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Non-linear transport phenomena in brain microvascular networks

Berg, Maxime and Merlo, Adlan and Davit, Yohan and Quintard, Michel and Lorthois, Sylvie Non-linear transport phenomena in brain microvascular networks. (2017) In: 9th International Conference on Porous Media - Interpore 2017, 8 May 2017 - 11 May 2017 (Rotterdam, Netherlands). (Unpublished)

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The cerebral microvascular system is key to a large variety of cerebral processes, including oxygen and nutrient delivery to brain cells as well as blood flow regulation as a function of neural activity. It plays a central role in numerous pathologies ranging from stroke to neurodegenerative diseases but the comprehension of the basic mechanisms involved is still largely incomplete. However recent anatomical and functional in-vivo imaging techniques, such as two photon microscopy together with optical manipulation of blood flow, have permitted significant breakthroughs [1]. These methods generate massive amounts of data that are difficult to interpret without proper theoretical and numerical frameworks. In this work, our goal is to develop models for hemodynamics and mass transport in the brain microcirculation, which can be later coupled with in-vivo measurement to understand and solve physiological problems involved in pathologies. To do so is challenging because the brain is a heterogeneous multiscale system with mechanisms occurring over a broad range of spatial and temporal scales. Further, mass and momentum transport are strongly coupled and exhibit non-linear behaviours, making it challenging to develop accurate macroscale models using homogenization techniques. Here, we consider the blood as a monophasic, non-Newtonian fluid whose rheology strongly depends on vessel diameter and discharge hematocrit (i.e. the volume fraction of RBCs in blood flowing through a given vessel). The repartition of RBCs between branches at bifurcations is notoriously difficult to describe, uneven and non-linear. The most popular approach consists in using empirical laws such as the one detailed in [2] to account for phase separation in simple bifurcation geometries. One important aspect of these empirical laws is that they connect flowrate and discharge hematocrit in a non-linear way, so that standard linear pore-network model may fail to capture important features of the flow and of the hemodynamics. For instance, recent work in [4] suggests that such empirical laws may yield strong non-linear effects whereby multiple stationary states with different stabilities are possible, at least for specific network configurations. In our computational framework, non-linear effects are captured using an algorithm based on an iterative solver, which was previously developed by our group (see [3]) and tested for large anatomical networks. To further assess its accuracy and the biological relevance of instabilities, we will present results of the solver for simple networks and compare these with experimental measurements recently obtained using microfluidics (illustrated in figure 1). We then go on to study larger anatomical networks that include thousands of vessels, check if instabilities can be triggered in such configurations, and evaluate their impact on the overall blood dynamics. Finally, we study oxygen transport within microvascular networks and coupling with the RBC distribution. The large size of anatomical networks makes it challenging to use numerical methods such as finite elements or finite differences directly. To circumvent this issue, we develop a mesh reduction approach. On the one hand, homogenization techniques [5] are first used to reduce the 3D transport equation inside the vessel to a 1D axial equation with exchange terms with the surrounding tissues. On the other hand, the transport in the tissues surrounding the vessels is described via a boundary element method (BEM) inspired by Hsu et Secomb [6]. This hybrid approach allows us to significantly reduce the number of unknowns, from hundred of thousands to about a thousand for a single vessel geometry.

Item Type:Conference or Workshop Item (Other)
Additional Information:No full-text document attached to this repository.
Audience (conference):International conference without published proceedings
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:
European Commission
Deposited On:11 Jan 2018 11:21

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