Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T14:01:10.847Z Has data issue: false hasContentIssue false
  • English
  • Français

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. [email protected]., [email protected]., 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. [email protected]., [email protected]., web page:
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cockburn, B. and Shu, C.W., Runge-Kutta, TVB projection discontinous Galerkin finite element methods for conservation laws II general framework. Math. Commun. 52 (1989) 411-435.
Denbow, M.L., Cox, P., Talbert, D. and Fisk, N.M., 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. CrossRef
Denbow, N.M., Cox, P., Taylor, M., Hammal, D.M. and Fisk, N.M., 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. CrossRef
L. Formaggia, F. Nobile and A. Quarteroni, 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.
L. Formaggia and A. Veneziani, Geometrical multiscale models of the cardiovascular system: from lumped parameters to 3d simulations. VKI Lecture Series (2003).
T.J. Pedley, The fluid mechanics of large blood vessels, volume First Edition, Cambridge University Press, Cambridge (1980).
Lomtev, I., Quillen, C.W. and Karniadakis, G., Spectral/hp methods for viscous compressible flows on unstructured 2d meshes. J. Comput. Phys. 144 (1998) 325-357. CrossRef
W.W. Nichols and M.F. O'Rourke, McDonald's Blood Flow in Arteries. Theoretical, experimental and clinical principles, volume Fourth Edition, Arnold, London (1998).
S.J. Sherwin, L. Formaggia, J. Peiro and V. Franke, 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).
S.J. Sherwin, V. Franke, J. Peiro and K. Parker, One-dimensional modelling of a vascular network in space-time variables. Submitted to J. Eng. Math. (2003).
S.J. Sherwin, Dispersion analysis of the continuous and discontinuous Galerkin formulations, in International Symposium on Discontinuous Galerkin Methods, Newport, RI (1999).
Smith, N.P., Pullan, A.J. and Hunter, P.J., An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62 (2002) 990-1018. CrossRef
T.Y.T. Tam, M.J.O. Taylor, L.Y. Wee, T. Vanderheydem and N.M. Fisk, Modified quintero staging system for twin-twin transfusion syndrome. Submitted to Ultrasound Obstet. Gynecol. (2003).
M.J.O. Taylor, M.L. Denbow, K.R. Duncan, T.G. Overton and N.M. Fisk, Anatenatal factors at diagnosis that predict outcome in twin-twin transfusion syndrome. Am. J. Obstet. Gynecol. (2000) 1023-1028.
Taylor, M.J.O., Denbow, M.L., Tanawattanacharoen, S., Gannon, C., Cox, P. and Fisk, N.M., Doppler detection of arterio-arterial anastomoses in monochorionic twins: feasibility and clinical application. Hum. Reprod. 15 (2000) 1632-1636. CrossRef
Taylor, M.J.O., Farquaharson, D., Cox, P.M. and Fisk, N.M., Identification of arterio-venous anastomoses in vivo in monochorionic twin pregnancies: preliminary report. Ultrasound Obstet. Gynecol. 16 (2000) 218-222. CrossRef
Taylor, M.J.O., Talbert, D.G. and Fisk, N.M., Mapping the monochorionic equator. Ultrasound Obstet. Gynecol. 14 (1999) 372-374. CrossRef
J.J. Wang and K.H. Parker, Wave propagation in a model of the arterial circulation. Submitted to J. Biomech. (2003).
Wee, L.Y. and Fisk, N.M., The twin-twin transfusion syndrome. Semin. Neonatol. 7 (2002) 187-202. CrossRef