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Numerical modelling of flow in lower urinary tract using high-resolution methods. (English) Zbl 1340.92014
Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 16. Proceedings of the 16th seminar (PANM), Dolní Maxov, Czech Republic, June 3–8, 2012. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-62-2). 21-28 (2013).
This work deals with urethra flow. For the simulation of this flow, the authors propose a numerical scheme based on finite volumes. The model of the bladder contraction consists of the following parts, the model of the time evolution \(\text{Ca}^{2+}\) concentration, the model of the time evolution of the phosphorylation of the light myosin chain, the model of the own contraction based on the growth and remodelling theory (GRT), and the irreversible thermodynamics. The whole voiding model consists of the detrusor smooth muscle cell model and the model of the urethra flow. It is described by a system of ordinary differential equations: 12 equations describing the bladder model and the detrusor contraction during voiding and \(2J\) equations of urethra flow, where \(J\) is the number of finite volumes in which the urethra region is divided.
For the entire collection see [Zbl 1277.65001].

92C35 Physiological flow
76Z05 Physiological flows
76M12 Finite volume methods applied to problems in fluid mechanics
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