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      Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms


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          Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symptoms can be easily attributed mistakenly to other common brain diseases. Mathematical models could highlight possible mechanisms of aneurismal development and suggest specialized biomarkers for aneurysms. Existing mathematical models of intracranial aneurysms focus on mechanical interactions between blood flow and arteries. However, these models cannot apply to microaneurysms since the anatomy and physiology at the length scale of cerebral microcirculation are different. In this paper we propose a mechanism for the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells. We model the blood as a non-local non-Newtonian incompressible fluid and solve analytically the Poiseuille flow of such a fluid through an axi-symmetric circular rigid and impermeable pipe in the presence of wall slip. The spatial derivatives of the proposed generalization of the rate of deformation tensor are expressed using Caputo fractional derivatives. The wall slip is represented by the classic Navier law and a generalization of this law involving fractional derivatives. Numerical simulations suggest that hypertension could contribute to microaneurysmal formation.

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          Most cited references 33

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          Glial regulation of the cerebral microvasculature.

          The brain is a heterogeneous organ with regionally varied and constantly changing energetic needs. Blood vessels in the brain are equipped with control mechanisms that match oxygen and glucose delivery through blood flow with the local metabolic demands that are imposed by neural activity. However, the cellular bases of this mechanism have remained elusive. A major advance has been the demonstration that astrocytes, cells with extensive contacts with both synapses and cerebral blood vessels, participate in the increases in flow evoked by synaptic activity. Their organization in nonoverlapping spatial domains indicates that they are uniquely positioned to shape the spatial distribution of the vascular responses that are evoked by neural activity. Astrocytic calcium is an important determinant of microvascular function and may regulate flow independently of synaptic activity. The involvement of astrocytes in neurovascular coupling has broad implications for the interpretation of functional imaging signals and for the understanding of brain diseases that are associated with neurovascular dysfunction.
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            Modeling Dynamic Architectures Using Dy-BIP

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              Glial cells dilate and constrict blood vessels: a mechanism of neurovascular coupling.

              Neuronal activity evokes localized changes in blood flow. Although this response, termed neurovascular coupling, is widely used to monitor human brain function and diagnose pathology, the cellular mechanisms that mediate the response remain unclear. We investigated the contribution of glial cells to neurovascular coupling in the acutely isolated mammalian retina. We found that light stimulation and glial cell stimulation can both evoke dilation or constriction of arterioles. Light-evoked and glial-evoked vasodilations were blocked by inhibitors of cytochrome P450 epoxygenase, the synthetic enzyme for epoxyeicosatrienoic acids. Vasoconstrictions, in contrast, were blocked by an inhibitor of omega-hydroxylase, which synthesizes 20-hydroxyeicosatetraenoic acid. Nitric oxide influenced whether vasodilations or vasoconstrictions were produced in response to light and glial stimulation. Light-evoked vasoactivity was blocked when neuron-to-glia signaling was interrupted by a purinergic antagonist. These results indicate that glial cells contribute to neurovascular coupling and suggest that regulation of blood flow may involve both vasodilating and vasoconstricting components.

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                12 January 2018


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                76Z05 (Primary) 92C50, 92C10 (Secondary)


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