Fighting bacteria with mathematics

The relevance of mathematical models extends far beyond the world of science—a fact made abundantly clear by the COVID-19 pandemic. Such models helped to forecast the spread of the virus, optimize vaccination strategies and assess containment measures. However, such models also have many other applications. In moder medicine, for example, they play a decisive role in understanding biological processes and help to improve clinical decisions. In her work in the Cluster of Excellence »Balance of the Microverse«, Prof. Dr Rosalind Allen deploys mathematical and biophysical models to investigate bacterial infections in urinary catheters.

By Juliane Seeber

Urinary catheters are essential pieces of healthcare equipment, especially in hospitals and care facilities. But while millions of these catheters are used every year, their use also entails certain risks. Catheter-associated urinary tract infections (UTIs) are among the most common hospital-acquired infections and can cause serious complications, including damage to the bladder or kidneys. Despite decades of research, we still lack a complete understanding of the mechanisms that lead to bacterial colonization of catheters. Rosalind Allen and her interdisciplinary team are now tackling this problem with a novel approach.

The research team have developed a mathematical model that describes different routes of infection and the dynamics of bacterial colonization. Their approach combines the outer surfaces of the catheter, the bladder, the flow of urine within the catheter and the inside surfaces of the catheter together in a single, integrative model. Simulations have enabled the researchers to identify key factors that influence the risk and progression of infections. 

Their model shows that the urine production rate—determined by the patient’s fluid intake—plays a central role. Increased fluid intake makes it possible to flush out bacteria in the urine more effectively, therefore reducing the risk of an infection. For short term catheterisation, however, the risk of infection is determined by the length of the catheter and the speed at which bacteria spread over the surface of the catheter.