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/ 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.
Mots clés : wave propagation, mathematical model, spectral/$hp$ element, arterial networks, monochorionic placentas, non-linear
@article{M2AN_2003__37_4_557_0,
author = {Franke, Victoria E. and Parker, Kim H. and Wee, Ling Y. and Fisk, Nicholas M. and Sherwin, Spencer J.},
title = {Time domain computational modelling of {1D} arterial networks in monochorionic placentas},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {557--580},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003047},
mrnumber = {2018430},
zbl = {1065.92017},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003047/}
}
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: Modélisation mathématique et analyse numérique PY - 2003 SP - 557 EP - 580 VL - 37 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003047/ DO - 10.1051/m2an:2003047 LA - en ID - M2AN_2003__37_4_557_0 ER -
%0 Journal Article %A Franke, Victoria E. %A Parker, Kim H. %A Wee, Ling Y. %A Fisk, Nicholas M. %A Sherwin, Spencer J. %T Time domain computational modelling of 1D arterial networks in monochorionic placentas %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 557-580 %V 37 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003047/ %R 10.1051/m2an:2003047 %G en %F M2AN_2003__37_4_557_0
Franke, Victoria E.; Parker, Kim H.; Wee, Ling Y.; Fisk, Nicholas M.; Sherwin, Spencer J. Time domain computational modelling of 1D arterial networks in monochorionic placentas. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 4, pp. 557-580. doi : 10.1051/m2an:2003047. http://www.numdam.org/articles/10.1051/m2an:2003047/
[1] and, TVB Runge-Kutta projection discontinous Galerkin finite element methods for conservation laws II general framework. Math. Commun. 52 (1989) 411-435. | Zbl
[2] ,, and, Colour doppler energy insonation of placental vasculature in monochorionic twins: absent arterio-arterial anastomoses in association with twin-to-twin transfusion syndrome. Br. J. Obstet. Gynecol. 105 (1998) 760-765.
[3] ,,, and, Placental angioarchitecture in monochorionic twin pregnancies: relationship to fetal growth, feto-fetal transfusion syndrome, fetofetal transfusion syndrome, and pregnancy outcome. Am. J. Obstet. Gynecol. 182 (2000) 417-426.
[4] , and, A one dimensional model for blood flow: application to vascular prosthesis, in Mathematical Modeling and Numerical Simulation in Continuum Mechanics, I. Babuska, T. Miyoshi, and P.G. Ciarlet Eds., Lect. Notes Comput. Sci. Eng. 19 (2002) 137-153. | Zbl
[5] and, Geometrical multiscale models of the cardiovascular system: from lumped parameters to 3d simulations. VKI Lecture Series (2003).
[6] , The fluid mechanics of large blood vessels, volume First Edition, Cambridge University Press, Cambridge (1980). | Zbl
[7] , and, Spectral/ methods for viscous compressible flows on unstructured 2d meshes. J. Comput. Phys. 144 (1998) 325-357. | Zbl
[8] and, McDonald's Blood Flow in Arteries. Theoretical, experimental and clinical principles, volume Fourth Edition, Arnold, London (1998).
[9] ,, and, Computational modelling of 1d blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Submitted to Int. J. Numer. Method Fluid (2003). | MR | Zbl
[10] ,, and, One-dimensional modelling of a vascular network in space-time variables. Submitted to J. Eng. Math. (2003). | MR
[11] , Dispersion analysis of the continuous and discontinuous Galerkin formulations, in International Symposium on Discontinuous Galerkin Methods, Newport, RI (1999). | Zbl
[12] , and, An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62 (2002) 990-1018. | Zbl
[13] ,,, and, Modified quintero staging system for twin-twin transfusion syndrome. Submitted to Ultrasound Obstet. Gynecol. (2003).
[14] ,,, and, Anatenatal factors at diagnosis that predict outcome in twin-twin transfusion syndrome. Am. J. Obstet. Gynecol. (2000) 1023-1028.
[15] ,,,, and, Doppler detection of arterio-arterial anastomoses in monochorionic twins: feasibility and clinical application. Hum. Reprod. 15 (2000) 1632-1636.
[16] ,, and, Identification of arterio-venous anastomoses in vivo in monochorionic twin pregnancies: preliminary report. Ultrasound Obstet. Gynecol. 16 (2000) 218-222.
[17] , and, Mapping the monochorionic equator. Ultrasound Obstet. Gynecol. 14 (1999) 372-374.
[18] and, Wave propagation in a model of the arterial circulation. Submitted to J. Biomech. (2003).
[19] and, The twin-twin transfusion syndrome. Semin. Neonatol. 7 (2002) 187-202.
Cité par Sources :
