The human body depends upon the flow of fluid for its sustenance, maintenance and repair. The airways of the lung and the cardiovascular and lymphatic systems can be regarded as branched networks of tubes through which fluid needs to flow at an appropriate rate. Substantial blockages in these tubes produce illness or death. Surprisingly little is understood about physiological fluid flow, which has become a substantial research area in recent decades.

Blood vessels and airways are reactive tubes that are sensitive to the effects of many chemicals (some of which are produced by the body as a control mechanism). At present, there is no adequate large-scale flow model that incorporates such effects. Even if vessel reactivity is ignored, the geometry of the cardiovascular system (or the lung) is so complex that calculating the fluid flow everywhere is not yet possible. However, by using appropriate mathematical models, it is possible to understand some of the main features of physiological fluid flow.

My research group has investigated various models of flow and transport through airways and arteries. Much of our work on physiological flows has focused on chaotic advection and swirling flows.


Fiona Tomkinson (née Laine-Pearson) and I have investigated chaotic advection in models of the lung, in collaboration with Akira Tsuda of the Harvard School of Public Health. As newborn children develop, the small airways of the lung become increasingly alveolated. The alveoli are cavities in which air can recirculate. As air sloshes in and out of the lung, the recirculation pattern is disturbed, which sets up chaotic motion for some fluid particles. This type of motion is called chaotic advection or Lagrangian chaos.

For some early results on chaos in a moving cavity with recirculation, see

Particle transport in a moving corner

Our analysis used Kolmogorov-Arnol'd-Moser theory to explain why particle transport is maximized in a particular region of the cavity.

For further publications on chaotic advection and particle transport, please refer to my publications list.


The geometry of the airways and the arterial network produces swirling flows, similar to the flows found in curved or twisted pipes.

David Gammack and I constructed the first analytic model of flow in twisted pipes with nonuniform helicity and torsion. This model has been applied to surgery for bypassing diseased arteries; it provides a basis for understanding why twisting a bypass graft may be beneficial. We have also investigated chaotic advection in nonuniform pipes, with application to High Frequency Ventilation (HFV) of premature babies.