June 24, 2021
Application of topological shooting to biological modelling
Thomas Geert de Jong, Xiamen University
Topological shooting is a technique for differential equations which is applied to prove the existence of solutions with specific monotonicity. It works by constructing (non-empty) open solution sets such that their complement necessarily contains the desired solutions. We applied this technique to two biological models. The first model is a biomechanical model for single-celled, non-branching fungal tip growth. To validate this model it has to be shown that the governing equations contain solutions corresponding to fungal growth. We showed that these solutions exist for a toy model using topological shooting. The second model describes Fickian diffusion of oxygen into core-shell geometry for encapsulating pancreatic Langerhan islets. These are of interest for the preparation of artificial pancreas for Diabetes type 1. We used topological shooting to show that solutions exist corresponding to viable diffusion of oxygen into the core-shell.