature values varying by several orders of magnitude. In this work, we rigorously quantified the variability of tracer distribution in the brain resulting from uncertainty in diffusion and convection model parameters. Methods Using the convection–diffusion–reaction equation, we simulated tracer distribution 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. Results In models of pure diffusion, the expected amount of tracer in the gray matter reached peak value after 15 h, while the white matter did not reach peak within 24 h with high likelihood. Models of the glymphatic system were similar qualitatively to the models of pure diffusion with respect to expected time to peak but displayed less variability. However, the expected time to peak was reduced to 11 h 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 h for the gray matter. Conclusion Even 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 large-scale directional structure is included in the glymphatic circulation.

Apparent diffusion coefficient estimates based on 24 hours tracer movement support glymphatic transport in human cerebral cortex

“…However, all these studies were done with modeling that was on the micro-scale over shorter time periods. To the authors' knowledge, the only other study 35 that has considered macroscopic modeling on the time-scales of hours and days, where uncertainties representing both variations in ADC and paravascular velocities where modelled with extensive testing using Monte Carlo methods. They found that, in particular, the CSF tracer distribution within the deep white matter found in 11 could not be explained by diffusion alone.…”

Realistic boundary conditions for perivascular pumping in the mouse brain reconcile theory, simulation, and experiment

“…Other osmotic processes might be at play. 145 Non-physiological flow induced by injection of tracer parti-146 cles has been offered as an explanation (24,(30)(31)(32)(33)(34), though 147 Mestre, Tithof et al (6) measured flow speeds that had in-148 significant dependence on whether injection was in progress, 149 and insignificant decay after injection ceased. Those authors 150 also demonstrated that altering the artery wall motion sub-151 stantially changed CSF flow characteristics and significantly 152 reduced the mean flow speed.…”

“…Hadaczek et al (18) proposed that the dilations and constric-28 tions traveling along artery walls with each heart beat might 29 drive CSF in the same direction, in a peristalsis-like mecha-30 nism they dubbed "perivascular pumping." As evidence, they 31 presented experimental results showing that macromolecules 32 injected into the central nervous systems of rats were trans-33 ported further in animals with beating hearts than in ani-34 mals whose hearts had recently been stopped. Iliff et al (19)…”

Modulating the Blood-Brain Barrier by Light Stimulation of Molecular-Targeted Nanoparticles

“…blood to the brain parenchyma by two main features, including the tight junction (TJ) complex that seals the paracellular space between the endothelial cells, and low level of transcytosis through the endothelium (5)(6)(7)(8). Prior approaches to circumvent the BBB have led to limited success: convection enhanced delivery has limited success in the clinical trials (9), intrathecal delivery has limited parenchymal penetration (10). Methods to increase BBB permeability such as using high osmotic mannitol have significant neurotoxicity (11,12).…”