Shock formation and non-linear dispersion in a microvascular capillary network.
Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhraeus effect, the Fåhraeus-Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhraeus effect, providing a novel mechanism for non-linear dispersion in microvascular networks.
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School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Richardson
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Waters
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Jensen
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D002196:Capillaries / Q000502:physiology*; D004912:Erythrocytes / Q000502:physiology; D006400:Hematocrit; D018056:Hemorheology / Q000379:methods; D006801:Humans; D008833:Microcirculation / Q000502:physiology*; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted