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Take it from the birds

Bodily functions are not something immediately associated with mathematics.

But Dr Alona Ben-Tal and her colleagues at the Institute of Natural and Mathematical Sciences are using mathematics to solve mysteries behind how breathing works, with implications for our treatment of diseases like chronic obstructive pulmonary disease (COPD). 

For the past thirteen years Dr Ben-Tal’s work has been focused on developing mathematical equations to describe how the human respiratory system works. Her latest research moved to another animal with a quite different way of breathing. The research, with Dr Emily Harvey, has developed a robust mathematical model of avian respiratory system for the first time.

“Birds and mammals have similar metabolic demands and cardiovascular systems, but they have evolved drastically different respiratory systems. Gas exchange in birds is unidirectional during both inspiration and expiration. Until now, how this unidirectional flow is generated, and the factors affecting it, have not been well understood.”

A novel mathematical model

The hypothesis has been that this is due to aerodynamic valving. To test this hypothesis, Dr Ben-Tal and Dr Harvey constructed a novel mathematical model that, unlike previous models, produces unidirectional flow through avian lungs consistently, even when the amplitude and frequency of breathing change.

The model was investigated both analytically and computationally and showed the importance of aerodynamic valving for generating strong air flow through the lungs. The lumped parameters approach used means that this model is generally applicable across all birds. 

She says this ‘comparative physiology’ opens up ways to understand the function of our own bodies better.

Implications for human health

“In healthy, resting mammals expiration is passive, in birds it is active – muscles contract to make it happen. The research could lead to the development of ways to help those who suffer from diseases such as COPD and asthma, where we see forced expiration.” 

Her interest in using mathematics to understand the human body started after studying non-linear systems for her PhD. 

“I realised that the human body is the ultimate non-linear system and was fascinated by its two oscillators – the heart and the lungs.”

“The mathematical modeling challenge is linking knowledge at the neural/animal level back into human systems.”


  • Associate Professor Alona Ben-Tal

    Associate Professor Alona Ben-Tal

    Associate Professor in Mathematics
    - School of Mathematical and Computational Sciences


    My research is truly interdisciplinary and lies in the fields of applied mathematics, dynamical systems, numerical methods and physiology. My main interest is the integrated behaviour of the cardiorespiratory system and over the years, I have studied different aspects of this system including lung mechanics, gas exchange, neural control of breathing and heart rate control. My research involves mathematical modelling at different levels of complexity and mathematical analysis using a variety of mathematical techniques.