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Modelling solute transport in the brain microcirculation: is it really well mixed inside the blood vessels?

Berg, Maxime and Davit, Yohan and Quintard, Michel and Lorthois, Sylvie Modelling solute transport in the brain microcirculation: is it really well mixed inside the blood vessels? (2020) Journal of Fluid Mechanics, 884 (A39). 1-43. ISSN 0022-1120

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Official URL: https://doi.org/10.1017/jfm.2019.866


Most network models describing solute transport in the brain microcirculation use the well-mixed hypothesis and assume that radial gradients inside the blood vessels are negligible. Recent experimental data suggest that these gradients, which may result from heterogeneities in the velocity field or consumption in the tissue, may in fact be important. Here, we study the validity of the well-mixed hypothesis in network models of solute transport using theoretical and computational approaches. We focus on regimes of weak coupling where the transport problem inside the vasculature is independent of the concentration field in the tissue. In these regimes, the boundary condition between vessels and tissue can be modelled by a Robin boundary condition. For this boundary condition and for a single cylindrical capillary, we derive a one-dimensional cross-section average transport problem with dispersion and exchange coefficients capturing the effects of radial gradients. We then extend this model to a network of connected tubes and solve the problem in a complex anatomical network. By comparing with results based on the well-mixed hypothesis, we find that dispersive effects are a fundamental component of transport in transient situations with relatively rapid injections, i.e. frequencies above one Hertz. For slowly varying signals and steady states, radial gradients also significantly impact the spatial distribution of vessel/tissue exchange for molecules that easily cross the blood brain barrier. This suggests that radial gradients cannot be systematically neglected and that there is a crucial need to determine the impact of spatio-temporal heterogeneities on transport in the brain microcirculation.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
ERC BrainMicroFlow GA615102 - NIH NCI IMAT R21CA214299 - CALMIP (Grant 2016-P1541)
Deposited On:20 Dec 2019 10:06

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