Porous Media Group
MSc project

Penalized Splitting in Modelling Structures of Live Tissues, 2020

Caroline Myklebust

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Advisors: Erik Hanson, Jan Martin Nordbotten

Short description of the project:

This thesis presents an addition to current mathematical models of vascular tissue. The hypothesis is that by penalizing splitting points in a structure, the optimal solution will include fewer splittings. As this becomes a matter of optimal resource allocation, the theory of Optimal Transport is presented. This is followed by describing a recent model of the structures of interest. To gain a deeper understanding of how to classify splitting points, their properties are studied both dynamically and using image processing. The results are two proposed PDEs that incorporate the splitting penalty properties.

Experiments show that both of the derived models can penalize splitting points. However, they both focus on removing the smallest splitting points of the structure. A closer examination yields that both models have successfully targeted some of the desired points.

Link to the thesis at Bora-UiB: https://bora.uib.no/bora-xmlui/handle/1956/22731