On the exact solution of the Riemann problem for blood flow in human veins, including collapse

C. Spiller, E.F. Toro, M.E. Vázquez-Cendón and C. Contarino

Applied Mathematics and Computation, 2017, vol. 303, issue C, 178-189

Abstract: We solve exactly the Riemann problem for the non-linear hyperbolic system governing blood flow in human veins and note that, as modeled here, veins do not admit complete collapse, that is zero cross-sectional area A. This means that the Cauchy problem will not admit zero cross-sectional areas as initial condition. In particular, rarefactions and shock waves (elastic jumps), classical waves in the conventional Riemann problem, cannot be connected to the zero state with A=0. Moreover, we show that the area A* between two rarefaction waves in the solution of the Riemann problem can never attain the value zero, unless the data velocity difference uR−uL tends to infinity. This is in sharp contrast to analogous systems such as blood flow in arteries, gas dynamics and shallow water flows, all of which admitting a vacuum state. We discuss the implications of these findings in the modelling of the human circulation system that includes the venous system.

Keywords: Blood flow; One-dimensional model; Veins; Collapse; Riemann problem (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:303:y:2017:i:c:p:178-189

DOI: 10.1016/j.amc.2017.01.024

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