Music & Mathematics Interrogate Brain Tumour Dissemination

Rachel Bearon (Mathematical Biology), Violaine See (Institute of Integrative Biology), Emily Howard (Composer), Lasse Rempe-Gillen (Pure Mathematics); EPSRC Liverpool Centre for Mathematics in Healthcare.

Glioblastoma (GBM) is the most common malignant brain tumour and has an extremely poor prognosis. New imaging data on glioblastoma cell movement in a 3D tissue environment (See) provides insight into how tumour cells move into normal brain tissue and how drugs can affect such cellular movement. Mathematical modelling (Bearon) is used to understand how heterogeneous cell behaviours impact tumour cell invasion.

This science was developed as a creative process through engagement with music (Howard) and pure mathematics (Rempe-Gillen), and in turn, the mathematics applied to health informed a new composition.

Below is a video of cells within a 3D spheroid. It was taken using a fluorescent light sheet microscope, and each light dot represents the nucleus of a cell. On the left is the processed data showing the trajectories of individual cells which are moving in the spheroid and invading into the surrounding gel.

Brain tumours can affect people of any age, with around 5,000 people diagnosed with a primary malignant brain tumour in the UK each year. Glioblastoma is the most common and deadliest type of brain cancer, because it moves and invades nearby healthy brain tissue, thereby damaging other parts of the brain. Therefore, the biggest challenge with glioblastoma is the migration of cancer cells, which cannot be controlled.

We recreate mini brain tumours in vitro and embed them in a gel resembling brain tissues. To understand the process of brain tumour cell migration, we follow in real-time, using high-end microscopes, how cells move out of the tumour environment towards their surroundings.

Using this experimental model, we can understand better why the cells invade and we can test drugs to stop them doing so. If we can catch the cells before they take off into other parts of the brain, we could make malignant tumours more manageable, and improve life expectancy and quality of life.

Dr Violaine See (Institute of Integrative Biology, University of Liverpool)

The study of random walks has a long mathematical history. We are investigating whether a persistent random walk model can capture the observed data by comparing the statistics of sample paths generated using equations which describe random movement over time (stochastic differential equations) with the statistics of the experimental data. We will also investigate how different drug treatments modify the movement statistics, and whether cells interact, for example by following paths created by other cells.

Dr Rachel Bearon (Mathematical Biology, University of Liverpool)

I have a long-term interest in Ada Lovelace’s idea to create a Calculus of the Nervous System: a mathematical model for how the brain would give rise to thought, and nerves to feelings. I first explored this in an orchestral piece entitled Calculus of the Nervous System written in 2011. Related works Axon (2013) for large orchestra and Afference (2014) for string quartet have since followed. This current collaboration presents me with the opportunity to explore real (rather than imaginary) data as well as to benefit from and contribute to conversations between biologists and mathematicians. I’m particularly interested in the nature of the motion and trajectories of outlier escaping cells as well as new mathematical models to map them.

Professor Emily Howard (Composer, RNCM)

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