Master's Thesis | Martin Berger

Master’s Thesis - An Application of Topological Data Analysis to Fibrin Networks

Topological data analysis (TDA) combines statistical inference methods with algebraic topology, allowing to identity the geometric structure within a dataset.

For my master’s thesis I developed a methodology to analyze microscopic images of fibrin networks using TDA.

Fibrin is a protein which is created from fibrinogen and is involved in blood clotting. Thus, it is of high interest how different volume replacements effect the natural fibrin net structure.

My thesis provides an introduction into the basics of algebraic topology, in particular simplicial complexes. We then discuss persistent homology, the building block of topological data analysis and it’s application to grayscale images.

For a shorter introduction to the field of topological data analysis, check my TDA lecture notes.

References

2020

Thromb. Haem.

Effect of Tranexamic Acid on Coagulation and Fibrin Clot Properties in Children Undergoing Craniofacial Surgery

Christian Fenger-Eriksen, Alexander D’Amore Lindholm, Lisbeth Krogh, Tobias Hell, Martin Berger, and 5 more authors

Thrombosis and Haemostasis, Jan 2020

Bib HTML

@article{FengerEriksen2020,
  doi = {10.1055/s-0039-3402762},
  year = {2020},
  month = jan,
  publisher = {Georg Thieme Verlag {KG}},
  volume = {120},
  number = {03},
  pages = {392--399},
  author = {Fenger-Eriksen, Christian and Lindholm, Alexander D{\textquotesingle}Amore and Krogh, Lisbeth and Hell, Tobias and Berger, Martin and Hermann, Martin and Fries, Dietmar and Juul, Niels and Rasmussen, Mads and Hvas, Anne-Mette},
  title = {Effect of Tranexamic Acid on Coagulation and Fibrin Clot Properties in Children Undergoing Craniofacial Surgery},
  journal = {Thrombosis and Haemostasis},
}