The brain microcirculation plays a key role in cerebral physiology and neuronal activation. In the case of degenerative diseases such as Alzheimer’s, severe deterioration of the microvascular networks (e.g. vascular occlusions) limit blood flow, thus oxygen and nutrients supply, to the cortex, eventually resulting in neurons death. In addition to functional neuroimaging, modelling is a valuable tool to investigate the impact of structural variations of the microvasculature on blood flow and mass transfers. In the brain microcirculation, the capillary bed contains the smallest vessels (1-10 μm in diameter) and presents a mesh-like structure embedded in the cerebral tissue. This is the main place of molecular exchange between blood and neurons. The capillary bed is fed and drained by larger arteriolar and venular tree-like vessels (10-100 μm in diameter). For the last decades, standard network approaches have significantly advanced our understanding of blood flow, mass transport and regulation mechanisms in the human brain microcirculation. By averaging flow equations over the vascular cross-sections, such approaches yield a one-dimensional model that involves much fewer variables compared to a full three-dimensional resolution of the flow. However, because of the high density of capillaries, such approaches are still computationally limited to relatively small volumes (<100 mm3). This constraint prevents applications at clinically relevant scales, since standard imaging techniques only yield much larger volumes (∼100 cm3), with a resolution of 1-10 mm3. To get around this computational cost, we present a hybrid approach for blood flow modelling where the capillaries are replaced by a continuous medium. This substitution makes sense since the capillary bed is dense and space-filling over a cut-off length of ∼50 μm. In this continuum, blood flow is characterized by effective properties (e.g. permeability) at the scale of a much larger representative volume. Furthermore, the domain is discretized on a coarse grid using the finite volume method, inducing an important computational gain. The arteriolar and venular trees cannot be homogenized because of their quasi-fractal structure, thus the network approach is used to model blood flow in the larger vessels. The main difficulty of the hybrid approach is to develop a proper coupling model at the points where arteriolar or venular vessels are connected to the continuum. Indeed, high pressure gradients build up at capillary-scale in the vicinity of the coupling points, and must be properly described at the continuum-scale. Such multiscale coupling has never been discussed in the context of brain microcirculation. Taking inspiration from the Peaceman “well model” developed for petroleum engineering, our coupling model relies on to use analytical solutions of the pressure field in the neighbourhood of the coupling points. The resulting equations yield a single linear system to solve for both the network part and the continuum (strong coupling). The accuracy of the hybrid model is evaluated by comparison with a classical network approach, for both very simple synthetic architectures involving no more than two couplings, and more complex ones, with anatomical arteriolar and venular trees displaying a large number of couplings. We show that the present approach is very accurate, since relative pressure errors are lower than 6 %. This lays the goundwork for introducing additional levels of complexity in the future (e.g. non uniform hematocrit). In the perspective of large-scale simulations and extension to mass transport, the hybrid approach has been implemented in a C++ code designed for High Performance Computing. It has been fully parallelized using Message Passing Interface standards and specialized libraries (e.g. PETSc). Since the present work is part of a larger project involving several collaborators, special care has been taken in developing efficient coding strategies.
| Identifer | oai:union.ndltd.org:univ-toulouse.fr/oai:oatao.univ-toulouse.fr:19543 |
| Date | 25 October 2017 |
| Creators | Peyrounette, Myriam |
| Contributors | Institut National Polytechnique de Toulouse - INPT (FRANCE), Institut de Mécanique des Fluides de Toulouse - IMFT (Toulouse, France) |
| Source Sets | Université de Toulouse |
| Language | English |
| Detected Language | English |
| Type | PhD Thesis, PeerReviewed, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | http://oatao.univ-toulouse.fr/19543/ |
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