How to tackle dementia with Mathematics

Posted by Roxana Aldea on 11 April 2017

A mother to her son, a husband to his wife, a grandmother to her granddaughter:

  • Where did I leave my keys?
  • What day is today?
  • Who are you?

Are these questions part of normal ageing or symptoms of dementia?

Understanding dementia

Dementia is not normal ageing and is characterised by cognitive deficits, memory loss and personality changes that compromise the independent living of more than 46 million people world-wide. The most common form of dementia is Alzheimer’s disease (AD) and has no effective intervention. I believe that the limited success in the discovery of long-term cure for AD could partly be due to incomplete understanding of its aetiology. For many years, AD was considered solely a neurodegenerative disease. Recently, however, a new paradigm has emerged. The presence of numerous vascular risk factors of AD has led to its classification as a vascular disease, increasing the complexity of pathology and the number of research pathways that need exploring.

Maths in medicine: a different approach

This is the type of problem that has motivated my decision of becoming a biophysicist. Given its complexity, it is unlikely that Alzheimer’s disease can be fully understood and treated through conventional biological sciences alone. Biophysical and mathematical models are powerful tools that have not yet been explored to their full potential in the biomedical and clinical fields. I have dedicated my PhD to bridging the gap between the neurodegeneration and the vascular pathology present in AD. Rather than looking through a microscope to brain tissue samples, I have been looking at Alzheimer’s dementia through the eyes of a physicist: physical principles from fluid dynamics and solid mechanics have been my strategy, mathematical models of cerebral blood vessels my tool and the pathology of Alzheimer’s dementia my target. Such a line of action could not have been successful without the guidance and mutual interest of my supervisors from Mathematical Sciences and Clinical Neuroanatomy.

Mathematics is the language that has allowed me to quantify physiological processes, to investigate multi-scale biological systems and to link disciplines such as Physics, Computer Science, Biology and Medicine. Despite its usefulness, mathematical modelling is an underrepresented approach in biomedical and clinical applications. Could it be due to the fact that for many Mathematics sounds like a foreign language difficult to grasp or could it be because scientists from biomedicine and clinical sciences remain sceptical to reductionist thinking?

The latter concern raises the question of how much physiological detail can be included in a mathematical model. My approach to this challenge can be summarised by the words of Albert Einstein:

“Everything should be made as simple as possible, but no simpler.”

The value of interdisciplinarity

Regarding the language of communication across the technological and biological sciences, I have learnt that the best strategy to engage with a biomedical audience is to keep the mathematical model as a black box and familiarise myself with the biological lexicon. In this way, my physical models take the shape of anatomical systems and mathematical equations express physiological processes. Embracing this strategy requires a large amount of self-teaching, high flexibility in communication and departure from the comfort zone of a mathematician or a physicist. It is nonetheless a thrilling way to develop unique skills and grow as a well-rounded scientist.

The interdisciplinary funding offered by EPSRC has offered me an amazing opportunity to develop projects that combine the flexibility of mathematical and physical modelling with the value of basic science and state-of-art neuroimaging in order to address the complexity of dementia. I believe that such an interdisciplinary perspective is the only path forward, contributing to a solid foundation for future successful treatments.

More information

To find out more about an interdisciplinary approach in the fight against dementia, please see the Carare group led by one of my supervisors.


In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.

Name: Roxana Aldea
Department: Institute for Complex Systems Simulation
Organisation: University of Southampton

Roxana is a fourth-year, EPSRC funded PhD student at the Institute for Complex Systems Simulations at University of Southampton. She was awarded The EPSRC Doctoral Prize Research Fellowship in 2017 which allows her to continue her interdisciplinary research in dementia.