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.”


  • Dr Alona Ben-Tal

    Dr Alona Ben-Tal

    Senior Lecturer
    - Institute of Natural and Mathematical Sciences


    My main area of research in recent years has been the cardio-respiratory system of mammals. I have developed simplified models of lung mechanics, gas exchange and neural control of breathing and studied different aspects of the integrated system. I have also studied the interactions between the heart and the lungs and contributed to a study of optimal nutritional intake of pregnant sheep and modelling high speed weighing systems.

Massey Contact Centre Mon - Fri 8:30am to 4:30pm 0800 MASSEY (+64 6 350 5701) TXT 5222 contact@massey.ac.nz Web chat Staff Alumni News Māori @ Massey