Scratch assays or wound healing assays are popular in vitro experiments that provide insights into cancer invasion and tissue repair processes. In these experiments, a sc​ratch is made on a cell monolayer and imaging of the re-conolisation of the scratched region is perfomed to quantify the migration rate of the cells.
In this talk, I will introduce three mathematical methods that I have been working on, motivated by these experiments.
I will begin introducing a new migration quantification method that deals with the non-uniformity of the scratch leading edge. This method fits experimental data more closely and provides a more accurate statistical classification of the migration rate between different assays.
Following, a cell age-structured population model will be introduced. The population evolution is modeled by a McKendrick-von Foerster partial differential equation. This model aims to explain the two phases of proliferation in scratch assays. At short time, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The conditions for the model to present this behavior is presented.
Finally, I will introduce a hybrid algorithm for coupling PDE and compartment based dynamics based on an error-variance estimator. The Fisher-KPP equation and its stochastic counterpart is consider as a test case, however, the framework can be extended to on-lattice reaction diffusion systems.
This work has been developed under the supervision of Dr. Thomas Carraro (Institute for Applied Mathematics, IWR, Heidelberg University), Dr. Tomas Alarcon (Centre de Recerca Matematica, Barcelona, Spain), Prof. Helen Byrne and Prof. Philip K Maini (Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford).