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

Published online by Cambridge University Press:  15 November 2003

Victoria E. Franke ,
Kim H. Parker ,
Ling Y. Wee ,
Nicholas M. Fisk  and
Spencer J. Sherwin
Victoria E. Franke
Affiliation:
Biomedical Flow Group, Department of Aeronautics, Imperial College London, South Kensington Campus London SW7 2AZ, UK. v.shenton@imperial.ac.uk., s.sherwin@imperial.ac.uk., web page:
Kim H. Parker
Affiliation:
Department of Bioengineering, Imperial College London, South Kensington Campus London SW7 2AZ, UK.
Ling Y. Wee
Affiliation:
Institute of Reproductive and Developmental Biology, Imperial College London at Queen Charlotte's Hospital, Hammersmith Campus.
Nicholas M. Fisk
Affiliation:
Institute of Reproductive and Developmental Biology, Imperial College London at Queen Charlotte's Hospital, Hammersmith Campus.
Spencer J. Sherwin
Affiliation:
Biomedical Flow Group, Department of Aeronautics, Imperial College London, South Kensington Campus London SW7 2AZ, UK. v.shenton@imperial.ac.uk., s.sherwin@imperial.ac.uk., web page:
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Abstract

In this paper we outline the hyperbolic system of governing equationsdescribing one-dimensional blood flow in arterial networks. Thissystem is numerically discretised using a discontinuous Galerkinformulation with a spectral/hp element spatial approximation. Weapply the numerical model to arterial networks in theplacenta. Starting with a single placenta we investigate the velocity waveformin the umbilical artery and its relationship with the distalbifurcation geometry and the terminal resistance. We then present resultsfor the waveform patterns and the volume fluxes throughout a simplifiedmodel of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. Theeffects of varying the time period of the two fetus' heart beats, increasing the input flux of one fetus and the role ofterminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by thecomputational model and demonstrate the applicability of themethods to the simulation of flows in arterial networks.

Keywords

Wave propagationmathematical modelspectral/hp elementarterial networksmonochorionicplacentasnon-linear.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 557 - 580
Copyright
© EDP Sciences, SMAI, 2003

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