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Approximate modelling of the leftward flow and morphogen transport in the embryonic node by specifying vorticity at the ciliated surface

Published online by Cambridge University Press:  13 December 2013

A. V. Kuznetsov ,
D. G. Blinov ,
A. A. Avramenko ,
I. V. Shevchuk ,
A. I. Tyrinov  and
I. A. Kuznetsov
A. V. Kuznetsov*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
D. G. Blinov
Affiliation:
Institute of Engineering Thermophysics, National Academy of Sciences, Kiev, Ukraine
A. A. Avramenko
Affiliation:
Institute of Engineering Thermophysics, National Academy of Sciences, Kiev, Ukraine
I. V. Shevchuk
Affiliation:
MBtech Group GmbH and Co. KGaA, 70736 Fellbach-Schmiden, Germany
A. I. Tyrinov
Affiliation:
Institute of Engineering Thermophysics, National Academy of Sciences, Kiev, Ukraine
I. A. Kuznetsov
Affiliation:
Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218-2694, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we have developed an approximate method for modelling the flow of embryonic fluid in a ventral node. We simplified the problem as flow in a two-dimensional cavity; the effect of rotating cilia was modelled by specifying a constant vorticity at the edge of the ciliated layer. We also developed an approximate solution for morphogen transport in the nodal pit. The solutions were obtained utilizing the proper generalized decomposition (PGD) method. We compared our approximate solutions with the results of numerical simulation of flow caused by the rotation of 81 cilia, and obtained reasonable agreement in most of the flow domain. We discuss locations where agreement is less accurate. The obtained semi-analytical solutions simplify the analysis of flow and morphogen distribution in a nodal pit.

JFM classification

Biological Fluid Dynamics: Biomedical flows Convection: Convection in cavities Nonlinear Dynamical Systems: Low-dimensional models
Type
Papers
Information
Journal of Fluid Mechanics , Volume 738 , 10 January 2014 , pp. 492 - 521
Copyright
©2013 Cambridge University Press 

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