# Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke; Kim H. Parker; Ling Y. Wee; Nicholas M. Fisk; Spencer J. Sherwin

- Volume: 37, Issue: 4, page 557-580
- ISSN: 0764-583X

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topFranke, Victoria E., et al. "Time domain computational modelling of 1D arterial networks in monochorionic placentas." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.4 (2003): 557-580. <http://eudml.org/doc/244652>.

@article{Franke2003,

abstract = {In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/$hp$ element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance. We then present results for the waveform patterns and the volume fluxes throughout a simplified model of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. The effects of varying the time period of the two fetus’ heart beats, increasing the input flux of one fetus and the role of terminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by the computational model and demonstrate the applicability of the methods to the simulation of flows in arterial networks.},

author = {Franke, Victoria E., Parker, Kim H., Wee, Ling Y., Fisk, Nicholas M., Sherwin, Spencer J.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {wave propagation; mathematical model; spectral/$hp$ element; arterial networks; monochorionic placentas; non-linear; Wave propagation; spectral/ hp element},

language = {eng},

number = {4},

pages = {557-580},

publisher = {EDP-Sciences},

title = {Time domain computational modelling of 1D arterial networks in monochorionic placentas},

url = {http://eudml.org/doc/244652},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Franke, Victoria E.

AU - Parker, Kim H.

AU - Wee, Ling Y.

AU - Fisk, Nicholas M.

AU - Sherwin, Spencer J.

TI - Time domain computational modelling of 1D arterial networks in monochorionic placentas

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 4

SP - 557

EP - 580

AB - In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/$hp$ element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance. We then present results for the waveform patterns and the volume fluxes throughout a simplified model of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. The effects of varying the time period of the two fetus’ heart beats, increasing the input flux of one fetus and the role of terminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by the computational model and demonstrate the applicability of the methods to the simulation of flows in arterial networks.

LA - eng

KW - wave propagation; mathematical model; spectral/$hp$ element; arterial networks; monochorionic placentas; non-linear; Wave propagation; spectral/ hp element

UR - http://eudml.org/doc/244652

ER -

## References

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