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A Mathematical Model of Lymphangiogenesis in a Zebrafish Embryo

Wertheim, Kenneth Y.; Roose, Tiina


Tiina Roose


The lymphatic system of a vertebrate is important in health and diseases. We propose a novel mathematical model to elucidate the lymphangiogenic processes in zebrafish embryos. Specifically, we are interested in the period when lymphatic endothelial cells (LECs) exit the posterior cardinal vein and migrate to the horizontal myoseptum of a zebrafish embryo. We wonder whether vascular endothelial growth factor C (VEGFC) is a morphogen and a chemotactic factor for these LECs. The model considers the interstitial flow driving convection, the reactive transport of VEGFC, and the changing dynamics of the extracellular matrix in the embryo. Simulations of the model illustrate that VEGFC behaves very differently in diffusion and convection-dominant scenarios. In the former case, it must bind to the matrix to establish a functional morphogen gradient. In the latter case, the opposite is true and the pressure field is the key determinant of what VEGFC may do to the LECs. Degradation of collagen I, a matrix component, by matrix metallopeptidase 2 controls the spatiotemporal dynamics of VEGFC. It controls whether diffusion or convection is dominant in the embryo; it can create channels of abundant VEGFC and scarce collagen I to facilitate lymphangiogenesis; when collagen I is insufficient, VEGFC cannot influence the LECs at all. We predict that VEGFC is a morphogen for the migrating LECs, but it is not a chemotactic factor for them.


Wertheim, K. Y., & Roose, T. (2017). A Mathematical Model of Lymphangiogenesis in a Zebrafish Embryo. Bulletin of Mathematical Biology, 79(4), 693-737.

Journal Article Type Article
Acceptance Date Jan 19, 2017
Online Publication Date Feb 23, 2017
Publication Date Apr 1, 2017
Deposit Date Jan 23, 2023
Publicly Available Date Feb 3, 2023
Journal Bulletin of Mathematical Biology
Print ISSN 0092-8240
Electronic ISSN 1522-9602
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 79
Issue 4
Pages 693-737
Keywords Mathematical model; Lymphangiogenesis; Zebrafish; VEGFC; Collagen I; MMP2
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© The Author(s) 2017. This article is published with open access at<br /> Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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