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A hybrid approach to model blood flow at the scale of the cortex in human brain microcirculation

Peyrounette, Myriam and Davit, Yohan and Lorthois, Sylvie A hybrid approach to model blood flow at the scale of the cortex in human brain microcirculation. (2017) In: Blood flow: current state and future prospects, 9 October 2017 - 11 October 2017 (Paris, France). (Unpublished)

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Abstract

The human brain microcirculation presents a dual multiscale architecture. On the one hand, the arteriolar and venular trees (10-100μm in vessel diameter) supply the cortex with blood, which carries oxygen and nutrients, and drain the metabolic waste. On the other hand, the capillaries (1-10μm in diameter) constitute a space-filling network connecting the larger arteriolar and venular trees. An important role of these capillaries is to facilitate molecular exchanges between blood and the cerebral tissue, therefore supporting the neuronal metabolic demand. Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction, which in turn may affect neuronal activity. Modelling is key in understanding such systems and the systemic impact of localized effects, such as capillary stalling occuring early in Alzheimer’s disease. In particular, network approaches, which model dynamics at the scale of individual vessels, have significantly advanced our understanding of blood flow, mass transfers and regulation mechanisms [1]. However, such methods are still intractable at clinically relevant scales, typically the whole cortex, primarily because of the computational cost associated with the huge number of vessels involved. Here, we present a hybrid approach to modelling blood flow in the microcirculation by treating the capillary bed as a continuum [2] and the arteriolar and venular trees as a network. The continuum model [3] characterizes the flow at a scale much larger than the length of a capillary and can be solved using finite volume methods on a coarse grid, therefore significantly decreasing the computational cost. The arteriolar and venular trees, however, have a quasifractal structure, thus cannot be homogenized and must be treated as a network. To capture the strong pressure gradients that build up in the vicinity of coupling sites, we introduce an analytical approximation (inspired by [4]) of the local pressure fields. The resulting coupling model consists in a single linear system describing both the network and continuum. Comparisons between the hybrid and full network approaches show very good agreement for simple configurations with one or two coupling points, as well as for realistic structures displaying more than 200 coupling points (local pressure errors < 6 %). The hybrid approach further yields an important computational gain, with an acceleration of 360 compared to the network approach. The accuracy and the computational benefit of the hybrid approach for blood flow modelling opens the way to include additional levels of complexity in the future and ultimately to simulate mass transfers in the whole brain. References [1] S.Lorthois et al., NeuroImage, 54, 1031–1042 & 2840–2853, (2011) [2] K.Erbertseder et al., PLoS ONE, 7, e31966, (2012) [3] Y.Davit et al., Advances in Water Resources, 62, 178–206, (2013) [4] D.Peaceman et al., Society of Petroleum Engineers Journal, 18, 183–194, (1978)

Item Type:Conference or Workshop Item (Poster)
Additional Information:No full-text document attached to this repository.
Audience (conference):International conference without published proceedings
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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)
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Funders:
ERC Consolidator BrainMicroFlow (GA615102)
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Deposited On:30 May 2018 06:44

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