Abstract
Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain—tens of billions—prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future.
Highlights
Blood flow through cerebral microcirculation is the primary driver of oxygen transport and waste removal in the cortex, making microcirculation fundamental to cerebral physiology [1,2,3]
Our goal is to assess the robustness of the coupling model and the relevance of strategies that have been adopted during its development
The first test case analyzes the impact of the size of finite volume (FV) cells on the accuracy of the model (Fig 6i(a))
Summary
Blood flow through cerebral microcirculation is the primary driver of oxygen transport and waste removal in the cortex, making microcirculation fundamental to cerebral physiology [1,2,3]. Obstructions of small vessels during strokes, long-term capillary rarefaction or lymphocyte stalling occurring early in Alzheimer’s Disease (AD) [5] may limit the transport of oxygen to the cerebral tissue and result in energy failure and neuronal death Understanding how these disease-induced modifications of the network architecture affect transport mechanisms in the brain is a fundamental challenge that may lead to clinical breakthroughs. One of the most complex aspect of the problem is that it involves a broad range of spatial scales [6], ranging from the scale of the whole brain (*10 cm, see Fig 1(a)) to the microscopic scale that we characterize here by the length of a capillary vessel lcap (*50 μm, see Fig 1(d)), with an intermediate macroscopic scale corresponding to the thickness of the cortex (*3 mm, see Fig 1(b)) This multiscale architecture makes it difficult to understand the mechanisms occurring at the different levels, and to understand and assess the systemic impact of localized effects
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