Speaker
Description
Endothelial cells organise within developing tissues to form a vascular network which remodels and matures over time. The mechanisms underlying network formation can be studied experimentally through the tube formation assay, and computationally using Cellular Potts Models or Partial Differential Equations. Such models offer a means to investigate proposed mechanisms which may drive endothelial network formation, such as chemotaxis, cell elongation-driven alignment, and mechanotaxis. However, using models to determine the effect of such processes on network formation remains a computational and theoretical challenge. Models produce time varying data with heterogeneous spatial structure, and the difficulty quantifying and comparing such simulated and experimental data hinders traditional modelling tasks such as parameter inference and model selection. We expand upon recent work \cite{tms} which proposes the combination Topological Data Analysis and Approximate Bayesian Computation to understand complex spatio-temporal models. We use experimental and simulated data from a recent modelling study \cite{falsifying} to quantify the effect of spatial model parameters on network formation. Using extended persistence \cite{extpers}, we derive eight topological feature types which evolve over time in model data. We compare continuum and cell-based approaches to network formation models, and describe how model mechanisms and model parameters affect their topological properties.
Bibliography
@article{falsifying,
title = {Falsifying computational models of endothelial cell network formation through quantitative comparison with in vitro models},
volume = {21},
issn = {1553-7358},
url = {https://dx.plos.org/10.1371/journal.pcbi.1012965},
doi = {10.1371/journal.pcbi.1012965},
language = {en},
number = {4},
urldate = {2026-03-15},
journal = {PLOS Computational Biology},
author = {Vergroesen, Tessa M. and Vermeulen, Vincent and Merks, Roeland M. H.},
editor = {Smith, Amber M},
month = apr,
year = {2025},
pages = {e1012965},
}
@article{tms,
title = {Topological model selection: a case-study in tumour-induced angiogenesis},
copyright = {https://creativecommons.org/licenses/by/4.0/},
issn = {1367-4811},
shorttitle = {Topological model selection},
url = {https://academic.oup.com/bioinformatics/advance-article/doi/10.1093/bioinformatics/btag065/8516556},
doi = {10.1093/bioinformatics/btag065},
language = {en},
urldate = {2026-03-15},
journal = {Bioinformatics},
author = {McDonald, Robert A and Byrne, Helen M and Harrington, Heather A and Thorne, Thomas and Stolz, Bernadette J},
editor = {Kendziorski, Christina},
month = mar,
year = {2026},
pages = {btag065},
}
@article{extpers,
title = {Extending {Persistence} {Using} {Poincaré} and {Lefschetz} {Duality}},
volume = {9},
copyright = {http://www.springer.com/tdm},
issn = {1615-3375, 1615-3383},
url = {http://link.springer.com/10.1007/s10208-008-9027-z},
doi = {10.1007/s10208-008-9027-z},
language = {en},
number = {1},
urldate = {2026-03-15},
journal = {Foundations of Computational Mathematics},
author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John},
month = feb,
year = {2009},
pages = {79--103},
}
