### Why don't circular wounds heal and a few other bloody problems

27 September 2019

Torbjörn ("Toby") Lundh

Department of Mathematical Sciences

Chalmers University of Technology & University of Gothenburg

Sweden

#### Abstract

The father of all physicians, Hippocrates, is believed to have stated the following question: Why do not circular wounds heal? Later, in Posterior Analytics I, Aristotle picked up Hippocrates' finding and moderated the statement somewhat: "*It belongs to the physician to know that circular wounds heal more slowly, but it belongs to the geometer to know the reasoned fact*".

We will discuss this ancient observation from both a bottom-up and a top-down viewpoint, that will lead us to the questions of what it is to "know the reasoned fact" and what a good model is and how many parameters can we deal with and still "reason"? One analogous model I have worked with together with Philip Maini at Oxford, is actually a parameter-free model based on a single (ill-posed) partial differential equation in order to formulate Hippocrates' problem in not only a medical way, but also in an analogous mathematical, physical, and numerical manner. In that way we might be able to "reason" about the "facts" to gain insight.

The second part of the seminar will be dedicated to three more concrete surgical questions: how to optimize a by-pass-graft, how to remove a stent, and how to obtain a predefined compression with a bandage (this last one is probably older than Hippocrates). We will discuss how these can be solved using a combination of basic mathematical and textile techniques.

current theory lunch schedule