# 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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 37.4 (2010): 557-580. <http://eudml.org/doc/194178>.

@article{Franke2010,

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},

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

language = {eng},

month = {3},

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/194178},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

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.; spectral/ hp element; monochorionic placentas; non-linear

UR - http://eudml.org/doc/194178

ER -

## References

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- L.Y. Wee and N.M. Fisk, The twin-twin transfusion syndrome. Semin. Neonatol.7 (2002) 187-202.

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