In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.
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e-mail: atsuda@hsph.harvard.edu
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January 2009
Research Papers
Hamiltonian Chaos in a Model Alveolus
F. S. Henry,
F. S. Henry
Molecular and Integrative Physiological Sciences
, Harvard School of Public Health, Boston, MA 02115
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F. E. Laine-Pearson,
F. E. Laine-Pearson
Department of Mathematics,
University of Surrey
, Guildford, UK
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A. Tsuda
e-mail: atsuda@hsph.harvard.edu
A. Tsuda
Molecular and Integrative Physiological Sciences
, Harvard School of Public Health, Boston, MA 02115
Search for other works by this author on:
F. S. Henry
Molecular and Integrative Physiological Sciences
, Harvard School of Public Health, Boston, MA 02115
F. E. Laine-Pearson
Department of Mathematics,
University of Surrey
, Guildford, UK
A. Tsuda
Molecular and Integrative Physiological Sciences
, Harvard School of Public Health, Boston, MA 02115e-mail: atsuda@hsph.harvard.edu
J Biomech Eng. Jan 2009, 131(1): 011006 (7 pages)
Published Online: November 19, 2008
Article history
Received:
June 15, 2007
Revised:
September 30, 2007
Published:
November 19, 2008
Citation
Henry, F. S., Laine-Pearson, F. E., and Tsuda, A. (November 19, 2008). "Hamiltonian Chaos in a Model Alveolus." ASME. J Biomech Eng. January 2009; 131(1): 011006. https://doi.org/10.1115/1.2953559
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