2014 journal article

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

JOURNAL OF FLUID MECHANICS, 738, 492–521.

By: A. Kuznetsov, D. Blinov*, A. Avramenko, I. Shevchuk, A. Tyrinov * & I. Kuznetsov

co-author countries: Ukraine πŸ‡ΊπŸ‡¦ United States of America πŸ‡ΊπŸ‡Έ
author keywords: biomedical flows; convection in cavities; low-dimensional models
Source: Web Of Science
Added: August 6, 2018

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.